1,1,252,0,9.743835," ","integrate(tan(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{15 \, a e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 75 \, a e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 150 \, a e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 150 \, a e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 75 \, 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) + 150 \, a e^{\left(8 i \, d x + 8 i \, c\right)} + 300 \, a e^{\left(6 i \, d x + 6 i \, c\right)} + 400 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 200 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 15 \, a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 46 \, a}{15 \, {\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,"-1/15*(15*a*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 75*a*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 150*a*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 150*a*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 75*a*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 150*a*e^(8*I*d*x + 8*I*c) + 300*a*e^(6*I*d*x + 6*I*c) + 400*a*e^(4*I*d*x + 4*I*c) + 200*a*e^(2*I*d*x + 2*I*c) + 15*a*log(e^(2*I*d*x + 2*I*c) + 1) + 46*a)/(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
2,1,204,0,2.610524," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{-3 i \, a e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 12 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 18 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 12 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) - 24 i \, a e^{\left(6 i \, d x + 6 i \, c\right)} - 36 i \, a e^{\left(4 i \, d x + 4 i \, c\right)} - 32 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} - 3 i \, a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 8 i \, a}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-3*I*a*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 12*I*a*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 18*I*a*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 12*I*a*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 24*I*a*e^(6*I*d*x + 6*I*c) - 36*I*a*e^(4*I*d*x + 4*I*c) - 32*I*a*e^(2*I*d*x + 2*I*c) - 3*I*a*log(e^(2*I*d*x + 2*I*c) + 1) - 8*I*a)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
3,1,156,0,1.382356," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{3 \, a e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 9 \, a e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 9 \, 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) + 18 \, a e^{\left(4 i \, d x + 4 i \, c\right)} + 18 \, a e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 8 \, a}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(3*a*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 9*a*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 9*a*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 18*a*e^(4*I*d*x + 4*I*c) + 18*a*e^(2*I*d*x + 2*I*c) + 3*a*log(e^(2*I*d*x + 2*I*c) + 1) + 8*a)/(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
4,1,107,0,2.045039," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{i \, a e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 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) + 4 i \, a e^{\left(2 i \, d x + 2 i \, c\right)} + i \, a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 i \, a}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(I*a*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 2*I*a*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 4*I*a*e^(2*I*d*x + 2*I*c) + I*a*log(e^(2*I*d*x + 2*I*c) + 1) + 2*I*a)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
5,1,58,0,0.457840," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{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) + a \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 \, a}{d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"-(a*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + a*log(e^(2*I*d*x + 2*I*c) + 1) + 2*a)/(d*e^(2*I*d*x + 2*I*c) + d)","A",0
6,1,18,0,2.350800," ","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
7,1,34,0,2.360961," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"-(2*a*log(tan(1/2*d*x + 1/2*c) + I) - a*log(tan(1/2*d*x + 1/2*c)))/d","A",0
8,1,75,0,1.530675," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{4 i \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 2 i \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-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 \, d}"," ",0,"-1/2*(4*I*a*log(tan(1/2*d*x + 1/2*c) + I) - 2*I*a*log(tan(1/2*d*x + 1/2*c)) - a*tan(1/2*d*x + 1/2*c) - (-2*I*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c))/d","B",0
9,1,102,0,0.608363," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 8 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 4 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 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}}}{8 \, d}"," ",0,"-1/8*(a*tan(1/2*d*x + 1/2*c)^2 - 16*a*log(tan(1/2*d*x + 1/2*c) + I) + 8*a*log(tan(1/2*d*x + 1/2*c)) - 4*I*a*tan(1/2*d*x + 1/2*c) - (12*a*tan(1/2*d*x + 1/2*c)^2 - 4*I*a*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
10,1,128,0,0.971920," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 i \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 24 i \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-44 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3 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)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 - 3*I*a*tan(1/2*d*x + 1/2*c)^2 + 48*I*a*log(tan(1/2*d*x + 1/2*c) + I) - 24*I*a*log(tan(1/2*d*x + 1/2*c)) - 15*a*tan(1/2*d*x + 1/2*c) - (-44*I*a*tan(1/2*d*x + 1/2*c)^3 - 15*a*tan(1/2*d*x + 1/2*c)^2 + 3*I*a*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
11,1,158,0,3.221431," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 384 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 192 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 120 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{400 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 - 8*I*a*tan(1/2*d*x + 1/2*c)^3 - 36*a*tan(1/2*d*x + 1/2*c)^2 + 384*a*log(tan(1/2*d*x + 1/2*c) + I) - 192*a*log(tan(1/2*d*x + 1/2*c)) + 120*I*a*tan(1/2*d*x + 1/2*c) + (400*a*tan(1/2*d*x + 1/2*c)^4 - 120*I*a*tan(1/2*d*x + 1/2*c)^3 - 36*a*tan(1/2*d*x + 1/2*c)^2 + 8*I*a*tan(1/2*d*x + 1/2*c) + 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
12,1,186,0,1.888120," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1920 i \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 960 i \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{-2192 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 180 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 i \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 - 15*I*a*tan(1/2*d*x + 1/2*c)^4 - 70*a*tan(1/2*d*x + 1/2*c)^3 + 180*I*a*tan(1/2*d*x + 1/2*c)^2 - 1920*I*a*log(tan(1/2*d*x + 1/2*c) + I) + 960*I*a*log(tan(1/2*d*x + 1/2*c)) + 660*a*tan(1/2*d*x + 1/2*c) + (-2192*I*a*tan(1/2*d*x + 1/2*c)^5 - 660*a*tan(1/2*d*x + 1/2*c)^4 + 180*I*a*tan(1/2*d*x + 1/2*c)^3 + 70*a*tan(1/2*d*x + 1/2*c)^2 - 15*I*a*tan(1/2*d*x + 1/2*c) - 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
13,1,274,0,2.941570," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{-30 i \, a^{2} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 150 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 300 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 300 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 150 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) - 270 i \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} - 600 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} - 740 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} - 400 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} - 30 i \, a^{2} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 86 i \, a^{2}}{15 \, {\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,"1/15*(-30*I*a^2*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 150*I*a^2*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 300*I*a^2*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 300*I*a^2*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 150*I*a^2*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 270*I*a^2*e^(8*I*d*x + 8*I*c) - 600*I*a^2*e^(6*I*d*x + 6*I*c) - 740*I*a^2*e^(4*I*d*x + 4*I*c) - 400*I*a^2*e^(2*I*d*x + 2*I*c) - 30*I*a^2*log(e^(2*I*d*x + 2*I*c) + 1) - 86*I*a^2)/(d*e^(10*I*d*x + 10*I*c) + 5*d*e^(8*I*d*x + 8*I*c) + 10*d*e^(6*I*d*x + 6*I*c) + 10*d*e^(4*I*d*x + 4*I*c) + 5*d*e^(2*I*d*x + 2*I*c) + d)","B",0
14,1,222,0,1.745805," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{2 \, {\left(3 \, a^{2} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 12 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 18 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 12 \, 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) + 21 \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} + 36 \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 29 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 3 \, a^{2} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 8 \, a^{2}\right)}}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"2/3*(3*a^2*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 12*a^2*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 18*a^2*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 12*a^2*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 21*a^2*e^(6*I*d*x + 6*I*c) + 36*a^2*e^(4*I*d*x + 4*I*c) + 29*a^2*e^(2*I*d*x + 2*I*c) + 3*a^2*log(e^(2*I*d*x + 2*I*c) + 1) + 8*a^2)/(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
15,1,170,0,1.133641," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{6 i \, a^{2} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 18 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 18 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) + 30 i \, a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} + 36 i \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 i \, a^{2} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 14 i \, a^{2}}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(6*I*a^2*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 18*I*a^2*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 18*I*a^2*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 30*I*a^2*e^(4*I*d*x + 4*I*c) + 36*I*a^2*e^(2*I*d*x + 2*I*c) + 6*I*a^2*log(e^(2*I*d*x + 2*I*c) + 1) + 14*I*a^2)/(d*e^(6*I*d*x + 6*I*c) + 3*d*e^(4*I*d*x + 4*I*c) + 3*d*e^(2*I*d*x + 2*I*c) + d)","B",0
16,1,116,0,0.607170," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(a^{2} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 \, 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) + 3 \, a^{2} e^{\left(2 i \, d x + 2 i \, c\right)} + a^{2} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 2 \, a^{2}\right)}}{d e^{\left(4 i \, d x + 4 i \, c\right)} + 2 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"-2*(a^2*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 2*a^2*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 3*a^2*e^(2*I*d*x + 2*I*c) + a^2*log(e^(2*I*d*x + 2*I*c) + 1) + 2*a^2)/(d*e^(4*I*d*x + 4*I*c) + 2*d*e^(2*I*d*x + 2*I*c) + d)","B",0
17,1,65,0,0.436584," ","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
18,1,68,0,0.963515," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 4 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d}"," ",0,"(a^2*log(tan(1/2*d*x + 1/2*c) + 1) - 4*a^2*log(tan(1/2*d*x + 1/2*c) + I) + a^2*log(tan(1/2*d*x + 1/2*c) - 1) + a^2*log(tan(1/2*d*x + 1/2*c)))/d","A",0
19,1,85,0,1.093893," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{8 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 4 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-4 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(8*I*a^2*log(tan(1/2*d*x + 1/2*c) + I) - 4*I*a^2*log(tan(1/2*d*x + 1/2*c)) - a^2*tan(1/2*d*x + 1/2*c) - (-4*I*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c))/d","B",0
20,1,116,0,1.879624," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 32 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 16 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{24 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 8 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 - 32*a^2*log(tan(1/2*d*x + 1/2*c) + I) + 16*a^2*log(tan(1/2*d*x + 1/2*c)) - 8*I*a^2*tan(1/2*d*x + 1/2*c) - (24*a^2*tan(1/2*d*x + 1/2*c)^2 - 8*I*a^2*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
21,1,146,0,1.563144," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 96 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 48 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 27 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-88 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 27 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 6 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 - 6*I*a^2*tan(1/2*d*x + 1/2*c)^2 + 96*I*a^2*log(tan(1/2*d*x + 1/2*c) + I) - 48*I*a^2*log(tan(1/2*d*x + 1/2*c)) - 27*a^2*tan(1/2*d*x + 1/2*c) - (-88*I*a^2*tan(1/2*d*x + 1/2*c)^3 - 27*a^2*tan(1/2*d*x + 1/2*c)^2 + 6*I*a^2*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
22,1,180,0,2.098986," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 768 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 384 \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 240 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{800 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 60 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 - 16*I*a^2*tan(1/2*d*x + 1/2*c)^3 - 60*a^2*tan(1/2*d*x + 1/2*c)^2 + 768*a^2*log(tan(1/2*d*x + 1/2*c) + I) - 384*a^2*log(tan(1/2*d*x + 1/2*c)) + 240*I*a^2*tan(1/2*d*x + 1/2*c) + (800*a^2*tan(1/2*d*x + 1/2*c)^4 - 240*I*a^2*tan(1/2*d*x + 1/2*c)^3 - 60*a^2*tan(1/2*d*x + 1/2*c)^2 + 16*I*a^2*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
23,1,212,0,2.872722," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 55 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1920 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 960 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{-2192 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 630 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 180 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 55 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 i \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 15*I*a^2*tan(1/2*d*x + 1/2*c)^4 - 55*a^2*tan(1/2*d*x + 1/2*c)^3 + 180*I*a^2*tan(1/2*d*x + 1/2*c)^2 - 1920*I*a^2*log(tan(1/2*d*x + 1/2*c) + I) + 960*I*a^2*log(tan(1/2*d*x + 1/2*c)) + 630*a^2*tan(1/2*d*x + 1/2*c) + (-2192*I*a^2*tan(1/2*d*x + 1/2*c)^5 - 630*a^2*tan(1/2*d*x + 1/2*c)^4 + 180*I*a^2*tan(1/2*d*x + 1/2*c)^3 + 55*a^2*tan(1/2*d*x + 1/2*c)^2 - 15*I*a^2*tan(1/2*d*x + 1/2*c) - 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
24,1,274,0,5.718928," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, {\left(30 \, a^{3} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 150 \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 300 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 300 \, 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) + 150 \, 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) + 240 \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} + 585 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 695 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 385 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 30 \, a^{3} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 83 \, a^{3}\right)}}{15 \, {\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,"2/15*(30*a^3*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 150*a^3*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 300*a^3*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 300*a^3*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 150*a^3*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 240*a^3*e^(8*I*d*x + 8*I*c) + 585*a^3*e^(6*I*d*x + 6*I*c) + 695*a^3*e^(4*I*d*x + 4*I*c) + 385*a^3*e^(2*I*d*x + 2*I*c) + 30*a^3*log(e^(2*I*d*x + 2*I*c) + 1) + 83*a^3)/(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
25,1,221,0,2.202099," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{4 i \, a^{3} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 16 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 24 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) + 16 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) + 24 i \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} + 46 i \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 36 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) + 10 i \, a^{3}}{d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d}"," ",0,"(4*I*a^3*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 16*I*a^3*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 24*I*a^3*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 16*I*a^3*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 24*I*a^3*e^(6*I*d*x + 6*I*c) + 46*I*a^3*e^(4*I*d*x + 4*I*c) + 36*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) + 10*I*a^3)/(d*e^(8*I*d*x + 8*I*c) + 4*d*e^(6*I*d*x + 6*I*c) + 6*d*e^(4*I*d*x + 4*I*c) + 4*d*e^(2*I*d*x + 2*I*c) + d)","B",0
26,1,170,0,0.748163," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(6 \, a^{3} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 18 \, 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) + 18 \, 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) + 24 \, a^{3} e^{\left(4 i \, d x + 4 i \, c\right)} + 33 \, a^{3} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 \, a^{3} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 13 \, a^{3}\right)}}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-2/3*(6*a^3*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 18*a^3*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 18*a^3*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 24*a^3*e^(4*I*d*x + 4*I*c) + 33*a^3*e^(2*I*d*x + 2*I*c) + 6*a^3*log(e^(2*I*d*x + 2*I*c) + 1) + 13*a^3)/(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
27,1,117,0,0.568705," ","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
28,1,123,0,1.216267," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{3 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 8 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 3 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1}}{d}"," ",0,"(3*a^3*log(tan(1/2*d*x + 1/2*c) + 1) - 8*a^3*log(tan(1/2*d*x + 1/2*c) + I) + 3*a^3*log(tan(1/2*d*x + 1/2*c) - 1) + a^3*log(tan(1/2*d*x + 1/2*c)) - (3*a^3*tan(1/2*d*x + 1/2*c)^2 - 2*I*a^3*tan(1/2*d*x + 1/2*c) - 3*a^3)/(tan(1/2*d*x + 1/2*c)^2 - 1))/d","B",0
29,1,119,0,2.896310," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-2 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 16 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 2 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - 6 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-6 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(-2*I*a^3*log(tan(1/2*d*x + 1/2*c) + 1) + 16*I*a^3*log(tan(1/2*d*x + 1/2*c) + I) - 2*I*a^3*log(tan(1/2*d*x + 1/2*c) - 1) - 6*I*a^3*log(tan(1/2*d*x + 1/2*c)) - a^3*tan(1/2*d*x + 1/2*c) - (-6*I*a^3*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c))/d","A",0
30,1,116,0,1.834206," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 64 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 32 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 12 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{48 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 - 64*a^3*log(tan(1/2*d*x + 1/2*c) + I) + 32*a^3*log(tan(1/2*d*x + 1/2*c)) - 12*I*a^3*tan(1/2*d*x + 1/2*c) - (48*a^3*tan(1/2*d*x + 1/2*c)^2 - 12*I*a^3*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
31,1,146,0,2.177016," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 192 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 96 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 51 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-176 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 51 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 9 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 - 9*I*a^3*tan(1/2*d*x + 1/2*c)^2 + 192*I*a^3*log(tan(1/2*d*x + 1/2*c) + I) - 96*I*a^3*log(tan(1/2*d*x + 1/2*c)) - 51*a^3*tan(1/2*d*x + 1/2*c) - (-176*I*a^3*tan(1/2*d*x + 1/2*c)^3 - 51*a^3*tan(1/2*d*x + 1/2*c)^2 + 9*I*a^3*tan(1/2*d*x + 1/2*c) + a^3)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
32,1,180,0,3.979823," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 108 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1536 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 768 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 456 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{1600 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 456 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 108 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a^3*tan(1/2*d*x + 1/2*c)^4 - 24*I*a^3*tan(1/2*d*x + 1/2*c)^3 - 108*a^3*tan(1/2*d*x + 1/2*c)^2 + 1536*a^3*log(tan(1/2*d*x + 1/2*c) + I) - 768*a^3*log(tan(1/2*d*x + 1/2*c)) + 456*I*a^3*tan(1/2*d*x + 1/2*c) + (1600*a^3*tan(1/2*d*x + 1/2*c)^4 - 456*I*a^3*tan(1/2*d*x + 1/2*c)^3 - 108*a^3*tan(1/2*d*x + 1/2*c)^2 + 24*I*a^3*tan(1/2*d*x + 1/2*c) + 3*a^3)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
33,1,212,0,7.421282," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 190 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 660 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7680 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 3840 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2460 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{-8768 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2460 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 660 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 190 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 45 i \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a^3*tan(1/2*d*x + 1/2*c)^5 - 45*I*a^3*tan(1/2*d*x + 1/2*c)^4 - 190*a^3*tan(1/2*d*x + 1/2*c)^3 + 660*I*a^3*tan(1/2*d*x + 1/2*c)^2 - 7680*I*a^3*log(tan(1/2*d*x + 1/2*c) + I) + 3840*I*a^3*log(tan(1/2*d*x + 1/2*c)) + 2460*a^3*tan(1/2*d*x + 1/2*c) + (-8768*I*a^3*tan(1/2*d*x + 1/2*c)^5 - 2460*a^3*tan(1/2*d*x + 1/2*c)^4 + 660*I*a^3*tan(1/2*d*x + 1/2*c)^3 + 190*a^3*tan(1/2*d*x + 1/2*c)^2 - 45*I*a^3*tan(1/2*d*x + 1/2*c) - 6*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
34,1,326,0,9.970797," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{4 \, {\left(30 \, a^{4} e^{\left(12 i \, d x + 12 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 180 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 450 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 600 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 450 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 180 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 270 \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} + 855 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 1350 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 1125 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 486 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 30 \, a^{4} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 86 \, a^{4}\right)}}{15 \, {\left(d e^{\left(12 i \, d x + 12 i \, c\right)} + 6 \, d e^{\left(10 i \, d x + 10 i \, c\right)} + 15 \, d e^{\left(8 i \, d x + 8 i \, c\right)} + 20 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 15 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 6 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"4/15*(30*a^4*e^(12*I*d*x + 12*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 180*a^4*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 450*a^4*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 600*a^4*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 450*a^4*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 180*a^4*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 270*a^4*e^(10*I*d*x + 10*I*c) + 855*a^4*e^(8*I*d*x + 8*I*c) + 1350*a^4*e^(6*I*d*x + 6*I*c) + 1125*a^4*e^(4*I*d*x + 4*I*c) + 486*a^4*e^(2*I*d*x + 2*I*c) + 30*a^4*log(e^(2*I*d*x + 2*I*c) + 1) + 86*a^4)/(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
35,1,274,0,2.093865," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{120 i \, a^{4} e^{\left(10 i \, d x + 10 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 600 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1200 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 1200 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 600 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 840 i \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} + 2220 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 2620 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 1460 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 120 i \, a^{4} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 316 i \, a^{4}}{15 \, {\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,"1/15*(120*I*a^4*e^(10*I*d*x + 10*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 600*I*a^4*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 1200*I*a^4*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 1200*I*a^4*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 600*I*a^4*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 840*I*a^4*e^(8*I*d*x + 8*I*c) + 2220*I*a^4*e^(6*I*d*x + 6*I*c) + 2620*I*a^4*e^(4*I*d*x + 4*I*c) + 1460*I*a^4*e^(2*I*d*x + 2*I*c) + 120*I*a^4*log(e^(2*I*d*x + 2*I*c) + 1) + 316*I*a^4)/(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
36,1,222,0,1.325036," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{4 \, {\left(6 \, a^{4} e^{\left(8 i \, d x + 8 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 24 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 36 \, a^{4} 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 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 30 \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} + 63 \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} + 50 \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} + 6 \, a^{4} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) + 14 \, a^{4}\right)}}{3 \, {\left(d e^{\left(8 i \, d x + 8 i \, c\right)} + 4 \, d e^{\left(6 i \, d x + 6 i \, c\right)} + 6 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 4 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"-4/3*(6*a^4*e^(8*I*d*x + 8*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 24*a^4*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 36*a^4*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 24*a^4*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) + 30*a^4*e^(6*I*d*x + 6*I*c) + 63*a^4*e^(4*I*d*x + 4*I*c) + 50*a^4*e^(2*I*d*x + 2*I*c) + 6*a^4*log(e^(2*I*d*x + 2*I*c) + 1) + 14*a^4)/(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
37,1,170,0,1.780240," ","integrate((a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{-24 i \, a^{4} e^{\left(6 i \, d x + 6 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 72 i \, a^{4} e^{\left(4 i \, d x + 4 i \, c\right)} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 72 i \, a^{4} 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^{4} e^{\left(4 i \, d x + 4 i \, c\right)} - 108 i \, a^{4} e^{\left(2 i \, d x + 2 i \, c\right)} - 24 i \, a^{4} \log\left(e^{\left(2 i \, d x + 2 i \, c\right)} + 1\right) - 44 i \, a^{4}}{3 \, {\left(d e^{\left(6 i \, d x + 6 i \, c\right)} + 3 \, d e^{\left(4 i \, d x + 4 i \, c\right)} + 3 \, d e^{\left(2 i \, d x + 2 i \, c\right)} + d\right)}}"," ",0,"1/3*(-24*I*a^4*e^(6*I*d*x + 6*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 72*I*a^4*e^(4*I*d*x + 4*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 72*I*a^4*e^(2*I*d*x + 2*I*c)*log(e^(2*I*d*x + 2*I*c) + 1) - 72*I*a^4*e^(4*I*d*x + 4*I*c) - 108*I*a^4*e^(2*I*d*x + 2*I*c) - 24*I*a^4*log(e^(2*I*d*x + 2*I*c) + 1) - 44*I*a^4)/(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
38,1,157,0,2.543540," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{14 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 32 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 14 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + 2 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \frac{21 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 46 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 21 \, a^{4}}{{\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 1\right)}^{2}}}{2 \, d}"," ",0,"1/2*(14*a^4*log(tan(1/2*d*x + 1/2*c) + 1) - 32*a^4*log(tan(1/2*d*x + 1/2*c) + I) + 14*a^4*log(tan(1/2*d*x + 1/2*c) - 1) + 2*a^4*log(tan(1/2*d*x + 1/2*c)) - (21*a^4*tan(1/2*d*x + 1/2*c)^4 - 16*I*a^4*tan(1/2*d*x + 1/2*c)^3 - 46*a^4*tan(1/2*d*x + 1/2*c)^2 + 16*I*a^4*tan(1/2*d*x + 1/2*c) + 21*a^4)/(tan(1/2*d*x + 1/2*c)^2 - 1)^2)/d","A",0
39,1,163,0,3.310709," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{-8 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) + 32 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 8 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) - 8 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-8 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4}}{\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)}}{2 \, d}"," ",0,"-1/2*(-8*I*a^4*log(tan(1/2*d*x + 1/2*c) + 1) + 32*I*a^4*log(tan(1/2*d*x + 1/2*c) + I) - 8*I*a^4*log(tan(1/2*d*x + 1/2*c) - 1) - 8*I*a^4*log(tan(1/2*d*x + 1/2*c)) - a^4*tan(1/2*d*x + 1/2*c) - (-8*I*a^4*tan(1/2*d*x + 1/2*c)^3 - 5*a^4*tan(1/2*d*x + 1/2*c)^2 + 8*I*a^4*tan(1/2*d*x + 1/2*c) + a^4)/(tan(1/2*d*x + 1/2*c)^3 - tan(1/2*d*x + 1/2*c)))/d","B",0
40,1,150,0,4.211278," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - 128 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 8 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1\right) + 56 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 16 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{84 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 16 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(a^4*tan(1/2*d*x + 1/2*c)^2 + 8*a^4*log(tan(1/2*d*x + 1/2*c) + 1) - 128*a^4*log(tan(1/2*d*x + 1/2*c) + I) + 8*a^4*log(tan(1/2*d*x + 1/2*c) - 1) + 56*a^4*log(tan(1/2*d*x + 1/2*c)) - 16*I*a^4*tan(1/2*d*x + 1/2*c) - (84*a^4*tan(1/2*d*x + 1/2*c)^2 - 16*I*a^4*tan(1/2*d*x + 1/2*c) - a^4)/tan(1/2*d*x + 1/2*c)^2)/d","A",0
41,1,146,0,5.641709," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 384 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 192 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 87 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{-352 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 87 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^4*tan(1/2*d*x + 1/2*c)^3 - 12*I*a^4*tan(1/2*d*x + 1/2*c)^2 + 384*I*a^4*log(tan(1/2*d*x + 1/2*c) + I) - 192*I*a^4*log(tan(1/2*d*x + 1/2*c)) - 87*a^4*tan(1/2*d*x + 1/2*c) - (-352*I*a^4*tan(1/2*d*x + 1/2*c)^3 - 87*a^4*tan(1/2*d*x + 1/2*c)^2 + 12*I*a^4*tan(1/2*d*x + 1/2*c) + a^4)/tan(1/2*d*x + 1/2*c)^3)/d","A",0
42,1,180,0,10.159931," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 32 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 3072 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) - 1536 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 864 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{3200 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 864 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 180 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 32 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a^4*tan(1/2*d*x + 1/2*c)^4 - 32*I*a^4*tan(1/2*d*x + 1/2*c)^3 - 180*a^4*tan(1/2*d*x + 1/2*c)^2 + 3072*a^4*log(tan(1/2*d*x + 1/2*c) + I) - 1536*a^4*log(tan(1/2*d*x + 1/2*c)) + 864*I*a^4*tan(1/2*d*x + 1/2*c) + (3200*a^4*tan(1/2*d*x + 1/2*c)^4 - 864*I*a^4*tan(1/2*d*x + 1/2*c)^3 - 180*a^4*tan(1/2*d*x + 1/2*c)^2 + 32*I*a^4*tan(1/2*d*x + 1/2*c) + 3*a^4)/tan(1/2*d*x + 1/2*c)^4)/d","A",0
43,1,212,0,46.777830," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 155 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 600 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 7680 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 3840 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + 2370 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{-8768 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2370 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 600 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 155 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^4*tan(1/2*d*x + 1/2*c)^5 - 30*I*a^4*tan(1/2*d*x + 1/2*c)^4 - 155*a^4*tan(1/2*d*x + 1/2*c)^3 + 600*I*a^4*tan(1/2*d*x + 1/2*c)^2 - 7680*I*a^4*log(tan(1/2*d*x + 1/2*c) + I) + 3840*I*a^4*log(tan(1/2*d*x + 1/2*c)) + 2370*a^4*tan(1/2*d*x + 1/2*c) + (-8768*I*a^4*tan(1/2*d*x + 1/2*c)^5 - 2370*a^4*tan(1/2*d*x + 1/2*c)^4 + 600*I*a^4*tan(1/2*d*x + 1/2*c)^3 + 155*a^4*tan(1/2*d*x + 1/2*c)^2 - 30*I*a^4*tan(1/2*d*x + 1/2*c) - 3*a^4)/tan(1/2*d*x + 1/2*c)^5)/d","A",0
44,1,245,0,63.611775," ","integrate(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 880 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 2835 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 30720 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + i\right) + 15360 \, a^{4} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 10080 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{37632 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 10080 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2835 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 880 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 i \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*(5*a^4*tan(1/2*d*x + 1/2*c)^6 - 48*I*a^4*tan(1/2*d*x + 1/2*c)^5 - 240*a^4*tan(1/2*d*x + 1/2*c)^4 + 880*I*a^4*tan(1/2*d*x + 1/2*c)^3 + 2835*a^4*tan(1/2*d*x + 1/2*c)^2 - 30720*a^4*log(tan(1/2*d*x + 1/2*c) + I) + 15360*a^4*log(tan(1/2*d*x + 1/2*c)) - 10080*I*a^4*tan(1/2*d*x + 1/2*c) - (37632*a^4*tan(1/2*d*x + 1/2*c)^6 - 10080*I*a^4*tan(1/2*d*x + 1/2*c)^5 - 2835*a^4*tan(1/2*d*x + 1/2*c)^4 + 880*I*a^4*tan(1/2*d*x + 1/2*c)^3 + 240*a^4*tan(1/2*d*x + 1/2*c)^2 - 48*I*a^4*tan(1/2*d*x + 1/2*c) - 5*a^4)/tan(1/2*d*x + 1/2*c)^6)/d","A",0
45,1,116,0,34.596291," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{33 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} + \frac{3 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a} + \frac{3 \, {\left(-11 i \, \tan\left(d x + c\right) - 9\right)}}{a {\left(\tan\left(d x + c\right) - i\right)}} + \frac{3 i \, a^{3} \tan\left(d x + c\right)^{4} - 4 \, a^{3} \tan\left(d x + c\right)^{3} - 12 i \, a^{3} \tan\left(d x + c\right)^{2} + 24 \, a^{3} \tan\left(d x + c\right)}{a^{4}}}{12 \, d}"," ",0,"-1/12*(33*I*log(tan(d*x + c) - I)/a + 3*I*log(I*tan(d*x + c) - 1)/a + 3*(-11*I*tan(d*x + c) - 9)/(a*(tan(d*x + c) - I)) + (3*I*a^3*tan(d*x + c)^4 - 4*a^3*tan(d*x + c)^3 - 12*I*a^3*tan(d*x + c)^2 + 24*a^3*tan(d*x + c))/a^4)/d","A",0
46,1,104,0,5.366927," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{3 \, \log\left(\tan\left(d x + c\right) + i\right)}{a} - \frac{27 \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a} + \frac{3 \, {\left(9 \, \tan\left(d x + c\right) - 7 i\right)}}{a {\left(\tan\left(d x + c\right) - i\right)}} - \frac{2 \, {\left(2 i \, a^{2} \tan\left(d x + c\right)^{3} - 3 \, a^{2} \tan\left(d x + c\right)^{2} - 12 i \, a^{2} \tan\left(d x + c\right)\right)}}{a^{3}}}{12 \, d}"," ",0,"1/12*(3*log(tan(d*x + c) + I)/a - 27*log(I*tan(d*x + c) + 1)/a + 3*(9*tan(d*x + c) - 7*I)/(a*(tan(d*x + c) - I)) - 2*(2*I*a^2*tan(d*x + c)^3 - 3*a^2*tan(d*x + c)^2 - 12*I*a^2*tan(d*x + c))/a^3)/d","A",0
47,1,87,0,5.614603," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-\frac{7 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{2 \, {\left(i \, a \tan\left(d x + c\right)^{2} - 2 \, a \tan\left(d x + c\right)\right)}}{a^{2}} - \frac{-7 i \, \tan\left(d x + c\right) - 5}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(-7*I*log(tan(d*x + c) - I)/a - I*log(-I*tan(d*x + c) + 1)/a + 2*(I*a*tan(d*x + c)^2 - 2*a*tan(d*x + c))/a^2 - (-7*I*tan(d*x + c) - 5)/(a*(tan(d*x + c) - I)))/d","A",0
48,1,70,0,2.415065," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left(\tan\left(d x + c\right) + i\right)}{a} - \frac{5 \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a} + \frac{4 i \, \tan\left(d x + c\right)}{a} + \frac{5 \, \tan\left(d x + c\right) - 3 i}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(log(tan(d*x + c) + I)/a - 5*log(-I*tan(d*x + c) - 1)/a + 4*I*tan(d*x + c)/a + (5*tan(d*x + c) - 3*I)/(a*(tan(d*x + c) - I)))/d","A",0
49,1,60,0,1.991077," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 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{-3 i \, \tan\left(d x + c\right) - 1}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(3*I*log(tan(d*x + c) - I)/a + I*log(I*tan(d*x + c) - 1)/a + (-3*I*tan(d*x + c) - 1)/(a*(tan(d*x + c) - I)))/d","A",0
50,1,58,0,0.592886," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{\log\left(\tan\left(d x + c\right) - i\right)}{a} - \frac{\log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a} - \frac{\tan\left(d x + c\right) + i}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(log(tan(d*x + c) - I)/a - log(-I*tan(d*x + c) + 1)/a - (tan(d*x + c) + I)/(a*(tan(d*x + c) - I)))/d","B",0
51,1,60,0,1.246239," ","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
52,1,72,0,0.873454," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{3 \, \log\left(\tan\left(d x + c\right) - i\right)}{a} + \frac{\log\left(i \, \tan\left(d x + c\right) - 1\right)}{a} - \frac{4 \, \log\left(\tan\left(d x + c\right)\right)}{a} - \frac{3 \, \tan\left(d x + c\right) - 5 i}{a {\left(\tan\left(d x + c\right) - i\right)}}}{4 \, d}"," ",0,"-1/4*(3*log(tan(d*x + c) - I)/a + log(I*tan(d*x + c) - 1)/a - 4*log(tan(d*x + c))/a - (3*tan(d*x + c) - 5*I)/(a*(tan(d*x + c) - I)))/d","A",0
53,1,91,0,1.825645," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{-\frac{10 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} + \frac{2 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a} + \frac{8 i \, \log\left(\tan\left(d x + c\right)\right)}{a} + \frac{\tan\left(d x + c\right)^{2} - 13 i \, \tan\left(d x + c\right) - 8}{{\left(-i \, \tan\left(d x + c\right)^{2} - \tan\left(d x + c\right)\right)} a}}{8 \, d}"," ",0,"-1/8*(-10*I*log(tan(d*x + c) - I)/a + 2*I*log(-I*tan(d*x + c) + 1)/a + 8*I*log(tan(d*x + c))/a + (tan(d*x + c)^2 - 13*I*tan(d*x + c) - 8)/((-I*tan(d*x + c)^2 - tan(d*x + c))*a))/d","A",0
54,1,105,0,1.478539," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{\log\left(\tan\left(d x + c\right) + i\right)}{a} + \frac{7 \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a} - \frac{8 \, \log\left(\tan\left(d x + c\right)\right)}{a} - \frac{7 \, \tan\left(d x + c\right) - 9 i}{a {\left(\tan\left(d x + c\right) - i\right)}} + \frac{2 \, {\left(6 \, \tan\left(d x + c\right)^{2} + 2 i \, \tan\left(d x + c\right) - 1\right)}}{a \tan\left(d x + c\right)^{2}}}{4 \, d}"," ",0,"1/4*(log(tan(d*x + c) + I)/a + 7*log(I*tan(d*x + c) + 1)/a - 8*log(tan(d*x + c))/a - (7*tan(d*x + c) - 9*I)/(a*(tan(d*x + c) - I)) + 2*(6*tan(d*x + c)^2 + 2*I*tan(d*x + c) - 1)/(a*tan(d*x + c)^2))/d","A",0
55,1,116,0,1.622376," ","integrate(cot(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{27 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a} - \frac{3 i \, \log\left(-i \, \tan\left(d x + c\right) + 1\right)}{a} - \frac{24 i \, \log\left(\tan\left(d x + c\right)\right)}{a} + \frac{3 \, {\left(-9 i \, \tan\left(d x + c\right) - 11\right)}}{a {\left(\tan\left(d x + c\right) - i\right)}} + \frac{2 i \, {\left(22 \, \tan\left(d x + c\right)^{3} + 12 i \, \tan\left(d x + c\right)^{2} - 3 \, \tan\left(d x + c\right) - 2 i\right)}}{a \tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(27*I*log(tan(d*x + c) - I)/a - 3*I*log(-I*tan(d*x + c) + 1)/a - 24*I*log(tan(d*x + c))/a + 3*(-9*I*tan(d*x + c) - 11)/(a*(tan(d*x + c) - I)) + 2*I*(22*tan(d*x + c)^3 + 12*I*tan(d*x + c)^2 - 3*tan(d*x + c) - 2*I)/(a*tan(d*x + c)^3))/d","A",0
56,1,111,0,20.890142," ","integrate(tan(d*x+c)^6/(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{294 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} + \frac{3 \, {\left(147 i \, \tan\left(d x + c\right)^{2} + 250 \, \tan\left(d x + c\right) - 107 i\right)}}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}} + \frac{16 \, {\left(a^{4} \tan\left(d x + c\right)^{3} + 3 i \, a^{4} \tan\left(d x + c\right)^{2} - 12 \, a^{4} \tan\left(d x + c\right)\right)}}{a^{6}}}{48 \, d}"," ",0,"-1/48*(6*I*log(tan(d*x + c) + I)/a^2 - 294*I*log(tan(d*x + c) - I)/a^2 + 3*(147*I*tan(d*x + c)^2 + 250*tan(d*x + c) - 107*I)/(a^2*(tan(d*x + c) - I)^2) + 16*(a^4*tan(d*x + c)^3 + 3*I*a^4*tan(d*x + c)^2 - 12*a^4*tan(d*x + c))/a^6)/d","A",0
57,1,98,0,13.781513," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{62 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} - \frac{8 \, {\left(a^{2} \tan\left(d x + c\right)^{2} + 4 i \, a^{2} \tan\left(d x + c\right)\right)}}{a^{4}} - \frac{93 \, \tan\left(d x + c\right)^{2} - 150 i \, \tan\left(d x + c\right) - 61}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"1/16*(2*log(tan(d*x + c) + I)/a^2 + 62*log(tan(d*x + c) - I)/a^2 - 8*(a^2*tan(d*x + c)^2 + 4*I*a^2*tan(d*x + c))/a^4 - (93*tan(d*x + c)^2 - 150*I*tan(d*x + c) - 61)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
58,1,79,0,6.809831," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{-\frac{2 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{34 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} + \frac{16 \, \tan\left(d x + c\right)}{a^{2}} + \frac{-51 i \, \tan\left(d x + c\right)^{2} - 74 \, \tan\left(d x + c\right) + 27 i}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(-2*I*log(tan(d*x + c) + I)/a^2 + 34*I*log(tan(d*x + c) - I)/a^2 + 16*tan(d*x + c)/a^2 + (-51*I*tan(d*x + c)^2 - 74*tan(d*x + c) + 27*I)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
59,1,69,0,2.617524," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{14 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} - \frac{21 \, \tan\left(d x + c\right)^{2} - 22 i \, \tan\left(d x + c\right) - 5}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(2*log(tan(d*x + c) + I)/a^2 + 14*log(tan(d*x + c) - I)/a^2 - (21*tan(d*x + c)^2 - 22*I*tan(d*x + c) - 5)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
60,1,72,0,1.414733," ","integrate(tan(d*x+c)^2/(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} - 6 \, \tan\left(d x + c\right) + 5 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 - 6*tan(d*x + c) + 5*I)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
61,1,70,0,0.960141," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{\log\left(\tan\left(2 \, d x + 2 \, c\right) - i\right)}{a^{2}} - \frac{\log\left(-i \, \tan\left(2 \, d x + 2 \, c\right) + 1\right)}{a^{2}} - \frac{\tan\left(2 \, d x + 2 \, c\right) + i}{a^{2} {\left(\tan\left(2 \, d x + 2 \, c\right) - i\right)}}}{16 \, d}"," ",0,"-1/16*(log(tan(2*d*x + 2*c) - I)/a^2 - log(-I*tan(2*d*x + 2*c) + 1)/a^2 - (tan(2*d*x + 2*c) + I)/(a^2*(tan(2*d*x + 2*c) - I)))/d","A",0
62,1,72,0,0.495955," ","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
63,1,81,0,1.487118," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{14 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} - \frac{16 \, \log\left(\tan\left(d x + c\right)\right)}{a^{2}} - \frac{21 \, \tan\left(d x + c\right)^{2} - 54 i \, \tan\left(d x + c\right) - 37}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(2*log(tan(d*x + c) + I)/a^2 + 14*log(tan(d*x + c) - I)/a^2 - 16*log(tan(d*x + c))/a^2 - (21*tan(d*x + c)^2 - 54*I*tan(d*x + c) - 37)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
64,1,109,0,1.940499," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{32 i \, \log\left(i \, \tan\left(d x + c\right)\right)}{a^{2}} - \frac{34 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{16 \, {\left(-2 i \, \tan\left(d x + c\right) + 1\right)}}{a^{2} \tan\left(d x + c\right)} + \frac{51 i \, \tan\left(d x + c\right)^{2} + 122 \, \tan\left(d x + c\right) - 75 i}{a^{2} {\left(\tan\left(d x + c\right) - i\right)}^{2}}}{16 \, d}"," ",0,"-1/16*(32*I*log(I*tan(d*x + c))/a^2 - 34*I*log(I*tan(d*x + c) + 1)/a^2 + 2*I*log(-I*tan(d*x + c) + 1)/a^2 + 16*(-2*I*tan(d*x + c) + 1)/(a^2*tan(d*x + c)) + (51*I*tan(d*x + c)^2 + 122*tan(d*x + c) - 75*I)/(a^2*(tan(d*x + c) - I)^2))/d","A",0
65,1,109,0,5.131838," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{2}} + \frac{124 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{2}} - \frac{128 \, \log\left(\tan\left(d x + c\right)\right)}{a^{2}} + \frac{3 \, \tan\left(d x + c\right)^{4} + 114 i \, \tan\left(d x + c\right)^{3} + 173 \, \tan\left(d x + c\right)^{2} - 32 i \, \tan\left(d x + c\right) + 16}{{\left(\tan\left(d x + c\right)^{2} - i \, \tan\left(d x + c\right)\right)}^{2} a^{2}}}{32 \, d}"," ",0,"1/32*(4*log(tan(d*x + c) + I)/a^2 + 124*log(tan(d*x + c) - I)/a^2 - 128*log(tan(d*x + c))/a^2 + (3*tan(d*x + c)^4 + 114*I*tan(d*x + c)^3 + 173*tan(d*x + c)^2 - 32*I*tan(d*x + c) + 16)/((tan(d*x + c)^2 - I*tan(d*x + c))^2*a^2))/d","A",0
66,1,111,0,30.469365," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{666 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{48 \, {\left(-i \, a^{3} \tan\left(d x + c\right)^{2} + 6 \, a^{3} \tan\left(d x + c\right)\right)}}{a^{6}} - \frac{1221 i \, \tan\left(d x + c\right)^{3} + 3075 \, \tan\left(d x + c\right)^{2} - 2619 i \, \tan\left(d x + c\right) - 749}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(666*I*log(tan(d*x + c) - I)/a^3 + 6*I*log(I*tan(d*x + c) - 1)/a^3 + 48*(-I*a^3*tan(d*x + c)^2 + 6*a^3*tan(d*x + c))/a^6 - (1221*I*tan(d*x + c)^3 + 3075*tan(d*x + c)^2 - 2619*I*tan(d*x + c) - 749)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
67,1,91,0,9.695694," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{3}} - \frac{294 \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{3}} + \frac{96 i \, \tan\left(d x + c\right)}{a^{3}} + \frac{539 \, \tan\left(d x + c\right)^{3} - 1245 i \, \tan\left(d x + c\right)^{2} - 981 \, \tan\left(d x + c\right) + 259 i}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*log(tan(d*x + c) + I)/a^3 - 294*log(I*tan(d*x + c) + 1)/a^3 + 96*I*tan(d*x + c)/a^3 + (539*tan(d*x + c)^3 - 1245*I*tan(d*x + c)^2 - 981*tan(d*x + c) + 259*I)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
68,1,80,0,4.094919," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-\frac{90 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{165 i \, \tan\left(d x + c\right)^{3} + 291 \, \tan\left(d x + c\right)^{2} - 171 i \, \tan\left(d x + c\right) - 29}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(-90*I*log(tan(d*x + c) - I)/a^3 - 6*I*log(-I*tan(d*x + c) + 1)/a^3 + (165*I*tan(d*x + c)^3 + 291*tan(d*x + c)^2 - 171*I*tan(d*x + c) - 29)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
69,1,81,0,2.589061," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{6 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{3}} - \frac{6 \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} - \frac{11 \, \tan\left(d x + c\right)^{3} + 51 i \, \tan\left(d x + c\right)^{2} + 75 \, \tan\left(d x + c\right) - 29 i}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"1/96*(6*log(tan(d*x + c) - I)/a^3 - 6*log(I*tan(d*x + c) - 1)/a^3 - (11*tan(d*x + c)^3 + 51*I*tan(d*x + c)^2 + 75*tan(d*x + c) - 29*I)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
70,1,80,0,4.665207," ","integrate(tan(d*x+c)^2/(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} - 21 i \, \tan\left(d x + c\right) - 3}{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 - 21*I*tan(d*x + c) - 3)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
71,1,81,0,1.828562," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{3}} - \frac{6 \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} - \frac{11 \, \tan\left(d x + c\right)^{3} - 45 i \, \tan\left(d x + c\right)^{2} - 69 \, \tan\left(d x + c\right) + 19 i}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(6*log(tan(d*x + c) - I)/a^3 - 6*log(I*tan(d*x + c) - 1)/a^3 - (11*tan(d*x + c)^3 - 45*I*tan(d*x + c)^2 - 69*tan(d*x + c) + 19*I)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
72,1,80,0,1.067099," ","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
73,1,93,0,2.627075," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{90 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{3}} + \frac{6 \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} - \frac{96 \, \log\left(\tan\left(d x + c\right)\right)}{a^{3}} - \frac{165 \, \tan\left(d x + c\right)^{3} - 579 i \, \tan\left(d x + c\right)^{2} - 699 \, \tan\left(d x + c\right) + 301 i}{a^{3} {\left(\tan\left(d x + c\right) - i\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(90*log(tan(d*x + c) - I)/a^3 + 6*log(I*tan(d*x + c) - 1)/a^3 - 96*log(tan(d*x + c))/a^3 - (165*tan(d*x + c)^3 - 579*I*tan(d*x + c)^2 - 699*tan(d*x + c) + 301*I)/(a^3*(tan(d*x + c) - I)^3))/d","A",0
74,1,119,0,3.710077," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{-\frac{294 i \, \log\left(i \, \tan\left(d x + c\right) + 1\right)}{a^{3}} + \frac{6 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{3}} + \frac{288 i \, \log\left(\tan\left(d x + c\right)\right)}{a^{3}} + \frac{96 \, {\left(-3 i \, \tan\left(d x + c\right) + 1\right)}}{a^{3} \tan\left(d x + c\right)} + \frac{539 \, \tan\left(d x + c\right)^{3} - 1821 i \, \tan\left(d x + c\right)^{2} - 2085 \, \tan\left(d x + c\right) + 819 i}{a^{3} {\left(i \, \tan\left(d x + c\right) + 1\right)}^{3}}}{96 \, d}"," ",0,"-1/96*(-294*I*log(I*tan(d*x + c) + 1)/a^3 + 6*I*log(I*tan(d*x + c) - 1)/a^3 + 288*I*log(tan(d*x + c))/a^3 + 96*(-3*I*tan(d*x + c) + 1)/(a^3*tan(d*x + c)) + (539*tan(d*x + c)^3 - 1821*I*tan(d*x + c)^2 - 2085*tan(d*x + c) + 819*I)/(a^3*(I*tan(d*x + c) + 1)^3))/d","A",0
75,1,100,0,22.102366," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 i \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{4}} - \frac{1548 i \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{4}} - \frac{384 \, \tan\left(d x + c\right)}{a^{4}} - \frac{-3225 i \, \tan\left(d x + c\right)^{4} - 10236 \, \tan\left(d x + c\right)^{3} + 12534 i \, \tan\left(d x + c\right)^{2} + 6908 \, \tan\left(d x + c\right) - 1433 i}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(12*I*log(tan(d*x + c) + I)/a^4 - 1548*I*log(tan(d*x + c) - I)/a^4 - 384*tan(d*x + c)/a^4 - (-3225*I*tan(d*x + c)^4 - 10236*tan(d*x + c)^3 + 12534*I*tan(d*x + c)^2 + 6908*tan(d*x + c) - 1433*I)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
76,1,89,0,9.652057," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{12 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{4}} + \frac{372 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{4}} - \frac{775 \, \tan\left(d x + c\right)^{4} - 1924 i \, \tan\left(d x + c\right)^{3} - 1866 \, \tan\left(d x + c\right)^{2} + 772 i \, \tan\left(d x + c\right) + 103}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"1/384*(12*log(tan(d*x + c) + I)/a^4 + 372*log(tan(d*x + c) - I)/a^4 - (775*tan(d*x + c)^4 - 1924*I*tan(d*x + c)^3 - 1866*tan(d*x + c)^2 + 772*I*tan(d*x + c) + 103)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
77,1,92,0,6.526147," ","integrate(tan(d*x+c)^4/(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} + 260 \, \tan\left(d x + c\right)^{3} - 522 i \, \tan\left(d x + c\right)^{2} - 388 \, \tan\left(d x + c\right) + 103 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 + 260*tan(d*x + c)^3 - 522*I*tan(d*x + c)^2 - 388*tan(d*x + c) + 103*I)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
78,1,88,0,3.492024," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{4}} - \frac{12 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{4}} + \frac{25 \, \tan\left(d x + c\right)^{4} - 124 i \, \tan\left(d x + c\right)^{3} - 54 \, \tan\left(d x + c\right)^{2} - 4 i \, \tan\left(d x + c\right) - 7}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(12*log(tan(d*x + c) + I)/a^4 - 12*log(tan(d*x + c) - I)/a^4 + (25*tan(d*x + c)^4 - 124*I*tan(d*x + c)^3 - 54*tan(d*x + c)^2 - 4*I*tan(d*x + c) - 7)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
79,1,87,0,2.554940," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{2 i \, \log\left(-i \, \tan\left(2 \, d x + 2 \, c\right) + 1\right)}{a^{4}} - \frac{2 i \, \log\left(-i \, \tan\left(2 \, d x + 2 \, c\right) - 1\right)}{a^{4}} + \frac{3 i \, \tan\left(2 \, d x + 2 \, c\right)^{2} - 6 \, \tan\left(2 \, d x + 2 \, c\right) + 5 i}{a^{4} {\left(\tan\left(2 \, d x + 2 \, c\right) - i\right)}^{2}}}{128 \, d}"," ",0,"-1/128*(2*I*log(-I*tan(2*d*x + 2*c) + 1)/a^4 - 2*I*log(-I*tan(2*d*x + 2*c) - 1)/a^4 + (3*I*tan(2*d*x + 2*c)^2 - 6*tan(2*d*x + 2*c) + 5*I)/(a^4*(tan(2*d*x + 2*c) - I)^2))/d","A",0
80,1,88,0,1.888961," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{12 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{4}} - \frac{12 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{4}} + \frac{25 \, \tan\left(d x + c\right)^{4} - 124 i \, \tan\left(d x + c\right)^{3} - 246 \, \tan\left(d x + c\right)^{2} + 252 i \, \tan\left(d x + c\right) + 57}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"1/384*(12*log(tan(d*x + c) + I)/a^4 - 12*log(tan(d*x + c) - I)/a^4 + (25*tan(d*x + c)^4 - 124*I*tan(d*x + c)^3 - 246*tan(d*x + c)^2 + 252*I*tan(d*x + c) + 57)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
81,1,92,0,0.832081," ","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
82,1,101,0,3.518425," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{12 \, \log\left(\tan\left(d x + c\right) + i\right)}{a^{4}} + \frac{372 \, \log\left(\tan\left(d x + c\right) - i\right)}{a^{4}} - \frac{384 \, \log\left(\tan\left(d x + c\right)\right)}{a^{4}} - \frac{775 \, \tan\left(d x + c\right)^{4} - 3460 i \, \tan\left(d x + c\right)^{3} - 5898 \, \tan\left(d x + c\right)^{2} + 4612 i \, \tan\left(d x + c\right) + 1447}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(12*log(tan(d*x + c) + I)/a^4 + 372*log(tan(d*x + c) - I)/a^4 - 384*log(tan(d*x + c))/a^4 - (775*tan(d*x + c)^4 - 3460*I*tan(d*x + c)^3 - 5898*tan(d*x + c)^2 + 4612*I*tan(d*x + c) + 1447)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
83,1,129,0,5.361595," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{1536 i \, \log\left(-i \, \tan\left(d x + c\right)\right)}{a^{4}} + \frac{12 i \, \log\left(i \, \tan\left(d x + c\right) - 1\right)}{a^{4}} - \frac{1548 i \, \log\left(-i \, \tan\left(d x + c\right) - 1\right)}{a^{4}} + \frac{384 \, {\left(-4 i \, \tan\left(d x + c\right) + 1\right)}}{a^{4} \tan\left(d x + c\right)} + \frac{3225 i \, \tan\left(d x + c\right)^{4} + 14076 \, \tan\left(d x + c\right)^{3} - 23286 i \, \tan\left(d x + c\right)^{2} - 17404 \, \tan\left(d x + c\right) + 5017 i}{a^{4} {\left(\tan\left(d x + c\right) - i\right)}^{4}}}{384 \, d}"," ",0,"-1/384*(1536*I*log(-I*tan(d*x + c))/a^4 + 12*I*log(I*tan(d*x + c) - 1)/a^4 - 1548*I*log(-I*tan(d*x + c) - 1)/a^4 + 384*(-4*I*tan(d*x + c) + 1)/(a^4*tan(d*x + c)) + (3225*I*tan(d*x + c)^4 + 14076*tan(d*x + c)^3 - 23286*I*tan(d*x + c)^2 - 17404*tan(d*x + c) + 5017*I)/(a^4*(tan(d*x + c) - I)^4))/d","A",0
84,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^2, x)","F",0
87,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a), x)","F",0
89,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c), x)","F",0
90,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^2, x)","F",0
91,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^3, x)","F",0
92,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c), x)","F",0
97,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^2, x)","F",0
98,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^3, x)","F",0
99,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(tan(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
101,0,0,0,0.000000," ","integrate(tan(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}} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*tan(d*x + c), x)","F",0
102,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c), x)","F",0
104,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^2, x)","F",0
105,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^3, x)","F",0
106,0,0,0,0.000000," ","integrate(cot(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}} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^4, x)","F",0
107,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,0,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{5}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^5/sqrt(I*a*tan(d*x + c) + a), x)","F",0
109,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/sqrt(I*a*tan(d*x + c) + a), x)","F",0
110,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{3}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/sqrt(I*a*tan(d*x + c) + a), x)","F",0
111,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/sqrt(I*a*tan(d*x + c) + a), x)","F",0
112,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
113,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(1/sqrt(I*a*tan(d*x + c) + a), x)","F",0
114,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
115,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/sqrt(I*a*tan(d*x + c) + a), x)","F",0
116,0,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{3}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^3/sqrt(I*a*tan(d*x + c) + a), x)","F",0
117,0,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{5}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^5/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
121,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
122,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-3/2), x)","F",0
123,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
124,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
125,0,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^3/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
126,0,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{5}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^5/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
127,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
128,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
129,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
130,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
131,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-5/2), x)","F",0
132,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
133,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-7/2), x)","F",0
135,1,154,0,3.726812," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2}{15} \, a d^{2} {\left(\frac{15 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{-3 i \, \sqrt{d \tan\left(f x + e\right)} d^{10} f^{4} \tan\left(f x + e\right)^{2} - 5 \, \sqrt{d \tan\left(f x + e\right)} d^{10} f^{4} \tan\left(f x + e\right) + 15 i \, \sqrt{d \tan\left(f x + e\right)} d^{10} f^{4}}{d^{10} f^{5}}\right)}"," ",0,"-2/15*a*d^2*(15*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) + (-3*I*sqrt(d*tan(f*x + e))*d^10*f^4*tan(f*x + e)^2 - 5*sqrt(d*tan(f*x + e))*d^10*f^4*tan(f*x + e) + 15*I*sqrt(d*tan(f*x + e))*d^10*f^4)/(d^10*f^5))","A",0
136,1,124,0,1.920036," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2}{3} \, a d {\left(\frac{3 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{-i \, \sqrt{d \tan\left(f x + e\right)} d^{3} f^{2} \tan\left(f x + e\right) - 3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f^{2}}{d^{3} f^{3}}\right)}"," ",0,"-2/3*a*d*(3*I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) + (-I*sqrt(d*tan(f*x + e))*d^3*f^2*tan(f*x + e) - 3*sqrt(d*tan(f*x + e))*d^3*f^2)/(d^3*f^3))","A",0
137,1,89,0,0.533504," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, a {\left(\frac{\sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{i \, \sqrt{d \tan\left(f x + e\right)} d}{f}\right)}}{d}"," ",0,"2*a*(sqrt(2)*d^(3/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) + I*sqrt(d*tan(f*x + e))*d/f)/d","A",0
138,1,67,0,1.168884," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} a \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}}"," ",0,"2*sqrt(2)*a*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(-I*d/sqrt(d^2) + 1))","C",0
139,1,89,0,0.914704," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, a {\left(\frac{i \, \sqrt{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{1}{\sqrt{d \tan\left(f x + e\right)} f}\right)}}{d}"," ",0,"2*a*(I*sqrt(2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) - 1/(sqrt(d*tan(f*x + e))*f))/d","C",0
140,1,109,0,3.383404," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{2}{3} \, a {\left(\frac{3 i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{5}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, d \tan\left(f x + e\right) + d}{\sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}\right)}"," ",0,"-2/3*a*(3*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(5/2)*f*(I*d/sqrt(d^2) + 1)) + (3*I*d*tan(f*x + e) + d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e)))","A",0
141,1,130,0,3.016044," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""giac"")","-\frac{2}{15} \, a {\left(\frac{15 i \, \sqrt{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{7}{2}} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{15 \, d^{2} \tan\left(f x + e\right)^{2} - 5 i \, d^{2} \tan\left(f x + e\right) - 3 \, d^{2}}{\sqrt{d \tan\left(f x + e\right)} d^{5} f \tan\left(f x + e\right)^{2}}\right)}"," ",0,"-2/15*a*(15*I*sqrt(2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(7/2)*f*(-I*d/sqrt(d^2) + 1)) - (15*d^2*tan(f*x + e)^2 - 5*I*d^2*tan(f*x + e) - 3*d^2)/(sqrt(d*tan(f*x + e))*d^5*f*tan(f*x + e)^2))","A",0
142,1,154,0,0.928854," ","integrate((d*tan(f*x+e))^(5/2)*(a-I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2}{15} \, a d^{2} {\left(\frac{15 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, \sqrt{d \tan\left(f x + e\right)} d^{10} f^{4} \tan\left(f x + e\right)^{2} - 5 \, \sqrt{d \tan\left(f x + e\right)} d^{10} f^{4} \tan\left(f x + e\right) - 15 i \, \sqrt{d \tan\left(f x + e\right)} d^{10} f^{4}}{d^{10} f^{5}}\right)}"," ",0,"-2/15*a*d^2*(15*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(-I*d/sqrt(d^2) + 1)) + (3*I*sqrt(d*tan(f*x + e))*d^10*f^4*tan(f*x + e)^2 - 5*sqrt(d*tan(f*x + e))*d^10*f^4*tan(f*x + e) - 15*I*sqrt(d*tan(f*x + e))*d^10*f^4)/(d^10*f^5))","A",0
143,1,124,0,0.732372," ","integrate((d*tan(f*x+e))^(3/2)*(a-I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2}{3} \, a d {\left(-\frac{3 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{i \, \sqrt{d \tan\left(f x + e\right)} d^{3} f^{2} \tan\left(f x + e\right) - 3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f^{2}}{d^{3} f^{3}}\right)}"," ",0,"-2/3*a*d*(-3*I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(-I*d/sqrt(d^2) + 1)) + (I*sqrt(d*tan(f*x + e))*d^3*f^2*tan(f*x + e) - 3*sqrt(d*tan(f*x + e))*d^3*f^2)/(d^3*f^3))","A",0
144,1,89,0,0.998717," ","integrate((d*tan(f*x+e))^(1/2)*(a-I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, a {\left(\frac{\sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{i \, \sqrt{d \tan\left(f x + e\right)} d}{f}\right)}}{d}"," ",0,"2*a*(sqrt(2)*d^(3/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(-I*d/sqrt(d^2) + 1)) - I*sqrt(d*tan(f*x + e))*d/f)/d","A",0
145,1,67,0,2.193676," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} a \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}}"," ",0,"2*sqrt(2)*a*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(I*d/sqrt(d^2) + 1))","C",0
146,1,89,0,0.779089," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, a {\left(-\frac{i \, \sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{1}{\sqrt{d \tan\left(f x + e\right)} f}\right)}}{d}"," ",0,"2*a*(-I*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - 1/(sqrt(d*tan(f*x + e))*f))/d","C",0
147,1,109,0,0.946437," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{2}{3} \, a {\left(-\frac{3 i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{5}{2}} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{-3 i \, d \tan\left(f x + e\right) + d}{\sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}\right)}"," ",0,"-2/3*a*(-3*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(5/2)*f*(-I*d/sqrt(d^2) + 1)) + (-3*I*d*tan(f*x + e) + d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e)))","A",0
148,1,130,0,1.909244," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""giac"")","-\frac{2}{15} \, a {\left(-\frac{15 i \, \sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{7}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{15 \, d^{2} \tan\left(f x + e\right)^{2} + 5 i \, d^{2} \tan\left(f x + e\right) - 3 \, d^{2}}{\sqrt{d \tan\left(f x + e\right)} d^{5} f \tan\left(f x + e\right)^{2}}\right)}"," ",0,"-2/15*a*(-15*I*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(7/2)*f*(I*d/sqrt(d^2) + 1)) - (15*d^2*tan(f*x + e)^2 + 5*I*d^2*tan(f*x + e) - 3*d^2)/(sqrt(d*tan(f*x + e))*d^5*f*tan(f*x + e)^2))","A",0
149,1,192,0,2.156692," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{4 \, \sqrt{2} a^{2} d^{\frac{5}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{30 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6} \tan\left(f x + e\right)^{3} - 84 i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6} \tan\left(f x + e\right)^{2} - 140 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6} \tan\left(f x + e\right) + 420 i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6}}{105 \, d^{7} f^{7}}"," ",0,"-4*sqrt(2)*a^2*d^(5/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) - 1/105*(30*sqrt(d*tan(f*x + e))*a^2*d^9*f^6*tan(f*x + e)^3 - 84*I*sqrt(d*tan(f*x + e))*a^2*d^9*f^6*tan(f*x + e)^2 - 140*sqrt(d*tan(f*x + e))*a^2*d^9*f^6*tan(f*x + e) + 420*I*sqrt(d*tan(f*x + e))*a^2*d^9*f^6)/(d^7*f^7)","A",0
150,1,163,0,1.748244," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{1}{15} \, {\left(\frac{60 i \, \sqrt{2} a^{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{6 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{10} f^{4} \tan\left(f x + e\right)^{2} - 20 i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{10} f^{4} \tan\left(f x + e\right) - 60 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{10} f^{4}}{d^{10} f^{5}}\right)} d"," ",0,"-1/15*(60*I*sqrt(2)*a^2*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) + (6*sqrt(d*tan(f*x + e))*a^2*d^10*f^4*tan(f*x + e)^2 - 20*I*sqrt(d*tan(f*x + e))*a^2*d^10*f^4*tan(f*x + e) - 60*sqrt(d*tan(f*x + e))*a^2*d^10*f^4)/(d^10*f^5))*d","A",0
151,1,130,0,1.540401," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{4 \, \sqrt{2} a^{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f^{2} \tan\left(f x + e\right) - 12 i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f^{2}}{3 \, d^{3} f^{3}}"," ",0,"4*sqrt(2)*a^2*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) - 1/3*(2*sqrt(d*tan(f*x + e))*a^2*d^3*f^2*tan(f*x + e) - 12*I*sqrt(d*tan(f*x + e))*a^2*d^3*f^2)/(d^3*f^3)","A",0
152,1,92,0,0.814513," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{4 i \, \sqrt{2} a^{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, \sqrt{d \tan\left(f x + e\right)} a^{2}}{d f}"," ",0,"4*I*sqrt(2)*a^2*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - 2*sqrt(d*tan(f*x + e))*a^2/(d*f)","C",0
153,1,93,0,3.143990," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\frac{4 i \, \sqrt{2} a^{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, a^{2}}{\sqrt{d \tan\left(f x + e\right)} f}}{d}"," ",0,"(4*I*sqrt(2)*a^2*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) - 2*a^2/(sqrt(d*tan(f*x + e))*f))/d","C",0
154,1,117,0,2.176260," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{4 i \, \sqrt{2} a^{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{5}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, {\left(6 i \, a^{2} d \tan\left(f x + e\right) + a^{2} d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}"," ",0,"-4*I*sqrt(2)*a^2*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(5/2)*f*(I*d/sqrt(d^2) + 1)) - 2/3*(6*I*a^2*d*tan(f*x + e) + a^2*d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e))","A",0
155,1,139,0,2.997752," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(7/2),x, algorithm=""giac"")","-\frac{4 i \, \sqrt{2} a^{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{7}{2}} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{60 \, a^{2} d^{2} \tan\left(f x + e\right)^{2} - 20 i \, a^{2} d^{2} \tan\left(f x + e\right) - 6 \, a^{2} d^{2}}{15 \, \sqrt{d \tan\left(f x + e\right)} d^{5} f \tan\left(f x + e\right)^{2}}"," ",0,"-4*I*sqrt(2)*a^2*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(7/2)*f*(-I*d/sqrt(d^2) + 1)) + 1/15*(60*a^2*d^2*tan(f*x + e)^2 - 20*I*a^2*d^2*tan(f*x + e) - 6*a^2*d^2)/(sqrt(d*tan(f*x + e))*d^5*f*tan(f*x + e)^2)","A",0
156,1,223,0,2.567360," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{8 \, \sqrt{2} a^{3} d^{\frac{5}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{70 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right)^{4} + 270 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right)^{3} - 504 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right)^{2} - 840 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right) + 2520 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8}}{315 \, d^{18} f^{9}}"," ",0,"-8*sqrt(2)*a^3*d^(5/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) - 1/315*(70*I*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e)^4 + 270*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e)^3 - 504*I*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e)^2 - 840*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e) + 2520*I*sqrt(d*tan(f*x + e))*a^3*d^20*f^8)/(d^18*f^9)","A",0
157,1,194,0,1.929541," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{105} \, {\left(\frac{840 i \, \sqrt{2} a^{3} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{30 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6} \tan\left(f x + e\right)^{3} + 126 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6} \tan\left(f x + e\right)^{2} - 280 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6} \tan\left(f x + e\right) - 840 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6}}{d^{21} f^{7}}\right)} d"," ",0,"-1/105*(840*I*sqrt(2)*a^3*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) + (30*I*sqrt(d*tan(f*x + e))*a^3*d^21*f^6*tan(f*x + e)^3 + 126*sqrt(d*tan(f*x + e))*a^3*d^21*f^6*tan(f*x + e)^2 - 280*I*sqrt(d*tan(f*x + e))*a^3*d^21*f^6*tan(f*x + e) - 840*sqrt(d*tan(f*x + e))*a^3*d^21*f^6)/(d^21*f^7))*d","A",0
158,1,161,0,1.543724," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{8 \, \sqrt{2} a^{3} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{10} f^{4} \tan\left(f x + e\right)^{2} + 10 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{10} f^{4} \tan\left(f x + e\right) - 40 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{10} f^{4}}{5 \, d^{10} f^{5}}"," ",0,"8*sqrt(2)*a^3*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(f*(I*d/sqrt(d^2) + 1)) - 1/5*(2*I*sqrt(d*tan(f*x + e))*a^3*d^10*f^4*tan(f*x + e)^2 + 10*sqrt(d*tan(f*x + e))*a^3*d^10*f^4*tan(f*x + e) - 40*I*sqrt(d*tan(f*x + e))*a^3*d^10*f^4)/(d^10*f^5)","A",0
159,1,130,0,1.395037," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{8 i \, \sqrt{2} a^{3} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, {\left(i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{5} f^{2} \tan\left(f x + e\right) + 9 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{5} f^{2}\right)}}{3 \, d^{6} f^{3}}"," ",0,"8*I*sqrt(2)*a^3*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - 2/3*(I*sqrt(d*tan(f*x + e))*a^3*d^5*f^2*tan(f*x + e) + 9*sqrt(d*tan(f*x + e))*a^3*d^5*f^2)/(d^6*f^3)","A",0
160,1,115,0,1.453830," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\frac{8 i \, \sqrt{2} a^{3} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{\sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, a^{3}}{\sqrt{d \tan\left(f x + e\right)} f} - \frac{2 i \, \sqrt{d \tan\left(f x + e\right)} a^{3}}{d f}}{d}"," ",0,"(8*I*sqrt(2)*a^3*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) - 2*a^3/(sqrt(d*tan(f*x + e))*f) - 2*I*sqrt(d*tan(f*x + e))*a^3/(d*f))/d","A",0
161,1,117,0,1.627996," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{8 i \, \sqrt{2} a^{3} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{5}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, {\left(9 i \, a^{3} d \tan\left(f x + e\right) + a^{3} d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}"," ",0,"-8*I*sqrt(2)*a^3*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(5/2)*f*(I*d/sqrt(d^2) + 1)) - 2/3*(9*I*a^3*d*tan(f*x + e) + a^3*d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e))","A",0
162,1,139,0,2.220660," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\frac{8 i \, \sqrt{2} a^{3} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{7}{2}} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{40 \, a^{3} d^{2} \tan\left(f x + e\right)^{2} - 10 i \, a^{3} d^{2} \tan\left(f x + e\right) - 2 \, a^{3} d^{2}}{5 \, \sqrt{d \tan\left(f x + e\right)} d^{5} f \tan\left(f x + e\right)^{2}}"," ",0,"8*I*sqrt(2)*a^3*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(7/2)*f*(-I*d/sqrt(d^2) + 1)) + 1/5*(40*a^3*d^2*tan(f*x + e)^2 - 10*I*a^3*d^2*tan(f*x + e) - 2*a^3*d^2)/(sqrt(d*tan(f*x + e))*d^5*f*tan(f*x + e)^2)","A",0
163,1,156,0,2.422931," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x, algorithm=""giac"")","\frac{8 i \, \sqrt{2} a^{3} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{d^{\frac{9}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{-840 i \, a^{3} d^{3} \tan\left(f x + e\right)^{3} - 280 \, a^{3} d^{3} \tan\left(f x + e\right)^{2} + 126 i \, a^{3} d^{3} \tan\left(f x + e\right) + 30 \, a^{3} d^{3}}{105 \, \sqrt{d \tan\left(f x + e\right)} d^{7} f \tan\left(f x + e\right)^{3}}"," ",0,"8*I*sqrt(2)*a^3*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(d^(9/2)*f*(I*d/sqrt(d^2) + 1)) - 1/105*(-840*I*a^3*d^3*tan(f*x + e)^3 - 280*a^3*d^3*tan(f*x + e)^2 + 126*I*a^3*d^3*tan(f*x + e) + 30*a^3*d^3)/(sqrt(d*tan(f*x + e))*d^7*f*tan(f*x + e)^3)","A",0
164,1,242,0,1.592482," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{1}{6} \, d^{3} {\left(\frac{18 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, \sqrt{d \tan\left(f x + e\right)} d}{{\left(d \tan\left(f x + e\right) - i \, d\right)} a f} + \frac{4 \, {\left(i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f^{2} \tan\left(f x + e\right) - 3 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f^{2}\right)}}{a^{3} d^{3} f^{3}}\right)}"," ",0,"-1/6*d^3*(18*sqrt(2)*sqrt(d)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(I*d/sqrt(d^2) + 1)) + 3*sqrt(2)*sqrt(d)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(-I*d/sqrt(d^2) + 1)) + 3*I*sqrt(d*tan(f*x + e))*d/((d*tan(f*x + e) - I*d)*a*f) + 4*(I*sqrt(d*tan(f*x + e))*a^2*d^3*f^2*tan(f*x + e) - 3*sqrt(d*tan(f*x + e))*a^2*d^3*f^2)/(a^3*d^3*f^3))","A",0
165,1,197,0,3.152363," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{1}{2} \, d^{2} {\left(\frac{4 i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{4 i \, \sqrt{d \tan\left(f x + e\right)}}{a f} + \frac{\sqrt{d \tan\left(f x + e\right)} d}{{\left(d \tan\left(f x + e\right) - i \, d\right)} a f}\right)}"," ",0,"-1/2*d^2*(4*I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(I*d/sqrt(d^2) + 1)) - I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(-I*d/sqrt(d^2) + 1)) + 4*I*sqrt(d*tan(f*x + e))/(a*f) + sqrt(d*tan(f*x + e))*d/((d*tan(f*x + e) - I*d)*a*f))","A",0
166,1,177,0,0.993619," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{1}{2} \, d {\left(\frac{i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{2 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{i \, \sqrt{d \tan\left(f x + e\right)} d}{{\left(d \tan\left(f x + e\right) - i \, d\right)} a f}\right)}"," ",0,"-1/2*d*(I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(I*d/sqrt(d^2) + 1)) + 2*I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(-I*d/sqrt(d^2) + 1)) - I*sqrt(d*tan(f*x + e))*d/((d*tan(f*x + e) - I*d)*a*f))","A",0
167,1,110,0,0.810041," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{\sqrt{d \tan\left(f x + e\right)} d^{2}}{{\left(d \tan\left(f x + e\right) - i \, d\right)} a f}}{2 \, d}"," ",0,"1/2*(sqrt(2)*d^(3/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*f*(I*d/sqrt(d^2) + 1)) + sqrt(d*tan(f*x + e))*d^2/((d*tan(f*x + e) - I*d)*a*f))/d","A",0
168,1,173,0,0.816659," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{2 \, a \sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a \sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{i \, \sqrt{d \tan\left(f x + e\right)}}{2 \, {\left(d \tan\left(f x + e\right) - i \, d\right)} a f}"," ",0,"1/2*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) - 1/2*I*sqrt(d*tan(f*x + e))/((d*tan(f*x + e) - I*d)*a*f)","A",0
169,1,202,0,2.469686," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{5 i \, d \tan\left(f x + e\right) + 4 \, d}{{\left(i \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) + \sqrt{d \tan\left(f x + e\right)} d\right)} a f} + \frac{4 i \, \sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a \sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{i \, \sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a \sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}}}{2 \, d}"," ",0,"-1/2*((5*I*d*tan(f*x + e) + 4*d)/((I*sqrt(d*tan(f*x + e))*d*tan(f*x + e) + sqrt(d*tan(f*x + e))*d)*a*f) + 4*I*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*sqrt(d)*f*(I*d/sqrt(d^2) + 1)) + I*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*sqrt(d)*f*(-I*d/sqrt(d^2) + 1)))/d","A",0
170,1,220,0,1.486643," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{2 \, a d^{\frac{5}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a d^{\frac{5}{2}} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{\sqrt{d \tan\left(f x + e\right)}}{2 \, {\left(i \, d \tan\left(f x + e\right) + d\right)} a d^{2} f} + \frac{2 \, {\left(3 i \, d \tan\left(f x + e\right) - d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} a d^{3} f \tan\left(f x + e\right)}"," ",0,"-1/2*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*d^(5/2)*f*(I*d/sqrt(d^2) + 1)) + 3*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a*d^(5/2)*f*(-I*d/sqrt(d^2) + 1)) - 1/2*sqrt(d*tan(f*x + e))/((I*d*tan(f*x + e) + d)*a*d^2*f) + 2/3*(3*I*d*tan(f*x + e) - d)/(sqrt(d*tan(f*x + e))*a*d^3*f*tan(f*x + e))","A",0
171,1,269,0,1.517053," ","integrate((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{24} \, d^{4} {\left(-\frac{141 i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{6 i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{3 \, {\left(15 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) - 13 i \, \sqrt{d \tan\left(f x + e\right)} d^{2}\right)}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f} - \frac{16 \, {\left(\sqrt{d \tan\left(f x + e\right)} a^{4} d^{3} f^{2} \tan\left(f x + e\right) + 6 i \, \sqrt{d \tan\left(f x + e\right)} a^{4} d^{3} f^{2}\right)}}{a^{6} d^{3} f^{3}}\right)}"," ",0,"1/24*d^4*(-141*I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(I*d/sqrt(d^2) + 1)) - 6*I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(-I*d/sqrt(d^2) + 1)) - 3*(15*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) - 13*I*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) - I*d)^2*a^2*f) - 16*(sqrt(d*tan(f*x + e))*a^4*d^3*f^2*tan(f*x + e) + 6*I*sqrt(d*tan(f*x + e))*a^4*d^3*f^2)/(a^6*d^3*f^3))","A",0
172,1,226,0,1.392305," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{1}{8} \, d^{3} {\left(\frac{23 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{16 \, \sqrt{d \tan\left(f x + e\right)}}{a^{2} f} - \frac{11 i \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) + 9 \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}\right)}"," ",0,"-1/8*d^3*(23*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(I*d/sqrt(d^2) + 1)) - 2*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(-I*d/sqrt(d^2) + 1)) + 16*sqrt(d*tan(f*x + e))/(a^2*f) - (11*I*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) + 9*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) - I*d)^2*a^2*f))","A",0
173,1,206,0,1.182806," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{8} \, d^{2} {\left(\frac{7 i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{2 i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{7 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) - 5 i \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}\right)}"," ",0,"1/8*d^2*(7*I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(I*d/sqrt(d^2) + 1)) + 2*I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(-I*d/sqrt(d^2) + 1)) + (7*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) - 5*I*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) - I*d)^2*a^2*f))","A",0
174,1,203,0,1.490875," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{8} \, d {\left(\frac{\sqrt{2} \sqrt{d} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{2 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{-3 i \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) - \sqrt{d \tan\left(f x + e\right)} d^{2}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}\right)}"," ",0,"1/8*d*(sqrt(2)*sqrt(d)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(I*d/sqrt(d^2) + 1)) + 2*sqrt(2)*sqrt(d)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(-I*d/sqrt(d^2) + 1)) + (-3*I*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) - sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) - I*d)^2*a^2*f))","A",0
175,1,205,0,1.086538," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{i \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 i \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{\sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right) - 3 i \, \sqrt{d \tan\left(f x + e\right)} d^{3}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}}{8 \, d}"," ",0,"1/8*(I*sqrt(2)*d^(3/2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(I*d/sqrt(d^2) + 1)) - 2*I*sqrt(2)*d^(3/2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*f*(-I*d/sqrt(d^2) + 1)) + (sqrt(d*tan(f*x + e))*d^3*tan(f*x + e) - 3*I*sqrt(d*tan(f*x + e))*d^3)/((d*tan(f*x + e) - I*d)^2*a^2*f))/d","A",0
176,1,198,0,1.689788," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{7 \, \sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{8 \, a^{2} \sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{\sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{4 \, a^{2} \sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{-5 i \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) - 7 \, \sqrt{d \tan\left(f x + e\right)} d}{8 \, {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}"," ",0,"7/8*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - 1/4*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) + 1/8*(-5*I*sqrt(d*tan(f*x + e))*d*tan(f*x + e) - 7*sqrt(d*tan(f*x + e))*d)/((d*tan(f*x + e) - I*d)^2*a^2*f)","A",0
177,1,221,0,3.838676," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} \sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{23 i \, \sqrt{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{2} \sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{16}{\sqrt{d \tan\left(f x + e\right)} a^{2} f} + \frac{9 \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) - 11 i \, \sqrt{d \tan\left(f x + e\right)} d}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}}{8 \, d}"," ",0,"-1/8*(2*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - 23*I*sqrt(2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*sqrt(d)*f*(I*d/sqrt(d^2) + 1)) + 16/(sqrt(d*tan(f*x + e))*a^2*f) + (9*sqrt(d*tan(f*x + e))*d*tan(f*x + e) - 11*I*sqrt(d*tan(f*x + e))*d)/((d*tan(f*x + e) - I*d)^2*a^2*f))/d","A",0
178,1,246,0,1.849094," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{47 \, \sqrt{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{8 \, a^{2} d^{\frac{5}{2}} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{\sqrt{2} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{4 \, a^{2} d^{\frac{5}{2}} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{13 i \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) + 15 \, \sqrt{d \tan\left(f x + e\right)} d}{8 \, {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} d^{2} f} + \frac{2 \, {\left(6 i \, d \tan\left(f x + e\right) - d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f \tan\left(f x + e\right)}"," ",0,"47/8*sqrt(2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*d^(5/2)*f*(I*d/sqrt(d^2) + 1)) - 1/4*sqrt(2)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^2*d^(5/2)*f*(-I*d/sqrt(d^2) + 1)) + 1/8*(13*I*sqrt(d*tan(f*x + e))*d*tan(f*x + e) + 15*sqrt(d*tan(f*x + e))*d)/((d*tan(f*x + e) - I*d)^2*a^2*d^2*f) + 2/3*(6*I*d*tan(f*x + e) - d)/(sqrt(d*tan(f*x + e))*a^2*d^3*f*tan(f*x + e))","A",0
179,1,251,0,3.333899," ","integrate((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{24} \, d^{4} {\left(\frac{87 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, \sqrt{2} \sqrt{d} \arctan\left(-\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{48 i \, \sqrt{d \tan\left(f x + e\right)}}{a^{3} f} - \frac{2 \, {\left(30 \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right)^{2} - 49 i \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right) - 21 \, \sqrt{d \tan\left(f x + e\right)} d^{3}\right)}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}\right)}"," ",0,"-1/24*d^4*(87*I*sqrt(2)*sqrt(d)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(I*d/sqrt(d^2) + 1)) + 3*I*sqrt(2)*sqrt(d)*arctan(-16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(-I*d/sqrt(d^2) + 1)) - 48*I*sqrt(d*tan(f*x + e))/(a^3*f) - 2*(30*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e)^2 - 49*I*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e) - 21*sqrt(d*tan(f*x + e))*d^3)/((d*tan(f*x + e) - I*d)^3*a^3*f))","A",0
180,1,231,0,2.493930," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{24} \, d^{3} {\left(-\frac{3 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{18 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{27 i \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right)^{2} + 38 \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right) - 15 i \, \sqrt{d \tan\left(f x + e\right)} d^{3}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}\right)}"," ",0,"-1/24*d^3*(-3*I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(I*d/sqrt(d^2) + 1)) - 18*I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(-I*d/sqrt(d^2) + 1)) + (27*I*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e)^2 + 38*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e) - 15*I*sqrt(d*tan(f*x + e))*d^3)/((d*tan(f*x + e) - I*d)^3*a^3*f))","A",0
181,1,216,0,3.230033," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{24} \, d^{2} {\left(\frac{3 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{2 \, {\left(3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right)^{2} - i \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right)\right)}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}\right)}"," ",0,"-1/24*d^2*(3*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(I*d/sqrt(d^2) + 1)) + 3*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(-I*d/sqrt(d^2) + 1)) + 2*(3*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e)^2 - I*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e))/((d*tan(f*x + e) - I*d)^3*a^3*f))","A",0
182,1,160,0,2.707795," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{24} \, d {\left(\frac{3 i \, \sqrt{2} \sqrt{d} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right)^{2} + 10 \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right) - 3 i \, \sqrt{d \tan\left(f x + e\right)} d^{3}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}\right)}"," ",0,"-1/24*d*(3*I*sqrt(2)*sqrt(d)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(I*d/sqrt(d^2) + 1)) + (3*I*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e)^2 + 10*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e) - 3*I*sqrt(d*tan(f*x + e))*d^3)/((d*tan(f*x + e) - I*d)^3*a^3*f))","A",0
183,1,207,0,5.611564," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{3 \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{3 \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{2 \, {\left(i \, \sqrt{d \tan\left(f x + e\right)} d^{4} \tan\left(f x + e\right) + 3 \, \sqrt{d \tan\left(f x + e\right)} d^{4}\right)}}{{\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}}{24 \, d}"," ",0,"1/24*(3*sqrt(2)*d^(3/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(I*d/sqrt(d^2) + 1)) - 3*sqrt(2)*d^(3/2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*f*(-I*d/sqrt(d^2) + 1)) - 2*(I*sqrt(d*tan(f*x + e))*d^4*tan(f*x + e) + 3*sqrt(d*tan(f*x + e))*d^4)/((d*tan(f*x + e) - I*d)^3*a^3*f))/d","A",0
184,1,227,0,5.045630," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{8 \, a^{3} \sqrt{d} f {\left(\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{3 i \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{4 \, a^{3} \sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} - \frac{15 i \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right)^{2} + 38 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) - 27 i \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{24 \, {\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}"," ",0,"1/8*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*sqrt(d)*f*(I*d/sqrt(d^2) + 1)) - 3/4*I*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) - 1/24*(15*I*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e)^2 + 38*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) - 27*I*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) - I*d)^3*a^3*f)","A",0
185,1,252,0,2.389063," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{87 \, \sqrt{2} \arctan\left(\frac{16 \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} \sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{3 i \, \sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d^{2}} \sqrt{d \tan\left(f x + e\right)}}{-8 i \, \sqrt{2} d^{\frac{3}{2}} + 8 \, \sqrt{2} \sqrt{d^{2}} \sqrt{d}}\right)}{a^{3} \sqrt{d} f {\left(-\frac{i \, d}{\sqrt{d^{2}}} + 1\right)}} + \frac{48}{\sqrt{d \tan\left(f x + e\right)} a^{3} f} + \frac{2 \, {\left(21 i \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right)^{2} + 49 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) - 30 i \, \sqrt{d \tan\left(f x + e\right)} d^{2}\right)}}{{\left(-i \, d \tan\left(f x + e\right) - d\right)}^{3} a^{3} f}}{24 \, d}"," ",0,"-1/24*(87*sqrt(2)*arctan(16*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) + 3*I*sqrt(2)*arctan(16*I*sqrt(d^2)*sqrt(d*tan(f*x + e))/(-8*I*sqrt(2)*d^(3/2) + 8*sqrt(2)*sqrt(d^2)*sqrt(d)))/(a^3*sqrt(d)*f*(-I*d/sqrt(d^2) + 1)) + 48/(sqrt(d*tan(f*x + e))*a^3*f) + 2*(21*I*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e)^2 + 49*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) - 30*I*sqrt(d*tan(f*x + e))*d^2)/((-I*d*tan(f*x + e) - d)^3*a^3*f))/d","A",0
186,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sqrt(tan(d*x + c)), x)","F",0
189,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/sqrt(tan(d*x + c)), x)","F",0
190,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c)^(3/2), x)","F",0
191,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c)^(5/2), x)","F",0
192,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c)^(7/2), x)","F",0
193,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/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/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)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)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)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/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)Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [28,-44]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [93,91]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-21,88]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-66,66]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedEvaluation time: 3.28int()  Error: Bad Argument Value","F(-2)",0
197,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(3/2), x)","F",0
198,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(5/2), x)","F",0
199,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(7/2), x)","F",0
200,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(9/2), x)","F",0
201,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/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/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)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)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)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/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)Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [28,-44]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [93,91]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-21,88]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-66,66]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-23,79]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [9,6]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedEvaluation time: 7.16int()  Error: Bad Argument Value","F(-2)",0
205,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),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/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)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)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)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/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)Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [28,-44]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [93,91]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-21,88]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-66,66]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-23,79]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [9,6]Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{4,[0,3]%%%}+%%%{-4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{4,[1,5]%%%}+%%%{-8,[1,3]%%%}+%%%{4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [-8,31]Warning, choosing root of [1,0,%%%{-2,[1,2]%%%}+%%%{2,[1,0]%%%}+%%%{-4,[0,3]%%%}+%%%{4,[0,1]%%%},0,%%%{1,[2,4]%%%}+%%%{-2,[2,2]%%%}+%%%{1,[2,0]%%%}+%%%{-4,[1,5]%%%}+%%%{8,[1,3]%%%}+%%%{-4,[1,1]%%%}+%%%{4,[0,6]%%%}+%%%{-8,[0,4]%%%}+%%%{4,[0,2]%%%}] at parameters values [2,97]Evaluation time: 7.93int()  Error: Bad Argument Value","F(-2)",0
206,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(5/2), x)","F",0
207,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(7/2), x)","F",0
208,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(9/2), x)","F",0
209,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(11/2), x)","F",0
210,0,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(7/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
211,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
212,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(3/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
213,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(I*a*tan(d*x + c) + a), x)","F",0
214,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*sqrt(tan(d*x + c))), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(3/2)), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(5/2)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(7/2)), x)","F",0
218,0,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{7}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(7/2)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
219,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/2)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
220,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(3/2)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
221,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
222,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c))), x)","F",0
223,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(3/2)), x)","F",0
224,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(5/2)), x)","F",0
225,0,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{9}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(9/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
226,0,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{7}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(7/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
227,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
228,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(3/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
229,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
230,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c))), x)","F",0
231,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(3/2)), x)","F",0
232,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(5/2)), x)","F",0
233,0,0,0,0.000000," ","integrate(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{10}{3}}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^(10/3)/(I*a*tan(d*x + c) + a), x)","F",0
234,0,0,0,0.000000," ","integrate(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{8}{3}}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^(8/3)/(I*a*tan(d*x + c) + a), x)","F",0
235,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{4}{3}}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^(4/3)/(I*a*tan(d*x + c) + a), x)","F",0
236,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{2}{3}}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^(2/3)/(I*a*tan(d*x + c) + a), x)","F",0
237,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)*tan(d*x + c)^(1/3)), x)","F",0
238,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)*tan(d*x + c)^(5/3)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)*tan(d*x + c)^(7/3)), x)","F",0
240,0,0,0,0.000000," ","integrate(tan(d*x+c)^(14/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{14}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(14/3)/(I*a*tan(d*x + c) + a)^2, x)","F",0
241,0,0,0,0.000000," ","integrate(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{10}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(10/3)/(I*a*tan(d*x + c) + a)^2, x)","F",0
242,0,0,0,0.000000," ","integrate(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{8}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(8/3)/(I*a*tan(d*x + c) + a)^2, x)","F",0
243,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{4}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(4/3)/(I*a*tan(d*x + c) + a)^2, x)","F",0
244,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{2}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(2/3)/(I*a*tan(d*x + c) + a)^2, x)","F",0
245,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*tan(d*x + c)^(1/3)), x)","F",0
246,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*tan(d*x + c)^(5/3)), x)","F",0
247,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*tan(d*x + c)^(7/3)), x)","F",0
248,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)*(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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Warning, choosing root of [1,0,0,0,0,0,%%%{-2,[1]%%%}] at parameters values [-97]Simplification assuming c near 0Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: 8.62Done","F(-2)",0
249,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)*(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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)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)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)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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: 8.84Done","F(-2)",0
250,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)*(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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: 8.7Done","F(-2)",0
251,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)Evaluation time: 8.25Done","F(-2)",0
252,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)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)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)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)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)Evaluation time: 9.48Done","F(-2)",0
253,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)Evaluation time: 8.61Done","F(-2)",0
254,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(3/2),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/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/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)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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Simplification assuming c near 0Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Warning, choosing root of [1,0,0,0,0,0,%%%{-2,[1]%%%}] at parameters values [-82]Warning, choosing root of [1,0,0,0,0,0,%%%{-2,[1]%%%}] at parameters values [7]Simplification assuming c near 0Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: 2.16Done","F(-2)",0
255,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(3/2),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/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/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)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)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)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)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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Warning, choosing root of [1,0,0,0,0,0,%%%{-2,[1]%%%}] at parameters values [-82]Simplification assuming c near 0Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: 2.38Done","F(-2)",0
256,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(3/2),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/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/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)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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification assuming a near 0Simplification assuming c near 0Simplification assuming d near 0Simplification assuming x near 0Warning, choosing root of [1,0,0,0,0,0,%%%{-2,[1]%%%}] at parameters values [-82]Simplification assuming c near 0Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Unable to check sign: (pi/x/2)>(-pi/x/2)Simplification 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: 1.88Done","F(-2)",0
257,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/3),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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)Algebraic extensions not allowed in a rootofAlgebraic extensions not allowed in a rootofEvaluation time: 8.49int()  Error: Bad Argument Value","F(-2)",0
258,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(2/3),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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)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)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)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)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)Evaluation time: 11.25Done","F(-2)",0
259,-2,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(4/3),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/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)sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueUnable 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)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)Evaluation time: 9.05Done","F(-2)",0
260,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{4}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(4/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
261,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{2}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(2/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
262,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(1/3)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
263,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(1/3)), x)","F",0
264,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(2/3)), x)","F",0
265,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(4/3)), x)","F",0
266,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{4}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(4/3)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
267,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{2}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(2/3)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
268,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{1}{3}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(1/3)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
269,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(1/3)), x)","F",0
270,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(2/3)), x)","F",0
271,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(4/3)), x)","F",0
272,0,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(1/3)*tan(d*x + c)^3, x)","F",0
273,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(1/3)*tan(d*x + c)^2, x)","F",0
274,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(1/3)*tan(d*x + c), x)","F",0
275,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(1/3), x)","F",0
276,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(1/3)*cot(d*x + c), x)","F",0
277,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(1/3)*cot(d*x + c)^2, x)","F",0
278,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),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/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)Not invertible Error: Bad Argument Value","F(-2)",0
279,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(2/3), x)","F",0
280,0,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3)*tan(d*x + c)^3, x)","F",0
281,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3)*tan(d*x + c)^2, x)","F",0
282,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3)*tan(d*x + c), x)","F",0
283,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3), x)","F",0
284,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3)*cot(d*x + c), x)","F",0
285,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3)*cot(d*x + c)^2, x)","F",0
286,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(4/3)*cot(d*x + c)^3, x)","F",0
287,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/3), x)","F",0
288,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^m/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
289,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
290,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
291,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
292,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
293,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
294,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-1/3), x)","F",0
295,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
296,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(I*a*tan(d*x + c) + a)^(1/3), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-2/3), x)","F",0
298,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{m}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^m/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
299,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
300,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
301,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
302,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
303,0,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(tan(d*x + c)/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-4/3), x)","F",0
305,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
306,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(I*a*tan(d*x + c) + a)^(4/3), x)","F",0
307,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(-5/3), x)","F",0
308,0,0,0,0.000000," ","integrate((e*tan(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 \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
309,0,0,0,0.000000," ","integrate((e*tan(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 \tan\left(d x + c\right)\right)^{m}\,{d x}"," ",0,"integrate((-I*a*tan(d*x + c) + a)*(e*tan(d*x + c))^m, x)","F",0
310,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^4,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{4} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^4*(d*tan(f*x + e))^n, x)","F",0
311,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(d*tan(f*x + e))^n, x)","F",0
312,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(d*tan(f*x + e))^n, x)","F",0
313,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
314,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(I*a*tan(f*x + e) + a), x)","F",0
315,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(I*a*tan(f*x + e) + a)^2, x)","F",0
316,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(I*a*tan(f*x + e) + a)^3, x)","F",0
317,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^4,x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(I*a*tan(f*x + e) + a)^4, x)","F",0
318,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a-I*a*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(-i \, a \tan\left(f x + e\right) + a\right)} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((-I*a*tan(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
319,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a-I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{-i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(-I*a*tan(f*x + e) + a), x)","F",0
320,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(3/2)*(d*tan(f*x + e))^n, x)","F",0
321,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(f x + e\right) + a} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
322,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{\sqrt{i \, a \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/sqrt(I*a*tan(f*x + e) + a), x)","F",0
323,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(I*a*tan(f*x + e) + a)^(3/2), x)","F",0
324,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
325,0,0,0,0.000000," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*tan(d*x + c)^4, x)","F",0
326,0,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*tan(d*x + c)^3, x)","F",0
327,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*tan(d*x + c)^2, x)","F",0
328,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*tan(d*x + c), x)","F",0
329,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m, x)","F",0
330,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*cot(d*x + c), x)","F",0
331,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*cot(d*x + c)^2, x)","F",0
332,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*tan(d*x + c)^(3/2), x)","F",0
333,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^m,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{m} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m*sqrt(tan(d*x + c)), x)","F",0
334,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{m}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m/sqrt(tan(d*x + c)), x)","F",0
335,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^m/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{m}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^m/tan(d*x + c)^(3/2), x)","F",0
336,1,314,0,1.658092," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e)),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(a d^{2} \sqrt{{\left| d \right|}} - a d {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, f} + \frac{\sqrt{2} {\left(a d^{2} \sqrt{{\left| d \right|}} - a d {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, f} + \frac{\sqrt{2} {\left(a d^{2} \sqrt{{\left| d \right|}} + a d {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, f} - \frac{\sqrt{2} {\left(a d^{2} \sqrt{{\left| d \right|}} + a d {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, f} + \frac{2 \, {\left(3 \, \sqrt{d \tan\left(f x + e\right)} a d^{2} f^{4} \tan\left(f x + e\right)^{2} + 5 \, \sqrt{d \tan\left(f x + e\right)} a d^{2} f^{4} \tan\left(f x + e\right) - 15 \, \sqrt{d \tan\left(f x + e\right)} a d^{2} f^{4}\right)}}{15 \, f^{5}}"," ",0,"1/2*sqrt(2)*(a*d^2*sqrt(abs(d)) - a*d*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + 1/2*sqrt(2)*(a*d^2*sqrt(abs(d)) - a*d*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + 1/4*sqrt(2)*(a*d^2*sqrt(abs(d)) + a*d*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f - 1/4*sqrt(2)*(a*d^2*sqrt(abs(d)) + a*d*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f + 2/15*(3*sqrt(d*tan(f*x + e))*a*d^2*f^4*tan(f*x + e)^2 + 5*sqrt(d*tan(f*x + e))*a*d^2*f^4*tan(f*x + e) - 15*sqrt(d*tan(f*x + e))*a*d^2*f^4)/f^5","B",0
337,1,290,0,1.122715," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{1}{12} \, d {\left(\frac{6 \, \sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{6 \, \sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{3 \, \sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} - \frac{3 \, \sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} - \frac{8 \, {\left(\sqrt{d \tan\left(f x + e\right)} a d^{3} f^{2} \tan\left(f x + e\right) + 3 \, \sqrt{d \tan\left(f x + e\right)} a d^{3} f^{2}\right)}}{d^{3} f^{3}}\right)}"," ",0,"-1/12*d*(6*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 6*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 3*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - 3*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - 8*(sqrt(d*tan(f*x + e))*a*d^3*f^2*tan(f*x + e) + 3*sqrt(d*tan(f*x + e))*a*d^3*f^2)/(d^3*f^3))","B",0
338,1,249,0,0.984471," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, \sqrt{d \tan\left(f x + e\right)} a}{f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d f} + \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d f}"," ",0,"2*sqrt(d*tan(f*x + e))*a/f - 1/2*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) - 1/2*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) - 1/4*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) + 1/4*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f)","B",0
339,1,232,0,0.755279," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d^{2} f} + \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d^{2} f} + \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d^{2} f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d^{2} f}"," ",0,"1/2*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) + 1/2*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) + 1/4*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) - 1/4*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f)","B",0
340,1,253,0,1.584780," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{\frac{8 \, a}{\sqrt{d \tan\left(f x + e\right)} f} - \frac{2 \, \sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} - \frac{2 \, \sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d^{2} f} + \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d^{2} f}}{4 \, d}"," ",0,"-1/4*(8*a/(sqrt(d*tan(f*x + e))*f) - 2*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) - 2*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) - sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) + sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f))/d","B",0
341,1,275,0,1.294986," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d^{4} f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d^{4} f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d^{4} f} + \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d^{4} f} - \frac{2 \, {\left(3 \, a d \tan\left(f x + e\right) + a d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}"," ",0,"-1/2*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^4*f) - 1/2*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^4*f) - 1/4*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^4*f) + 1/4*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^4*f) - 2/3*(3*a*d*tan(f*x + e) + a*d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e))","B",0
342,1,295,0,1.801003," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d^{5} f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} - a {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{2 \, d^{5} f} - \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d^{5} f} + \frac{\sqrt{2} {\left(a d \sqrt{{\left| d \right|}} + a {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{4 \, d^{5} f} + \frac{2 \, {\left(15 \, a d^{2} \tan\left(f x + e\right)^{2} - 5 \, a d^{2} \tan\left(f x + e\right) - 3 \, a d^{2}\right)}}{15 \, \sqrt{d \tan\left(f x + e\right)} d^{5} f \tan\left(f x + e\right)^{2}}"," ",0,"-1/2*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^5*f) - 1/2*sqrt(2)*(a*d*sqrt(abs(d)) - a*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^5*f) - 1/4*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^5*f) + 1/4*sqrt(2)*(a*d*sqrt(abs(d)) + a*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^5*f) + 2/15*(15*a*d^2*tan(f*x + e)^2 - 5*a*d^2*tan(f*x + e) - 3*a*d^2)/(sqrt(d*tan(f*x + e))*d^5*f*tan(f*x + e)^2)","B",0
343,1,293,0,2.034081," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\sqrt{2} a^{2} d^{2} \sqrt{{\left| d \right|}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} + \frac{\sqrt{2} a^{2} d^{2} \sqrt{{\left| d \right|}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} + \frac{\sqrt{2} a^{2} d^{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} - \frac{\sqrt{2} a^{2} d^{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} + \frac{2 \, {\left(5 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6} \tan\left(f x + e\right)^{3} + 14 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6} \tan\left(f x + e\right)^{2} - 70 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{9} f^{6}\right)}}{35 \, d^{7} f^{7}}"," ",0,"sqrt(2)*a^2*d^2*sqrt(abs(d))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + sqrt(2)*a^2*d^2*sqrt(abs(d))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + 1/2*sqrt(2)*a^2*d^2*sqrt(abs(d))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f - 1/2*sqrt(2)*a^2*d^2*sqrt(abs(d))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f + 2/35*(5*sqrt(d*tan(f*x + e))*a^2*d^9*f^6*tan(f*x + e)^3 + 14*sqrt(d*tan(f*x + e))*a^2*d^9*f^6*tan(f*x + e)^2 - 70*sqrt(d*tan(f*x + e))*a^2*d^9*f^6)/(d^7*f^7)","A",0
344,1,274,0,1.891694," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{1}{30} \, {\left(\frac{30 \, \sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{30 \, \sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} - \frac{15 \, \sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} + \frac{15 \, \sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} - \frac{4 \, {\left(3 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{10} f^{4} \tan\left(f x + e\right)^{2} + 10 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{10} f^{4} \tan\left(f x + e\right)\right)}}{d^{10} f^{5}}\right)} d"," ",0,"-1/30*(30*sqrt(2)*a^2*abs(d)^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 30*sqrt(2)*a^2*abs(d)^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) - 15*sqrt(2)*a^2*abs(d)^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) + 15*sqrt(2)*a^2*abs(d)^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - 4*(3*sqrt(d*tan(f*x + e))*a^2*d^10*f^4*tan(f*x + e)^2 + 10*sqrt(d*tan(f*x + e))*a^2*d^10*f^4*tan(f*x + e))/(d^10*f^5))*d","A",0
345,1,249,0,0.948155," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\sqrt{2} a^{2} \sqrt{{\left| d \right|}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} - \frac{\sqrt{2} a^{2} \sqrt{{\left| d \right|}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} - \frac{\sqrt{2} a^{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} + \frac{\sqrt{2} a^{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} + \frac{2 \, {\left(\sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f^{2} \tan\left(f x + e\right) + 6 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f^{2}\right)}}{3 \, d^{3} f^{3}}"," ",0,"-sqrt(2)*a^2*sqrt(abs(d))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f - sqrt(2)*a^2*sqrt(abs(d))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f - 1/2*sqrt(2)*a^2*sqrt(abs(d))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f + 1/2*sqrt(2)*a^2*sqrt(abs(d))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f + 2/3*(sqrt(d*tan(f*x + e))*a^2*d^3*f^2*tan(f*x + e) + 6*sqrt(d*tan(f*x + e))*a^2*d^3*f^2)/(d^3*f^3)","A",0
346,1,222,0,1.017377," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} + \frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} - \frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{2} f} + \frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{2} f} + \frac{2 \, \sqrt{d \tan\left(f x + e\right)} a^{2}}{d f}"," ",0,"sqrt(2)*a^2*abs(d)^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) + sqrt(2)*a^2*abs(d)^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) - 1/2*sqrt(2)*a^2*abs(d)^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) + 1/2*sqrt(2)*a^2*abs(d)^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) + 2*sqrt(d*tan(f*x + e))*a^2/(d*f)","A",0
347,1,225,0,1.721687," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} a^{2} \sqrt{{\left| d \right|}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{2 \, \sqrt{2} a^{2} \sqrt{{\left| d \right|}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{\sqrt{2} a^{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} - \frac{\sqrt{2} a^{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} - \frac{4 \, a^{2}}{\sqrt{d \tan\left(f x + e\right)} f}}{2 \, d}"," ",0,"1/2*(2*sqrt(2)*a^2*sqrt(abs(d))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 2*sqrt(2)*a^2*sqrt(abs(d))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + sqrt(2)*a^2*sqrt(abs(d))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - sqrt(2)*a^2*sqrt(abs(d))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - 4*a^2/(sqrt(d*tan(f*x + e))*f))/d","A",0
348,1,249,0,3.327951," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{4} f} - \frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{4} f} + \frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{4} f} - \frac{\sqrt{2} a^{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{4} f} - \frac{2 \, {\left(6 \, a^{2} d \tan\left(f x + e\right) + a^{2} d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}"," ",0,"-sqrt(2)*a^2*abs(d)^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^4*f) - sqrt(2)*a^2*abs(d)^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^4*f) + 1/2*sqrt(2)*a^2*abs(d)^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^4*f) - 1/2*sqrt(2)*a^2*abs(d)^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^4*f) - 2/3*(6*a^2*d*tan(f*x + e) + a^2*d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e))","A",0
349,1,446,0,3.292812," ","integrate((d*tan(f*x+e))^(7/2)*(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a^{3} d^{3} \sqrt{{\left| d \right|}} + a^{3} d^{2} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} + \frac{\sqrt{2} {\left(a^{3} d^{3} \sqrt{{\left| d \right|}} + a^{3} d^{2} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} - \frac{{\left(\sqrt{2} a^{3} d^{3} \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} d^{2} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} - \frac{{\left(\sqrt{2} a^{3} d^{3} \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} d^{2} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} + \frac{2 \, {\left(105 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{25} f^{10} \tan\left(f x + e\right)^{5} + 385 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{25} f^{10} \tan\left(f x + e\right)^{4} + 330 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{25} f^{10} \tan\left(f x + e\right)^{3} - 462 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{25} f^{10} \tan\left(f x + e\right)^{2} - 770 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{25} f^{10} \tan\left(f x + e\right) + 2310 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{25} f^{10}\right)}}{1155 \, d^{22} f^{11}}"," ",0,"-1/2*sqrt(2)*(a^3*d^3*sqrt(abs(d)) + a^3*d^2*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f + 1/2*sqrt(2)*(a^3*d^3*sqrt(abs(d)) + a^3*d^2*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f - (sqrt(2)*a^3*d^3*sqrt(abs(d)) - sqrt(2)*a^3*d^2*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f - (sqrt(2)*a^3*d^3*sqrt(abs(d)) - sqrt(2)*a^3*d^2*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + 2/1155*(105*sqrt(d*tan(f*x + e))*a^3*d^25*f^10*tan(f*x + e)^5 + 385*sqrt(d*tan(f*x + e))*a^3*d^25*f^10*tan(f*x + e)^4 + 330*sqrt(d*tan(f*x + e))*a^3*d^25*f^10*tan(f*x + e)^3 - 462*sqrt(d*tan(f*x + e))*a^3*d^25*f^10*tan(f*x + e)^2 - 770*sqrt(d*tan(f*x + e))*a^3*d^25*f^10*tan(f*x + e) + 2310*sqrt(d*tan(f*x + e))*a^3*d^25*f^10)/(d^22*f^11)","B",0
350,1,405,0,2.789500," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(a^{3} d^{2} \sqrt{{\left| d \right|}} - a^{3} d {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} - \frac{\sqrt{2} {\left(a^{3} d^{2} \sqrt{{\left| d \right|}} - a^{3} d {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, f} + \frac{{\left(\sqrt{2} a^{3} d^{2} \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} d {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} + \frac{{\left(\sqrt{2} a^{3} d^{2} \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} d {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{f} + \frac{2 \, {\left(35 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right)^{4} + 135 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right)^{3} + 126 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right)^{2} - 210 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8} \tan\left(f x + e\right) - 630 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{20} f^{8}\right)}}{315 \, d^{18} f^{9}}"," ",0,"1/2*sqrt(2)*(a^3*d^2*sqrt(abs(d)) - a^3*d*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f - 1/2*sqrt(2)*(a^3*d^2*sqrt(abs(d)) - a^3*d*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/f + (sqrt(2)*a^3*d^2*sqrt(abs(d)) + sqrt(2)*a^3*d*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + (sqrt(2)*a^3*d^2*sqrt(abs(d)) + sqrt(2)*a^3*d*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/f + 2/315*(35*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e)^4 + 135*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e)^3 + 126*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e)^2 - 210*sqrt(d*tan(f*x + e))*a^3*d^20*f^8*tan(f*x + e) - 630*sqrt(d*tan(f*x + e))*a^3*d^20*f^8)/(d^18*f^9)","B",0
351,1,379,0,2.250101," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{1}{210} \, d {\left(\frac{105 \, \sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} - \frac{105 \, \sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d f} + \frac{210 \, {\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{210 \, {\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{4 \, {\left(15 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6} \tan\left(f x + e\right)^{3} + 63 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6} \tan\left(f x + e\right)^{2} + 70 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6} \tan\left(f x + e\right) - 210 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{21} f^{6}\right)}}{d^{21} f^{7}}\right)}"," ",0,"1/210*d*(105*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - 105*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) + 210*(sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 210*(sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 4*(15*sqrt(d*tan(f*x + e))*a^3*d^21*f^6*tan(f*x + e)^3 + 63*sqrt(d*tan(f*x + e))*a^3*d^21*f^6*tan(f*x + e)^2 + 70*sqrt(d*tan(f*x + e))*a^3*d^21*f^6*tan(f*x + e) - 210*sqrt(d*tan(f*x + e))*a^3*d^21*f^6)/(d^21*f^7))","B",0
352,1,344,0,1.562787," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} - a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d f} + \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} - a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d f} + \frac{2 \, {\left(\sqrt{d \tan\left(f x + e\right)} a^{3} d^{10} f^{4} \tan\left(f x + e\right)^{2} + 5 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{10} f^{4} \tan\left(f x + e\right) + 10 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{10} f^{4}\right)}}{5 \, d^{10} f^{5}}"," ",0,"-1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) - a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) + 1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) - a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) + sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) + sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d*f) + 2/5*(sqrt(d*tan(f*x + e))*a^3*d^10*f^4*tan(f*x + e)^2 + 5*sqrt(d*tan(f*x + e))*a^3*d^10*f^4*tan(f*x + e) + 10*sqrt(d*tan(f*x + e))*a^3*d^10*f^4)/(d^10*f^5)","B",0
353,1,313,0,1.401154," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{2} f} + \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{2} f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} + \frac{2 \, {\left(\sqrt{d \tan\left(f x + e\right)} a^{3} d^{5} f^{2} \tan\left(f x + e\right) + 9 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{5} f^{2}\right)}}{3 \, d^{6} f^{3}}"," ",0,"-1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) + 1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) + 2/3*(sqrt(d*tan(f*x + e))*a^3*d^5*f^2*tan(f*x + e) + 9*sqrt(d*tan(f*x + e))*a^3*d^5*f^2)/(d^6*f^3)","B",0
354,1,299,0,1.559405," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{\frac{4 \, a^{3}}{\sqrt{d \tan\left(f x + e\right)} f} - \frac{4 \, \sqrt{d \tan\left(f x + e\right)} a^{3}}{d f} - \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} - a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d^{2} f} + \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} - a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{d^{2} f} - \frac{2 \, {\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f} - \frac{2 \, {\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{2} f}}{2 \, d}"," ",0,"-1/2*(4*a^3/(sqrt(d*tan(f*x + e))*f) - 4*sqrt(d*tan(f*x + e))*a^3/(d*f) - sqrt(2)*(a^3*d*sqrt(abs(d)) - a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) + sqrt(2)*(a^3*d*sqrt(abs(d)) - a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^2*f) - 2*(sqrt(2)*a^3*d*sqrt(abs(d)) + sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f) - 2*(sqrt(2)*a^3*d*sqrt(abs(d)) + sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^2*f))/d","B",0
355,1,299,0,1.591844," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{4} f} - \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{4} f} + \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{4} f} + \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{4} f} - \frac{2 \, {\left(9 \, a^{3} d \tan\left(f x + e\right) + a^{3} d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} f \tan\left(f x + e\right)}"," ",0,"1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^4*f) - 1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^4*f) + (sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^4*f) + (sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^4*f) - 2/3*(9*a^3*d*tan(f*x + e) + a^3*d)/(sqrt(d*tan(f*x + e))*d^3*f*tan(f*x + e))","B",0
356,1,322,0,1.744113," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} - a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{5} f} + \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} - a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{5} f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{5} f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} + \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{5} f} - \frac{2 \, {\left(10 \, a^{3} d^{2} \tan\left(f x + e\right)^{2} + 5 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}\right)}}{5 \, \sqrt{d \tan\left(f x + e\right)} d^{5} f \tan\left(f x + e\right)^{2}}"," ",0,"-1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) - a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^5*f) + 1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) - a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^5*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) + sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^5*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) + sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^5*f) - 2/5*(10*a^3*d^2*tan(f*x + e)^2 + 5*a^3*d^2*tan(f*x + e) + a^3*d^2)/(sqrt(d*tan(f*x + e))*d^5*f*tan(f*x + e)^2)","B",0
357,1,340,0,2.773521," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{6} f} + \frac{\sqrt{2} {\left(a^{3} d \sqrt{{\left| d \right|}} + a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{2 \, d^{6} f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{6} f} - \frac{{\left(\sqrt{2} a^{3} d \sqrt{{\left| d \right|}} - \sqrt{2} a^{3} {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{d^{6} f} + \frac{2 \, {\left(210 \, a^{3} d^{3} \tan\left(f x + e\right)^{3} - 70 \, a^{3} d^{3} \tan\left(f x + e\right)^{2} - 63 \, a^{3} d^{3} \tan\left(f x + e\right) - 15 \, a^{3} d^{3}\right)}}{105 \, \sqrt{d \tan\left(f x + e\right)} d^{7} f \tan\left(f x + e\right)^{3}}"," ",0,"-1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^6*f) + 1/2*sqrt(2)*(a^3*d*sqrt(abs(d)) + a^3*abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(d^6*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^6*f) - (sqrt(2)*a^3*d*sqrt(abs(d)) - sqrt(2)*a^3*abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(d^6*f) + 2/105*(210*a^3*d^3*tan(f*x + e)^3 - 70*a^3*d^3*tan(f*x + e)^2 - 63*a^3*d^3*tan(f*x + e) - 15*a^3*d^3)/(sqrt(d*tan(f*x + e))*d^7*f*tan(f*x + e)^3)","B",0
358,1,284,0,1.062229," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{1}{8} \, d^{2} {\left(\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a d f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a d f} + \frac{8 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a d f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a d f} - \frac{16 \, \sqrt{d \tan\left(f x + e\right)}}{a f}\right)}"," ",0,"-1/8*d^2*(2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d*f) + 2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d*f) + 8*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*f) + sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d*f) - sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d*f) - 16*sqrt(d*tan(f*x + e))/(a*f))","B",0
359,1,263,0,1.055844," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{1}{8} \, d {\left(\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a d f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a d f} - \frac{8 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a d f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a d f}\right)}"," ",0,"-1/8*d*(2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d*f) + 2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d*f) - 8*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*f) + sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d*f) - sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d*f))","B",0
360,1,253,0,0.978920," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a f} - \frac{8 \, d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a f}}{8 \, d}"," ",0,"1/8*(2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*f) + 2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*f) - 8*d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*f) + sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*f) - sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*f))/d","B",0
361,1,260,0,0.926392," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x, algorithm=""giac"")","\frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a d^{2} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a d^{2} f} + \frac{\arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a \sqrt{d} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a d^{2} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a d^{2} f}"," ",0,"1/4*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d^2*f) + 1/4*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d^2*f) + arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*sqrt(d)*f) + 1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d^2*f) - 1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d^2*f)","B",0
362,1,284,0,1.363049," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a d^{2} f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a d^{2} f} + \frac{8 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a \sqrt{d} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a d^{2} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a d^{2} f} + \frac{16}{\sqrt{d \tan\left(f x + e\right)} a f}}{8 \, d}"," ",0,"-1/8*(2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d^2*f) + 2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d^2*f) + 8*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*sqrt(d)*f) + sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d^2*f) - sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d^2*f) + 16/(sqrt(d*tan(f*x + e))*a*f))/d","B",0
363,1,305,0,1.506423," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a d^{4} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a d^{4} f} + \frac{\arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a d^{\frac{5}{2}} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a d^{4} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a d^{4} f} + \frac{2 \, {\left(3 \, d \tan\left(f x + e\right) - d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} a d^{3} f \tan\left(f x + e\right)}"," ",0,"-1/4*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d^4*f) - 1/4*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a*d^4*f) + arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*d^(5/2)*f) - 1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d^4*f) + 1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a*d^4*f) + 2/3*(3*d*tan(f*x + e) - d)/(sqrt(d*tan(f*x + e))*a*d^3*f*tan(f*x + e))","B",0
364,1,254,0,1.600724," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{1}{8} \, d^{2} {\left(\frac{2 \, \sqrt{2} \sqrt{{\left| d \right|}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} f} + \frac{2 \, \sqrt{2} \sqrt{{\left| d \right|}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} f} + \frac{\sqrt{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} f} - \frac{\sqrt{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} f} - \frac{12 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2} f} + \frac{4 \, \sqrt{d \tan\left(f x + e\right)} d}{{\left(d \tan\left(f x + e\right) + d\right)} a^{2} f}\right)}"," ",0,"-1/8*d^2*(2*sqrt(2)*sqrt(abs(d))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*f) + 2*sqrt(2)*sqrt(abs(d))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*f) + sqrt(2)*sqrt(abs(d))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*f) - sqrt(2)*sqrt(abs(d))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*f) - 12*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*f) + 4*sqrt(d*tan(f*x + e))*d/((d*tan(f*x + e) + d)*a^2*f))","A",0
365,1,264,0,1.306516," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{8} \, d {\left(\frac{2 \, \sqrt{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} d f} + \frac{2 \, \sqrt{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} d f} - \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} d f} + \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} d f} - \frac{4 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2} f} + \frac{4 \, \sqrt{d \tan\left(f x + e\right)} d}{{\left(d \tan\left(f x + e\right) + d\right)} a^{2} f}\right)}"," ",0,"1/8*d*(2*sqrt(2)*abs(d)^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d*f) + 2*sqrt(2)*abs(d)^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d*f) - sqrt(2)*abs(d)^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d*f) + sqrt(2)*abs(d)^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d*f) - 4*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*f) + 4*sqrt(d*tan(f*x + e))*d/((d*tan(f*x + e) + d)*a^2*f))","A",0
366,1,260,0,1.202476," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} d \sqrt{{\left| d \right|}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} f} + \frac{2 \, \sqrt{2} d \sqrt{{\left| d \right|}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} f} + \frac{\sqrt{2} d \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} f} - \frac{\sqrt{2} d \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} f} - \frac{4 \, d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2} f} - \frac{4 \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{{\left(d \tan\left(f x + e\right) + d\right)} a^{2} f}}{8 \, d}"," ",0,"1/8*(2*sqrt(2)*d*sqrt(abs(d))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*f) + 2*sqrt(2)*d*sqrt(abs(d))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*f) + sqrt(2)*d*sqrt(abs(d))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*f) - sqrt(2)*d*sqrt(abs(d))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*f) - 4*d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*f) - 4*sqrt(d*tan(f*x + e))*d^2/((d*tan(f*x + e) + d)*a^2*f))/d","A",0
367,1,261,0,1.178239," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a^{2} d^{2} f} - \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a^{2} d^{2} f} + \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a^{2} d^{2} f} - \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a^{2} d^{2} f} + \frac{3 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{2 \, a^{2} \sqrt{d} f} + \frac{\sqrt{d \tan\left(f x + e\right)}}{2 \, {\left(d \tan\left(f x + e\right) + d\right)} a^{2} f}"," ",0,"-1/4*sqrt(2)*abs(d)^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d^2*f) - 1/4*sqrt(2)*abs(d)^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d^2*f) + 1/8*sqrt(2)*abs(d)^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d^2*f) - 1/8*sqrt(2)*abs(d)^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d^2*f) + 3/2*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*sqrt(d)*f) + 1/2*sqrt(d*tan(f*x + e))/((d*tan(f*x + e) + d)*a^2*f)","A",0
368,1,291,0,1.817160," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} \sqrt{{\left| d \right|}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} d f} + \frac{2 \, \sqrt{2} \sqrt{{\left| d \right|}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{2} d f} + \frac{\sqrt{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} d f} - \frac{\sqrt{2} \sqrt{{\left| d \right|}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{2} d f} + \frac{20 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2} \sqrt{d} f} + \frac{4 \, {\left(5 \, d \tan\left(f x + e\right) + 4 \, d\right)}}{{\left(\sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) + \sqrt{d \tan\left(f x + e\right)} d\right)} a^{2} f}}{8 \, d}"," ",0,"-1/8*(2*sqrt(2)*sqrt(abs(d))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d*f) + 2*sqrt(2)*sqrt(abs(d))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d*f) + sqrt(2)*sqrt(abs(d))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d*f) - sqrt(2)*sqrt(abs(d))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d*f) + 20*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*sqrt(d)*f) + 4*(5*d*tan(f*x + e) + 4*d)/((sqrt(d*tan(f*x + e))*d*tan(f*x + e) + sqrt(d*tan(f*x + e))*d)*a^2*f))/d","A",0
369,1,309,0,2.161117," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a^{2} d^{4} f} + \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{4 \, a^{2} d^{4} f} - \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a^{2} d^{4} f} + \frac{\sqrt{2} {\left| d \right|}^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{8 \, a^{2} d^{4} f} + \frac{7 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{2 \, a^{2} d^{\frac{5}{2}} f} + \frac{\sqrt{d \tan\left(f x + e\right)}}{2 \, {\left(d \tan\left(f x + e\right) + d\right)} a^{2} d^{2} f} + \frac{2 \, {\left(6 \, d \tan\left(f x + e\right) - d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} f \tan\left(f x + e\right)}"," ",0,"1/4*sqrt(2)*abs(d)^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d^4*f) + 1/4*sqrt(2)*abs(d)^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^2*d^4*f) - 1/8*sqrt(2)*abs(d)^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d^4*f) + 1/8*sqrt(2)*abs(d)^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^2*d^4*f) + 7/2*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*d^(5/2)*f) + 1/2*sqrt(d*tan(f*x + e))/((d*tan(f*x + e) + d)*a^2*d^2*f) + 2/3*(6*d*tan(f*x + e) - d)/(sqrt(d*tan(f*x + e))*a^2*d^3*f*tan(f*x + e))","A",0
370,1,345,0,3.142513," ","integrate((d*tan(f*x+e))^(9/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{1}{16} \, d^{4} {\left(\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} - \frac{62 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} + \frac{32 \, \sqrt{d \tan\left(f x + e\right)}}{a^{3} f} + \frac{2 \, {\left(13 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) + 11 \, \sqrt{d \tan\left(f x + e\right)} d^{2}\right)}}{{\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}\right)}"," ",0,"1/16*d^4*(2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) + 2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) - 62*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*f) + sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) - sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) + 32*sqrt(d*tan(f*x + e))/(a^3*f) + 2*(13*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) + 11*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) + d)^2*a^3*f))","B",0
371,1,326,0,3.825522," ","integrate((d*tan(f*x+e))^(7/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{16} \, d^{3} {\left(\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} - \frac{22 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} + \frac{2 \, {\left(9 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) + 7 \, \sqrt{d \tan\left(f x + e\right)} d^{2}\right)}}{{\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}\right)}"," ",0,"-1/16*d^3*(2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) + 2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) - 22*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*f) + sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) - sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) + 2*(9*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) + 7*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) + d)^2*a^3*f))","B",0
372,1,326,0,3.937736," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{1}{16} \, d^{2} {\left(\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} - \frac{2 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} - \frac{2 \, {\left(5 \, \sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) + 3 \, \sqrt{d \tan\left(f x + e\right)} d^{2}\right)}}{{\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}\right)}"," ",0,"-1/16*d^2*(2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) + 2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) - 2*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*f) + sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) - sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) - 2*(5*sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) + 3*sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) + d)^2*a^3*f))","B",0
373,1,323,0,2.039397," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{1}{16} \, d {\left(\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d f} - \frac{10 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d f} - \frac{2 \, {\left(\sqrt{d \tan\left(f x + e\right)} d^{2} \tan\left(f x + e\right) - \sqrt{d \tan\left(f x + e\right)} d^{2}\right)}}{{\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}\right)}"," ",0,"1/16*d*(2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) + 2*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d*f) - 10*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*f) + sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) - sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d*f) - 2*(sqrt(d*tan(f*x + e))*d^2*tan(f*x + e) - sqrt(d*tan(f*x + e))*d^2)/((d*tan(f*x + e) + d)^2*a^3*f))","B",0
374,1,314,0,1.626170," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} f} + \frac{2 \, d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} f} - \frac{2 \, {\left(3 \, \sqrt{d \tan\left(f x + e\right)} d^{3} \tan\left(f x + e\right) + 5 \, \sqrt{d \tan\left(f x + e\right)} d^{3}\right)}}{{\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}}{16 \, d}"," ",0,"1/16*(2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*f) + 2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*f) + 2*d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*f) + sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*f) - sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*f) - 2*(3*sqrt(d*tan(f*x + e))*d^3*tan(f*x + e) + 5*sqrt(d*tan(f*x + e))*d^3)/((d*tan(f*x + e) + d)^2*a^3*f))/d","B",0
375,1,318,0,3.167683," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{8 \, a^{3} d^{2} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{8 \, a^{3} d^{2} f} + \frac{11 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{8 \, a^{3} \sqrt{d} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{16 \, a^{3} d^{2} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{16 \, a^{3} d^{2} f} + \frac{7 \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) + 9 \, \sqrt{d \tan\left(f x + e\right)} d}{8 \, {\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}"," ",0,"-1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d^2*f) - 1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d^2*f) + 11/8*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*sqrt(d)*f) - 1/16*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d^2*f) + 1/16*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d^2*f) + 1/8*(7*sqrt(d*tan(f*x + e))*d*tan(f*x + e) + 9*sqrt(d*tan(f*x + e))*d)/((d*tan(f*x + e) + d)^2*a^3*f)","B",0
376,1,341,0,2.430110," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d^{2} f} + \frac{2 \, \sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{a^{3} d^{2} f} + \frac{62 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} \sqrt{d} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d^{2} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{a^{3} d^{2} f} + \frac{32}{\sqrt{d \tan\left(f x + e\right)} a^{3} f} + \frac{2 \, {\left(11 \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) + 13 \, \sqrt{d \tan\left(f x + e\right)} d\right)}}{{\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} f}}{16 \, d}"," ",0,"-1/16*(2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d^2*f) + 2*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d^2*f) + 62*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*sqrt(d)*f) + sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d^2*f) - sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d^2*f) + 32/(sqrt(d*tan(f*x + e))*a^3*f) + 2*(11*sqrt(d*tan(f*x + e))*d*tan(f*x + e) + 13*sqrt(d*tan(f*x + e))*d)/((d*tan(f*x + e) + d)^2*a^3*f))/d","B",0
377,1,366,0,3.076140," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{8 \, a^{3} d^{4} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} + {\left| d \right|}^{\frac{3}{2}}\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{{\left| d \right|}} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{{\left| d \right|}}}\right)}{8 \, a^{3} d^{4} f} + \frac{59 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{8 \, a^{3} d^{\frac{5}{2}} f} + \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{16 \, a^{3} d^{4} f} - \frac{\sqrt{2} {\left(d \sqrt{{\left| d \right|}} - {\left| d \right|}^{\frac{3}{2}}\right)} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{{\left| d \right|}} + {\left| d \right|}\right)}{16 \, a^{3} d^{4} f} + \frac{15 \, \sqrt{d \tan\left(f x + e\right)} d \tan\left(f x + e\right) + 17 \, \sqrt{d \tan\left(f x + e\right)} d}{8 \, {\left(d \tan\left(f x + e\right) + d\right)}^{2} a^{3} d^{2} f} + \frac{2 \, {\left(9 \, d \tan\left(f x + e\right) - d\right)}}{3 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{3} f \tan\left(f x + e\right)}"," ",0,"1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) + 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d^4*f) + 1/8*sqrt(2)*(d*sqrt(abs(d)) + abs(d)^(3/2))*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(abs(d)) - 2*sqrt(d*tan(f*x + e)))/sqrt(abs(d)))/(a^3*d^4*f) + 59/8*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*d^(5/2)*f) + 1/16*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d^4*f) - 1/16*sqrt(2)*(d*sqrt(abs(d)) - abs(d)^(3/2))*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(abs(d)) + abs(d))/(a^3*d^4*f) + 1/8*(15*sqrt(d*tan(f*x + e))*d*tan(f*x + e) + 17*sqrt(d*tan(f*x + e))*d)/((d*tan(f*x + e) + d)^2*a^3*d^2*f) + 2/3*(9*d*tan(f*x + e) - d)/(sqrt(d*tan(f*x + e))*a^3*d^3*f*tan(f*x + e))","B",0
378,1,278,0,1.201781," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^5,x, algorithm=""giac"")","-\frac{\sqrt{2 \, \sqrt{2} - 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{2 \, \sqrt{2} - 2} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{2 \, \sqrt{2} + 2} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{\sqrt{2 \, \sqrt{2} + 2} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, {\left(35 \, f^{8} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{9}{2}} - 135 \, f^{8} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{7}{2}} + 126 \, f^{8} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}} + 315 \, f^{8} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{315 \, f^{9}}"," ",0,"-1/2*sqrt(2*sqrt(2) - 2)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(2*sqrt(2) - 2)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/4*sqrt(2*sqrt(2) + 2)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/4*sqrt(2*sqrt(2) + 2)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/315*(35*f^8*(tan(f*x + e) + 1)^(9/2) - 135*f^8*(tan(f*x + e) + 1)^(7/2) + 126*f^8*(tan(f*x + e) + 1)^(5/2) + 315*f^8*sqrt(tan(f*x + e) + 1))/f^9","A",0
379,1,262,0,0.979688," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^3,x, algorithm=""giac"")","\frac{\sqrt{2 \, \sqrt{2} - 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{2 \, \sqrt{2} - 2} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{2 \, \sqrt{2} + 2} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} - \frac{\sqrt{2 \, \sqrt{2} + 2} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, {\left(3 \, f^{4} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}} - 5 \, f^{4} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} - 15 \, f^{4} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{15 \, f^{5}}"," ",0,"1/2*sqrt(2*sqrt(2) - 2)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/2*sqrt(2*sqrt(2) - 2)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/4*sqrt(2*sqrt(2) + 2)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f - 1/4*sqrt(2*sqrt(2) + 2)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/15*(3*f^4*(tan(f*x + e) + 1)^(5/2) - 5*f^4*(tan(f*x + e) + 1)^(3/2) - 15*f^4*sqrt(tan(f*x + e) + 1))/f^5","A",0
380,1,224,0,1.076898," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e),x, algorithm=""giac"")","-\frac{\sqrt{2 \, \sqrt{2} - 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{2 \, \sqrt{2} - 2} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{2 \, \sqrt{2} + 2} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{\sqrt{2 \, \sqrt{2} + 2} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, \sqrt{\tan\left(f x + e\right) + 1}}{f}"," ",0,"-1/2*sqrt(2*sqrt(2) - 2)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(2*sqrt(2) - 2)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/4*sqrt(2*sqrt(2) + 2)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/4*sqrt(2*sqrt(2) + 2)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2*sqrt(tan(f*x + e) + 1)/f","A",0
381,0,0,0,0.000000," ","integrate(cot(f*x+e)*(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{\tan\left(f x + e\right) + 1} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*cot(f*x + e), x)","F",0
382,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{\tan\left(f x + e\right) + 1} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*cot(f*x + e)^3, x)","F",0
383,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{\tan\left(f x + e\right) + 1} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*cot(f*x + e)^5, x)","F",0
384,1,246,0,1.055730," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^4,x, algorithm=""giac"")","\frac{\sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{2 \, \sqrt{2} + 2} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{2 \, \sqrt{2} - 2} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{\sqrt{2 \, \sqrt{2} - 2} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, {\left(5 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{7}{2}} - 14 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}}\right)}}{35 \, f^{7}}"," ",0,"1/2*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/2*sqrt(2*sqrt(2) + 2)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/4*sqrt(2*sqrt(2) - 2)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/4*sqrt(2*sqrt(2) - 2)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/35*(5*f^6*(tan(f*x + e) + 1)^(7/2) - 14*f^6*(tan(f*x + e) + 1)^(5/2))/f^7","A",0
385,1,224,0,1.017930," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^2,x, algorithm=""giac"")","\frac{2 \, {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}}}{3 \, f} - \frac{\sqrt{2 \, \sqrt{2} + 2} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{2 \, \sqrt{2} + 2} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{2 \, \sqrt{2} - 2} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} - \frac{\sqrt{2 \, \sqrt{2} - 2} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f}"," ",0,"2/3*(tan(f*x + e) + 1)^(3/2)/f - 1/2*sqrt(2*sqrt(2) + 2)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(2*sqrt(2) + 2)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/4*sqrt(2*sqrt(2) - 2)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f - 1/4*sqrt(2*sqrt(2) - 2)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f","A",0
386,1,266,0,2.235919," ","integrate((1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{{\left(f^{2} \sqrt{\sqrt{2} + 1} + f \sqrt{\sqrt{2} - 1} {\left| f \right|}\right)} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f^{3}} + \frac{{\left(f^{2} \sqrt{\sqrt{2} + 1} + f \sqrt{\sqrt{2} - 1} {\left| f \right|}\right)} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f^{3}} + \frac{{\left(f^{2} \sqrt{\sqrt{2} - 1} - f \sqrt{\sqrt{2} + 1} {\left| f \right|}\right)} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f^{3}} - \frac{{\left(f^{2} \sqrt{\sqrt{2} - 1} - f \sqrt{\sqrt{2} + 1} {\left| f \right|}\right)} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f^{3}}"," ",0,"1/2*(f^2*sqrt(sqrt(2) + 1) + f*sqrt(sqrt(2) - 1)*abs(f))*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f^3 + 1/2*(f^2*sqrt(sqrt(2) + 1) + f*sqrt(sqrt(2) - 1)*abs(f))*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f^3 + 1/4*(f^2*sqrt(sqrt(2) - 1) - f*sqrt(sqrt(2) + 1)*abs(f))*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f^3 - 1/4*(f^2*sqrt(sqrt(2) - 1) - f*sqrt(sqrt(2) + 1)*abs(f))*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f^3","A",0
387,-2,0,0,0.000000," ","integrate(cot(f*x+e)^2*(1+tan(f*x+e))^(1/2),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)(3616*sqrt(sqrt(2)-1)*f^2-3616*sqrt(sqrt(2)+1)*f*abs(f))/14464/f^3*ln(tan(f*x+exp(1))+1-(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))+(-3616*sqrt(sqrt(2)+1)*f^2-3616*sqrt(sqrt(2)-1)*f*abs(f))/7232/f^3*atan((sqrt(tan(f*x+exp(1))+1)-sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+(-3616*sqrt(sqrt(2)-1)*f^2+3616*sqrt(sqrt(2)+1)*f*abs(f))/14464/f^3*ln(tan(f*x+exp(1))+1+(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))-(3616*sqrt(sqrt(2)+1)*f^2+3616*sqrt(sqrt(2)-1)*f*abs(f))/7232/f^3*atan((sqrt(tan(f*x+exp(1))+1)+sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+1/2/f*ln(abs(sqrt(tan(f*x+exp(1))+1)-1))-1/2/f*ln(sqrt(tan(f*x+exp(1))+1)+1)-sqrt(tan(f*x+exp(1))+1)/f/tan(f*x+exp(1))","F(-2)",0
388,-2,0,0,0.000000," ","integrate(cot(f*x+e)^4*(1+tan(f*x+e))^(1/2),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)(-3616*sqrt(sqrt(2)-1)*f^2+3616*sqrt(sqrt(2)+1)*f*abs(f))/14464/f^3*ln(tan(f*x+exp(1))+1-(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))+(3616*sqrt(sqrt(2)+1)*f^2+3616*sqrt(sqrt(2)-1)*f*abs(f))/7232/f^3*atan((sqrt(tan(f*x+exp(1))+1)-sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+(3616*sqrt(sqrt(2)-1)*f^2-3616*sqrt(sqrt(2)+1)*f*abs(f))/14464/f^3*ln(tan(f*x+exp(1))+1+(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))-(-3616*sqrt(sqrt(2)+1)*f^2-3616*sqrt(sqrt(2)-1)*f*abs(f))/7232/f^3*atan((sqrt(tan(f*x+exp(1))+1)+sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))-7/16/f*ln(abs(sqrt(tan(f*x+exp(1))+1)-1))+7/16/f*ln(sqrt(tan(f*x+exp(1))+1)+1)+(27*sqrt(tan(f*x+exp(1))+1)*(tan(f*x+exp(1))+1)^2-56*sqrt(tan(f*x+exp(1))+1)*(tan(f*x+exp(1))+1)+21*sqrt(tan(f*x+exp(1))+1))/24/f/tan(f*x+exp(1))^3","F(-2)",0
389,1,286,0,1.601807," ","integrate(tan(f*x+e)^5*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{2 \, {\left(21 \, f^{10} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{11}{2}} - 77 \, f^{10} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{9}{2}} + 66 \, f^{10} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{7}{2}} + 77 \, f^{10} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} + 231 \, f^{10} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{231 \, f^{11}}"," ",0,"-sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/2*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/231*(21*f^10*(tan(f*x + e) + 1)^(11/2) - 77*f^10*(tan(f*x + e) + 1)^(9/2) + 66*f^10*(tan(f*x + e) + 1)^(7/2) + 77*f^10*(tan(f*x + e) + 1)^(3/2) + 231*f^10*sqrt(tan(f*x + e) + 1))/f^11","A",0
390,1,268,0,2.365221," ","integrate(tan(f*x+e)^3*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} + \frac{\sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} + \frac{\sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} - \frac{\sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{2 \, {\left(15 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{7}{2}} - 21 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}} - 35 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} - 105 \, f^{6} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{105 \, f^{7}}"," ",0,"sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/2*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f - 1/2*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/105*(15*f^6*(tan(f*x + e) + 1)^(7/2) - 21*f^6*(tan(f*x + e) + 1)^(5/2) - 35*f^6*(tan(f*x + e) + 1)^(3/2) - 105*f^6*sqrt(tan(f*x + e) + 1))/f^7","A",0
391,1,237,0,1.151916," ","integrate(tan(f*x+e)*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{2 \, {\left(f^{2} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} + 3 \, f^{2} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{3 \, f^{3}}"," ",0,"-sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/2*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/3*(f^2*(tan(f*x + e) + 1)^(3/2) + 3*f^2*sqrt(tan(f*x + e) + 1))/f^3","A",0
392,0,0,0,0.000000," ","integrate(cot(f*x+e)*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*cot(f*x + e), x)","F",0
393,0,0,0,0.000000," ","integrate(cot(f*x+e)^3*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*cot(f*x + e)^3, x)","F",0
394,0,0,0,0.000000," ","integrate(cot(f*x+e)^5*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*cot(f*x + e)^5, x)","F",0
395,1,252,0,1.786817," ","integrate(tan(f*x+e)^4*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} + \frac{\sqrt{\sqrt{2} - 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} + 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} + 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{2 \, {\left(7 \, f^{8} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{9}{2}} - 18 \, f^{8} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{7}{2}} + 63 \, f^{8} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{63 \, f^{9}}"," ",0,"sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + sqrt(sqrt(2) - 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(sqrt(2) + 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/2*sqrt(sqrt(2) + 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/63*(7*f^8*(tan(f*x + e) + 1)^(9/2) - 18*f^8*(tan(f*x + e) + 1)^(7/2) + 63*f^8*sqrt(tan(f*x + e) + 1))/f^9","A",0
396,1,237,0,1.304048," ","integrate(tan(f*x+e)^2*(1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{\sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} - 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} + \frac{\sqrt{\sqrt{2} + 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} - \frac{\sqrt{\sqrt{2} + 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{2 \, {\left(f^{4} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}} - 5 \, f^{4} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{5 \, f^{5}}"," ",0,"-sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - sqrt(sqrt(2) - 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/2*sqrt(sqrt(2) + 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f - 1/2*sqrt(sqrt(2) + 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/5*(f^4*(tan(f*x + e) + 1)^(5/2) - 5*f^4*sqrt(tan(f*x + e) + 1))/f^5","A",0
397,1,214,0,2.059049," ","integrate((1+tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} + \frac{\sqrt{\sqrt{2} - 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{f} - \frac{\sqrt{\sqrt{2} + 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} + 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{2 \, f} + \frac{2 \, \sqrt{\tan\left(f x + e\right) + 1}}{f}"," ",0,"sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + sqrt(sqrt(2) - 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(sqrt(2) + 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/2*sqrt(sqrt(2) + 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2*sqrt(tan(f*x + e) + 1)/f","A",0
398,-2,0,0,0.000000," ","integrate(cot(f*x+e)^2*(1+tan(f*x+e))^(3/2),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)(-1808*sqrt(2*(sqrt(2)-1))*f^2-1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/7232/f^3*ln(tan(f*x+exp(1))+1-(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))+(-1808*sqrt(2*(sqrt(2)+1))*f^2+1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/3616/f^3*atan((sqrt(tan(f*x+exp(1))+1)-sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+(1808*sqrt(2*(sqrt(2)-1))*f^2+1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/7232/f^3*ln(tan(f*x+exp(1))+1+(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))-(1808*sqrt(2*(sqrt(2)+1))*f^2-1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/3616/f^3*atan((sqrt(tan(f*x+exp(1))+1)+sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+3/2/f*ln(abs(sqrt(tan(f*x+exp(1))+1)-1))-3/2/f*ln(sqrt(tan(f*x+exp(1))+1)+1)-sqrt(tan(f*x+exp(1))+1)/f/tan(f*x+exp(1))","F(-2)",0
399,-2,0,0,0.000000," ","integrate(cot(f*x+e)^4*(1+tan(f*x+e))^(3/2),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)(1808*sqrt(2*(sqrt(2)-1))*f^2+1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/7232/f^3*ln(tan(f*x+exp(1))+1-(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))+(1808*sqrt(2*(sqrt(2)+1))*f^2-1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/3616/f^3*atan((sqrt(tan(f*x+exp(1))+1)-sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+(-1808*sqrt(2*(sqrt(2)-1))*f^2-1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/7232/f^3*ln(tan(f*x+exp(1))+1+(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))-(-1808*sqrt(2*(sqrt(2)+1))*f^2+1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/3616/f^3*atan((sqrt(tan(f*x+exp(1))+1)+sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))-25/16/f*ln(abs(sqrt(tan(f*x+exp(1))+1)-1))+25/16/f*ln(sqrt(tan(f*x+exp(1))+1)+1)+(21*sqrt(tan(f*x+exp(1))+1)*(tan(f*x+exp(1))+1)^2-56*sqrt(tan(f*x+exp(1))+1)*(tan(f*x+exp(1))+1)+27*sqrt(tan(f*x+exp(1))+1))/24/f/tan(f*x+exp(1))^3","F(-2)",0
400,1,254,0,1.146298," ","integrate(tan(f*x+e)^5/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} - 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{\sqrt{2} + 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{\sqrt{\sqrt{2} + 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, {\left(15 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{7}{2}} - 63 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}} + 70 \, f^{6} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\right)}}{105 \, f^{7}}"," ",0,"1/2*sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/2*sqrt(sqrt(2) - 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/4*sqrt(sqrt(2) + 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/4*sqrt(sqrt(2) + 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/105*(15*f^6*(tan(f*x + e) + 1)^(7/2) - 63*f^6*(tan(f*x + e) + 1)^(5/2) + 70*f^6*(tan(f*x + e) + 1)^(3/2))/f^7","A",0
401,1,237,0,1.140029," ","integrate(tan(f*x+e)^3/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\sqrt{2} - 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{\sqrt{2} - 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} + 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} - \frac{\sqrt{\sqrt{2} + 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, {\left(f^{2} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} - 3 \, f^{2} \sqrt{\tan\left(f x + e\right) + 1}\right)}}{3 \, f^{3}}"," ",0,"-1/2*sqrt(sqrt(2) - 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(sqrt(2) - 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/4*sqrt(sqrt(2) + 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f - 1/4*sqrt(sqrt(2) + 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/3*(f^2*(tan(f*x + e) + 1)^(3/2) - 3*f^2*sqrt(tan(f*x + e) + 1))/f^3","A",0
402,1,282,0,1.244874," ","integrate(tan(f*x+e)/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} + 2} - f \sqrt{2 \, \sqrt{2} - 2} {\left| f \right|}\right)} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{4 \, f^{3}} + \frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} + 2} - f \sqrt{2 \, \sqrt{2} - 2} {\left| f \right|}\right)} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{4 \, f^{3}} - \frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} - 2} + f \sqrt{2 \, \sqrt{2} + 2} {\left| f \right|}\right)} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{8 \, f^{3}} + \frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} - 2} + f \sqrt{2 \, \sqrt{2} + 2} {\left| f \right|}\right)} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{8 \, f^{3}}"," ",0,"1/4*(f^2*sqrt(2*sqrt(2) + 2) - f*sqrt(2*sqrt(2) - 2)*abs(f))*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f^3 + 1/4*(f^2*sqrt(2*sqrt(2) + 2) - f*sqrt(2*sqrt(2) - 2)*abs(f))*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f^3 - 1/8*(f^2*sqrt(2*sqrt(2) - 2) + f*sqrt(2*sqrt(2) + 2)*abs(f))*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f^3 + 1/8*(f^2*sqrt(2*sqrt(2) - 2) + f*sqrt(2*sqrt(2) + 2)*abs(f))*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f^3","B",0
403,0,0,0,0.000000," ","integrate(cot(f*x+e)/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(f x + e\right)}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(cot(f*x + e)/sqrt(tan(f*x + e) + 1), x)","F",0
404,0,0,0,0.000000," ","integrate(cot(f*x+e)^3/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(f x + e\right)^{3}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(cot(f*x + e)^3/sqrt(tan(f*x + e) + 1), x)","F",0
405,0,0,0,0.000000," ","integrate(cot(f*x+e)^5/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(f x + e\right)^{5}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(cot(f*x + e)^5/sqrt(tan(f*x + e) + 1), x)","F",0
406,1,238,0,1.181344," ","integrate(tan(f*x+e)^4/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} + \frac{\sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} - \frac{\sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, {\left(3 \, f^{4} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{5}{2}} - 10 \, f^{4} {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}}\right)}}{15 \, f^{5}}"," ",0,"1/2*sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/2*sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f + 1/4*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f - 1/4*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2/15*(3*f^4*(tan(f*x + e) + 1)^(5/2) - 10*f^4*(tan(f*x + e) + 1)^(3/2))/f^5","A",0
407,1,216,0,1.065246," ","integrate(tan(f*x+e)^2/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{\sqrt{2} + 1} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{\sqrt{2} + 1} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{2 \, f} - \frac{\sqrt{\sqrt{2} - 1} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{\sqrt{\sqrt{2} - 1} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{4 \, f} + \frac{2 \, \sqrt{\tan\left(f x + e\right) + 1}}{f}"," ",0,"-1/2*sqrt(sqrt(2) + 1)*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/2*sqrt(sqrt(2) + 1)*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f - 1/4*sqrt(sqrt(2) - 1)*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 1/4*sqrt(sqrt(2) - 1)*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f + 2*sqrt(tan(f*x + e) + 1)/f","A",0
408,1,282,0,0.804941," ","integrate(1/(1+tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} - 2} + f \sqrt{2 \, \sqrt{2} + 2} {\left| f \right|}\right)} \arctan\left(\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} + 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{4 \, f^{3}} + \frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} - 2} + f \sqrt{2 \, \sqrt{2} + 2} {\left| f \right|}\right)} \arctan\left(-\frac{2^{\frac{3}{4}} {\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} - 2 \, \sqrt{\tan\left(f x + e\right) + 1}\right)}}{2 \, \sqrt{-\sqrt{2} + 2}}\right)}{4 \, f^{3}} + \frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} + 2} - f \sqrt{2 \, \sqrt{2} - 2} {\left| f \right|}\right)} \log\left(2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{8 \, f^{3}} - \frac{{\left(f^{2} \sqrt{2 \, \sqrt{2} + 2} - f \sqrt{2 \, \sqrt{2} - 2} {\left| f \right|}\right)} \log\left(-2^{\frac{1}{4}} \sqrt{\sqrt{2} + 2} \sqrt{\tan\left(f x + e\right) + 1} + \sqrt{2} + \tan\left(f x + e\right) + 1\right)}{8 \, f^{3}}"," ",0,"1/4*(f^2*sqrt(2*sqrt(2) - 2) + f*sqrt(2*sqrt(2) + 2)*abs(f))*arctan(1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) + 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f^3 + 1/4*(f^2*sqrt(2*sqrt(2) - 2) + f*sqrt(2*sqrt(2) + 2)*abs(f))*arctan(-1/2*2^(3/4)*(2^(1/4)*sqrt(sqrt(2) + 2) - 2*sqrt(tan(f*x + e) + 1))/sqrt(-sqrt(2) + 2))/f^3 + 1/8*(f^2*sqrt(2*sqrt(2) + 2) - f*sqrt(2*sqrt(2) - 2)*abs(f))*log(2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f^3 - 1/8*(f^2*sqrt(2*sqrt(2) + 2) - f*sqrt(2*sqrt(2) - 2)*abs(f))*log(-2^(1/4)*sqrt(sqrt(2) + 2)*sqrt(tan(f*x + e) + 1) + sqrt(2) + tan(f*x + e) + 1)/f^3","A",0
409,-2,0,0,0.000000," ","integrate(cot(f*x+e)^2/(1+tan(f*x+e))^(1/2),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)2*((1808*sqrt(2*(sqrt(2)+1))*f^2-1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/28928/f^3*ln(tan(f*x+exp(1))+1-(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))+(-1808*sqrt(2*(sqrt(2)-1))*f^2-1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/14464/f^3*atan((sqrt(tan(f*x+exp(1))+1)-sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+(-1808*sqrt(2*(sqrt(2)+1))*f^2+1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/28928/f^3*ln(tan(f*x+exp(1))+1+(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))-(1808*sqrt(2*(sqrt(2)-1))*f^2+1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/14464/f^3*atan((sqrt(tan(f*x+exp(1))+1)+sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))-1/4/f*ln(abs(sqrt(tan(f*x+exp(1))+1)-1))+1/4/f*ln(sqrt(tan(f*x+exp(1))+1)+1)-sqrt(tan(f*x+exp(1))+1)/2/f/tan(f*x+exp(1)))","F(-2)",0
410,-2,0,0,0.000000," ","integrate(cot(f*x+e)^4/(1+tan(f*x+e))^(1/2),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)2*((-1808*sqrt(2*(sqrt(2)+1))*f^2+1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/28928/f^3*ln(tan(f*x+exp(1))+1-(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))+(1808*sqrt(2*(sqrt(2)-1))*f^2+1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/14464/f^3*atan((sqrt(tan(f*x+exp(1))+1)-sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+(1808*sqrt(2*(sqrt(2)+1))*f^2-1808*sqrt(2*(sqrt(2)-1))*f*abs(f))/28928/f^3*ln(tan(f*x+exp(1))+1+(2*f/f)^(1/4)*sqrt(2+sqrt(2))*sqrt(tan(f*x+exp(1))+1)+(2*f/f)^(1/4)*(2*f/f)^(1/4))-(-1808*sqrt(2*(sqrt(2)-1))*f^2-1808*sqrt(2*(sqrt(2)+1))*f*abs(f))/14464/f^3*atan((sqrt(tan(f*x+exp(1))+1)+sqrt(2+sqrt(2))/2*(2*f/f)^(1/4))/sqrt(2-sqrt(2))*2/(2*f/f)^(1/4))+3/32/f*ln(abs(sqrt(tan(f*x+exp(1))+1)-1))-3/32/f*ln(sqrt(tan(f*x+exp(1))+1)+1)+(9*sqrt(tan(f*x+exp(1))+1)*(tan(f*x+exp(1))+1)^2-8*sqrt(tan(f*x+exp(1))+1)*(tan(f*x+exp(1))+1)-9*sqrt(tan(f*x+exp(1))+1))/48/f/tan(f*x+exp(1))^3)","F(-2)",0
411,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+a*tan(f*x+e))^m,x, algorithm=""giac"")","\int {\left(a \tan\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((a*tan(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
412,1,947,0,23.202800," ","integrate(tan(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{60 \, b d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 30 \, a \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)^{5} \tan\left(c\right)^{5} - 300 \, b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 45 \, a \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 150 \, a \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)^{4} \tan\left(c\right)^{4} + 60 \, b \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 60 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 600 \, b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 30 \, a \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 165 \, a \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 30 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 20 \, b \tan\left(d x\right)^{5} \tan\left(c\right)^{2} + 300 \, a \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)^{3} \tan\left(c\right)^{3} - 300 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 300 \, b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 20 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{5} - 15 \, a \tan\left(d x\right)^{5} \tan\left(c\right) - 600 \, b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 150 \, a \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 180 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 150 \, a \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 15 \, a \tan\left(d x\right) \tan\left(c\right)^{5} + 12 \, b \tan\left(d x\right)^{5} + 100 \, b \tan\left(d x\right)^{4} \tan\left(c\right) - 300 \, a \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} + 600 \, b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 600 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 100 \, b \tan\left(d x\right) \tan\left(c\right)^{4} + 12 \, b \tan\left(c\right)^{5} + 15 \, a \tan\left(d x\right)^{4} + 300 \, b d x \tan\left(d x\right) \tan\left(c\right) + 150 \, a \tan\left(d x\right)^{3} \tan\left(c\right) - 180 \, a \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 150 \, a \tan\left(d x\right) \tan\left(c\right)^{3} + 15 \, a \tan\left(c\right)^{4} - 20 \, b \tan\left(d x\right)^{3} + 150 \, a \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) \tan\left(c\right) - 300 \, b \tan\left(d x\right)^{2} \tan\left(c\right) - 300 \, b \tan\left(d x\right) \tan\left(c\right)^{2} - 20 \, b \tan\left(c\right)^{3} - 60 \, b d x - 30 \, a \tan\left(d x\right)^{2} + 165 \, a \tan\left(d x\right) \tan\left(c\right) - 30 \, a \tan\left(c\right)^{2} - 30 \, a \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) + 60 \, b \tan\left(d x\right) + 60 \, b \tan\left(c\right) - 45 \, a}{60 \, {\left(d \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 5 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 10 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 10 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 5 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/60*(60*b*d*x*tan(d*x)^5*tan(c)^5 + 30*a*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)^5*tan(c)^5 - 300*b*d*x*tan(d*x)^4*tan(c)^4 + 45*a*tan(d*x)^5*tan(c)^5 - 150*a*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)^4*tan(c)^4 + 60*b*tan(d*x)^5*tan(c)^4 + 60*b*tan(d*x)^4*tan(c)^5 + 600*b*d*x*tan(d*x)^3*tan(c)^3 + 30*a*tan(d*x)^5*tan(c)^3 - 165*a*tan(d*x)^4*tan(c)^4 + 30*a*tan(d*x)^3*tan(c)^5 - 20*b*tan(d*x)^5*tan(c)^2 + 300*a*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)^3*tan(c)^3 - 300*b*tan(d*x)^4*tan(c)^3 - 300*b*tan(d*x)^3*tan(c)^4 - 20*b*tan(d*x)^2*tan(c)^5 - 15*a*tan(d*x)^5*tan(c) - 600*b*d*x*tan(d*x)^2*tan(c)^2 - 150*a*tan(d*x)^4*tan(c)^2 + 180*a*tan(d*x)^3*tan(c)^3 - 150*a*tan(d*x)^2*tan(c)^4 - 15*a*tan(d*x)*tan(c)^5 + 12*b*tan(d*x)^5 + 100*b*tan(d*x)^4*tan(c) - 300*a*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 + 600*b*tan(d*x)^3*tan(c)^2 + 600*b*tan(d*x)^2*tan(c)^3 + 100*b*tan(d*x)*tan(c)^4 + 12*b*tan(c)^5 + 15*a*tan(d*x)^4 + 300*b*d*x*tan(d*x)*tan(c) + 150*a*tan(d*x)^3*tan(c) - 180*a*tan(d*x)^2*tan(c)^2 + 150*a*tan(d*x)*tan(c)^3 + 15*a*tan(c)^4 - 20*b*tan(d*x)^3 + 150*a*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)*tan(c) - 300*b*tan(d*x)^2*tan(c) - 300*b*tan(d*x)*tan(c)^2 - 20*b*tan(c)^3 - 60*b*d*x - 30*a*tan(d*x)^2 + 165*a*tan(d*x)*tan(c) - 30*a*tan(c)^2 - 30*a*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)) + 60*b*tan(d*x) + 60*b*tan(c) - 45*a)/(d*tan(d*x)^5*tan(c)^5 - 5*d*tan(d*x)^4*tan(c)^4 + 10*d*tan(d*x)^3*tan(c)^3 - 10*d*tan(d*x)^2*tan(c)^2 + 5*d*tan(d*x)*tan(c) - d)","B",0
413,1,716,0,6.460073," ","integrate(tan(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} - 6 \, b \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)^{4} \tan\left(c\right)^{4} - 48 \, a d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 9 \, b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 24 \, b \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)^{3} \tan\left(c\right)^{3} + 12 \, a \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 12 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 72 \, 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} + 24 \, b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 4 \, a \tan\left(d x\right)^{4} \tan\left(c\right) - 36 \, b \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} - 48 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 48 \, a \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 4 \, a \tan\left(d x\right) \tan\left(c\right)^{4} + 3 \, b \tan\left(d x\right)^{4} - 48 \, a d x \tan\left(d x\right) \tan\left(c\right) + 24 \, b \tan\left(d x\right)^{3} \tan\left(c\right) - 12 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 24 \, b \tan\left(d x\right) \tan\left(c\right)^{3} + 3 \, b \tan\left(c\right)^{4} + 4 \, a \tan\left(d x\right)^{3} + 24 \, b \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) \tan\left(c\right) + 48 \, a \tan\left(d x\right)^{2} \tan\left(c\right) + 48 \, a \tan\left(d x\right) \tan\left(c\right)^{2} + 4 \, a \tan\left(c\right)^{3} + 12 \, a d x - 6 \, b \tan\left(d x\right)^{2} + 24 \, b \tan\left(d x\right) \tan\left(c\right) - 6 \, b \tan\left(c\right)^{2} - 6 \, b \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) - 12 \, a \tan\left(d x\right) - 12 \, a \tan\left(c\right) - 9 \, b}{12 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"1/12*(12*a*d*x*tan(d*x)^4*tan(c)^4 - 6*b*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)^4*tan(c)^4 - 48*a*d*x*tan(d*x)^3*tan(c)^3 - 9*b*tan(d*x)^4*tan(c)^4 + 24*b*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)^3*tan(c)^3 + 12*a*tan(d*x)^4*tan(c)^3 + 12*a*tan(d*x)^3*tan(c)^4 + 72*a*d*x*tan(d*x)^2*tan(c)^2 - 6*b*tan(d*x)^4*tan(c)^2 + 24*b*tan(d*x)^3*tan(c)^3 - 6*b*tan(d*x)^2*tan(c)^4 - 4*a*tan(d*x)^4*tan(c) - 36*b*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 - 48*a*tan(d*x)^3*tan(c)^2 - 48*a*tan(d*x)^2*tan(c)^3 - 4*a*tan(d*x)*tan(c)^4 + 3*b*tan(d*x)^4 - 48*a*d*x*tan(d*x)*tan(c) + 24*b*tan(d*x)^3*tan(c) - 12*b*tan(d*x)^2*tan(c)^2 + 24*b*tan(d*x)*tan(c)^3 + 3*b*tan(c)^4 + 4*a*tan(d*x)^3 + 24*b*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)*tan(c) + 48*a*tan(d*x)^2*tan(c) + 48*a*tan(d*x)*tan(c)^2 + 4*a*tan(c)^3 + 12*a*d*x - 6*b*tan(d*x)^2 + 24*b*tan(d*x)*tan(c) - 6*b*tan(c)^2 - 6*b*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)) - 12*a*tan(d*x) - 12*a*tan(c) - 9*b)/(d*tan(d*x)^4*tan(c)^4 - 4*d*tan(d*x)^3*tan(c)^3 + 6*d*tan(d*x)^2*tan(c)^2 - 4*d*tan(d*x)*tan(c) + d)","B",0
414,1,515,0,3.059325," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{6 \, b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 3 \, a \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)^{3} \tan\left(c\right)^{3} - 18 \, b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, a \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 9 \, a \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} + 6 \, b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 6 \, b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 18 \, b d x \tan\left(d x\right) \tan\left(c\right) + 3 \, a \tan\left(d x\right)^{3} \tan\left(c\right) - 3 \, a \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, a \tan\left(d x\right) \tan\left(c\right)^{3} - 2 \, b \tan\left(d x\right)^{3} + 9 \, a \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) \tan\left(c\right) - 18 \, b \tan\left(d x\right)^{2} \tan\left(c\right) - 18 \, b \tan\left(d x\right) \tan\left(c\right)^{2} - 2 \, b \tan\left(c\right)^{3} - 6 \, b d x - 3 \, a \tan\left(d x\right)^{2} + 3 \, a \tan\left(d x\right) \tan\left(c\right) - 3 \, a \tan\left(c\right)^{2} - 3 \, a \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) + 6 \, b \tan\left(d x\right) + 6 \, b \tan\left(c\right) - 3 \, a}{6 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"1/6*(6*b*d*x*tan(d*x)^3*tan(c)^3 + 3*a*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)^3*tan(c)^3 - 18*b*d*x*tan(d*x)^2*tan(c)^2 + 3*a*tan(d*x)^3*tan(c)^3 - 9*a*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 + 6*b*tan(d*x)^3*tan(c)^2 + 6*b*tan(d*x)^2*tan(c)^3 + 18*b*d*x*tan(d*x)*tan(c) + 3*a*tan(d*x)^3*tan(c) - 3*a*tan(d*x)^2*tan(c)^2 + 3*a*tan(d*x)*tan(c)^3 - 2*b*tan(d*x)^3 + 9*a*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)*tan(c) - 18*b*tan(d*x)^2*tan(c) - 18*b*tan(d*x)*tan(c)^2 - 2*b*tan(c)^3 - 6*b*d*x - 3*a*tan(d*x)^2 + 3*a*tan(d*x)*tan(c) - 3*a*tan(c)^2 - 3*a*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)) + 6*b*tan(d*x) + 6*b*tan(c) - 3*a)/(d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c) - d)","B",0
415,1,327,0,3.109859," ","integrate(tan(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} - b \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} - 4 \, a d x \tan\left(d x\right) \tan\left(c\right) - b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 2 \, b \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) \tan\left(c\right) + 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} - b \tan\left(c\right)^{2} - b \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 \tan\left(d x\right) - 2 \, a \tan\left(c\right) - b}{2 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/2*(2*a*d*x*tan(d*x)^2*tan(c)^2 - b*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 - 4*a*d*x*tan(d*x)*tan(c) - b*tan(d*x)^2*tan(c)^2 + 2*b*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)*tan(c) + 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 - b*tan(c)^2 - b*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*tan(d*x) - 2*a*tan(c) - b)/(d*tan(d*x)^2*tan(c)^2 - 2*d*tan(d*x)*tan(c) + d)","B",0
416,1,174,0,0.603684," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, b d x \tan\left(d x\right) \tan\left(c\right) + a \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) \tan\left(c\right) - 2 \, b d x - a \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 \, b \tan\left(d x\right) + 2 \, b \tan\left(c\right)}{2 \, {\left(d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/2*(2*b*d*x*tan(d*x)*tan(c) + a*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)*tan(c) - 2*b*d*x - a*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*b*tan(d*x) + 2*b*tan(c))/(d*tan(d*x)*tan(c) - d)","B",0
417,1,18,0,0.387748," ","integrate(a+b*tan(d*x+c),x, algorithm=""giac"")","a x - \frac{b \log\left({\left| \cos\left(d x + c\right) \right|}\right)}{d}"," ",0,"a*x - b*log(abs(cos(d*x + c)))/d","A",0
418,1,42,0,0.585341," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{{\left(d x + c\right)} b - a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right)}{d}"," ",0,"((d*x + c)*b - a*log(tan(1/2*d*x + 1/2*c)^2 + 1) + a*log(abs(tan(1/2*d*x + 1/2*c))))/d","B",0
419,1,83,0,0.815078," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{2 \, {\left(d x + c\right)} a + 2 \, b \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 2 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{2 \, b \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 \, d}"," ",0,"-1/2*(2*(d*x + c)*a + 2*b*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 2*b*log(abs(tan(1/2*d*x + 1/2*c))) - a*tan(1/2*d*x + 1/2*c) + (2*b*tan(1/2*d*x + 1/2*c) + a)/tan(1/2*d*x + 1/2*c))/d","B",0
420,1,113,0,0.872055," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, {\left(d x + c\right)} b - 8 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 8 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 4 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{12 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b \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}}}{8 \, d}"," ",0,"-1/8*(a*tan(1/2*d*x + 1/2*c)^2 + 8*(d*x + c)*b - 8*a*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 8*a*log(abs(tan(1/2*d*x + 1/2*c))) - 4*b*tan(1/2*d*x + 1/2*c) - (12*a*tan(1/2*d*x + 1/2*c)^2 - 4*b*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
421,1,140,0,1.079132," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 3 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, {\left(d x + c\right)} a + 24 \, b \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 24 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{44 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 3 \, b \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)^{3}}}{24 \, d}"," ",0,"1/24*(a*tan(1/2*d*x + 1/2*c)^3 - 3*b*tan(1/2*d*x + 1/2*c)^2 + 24*(d*x + c)*a + 24*b*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 24*b*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a*tan(1/2*d*x + 1/2*c) + (44*b*tan(1/2*d*x + 1/2*c)^3 + 15*a*tan(1/2*d*x + 1/2*c)^2 - 3*b*tan(1/2*d*x + 1/2*c) - a)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
422,1,169,0,1.766499," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{3 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 192 \, {\left(d x + c\right)} b + 192 \, a \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, a \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + \frac{400 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 120 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a*tan(1/2*d*x + 1/2*c)^4 - 8*b*tan(1/2*d*x + 1/2*c)^3 - 36*a*tan(1/2*d*x + 1/2*c)^2 - 192*(d*x + c)*b + 192*a*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*a*log(abs(tan(1/2*d*x + 1/2*c))) + 120*b*tan(1/2*d*x + 1/2*c) + (400*a*tan(1/2*d*x + 1/2*c)^4 - 120*b*tan(1/2*d*x + 1/2*c)^3 - 36*a*tan(1/2*d*x + 1/2*c)^2 + 8*b*tan(1/2*d*x + 1/2*c) + 3*a)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
423,1,198,0,2.037507," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{6 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 960 \, {\left(d x + c\right)} a - 960 \, b \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 960 \, b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - \frac{2192 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 180 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a*tan(1/2*d*x + 1/2*c)^5 - 15*b*tan(1/2*d*x + 1/2*c)^4 - 70*a*tan(1/2*d*x + 1/2*c)^3 + 180*b*tan(1/2*d*x + 1/2*c)^2 - 960*(d*x + c)*a - 960*b*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 960*b*log(abs(tan(1/2*d*x + 1/2*c))) + 660*a*tan(1/2*d*x + 1/2*c) - (2192*b*tan(1/2*d*x + 1/2*c)^5 + 660*a*tan(1/2*d*x + 1/2*c)^4 - 180*b*tan(1/2*d*x + 1/2*c)^3 - 70*a*tan(1/2*d*x + 1/2*c)^2 + 15*b*tan(1/2*d*x + 1/2*c) + 6*a)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
424,1,1315,0,22.577652," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{30 \, a^{2} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 30 \, b^{2} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 30 \, a b \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)^{5} \tan\left(c\right)^{5} - 150 \, a^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 150 \, b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 45 \, a b \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 150 \, a b \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)^{4} \tan\left(c\right)^{4} + 30 \, a^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} - 30 \, b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 30 \, a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} - 30 \, b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 300 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 300 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 30 \, a b \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 165 \, a b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 30 \, a b \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 10 \, a^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} + 10 \, b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} - 300 \, a b \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)^{3} \tan\left(c\right)^{3} - 150 \, a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 150 \, b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 150 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 150 \, b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 10 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} + 10 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} + 15 \, a b \tan\left(d x\right)^{5} \tan\left(c\right) - 300 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 300 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 150 \, a b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 180 \, a b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 150 \, a b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 15 \, a b \tan\left(d x\right) \tan\left(c\right)^{5} - 6 \, b^{2} \tan\left(d x\right)^{5} + 20 \, a^{2} \tan\left(d x\right)^{4} \tan\left(c\right) - 50 \, b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) + 300 \, a b \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} + 240 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 300 \, b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 240 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 300 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 20 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{4} - 50 \, b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} - 6 \, b^{2} \tan\left(c\right)^{5} - 15 \, a b \tan\left(d x\right)^{4} + 150 \, a^{2} d x \tan\left(d x\right) \tan\left(c\right) - 150 \, b^{2} d x \tan\left(d x\right) \tan\left(c\right) - 150 \, a b \tan\left(d x\right)^{3} \tan\left(c\right) + 180 \, a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 150 \, a b \tan\left(d x\right) \tan\left(c\right)^{3} - 15 \, a b \tan\left(c\right)^{4} - 10 \, a^{2} \tan\left(d x\right)^{3} + 10 \, b^{2} \tan\left(d x\right)^{3} - 150 \, a b \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) \tan\left(c\right) - 150 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) + 150 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 150 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 150 \, b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 10 \, a^{2} \tan\left(c\right)^{3} + 10 \, b^{2} \tan\left(c\right)^{3} - 30 \, a^{2} d x + 30 \, b^{2} d x + 30 \, a b \tan\left(d x\right)^{2} - 165 \, a b \tan\left(d x\right) \tan\left(c\right) + 30 \, a b \tan\left(c\right)^{2} + 30 \, a b \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) + 30 \, a^{2} \tan\left(d x\right) - 30 \, b^{2} \tan\left(d x\right) + 30 \, a^{2} \tan\left(c\right) - 30 \, b^{2} \tan\left(c\right) + 45 \, a b}{30 \, {\left(d \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 5 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 10 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 10 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 5 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"1/30*(30*a^2*d*x*tan(d*x)^5*tan(c)^5 - 30*b^2*d*x*tan(d*x)^5*tan(c)^5 - 30*a*b*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)^5*tan(c)^5 - 150*a^2*d*x*tan(d*x)^4*tan(c)^4 + 150*b^2*d*x*tan(d*x)^4*tan(c)^4 - 45*a*b*tan(d*x)^5*tan(c)^5 + 150*a*b*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)^4*tan(c)^4 + 30*a^2*tan(d*x)^5*tan(c)^4 - 30*b^2*tan(d*x)^5*tan(c)^4 + 30*a^2*tan(d*x)^4*tan(c)^5 - 30*b^2*tan(d*x)^4*tan(c)^5 + 300*a^2*d*x*tan(d*x)^3*tan(c)^3 - 300*b^2*d*x*tan(d*x)^3*tan(c)^3 - 30*a*b*tan(d*x)^5*tan(c)^3 + 165*a*b*tan(d*x)^4*tan(c)^4 - 30*a*b*tan(d*x)^3*tan(c)^5 - 10*a^2*tan(d*x)^5*tan(c)^2 + 10*b^2*tan(d*x)^5*tan(c)^2 - 300*a*b*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)^3*tan(c)^3 - 150*a^2*tan(d*x)^4*tan(c)^3 + 150*b^2*tan(d*x)^4*tan(c)^3 - 150*a^2*tan(d*x)^3*tan(c)^4 + 150*b^2*tan(d*x)^3*tan(c)^4 - 10*a^2*tan(d*x)^2*tan(c)^5 + 10*b^2*tan(d*x)^2*tan(c)^5 + 15*a*b*tan(d*x)^5*tan(c) - 300*a^2*d*x*tan(d*x)^2*tan(c)^2 + 300*b^2*d*x*tan(d*x)^2*tan(c)^2 + 150*a*b*tan(d*x)^4*tan(c)^2 - 180*a*b*tan(d*x)^3*tan(c)^3 + 150*a*b*tan(d*x)^2*tan(c)^4 + 15*a*b*tan(d*x)*tan(c)^5 - 6*b^2*tan(d*x)^5 + 20*a^2*tan(d*x)^4*tan(c) - 50*b^2*tan(d*x)^4*tan(c) + 300*a*b*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 + 240*a^2*tan(d*x)^3*tan(c)^2 - 300*b^2*tan(d*x)^3*tan(c)^2 + 240*a^2*tan(d*x)^2*tan(c)^3 - 300*b^2*tan(d*x)^2*tan(c)^3 + 20*a^2*tan(d*x)*tan(c)^4 - 50*b^2*tan(d*x)*tan(c)^4 - 6*b^2*tan(c)^5 - 15*a*b*tan(d*x)^4 + 150*a^2*d*x*tan(d*x)*tan(c) - 150*b^2*d*x*tan(d*x)*tan(c) - 150*a*b*tan(d*x)^3*tan(c) + 180*a*b*tan(d*x)^2*tan(c)^2 - 150*a*b*tan(d*x)*tan(c)^3 - 15*a*b*tan(c)^4 - 10*a^2*tan(d*x)^3 + 10*b^2*tan(d*x)^3 - 150*a*b*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)*tan(c) - 150*a^2*tan(d*x)^2*tan(c) + 150*b^2*tan(d*x)^2*tan(c) - 150*a^2*tan(d*x)*tan(c)^2 + 150*b^2*tan(d*x)*tan(c)^2 - 10*a^2*tan(c)^3 + 10*b^2*tan(c)^3 - 30*a^2*d*x + 30*b^2*d*x + 30*a*b*tan(d*x)^2 - 165*a*b*tan(d*x)*tan(c) + 30*a*b*tan(c)^2 + 30*a*b*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)) + 30*a^2*tan(d*x) - 30*b^2*tan(d*x) + 30*a^2*tan(c) - 30*b^2*tan(c) + 45*a*b)/(d*tan(d*x)^5*tan(c)^5 - 5*d*tan(d*x)^4*tan(c)^4 + 10*d*tan(d*x)^3*tan(c)^3 - 10*d*tan(d*x)^2*tan(c)^2 + 5*d*tan(d*x)*tan(c) - d)","B",0
425,1,1262,0,8.390379," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{24 \, a b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 6 \, a^{2} \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)^{4} \tan\left(c\right)^{4} - 6 \, b^{2} \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)^{4} \tan\left(c\right)^{4} - 96 \, a b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 9 \, b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 24 \, a^{2} \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)^{3} \tan\left(c\right)^{3} + 24 \, b^{2} \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)^{3} \tan\left(c\right)^{3} + 24 \, a b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 24 \, a b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 144 \, a b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, a^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 6 \, b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 12 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 24 \, b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 6 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 8 \, a b \tan\left(d x\right)^{4} \tan\left(c\right) + 36 \, a^{2} \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} - 36 \, b^{2} \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} - 96 \, a b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 96 \, a b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 8 \, a b \tan\left(d x\right) \tan\left(c\right)^{4} + 3 \, b^{2} \tan\left(d x\right)^{4} - 96 \, a b d x \tan\left(d x\right) \tan\left(c\right) - 12 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right) + 24 \, b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) + 12 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 12 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 12 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{3} + 24 \, b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} + 3 \, b^{2} \tan\left(c\right)^{4} + 8 \, a b \tan\left(d x\right)^{3} - 24 \, a^{2} \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) \tan\left(c\right) + 24 \, b^{2} \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) \tan\left(c\right) + 96 \, a b \tan\left(d x\right)^{2} \tan\left(c\right) + 96 \, a b \tan\left(d x\right) \tan\left(c\right)^{2} + 8 \, a b \tan\left(c\right)^{3} + 24 \, a b d x + 6 \, a^{2} \tan\left(d x\right)^{2} - 6 \, b^{2} \tan\left(d x\right)^{2} - 12 \, a^{2} \tan\left(d x\right) \tan\left(c\right) + 24 \, b^{2} \tan\left(d x\right) \tan\left(c\right) + 6 \, a^{2} \tan\left(c\right)^{2} - 6 \, b^{2} \tan\left(c\right)^{2} + 6 \, a^{2} \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) - 6 \, b^{2} \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) - 24 \, a b \tan\left(d x\right) - 24 \, a b \tan\left(c\right) + 6 \, a^{2} - 9 \, b^{2}}{12 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"1/12*(24*a*b*d*x*tan(d*x)^4*tan(c)^4 + 6*a^2*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)^4*tan(c)^4 - 6*b^2*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)^4*tan(c)^4 - 96*a*b*d*x*tan(d*x)^3*tan(c)^3 + 6*a^2*tan(d*x)^4*tan(c)^4 - 9*b^2*tan(d*x)^4*tan(c)^4 - 24*a^2*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)^3*tan(c)^3 + 24*b^2*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)^3*tan(c)^3 + 24*a*b*tan(d*x)^4*tan(c)^3 + 24*a*b*tan(d*x)^3*tan(c)^4 + 144*a*b*d*x*tan(d*x)^2*tan(c)^2 + 6*a^2*tan(d*x)^4*tan(c)^2 - 6*b^2*tan(d*x)^4*tan(c)^2 - 12*a^2*tan(d*x)^3*tan(c)^3 + 24*b^2*tan(d*x)^3*tan(c)^3 + 6*a^2*tan(d*x)^2*tan(c)^4 - 6*b^2*tan(d*x)^2*tan(c)^4 - 8*a*b*tan(d*x)^4*tan(c) + 36*a^2*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 - 36*b^2*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 - 96*a*b*tan(d*x)^3*tan(c)^2 - 96*a*b*tan(d*x)^2*tan(c)^3 - 8*a*b*tan(d*x)*tan(c)^4 + 3*b^2*tan(d*x)^4 - 96*a*b*d*x*tan(d*x)*tan(c) - 12*a^2*tan(d*x)^3*tan(c) + 24*b^2*tan(d*x)^3*tan(c) + 12*a^2*tan(d*x)^2*tan(c)^2 - 12*b^2*tan(d*x)^2*tan(c)^2 - 12*a^2*tan(d*x)*tan(c)^3 + 24*b^2*tan(d*x)*tan(c)^3 + 3*b^2*tan(c)^4 + 8*a*b*tan(d*x)^3 - 24*a^2*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)*tan(c) + 24*b^2*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)*tan(c) + 96*a*b*tan(d*x)^2*tan(c) + 96*a*b*tan(d*x)*tan(c)^2 + 8*a*b*tan(c)^3 + 24*a*b*d*x + 6*a^2*tan(d*x)^2 - 6*b^2*tan(d*x)^2 - 12*a^2*tan(d*x)*tan(c) + 24*b^2*tan(d*x)*tan(c) + 6*a^2*tan(c)^2 - 6*b^2*tan(c)^2 + 6*a^2*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)) - 6*b^2*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)) - 24*a*b*tan(d*x) - 24*a*b*tan(c) + 6*a^2 - 9*b^2)/(d*tan(d*x)^4*tan(c)^4 - 4*d*tan(d*x)^3*tan(c)^3 + 6*d*tan(d*x)^2*tan(c)^2 - 4*d*tan(d*x)*tan(c) + d)","B",0
426,1,675,0,2.681971," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, a b \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)^{3} \tan\left(c\right)^{3} - 9 \, a^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 9 \, b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 3 \, a b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 9 \, a b \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} + 3 \, a^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 3 \, b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 3 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 3 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 9 \, a^{2} d x \tan\left(d x\right) \tan\left(c\right) - 9 \, b^{2} d x \tan\left(d x\right) \tan\left(c\right) - 3 \, a b \tan\left(d x\right)^{3} \tan\left(c\right) + 3 \, a b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 3 \, a b \tan\left(d x\right) \tan\left(c\right)^{3} + b^{2} \tan\left(d x\right)^{3} - 9 \, a b \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) \tan\left(c\right) - 6 \, a^{2} \tan\left(d x\right)^{2} \tan\left(c\right) + 9 \, b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 6 \, a^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + 9 \, b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} + b^{2} \tan\left(c\right)^{3} - 3 \, a^{2} d x + 3 \, b^{2} d x + 3 \, a b \tan\left(d x\right)^{2} - 3 \, a b \tan\left(d x\right) \tan\left(c\right) + 3 \, a b \tan\left(c\right)^{2} + 3 \, a b \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) + 3 \, a^{2} \tan\left(d x\right) - 3 \, b^{2} \tan\left(d x\right) + 3 \, a^{2} \tan\left(c\right) - 3 \, b^{2} \tan\left(c\right) + 3 \, a b}{3 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/3*(3*a^2*d*x*tan(d*x)^3*tan(c)^3 - 3*b^2*d*x*tan(d*x)^3*tan(c)^3 - 3*a*b*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)^3*tan(c)^3 - 9*a^2*d*x*tan(d*x)^2*tan(c)^2 + 9*b^2*d*x*tan(d*x)^2*tan(c)^2 - 3*a*b*tan(d*x)^3*tan(c)^3 + 9*a*b*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 + 3*a^2*tan(d*x)^3*tan(c)^2 - 3*b^2*tan(d*x)^3*tan(c)^2 + 3*a^2*tan(d*x)^2*tan(c)^3 - 3*b^2*tan(d*x)^2*tan(c)^3 + 9*a^2*d*x*tan(d*x)*tan(c) - 9*b^2*d*x*tan(d*x)*tan(c) - 3*a*b*tan(d*x)^3*tan(c) + 3*a*b*tan(d*x)^2*tan(c)^2 - 3*a*b*tan(d*x)*tan(c)^3 + b^2*tan(d*x)^3 - 9*a*b*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)*tan(c) - 6*a^2*tan(d*x)^2*tan(c) + 9*b^2*tan(d*x)^2*tan(c) - 6*a^2*tan(d*x)*tan(c)^2 + 9*b^2*tan(d*x)*tan(c)^2 + b^2*tan(c)^3 - 3*a^2*d*x + 3*b^2*d*x + 3*a*b*tan(d*x)^2 - 3*a*b*tan(d*x)*tan(c) + 3*a*b*tan(c)^2 + 3*a*b*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)) + 3*a^2*tan(d*x) - 3*b^2*tan(d*x) + 3*a^2*tan(c) - 3*b^2*tan(c) + 3*a*b)/(d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c) - d)","B",0
427,1,554,0,2.152120," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, a b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + a^{2} \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} - b^{2} \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} - 8 \, a b d x \tan\left(d x\right) \tan\left(c\right) - b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, a^{2} \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) \tan\left(c\right) + 2 \, b^{2} \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) \tan\left(c\right) + 4 \, a b \tan\left(d x\right)^{2} \tan\left(c\right) + 4 \, a b \tan\left(d x\right) \tan\left(c\right)^{2} + 4 \, a b d x - b^{2} \tan\left(d x\right)^{2} - b^{2} \tan\left(c\right)^{2} + a^{2} \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) - b^{2} \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) - 4 \, a b \tan\left(d x\right) - 4 \, a b \tan\left(c\right) - b^{2}}{2 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/2*(4*a*b*d*x*tan(d*x)^2*tan(c)^2 + a^2*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 - b^2*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 - 8*a*b*d*x*tan(d*x)*tan(c) - b^2*tan(d*x)^2*tan(c)^2 - 2*a^2*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)*tan(c) + 2*b^2*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)*tan(c) + 4*a*b*tan(d*x)^2*tan(c) + 4*a*b*tan(d*x)*tan(c)^2 + 4*a*b*d*x - b^2*tan(d*x)^2 - b^2*tan(c)^2 + a^2*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)) - b^2*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)) - 4*a*b*tan(d*x) - 4*a*b*tan(c) - b^2)/(d*tan(d*x)^2*tan(c)^2 - 2*d*tan(d*x)*tan(c) + d)","B",0
428,1,201,0,0.964877," ","integrate((a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} d x \tan\left(d x\right) \tan\left(c\right) - b^{2} d x \tan\left(d x\right) \tan\left(c\right) - a b \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) \tan\left(c\right) - a^{2} d x + b^{2} d x + a b \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) - b^{2} \tan\left(d x\right) - b^{2} \tan\left(c\right)}{d \tan\left(d x\right) \tan\left(c\right) - d}"," ",0,"(a^2*d*x*tan(d*x)*tan(c) - b^2*d*x*tan(d*x)*tan(c) - a*b*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)*tan(c) - a^2*d*x + b^2*d*x + a*b*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)) - b^2*tan(d*x) - b^2*tan(c))/(d*tan(d*x)*tan(c) - d)","B",0
429,1,50,0,1.503551," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{4 \, {\left(d x + c\right)} a b + 2 \, a^{2} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b + 2*a^2*log(abs(tan(d*x + c))) - (a^2 - b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
430,1,98,0,1.429241," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{4 \, a b \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 4 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} + \frac{4 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}}{2 \, d}"," ",0,"-1/2*(4*a*b*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 4*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - a^2*tan(1/2*d*x + 1/2*c) + 2*(a^2 - b^2)*(d*x + c) + (4*a*b*tan(1/2*d*x + 1/2*c) + a^2)/tan(1/2*d*x + 1/2*c))/d","B",0
431,1,154,0,1.775823," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 16 \, {\left(d x + c\right)} a b - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 8 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{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} - 8 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(a^2*tan(1/2*d*x + 1/2*c)^2 + 16*(d*x + c)*a*b - 8*a*b*tan(1/2*d*x + 1/2*c) - 8*(a^2 - b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 8*(a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (12*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 8*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
432,1,191,0,2.405131," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 48 \, a b \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 48 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - 15 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 12 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} + \frac{88 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, 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} - 6 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^2*tan(1/2*d*x + 1/2*c)^3 - 6*a*b*tan(1/2*d*x + 1/2*c)^2 + 48*a*b*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 48*a*b*log(abs(tan(1/2*d*x + 1/2*c))) - 15*a^2*tan(1/2*d*x + 1/2*c) + 12*b^2*tan(1/2*d*x + 1/2*c) + 24*(a^2 - b^2)*(d*x + c) + (88*a*b*tan(1/2*d*x + 1/2*c)^3 + 15*a^2*tan(1/2*d*x + 1/2*c)^2 - 12*b^2*tan(1/2*d*x + 1/2*c)^2 - 6*a*b*tan(1/2*d*x + 1/2*c) - a^2)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
433,1,248,0,2.430347," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, 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} - 384 \, {\left(d x + c\right)} a b + 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 192 \, {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{400 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 400 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, 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} + 16 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a^2*tan(1/2*d*x + 1/2*c)^4 - 16*a*b*tan(1/2*d*x + 1/2*c)^3 - 36*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 - 384*(d*x + c)*a*b + 240*a*b*tan(1/2*d*x + 1/2*c) + 192*(a^2 - b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*(a^2 - b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (400*a^2*tan(1/2*d*x + 1/2*c)^4 - 400*b^2*tan(1/2*d*x + 1/2*c)^4 - 240*a*b*tan(1/2*d*x + 1/2*c)^3 - 36*a^2*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*tan(1/2*d*x + 1/2*c)^2 + 16*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
434,1,287,0,3.411582," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 180 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 960 \, a b \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 960 \, a b \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 300 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{2192 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 330 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 300 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 180 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, a^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 20 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 15 \, a b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{2}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^2*tan(1/2*d*x + 1/2*c)^5 - 15*a*b*tan(1/2*d*x + 1/2*c)^4 - 35*a^2*tan(1/2*d*x + 1/2*c)^3 + 20*b^2*tan(1/2*d*x + 1/2*c)^3 + 180*a*b*tan(1/2*d*x + 1/2*c)^2 - 960*a*b*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 960*a*b*log(abs(tan(1/2*d*x + 1/2*c))) + 330*a^2*tan(1/2*d*x + 1/2*c) - 300*b^2*tan(1/2*d*x + 1/2*c) - 480*(a^2 - b^2)*(d*x + c) - (2192*a*b*tan(1/2*d*x + 1/2*c)^5 + 330*a^2*tan(1/2*d*x + 1/2*c)^4 - 300*b^2*tan(1/2*d*x + 1/2*c)^4 - 180*a*b*tan(1/2*d*x + 1/2*c)^3 - 35*a^2*tan(1/2*d*x + 1/2*c)^2 + 20*b^2*tan(1/2*d*x + 1/2*c)^2 + 15*a*b*tan(1/2*d*x + 1/2*c) + 3*a^2)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
435,1,1997,0,36.515309," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{180 \, a^{2} b d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 60 \, b^{3} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 30 \, a^{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)^{5} \tan\left(c\right)^{5} - 90 \, a b^{2} \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)^{5} \tan\left(c\right)^{5} - 900 \, a^{2} b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 300 \, b^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 30 \, a^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 135 \, a b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 150 \, a^{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)^{4} \tan\left(c\right)^{4} + 450 \, a b^{2} \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)^{4} \tan\left(c\right)^{4} + 180 \, a^{2} b \tan\left(d x\right)^{5} \tan\left(c\right)^{4} - 60 \, b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 180 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{5} - 60 \, b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 1800 \, a^{2} b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 600 \, b^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 30 \, a^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 90 \, a b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 90 \, a^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 495 \, a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 30 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 90 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 60 \, a^{2} b \tan\left(d x\right)^{5} \tan\left(c\right)^{2} + 20 \, b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} + 300 \, a^{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)^{3} \tan\left(c\right)^{3} - 900 \, a b^{2} \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)^{3} \tan\left(c\right)^{3} - 900 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 300 \, b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 900 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 300 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 60 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{5} + 20 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} + 45 \, a b^{2} \tan\left(d x\right)^{5} \tan\left(c\right) - 1800 \, a^{2} b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 600 \, b^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 90 \, a^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 450 \, a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 120 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 540 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 90 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 450 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 45 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{5} - 12 \, b^{3} \tan\left(d x\right)^{5} + 120 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right) - 100 \, b^{3} \tan\left(d x\right)^{4} \tan\left(c\right) - 300 \, a^{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} + 900 \, a b^{2} \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} + 1440 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 600 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 1440 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 600 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 120 \, a^{2} b \tan\left(d x\right) \tan\left(c\right)^{4} - 100 \, b^{3} \tan\left(d x\right) \tan\left(c\right)^{4} - 12 \, b^{3} \tan\left(c\right)^{5} - 45 \, a b^{2} \tan\left(d x\right)^{4} + 900 \, a^{2} b d x \tan\left(d x\right) \tan\left(c\right) - 300 \, b^{3} d x \tan\left(d x\right) \tan\left(c\right) + 90 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right) - 450 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) - 120 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 540 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 90 \, a^{3} \tan\left(d x\right) \tan\left(c\right)^{3} - 450 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} - 45 \, a b^{2} \tan\left(c\right)^{4} - 60 \, a^{2} b \tan\left(d x\right)^{3} + 20 \, b^{3} \tan\left(d x\right)^{3} + 150 \, a^{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) \tan\left(c\right) - 450 \, a b^{2} \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) \tan\left(c\right) - 900 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right) + 300 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right) - 900 \, a^{2} b \tan\left(d x\right) \tan\left(c\right)^{2} + 300 \, b^{3} \tan\left(d x\right) \tan\left(c\right)^{2} - 60 \, a^{2} b \tan\left(c\right)^{3} + 20 \, b^{3} \tan\left(c\right)^{3} - 180 \, a^{2} b d x + 60 \, b^{3} d x - 30 \, a^{3} \tan\left(d x\right)^{2} + 90 \, a b^{2} \tan\left(d x\right)^{2} + 90 \, a^{3} \tan\left(d x\right) \tan\left(c\right) - 495 \, a b^{2} \tan\left(d x\right) \tan\left(c\right) - 30 \, a^{3} \tan\left(c\right)^{2} + 90 \, a b^{2} \tan\left(c\right)^{2} - 30 \, a^{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) + 90 \, a b^{2} \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) + 180 \, a^{2} b \tan\left(d x\right) - 60 \, b^{3} \tan\left(d x\right) + 180 \, a^{2} b \tan\left(c\right) - 60 \, b^{3} \tan\left(c\right) - 30 \, a^{3} + 135 \, a b^{2}}{60 \, {\left(d \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 5 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 10 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 10 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 5 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"1/60*(180*a^2*b*d*x*tan(d*x)^5*tan(c)^5 - 60*b^3*d*x*tan(d*x)^5*tan(c)^5 + 30*a^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)^5*tan(c)^5 - 90*a*b^2*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)^5*tan(c)^5 - 900*a^2*b*d*x*tan(d*x)^4*tan(c)^4 + 300*b^3*d*x*tan(d*x)^4*tan(c)^4 + 30*a^3*tan(d*x)^5*tan(c)^5 - 135*a*b^2*tan(d*x)^5*tan(c)^5 - 150*a^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)^4*tan(c)^4 + 450*a*b^2*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)^4*tan(c)^4 + 180*a^2*b*tan(d*x)^5*tan(c)^4 - 60*b^3*tan(d*x)^5*tan(c)^4 + 180*a^2*b*tan(d*x)^4*tan(c)^5 - 60*b^3*tan(d*x)^4*tan(c)^5 + 1800*a^2*b*d*x*tan(d*x)^3*tan(c)^3 - 600*b^3*d*x*tan(d*x)^3*tan(c)^3 + 30*a^3*tan(d*x)^5*tan(c)^3 - 90*a*b^2*tan(d*x)^5*tan(c)^3 - 90*a^3*tan(d*x)^4*tan(c)^4 + 495*a*b^2*tan(d*x)^4*tan(c)^4 + 30*a^3*tan(d*x)^3*tan(c)^5 - 90*a*b^2*tan(d*x)^3*tan(c)^5 - 60*a^2*b*tan(d*x)^5*tan(c)^2 + 20*b^3*tan(d*x)^5*tan(c)^2 + 300*a^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)^3*tan(c)^3 - 900*a*b^2*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)^3*tan(c)^3 - 900*a^2*b*tan(d*x)^4*tan(c)^3 + 300*b^3*tan(d*x)^4*tan(c)^3 - 900*a^2*b*tan(d*x)^3*tan(c)^4 + 300*b^3*tan(d*x)^3*tan(c)^4 - 60*a^2*b*tan(d*x)^2*tan(c)^5 + 20*b^3*tan(d*x)^2*tan(c)^5 + 45*a*b^2*tan(d*x)^5*tan(c) - 1800*a^2*b*d*x*tan(d*x)^2*tan(c)^2 + 600*b^3*d*x*tan(d*x)^2*tan(c)^2 - 90*a^3*tan(d*x)^4*tan(c)^2 + 450*a*b^2*tan(d*x)^4*tan(c)^2 + 120*a^3*tan(d*x)^3*tan(c)^3 - 540*a*b^2*tan(d*x)^3*tan(c)^3 - 90*a^3*tan(d*x)^2*tan(c)^4 + 450*a*b^2*tan(d*x)^2*tan(c)^4 + 45*a*b^2*tan(d*x)*tan(c)^5 - 12*b^3*tan(d*x)^5 + 120*a^2*b*tan(d*x)^4*tan(c) - 100*b^3*tan(d*x)^4*tan(c) - 300*a^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 + 900*a*b^2*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 + 1440*a^2*b*tan(d*x)^3*tan(c)^2 - 600*b^3*tan(d*x)^3*tan(c)^2 + 1440*a^2*b*tan(d*x)^2*tan(c)^3 - 600*b^3*tan(d*x)^2*tan(c)^3 + 120*a^2*b*tan(d*x)*tan(c)^4 - 100*b^3*tan(d*x)*tan(c)^4 - 12*b^3*tan(c)^5 - 45*a*b^2*tan(d*x)^4 + 900*a^2*b*d*x*tan(d*x)*tan(c) - 300*b^3*d*x*tan(d*x)*tan(c) + 90*a^3*tan(d*x)^3*tan(c) - 450*a*b^2*tan(d*x)^3*tan(c) - 120*a^3*tan(d*x)^2*tan(c)^2 + 540*a*b^2*tan(d*x)^2*tan(c)^2 + 90*a^3*tan(d*x)*tan(c)^3 - 450*a*b^2*tan(d*x)*tan(c)^3 - 45*a*b^2*tan(c)^4 - 60*a^2*b*tan(d*x)^3 + 20*b^3*tan(d*x)^3 + 150*a^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)*tan(c) - 450*a*b^2*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)*tan(c) - 900*a^2*b*tan(d*x)^2*tan(c) + 300*b^3*tan(d*x)^2*tan(c) - 900*a^2*b*tan(d*x)*tan(c)^2 + 300*b^3*tan(d*x)*tan(c)^2 - 60*a^2*b*tan(c)^3 + 20*b^3*tan(c)^3 - 180*a^2*b*d*x + 60*b^3*d*x - 30*a^3*tan(d*x)^2 + 90*a*b^2*tan(d*x)^2 + 90*a^3*tan(d*x)*tan(c) - 495*a*b^2*tan(d*x)*tan(c) - 30*a^3*tan(c)^2 + 90*a*b^2*tan(c)^2 - 30*a^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)) + 90*a*b^2*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)) + 180*a^2*b*tan(d*x) - 60*b^3*tan(d*x) + 180*a^2*b*tan(c) - 60*b^3*tan(c) - 30*a^3 + 135*a*b^2)/(d*tan(d*x)^5*tan(c)^5 - 5*d*tan(d*x)^4*tan(c)^4 + 10*d*tan(d*x)^3*tan(c)^3 - 10*d*tan(d*x)^2*tan(c)^2 + 5*d*tan(d*x)*tan(c) - d)","B",0
436,1,1485,0,11.357279," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{4 \, a^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 12 \, a b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 6 \, a^{2} b \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)^{4} \tan\left(c\right)^{4} + 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)^{4} \tan\left(c\right)^{4} - 16 \, a^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 48 \, a b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 3 \, b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 24 \, a^{2} b \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)^{3} \tan\left(c\right)^{3} - 8 \, 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)^{3} \tan\left(c\right)^{3} + 4 \, a^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 12 \, a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 4 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 12 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 24 \, a^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 72 \, a b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 6 \, a^{2} b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 2 \, b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 12 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 8 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 2 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 4 \, a b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) - 36 \, a^{2} b \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} + 12 \, 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} - 12 \, a^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 48 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 12 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 48 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 4 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} - b^{3} \tan\left(d x\right)^{4} - 16 \, a^{3} d x \tan\left(d x\right) \tan\left(c\right) + 48 \, a b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 12 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right) - 8 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right) - 12 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 4 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 12 \, a^{2} b \tan\left(d x\right) \tan\left(c\right)^{3} - 8 \, b^{3} \tan\left(d x\right) \tan\left(c\right)^{3} - b^{3} \tan\left(c\right)^{4} - 4 \, a b^{2} \tan\left(d x\right)^{3} + 24 \, a^{2} b \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) \tan\left(c\right) - 8 \, 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) \tan\left(c\right) + 12 \, a^{3} \tan\left(d x\right)^{2} \tan\left(c\right) - 48 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) + 12 \, a^{3} \tan\left(d x\right) \tan\left(c\right)^{2} - 48 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 4 \, a b^{2} \tan\left(c\right)^{3} + 4 \, a^{3} d x - 12 \, a b^{2} d x - 6 \, a^{2} b \tan\left(d x\right)^{2} + 2 \, b^{3} \tan\left(d x\right)^{2} + 12 \, a^{2} b \tan\left(d x\right) \tan\left(c\right) - 8 \, b^{3} \tan\left(d x\right) \tan\left(c\right) - 6 \, a^{2} b \tan\left(c\right)^{2} + 2 \, b^{3} \tan\left(c\right)^{2} - 6 \, a^{2} b \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 \, 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) - 4 \, a^{3} \tan\left(d x\right) + 12 \, a b^{2} \tan\left(d x\right) - 4 \, a^{3} \tan\left(c\right) + 12 \, a b^{2} \tan\left(c\right) - 6 \, a^{2} b + 3 \, b^{3}}{4 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/4*(4*a^3*d*x*tan(d*x)^4*tan(c)^4 - 12*a*b^2*d*x*tan(d*x)^4*tan(c)^4 - 6*a^2*b*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)^4*tan(c)^4 + 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)^4*tan(c)^4 - 16*a^3*d*x*tan(d*x)^3*tan(c)^3 + 48*a*b^2*d*x*tan(d*x)^3*tan(c)^3 - 6*a^2*b*tan(d*x)^4*tan(c)^4 + 3*b^3*tan(d*x)^4*tan(c)^4 + 24*a^2*b*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)^3*tan(c)^3 - 8*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)^3*tan(c)^3 + 4*a^3*tan(d*x)^4*tan(c)^3 - 12*a*b^2*tan(d*x)^4*tan(c)^3 + 4*a^3*tan(d*x)^3*tan(c)^4 - 12*a*b^2*tan(d*x)^3*tan(c)^4 + 24*a^3*d*x*tan(d*x)^2*tan(c)^2 - 72*a*b^2*d*x*tan(d*x)^2*tan(c)^2 - 6*a^2*b*tan(d*x)^4*tan(c)^2 + 2*b^3*tan(d*x)^4*tan(c)^2 + 12*a^2*b*tan(d*x)^3*tan(c)^3 - 8*b^3*tan(d*x)^3*tan(c)^3 - 6*a^2*b*tan(d*x)^2*tan(c)^4 + 2*b^3*tan(d*x)^2*tan(c)^4 + 4*a*b^2*tan(d*x)^4*tan(c) - 36*a^2*b*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 + 12*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 - 12*a^3*tan(d*x)^3*tan(c)^2 + 48*a*b^2*tan(d*x)^3*tan(c)^2 - 12*a^3*tan(d*x)^2*tan(c)^3 + 48*a*b^2*tan(d*x)^2*tan(c)^3 + 4*a*b^2*tan(d*x)*tan(c)^4 - b^3*tan(d*x)^4 - 16*a^3*d*x*tan(d*x)*tan(c) + 48*a*b^2*d*x*tan(d*x)*tan(c) + 12*a^2*b*tan(d*x)^3*tan(c) - 8*b^3*tan(d*x)^3*tan(c) - 12*a^2*b*tan(d*x)^2*tan(c)^2 + 4*b^3*tan(d*x)^2*tan(c)^2 + 12*a^2*b*tan(d*x)*tan(c)^3 - 8*b^3*tan(d*x)*tan(c)^3 - b^3*tan(c)^4 - 4*a*b^2*tan(d*x)^3 + 24*a^2*b*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)*tan(c) - 8*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)*tan(c) + 12*a^3*tan(d*x)^2*tan(c) - 48*a*b^2*tan(d*x)^2*tan(c) + 12*a^3*tan(d*x)*tan(c)^2 - 48*a*b^2*tan(d*x)*tan(c)^2 - 4*a*b^2*tan(c)^3 + 4*a^3*d*x - 12*a*b^2*d*x - 6*a^2*b*tan(d*x)^2 + 2*b^3*tan(d*x)^2 + 12*a^2*b*tan(d*x)*tan(c) - 8*b^3*tan(d*x)*tan(c) - 6*a^2*b*tan(c)^2 + 2*b^3*tan(c)^2 - 6*a^2*b*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*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)) - 4*a^3*tan(d*x) + 12*a*b^2*tan(d*x) - 4*a^3*tan(c) + 12*a*b^2*tan(c) - 6*a^2*b + 3*b^3)/(d*tan(d*x)^4*tan(c)^4 - 4*d*tan(d*x)^3*tan(c)^3 + 6*d*tan(d*x)^2*tan(c)^2 - 4*d*tan(d*x)*tan(c) + d)","B",0
437,1,993,0,3.873581," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{18 \, a^{2} b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, b^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 3 \, a^{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)^{3} \tan\left(c\right)^{3} - 9 \, a b^{2} \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)^{3} \tan\left(c\right)^{3} - 54 \, a^{2} b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 18 \, b^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 9 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 9 \, a^{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} + 27 \, a b^{2} \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} + 18 \, a^{2} b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 6 \, b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 18 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 6 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 54 \, a^{2} b d x \tan\left(d x\right) \tan\left(c\right) - 18 \, b^{3} d x \tan\left(d x\right) \tan\left(c\right) - 9 \, a b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) + 9 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 9 \, a b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} + 2 \, b^{3} \tan\left(d x\right)^{3} + 9 \, a^{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) \tan\left(c\right) - 27 \, a b^{2} \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) \tan\left(c\right) - 36 \, a^{2} b \tan\left(d x\right)^{2} \tan\left(c\right) + 18 \, b^{3} \tan\left(d x\right)^{2} \tan\left(c\right) - 36 \, a^{2} b \tan\left(d x\right) \tan\left(c\right)^{2} + 18 \, b^{3} \tan\left(d x\right) \tan\left(c\right)^{2} + 2 \, b^{3} \tan\left(c\right)^{3} - 18 \, a^{2} b d x + 6 \, b^{3} d x + 9 \, a b^{2} \tan\left(d x\right)^{2} - 9 \, a b^{2} \tan\left(d x\right) \tan\left(c\right) + 9 \, a b^{2} \tan\left(c\right)^{2} - 3 \, a^{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) + 9 \, a b^{2} \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) + 18 \, a^{2} b \tan\left(d x\right) - 6 \, b^{3} \tan\left(d x\right) + 18 \, a^{2} b \tan\left(c\right) - 6 \, b^{3} \tan\left(c\right) + 9 \, a b^{2}}{6 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/6*(18*a^2*b*d*x*tan(d*x)^3*tan(c)^3 - 6*b^3*d*x*tan(d*x)^3*tan(c)^3 + 3*a^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)^3*tan(c)^3 - 9*a*b^2*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)^3*tan(c)^3 - 54*a^2*b*d*x*tan(d*x)^2*tan(c)^2 + 18*b^3*d*x*tan(d*x)^2*tan(c)^2 - 9*a*b^2*tan(d*x)^3*tan(c)^3 - 9*a^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 + 27*a*b^2*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 + 18*a^2*b*tan(d*x)^3*tan(c)^2 - 6*b^3*tan(d*x)^3*tan(c)^2 + 18*a^2*b*tan(d*x)^2*tan(c)^3 - 6*b^3*tan(d*x)^2*tan(c)^3 + 54*a^2*b*d*x*tan(d*x)*tan(c) - 18*b^3*d*x*tan(d*x)*tan(c) - 9*a*b^2*tan(d*x)^3*tan(c) + 9*a*b^2*tan(d*x)^2*tan(c)^2 - 9*a*b^2*tan(d*x)*tan(c)^3 + 2*b^3*tan(d*x)^3 + 9*a^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)*tan(c) - 27*a*b^2*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)*tan(c) - 36*a^2*b*tan(d*x)^2*tan(c) + 18*b^3*tan(d*x)^2*tan(c) - 36*a^2*b*tan(d*x)*tan(c)^2 + 18*b^3*tan(d*x)*tan(c)^2 + 2*b^3*tan(c)^3 - 18*a^2*b*d*x + 6*b^3*d*x + 9*a*b^2*tan(d*x)^2 - 9*a*b^2*tan(d*x)*tan(c) + 9*a*b^2*tan(c)^2 - 3*a^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)) + 9*a*b^2*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)) + 18*a^2*b*tan(d*x) - 6*b^3*tan(d*x) + 18*a^2*b*tan(c) - 6*b^3*tan(c) + 9*a*b^2)/(d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c) - d)","B",0
438,1,603,0,1.285414," ","integrate((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} - 3 \, a^{2} b \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} + 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} - 4 \, a^{3} d x \tan\left(d x\right) \tan\left(c\right) + 12 \, a b^{2} d x \tan\left(d x\right) \tan\left(c\right) + b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, a^{2} b \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) \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(d x\right) \tan\left(c\right) - 6 \, a b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 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 + b^{3} \tan\left(d x\right)^{2} + b^{3} \tan\left(c\right)^{2} - 3 \, a^{2} b \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) + 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) + 6 \, a b^{2} \tan\left(d x\right) + 6 \, a b^{2} \tan\left(c\right) + b^{3}}{2 \, {\left(d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"1/2*(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 - 3*a^2*b*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 + 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 - 4*a^3*d*x*tan(d*x)*tan(c) + 12*a*b^2*d*x*tan(d*x)*tan(c) + b^3*tan(d*x)^2*tan(c)^2 + 6*a^2*b*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)*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(d*x)*tan(c) - 6*a*b^2*tan(d*x)^2*tan(c) - 6*a*b^2*tan(d*x)*tan(c)^2 + 2*a^3*d*x - 6*a*b^2*d*x + b^3*tan(d*x)^2 + b^3*tan(c)^2 - 3*a^2*b*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)) + 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)) + 6*a*b^2*tan(d*x) + 6*a*b^2*tan(c) + b^3)/(d*tan(d*x)^2*tan(c)^2 - 2*d*tan(d*x)*tan(c) + d)","B",0
439,1,72,0,2.621937," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{2 \, a^{3} \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 2 \, b^{3} \tan\left(d x + c\right) + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} - {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*a^3*log(abs(tan(d*x + c))) + 2*b^3*tan(d*x + c) + 2*(3*a^2*b - b^3)*(d*x + c) - (a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
440,1,88,0,5.350548," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{2} b \log\left({\left| \tan\left(d x + c\right) \right|}\right) - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} - {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{2 \, {\left(3 \, a^{2} b \tan\left(d x + c\right) + a^{3}\right)}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(6*a^2*b*log(abs(tan(d*x + c))) - 2*(a^3 - 3*a*b^2)*(d*x + c) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1) - 2*(3*a^2*b*tan(d*x + c) + a^3)/tan(d*x + c))/d","A",0
441,1,171,0,3.581879," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} - 8 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 8 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{12 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(a^3*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) + 8*(3*a^2*b - b^3)*(d*x + c) - 8*(a^3 - 3*a*b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 8*(a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) - (12*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^2*b*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^2)/d","B",0
442,1,236,0,5.934270," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 9 \, a^{2} b \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) + 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} + 24 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 24 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{132 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 44 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 36 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 9 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^3*tan(1/2*d*x + 1/2*c)^3 - 9*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^3*tan(1/2*d*x + 1/2*c) + 36*a*b^2*tan(1/2*d*x + 1/2*c) + 24*(a^3 - 3*a*b^2)*(d*x + c) + 24*(3*a^2*b - b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 24*(3*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (132*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 44*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*a^3*tan(1/2*d*x + 1/2*c)^2 - 36*a*b^2*tan(1/2*d*x + 1/2*c)^2 - 9*a^2*b*tan(1/2*d*x + 1/2*c) - a^3)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
443,1,301,0,7.081201," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{3 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 192 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} + 192 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{400 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1200 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 360 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 96 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 72 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a^3*tan(1/2*d*x + 1/2*c)^4 - 24*a^2*b*tan(1/2*d*x + 1/2*c)^3 - 36*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 360*a^2*b*tan(1/2*d*x + 1/2*c) - 96*b^3*tan(1/2*d*x + 1/2*c) - 192*(3*a^2*b - b^3)*(d*x + c) + 192*(a^3 - 3*a*b^2)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*(a^3 - 3*a*b^2)*log(abs(tan(1/2*d*x + 1/2*c))) + (400*a^3*tan(1/2*d*x + 1/2*c)^4 - 1200*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 360*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 96*b^3*tan(1/2*d*x + 1/2*c)^3 - 36*a^3*tan(1/2*d*x + 1/2*c)^2 + 72*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 24*a^2*b*tan(1/2*d*x + 1/2*c) + 3*a^3)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
444,1,370,0,9.656919," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{6 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 70 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 540 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 660 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1800 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 960 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} - 960 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 960 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{6576 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 2192 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 660 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1800 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 540 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 70 \, a^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 45 \, a^{2} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, a^{3}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{960 \, d}"," ",0,"1/960*(6*a^3*tan(1/2*d*x + 1/2*c)^5 - 45*a^2*b*tan(1/2*d*x + 1/2*c)^4 - 70*a^3*tan(1/2*d*x + 1/2*c)^3 + 120*a*b^2*tan(1/2*d*x + 1/2*c)^3 + 540*a^2*b*tan(1/2*d*x + 1/2*c)^2 - 120*b^3*tan(1/2*d*x + 1/2*c)^2 + 660*a^3*tan(1/2*d*x + 1/2*c) - 1800*a*b^2*tan(1/2*d*x + 1/2*c) - 960*(a^3 - 3*a*b^2)*(d*x + c) - 960*(3*a^2*b - b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 960*(3*a^2*b - b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - (6576*a^2*b*tan(1/2*d*x + 1/2*c)^5 - 2192*b^3*tan(1/2*d*x + 1/2*c)^5 + 660*a^3*tan(1/2*d*x + 1/2*c)^4 - 1800*a*b^2*tan(1/2*d*x + 1/2*c)^4 - 540*a^2*b*tan(1/2*d*x + 1/2*c)^3 + 120*b^3*tan(1/2*d*x + 1/2*c)^3 - 70*a^3*tan(1/2*d*x + 1/2*c)^2 + 120*a*b^2*tan(1/2*d*x + 1/2*c)^2 + 45*a^2*b*tan(1/2*d*x + 1/2*c) + 6*a^3)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
445,1,3385,0,75.813435," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{240 \, a^{3} b d x \tan\left(d x\right)^{6} \tan\left(c\right)^{6} - 240 \, a b^{3} d x \tan\left(d x\right)^{6} \tan\left(c\right)^{6} + 30 \, a^{4} \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)^{6} \tan\left(c\right)^{6} - 180 \, a^{2} b^{2} \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)^{6} \tan\left(c\right)^{6} + 30 \, b^{4} \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)^{6} \tan\left(c\right)^{6} - 1440 \, a^{3} b d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 1440 \, a b^{3} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 30 \, a^{4} \tan\left(d x\right)^{6} \tan\left(c\right)^{6} - 270 \, a^{2} b^{2} \tan\left(d x\right)^{6} \tan\left(c\right)^{6} + 55 \, b^{4} \tan\left(d x\right)^{6} \tan\left(c\right)^{6} - 180 \, a^{4} \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)^{5} \tan\left(c\right)^{5} + 1080 \, a^{2} b^{2} \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)^{5} \tan\left(c\right)^{5} - 180 \, b^{4} \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)^{5} \tan\left(c\right)^{5} + 240 \, a^{3} b \tan\left(d x\right)^{6} \tan\left(c\right)^{5} - 240 \, a b^{3} \tan\left(d x\right)^{6} \tan\left(c\right)^{5} + 240 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{6} - 240 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{6} + 3600 \, a^{3} b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 3600 \, a b^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 30 \, a^{4} \tan\left(d x\right)^{6} \tan\left(c\right)^{4} - 180 \, a^{2} b^{2} \tan\left(d x\right)^{6} \tan\left(c\right)^{4} + 30 \, b^{4} \tan\left(d x\right)^{6} \tan\left(c\right)^{4} - 120 \, a^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 1260 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 270 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 30 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{6} - 180 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{6} + 30 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{6} - 80 \, a^{3} b \tan\left(d x\right)^{6} \tan\left(c\right)^{3} + 80 \, a b^{3} \tan\left(d x\right)^{6} \tan\left(c\right)^{3} + 450 \, a^{4} \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)^{4} \tan\left(c\right)^{4} - 2700 \, a^{2} b^{2} \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)^{4} \tan\left(c\right)^{4} + 450 \, b^{4} \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)^{4} \tan\left(c\right)^{4} - 1440 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 1440 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} - 1440 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 1440 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} - 80 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{6} + 80 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{6} + 90 \, a^{2} b^{2} \tan\left(d x\right)^{6} \tan\left(c\right)^{2} - 15 \, b^{4} \tan\left(d x\right)^{6} \tan\left(c\right)^{2} - 4800 \, a^{3} b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 4800 \, a b^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 120 \, a^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 1080 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} - 180 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 210 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 2070 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 495 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 120 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 1080 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} - 180 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 90 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{6} - 15 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{6} - 48 \, a b^{3} \tan\left(d x\right)^{6} \tan\left(c\right) + 240 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{2} - 480 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} - 600 \, a^{4} \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)^{3} \tan\left(c\right)^{3} + 3600 \, a^{2} b^{2} \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)^{3} \tan\left(c\right)^{3} - 600 \, b^{4} \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)^{3} \tan\left(c\right)^{3} + 3120 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 3600 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 3120 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 3600 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 240 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{5} - 480 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} - 48 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{6} + 10 \, b^{4} \tan\left(d x\right)^{6} - 180 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right) + 90 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right) + 3600 \, a^{3} b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 3600 \, a b^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 180 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 1800 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 450 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 240 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 2160 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 360 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 180 \, a^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 1800 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 450 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 180 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{5} + 90 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{5} + 10 \, b^{4} \tan\left(c\right)^{6} + 48 \, a b^{3} \tan\left(d x\right)^{5} - 240 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right) + 480 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right) + 450 \, a^{4} \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} - 2700 \, a^{2} b^{2} \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} + 450 \, b^{4} \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} - 3120 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 3600 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 3120 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 3600 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 240 \, a^{3} b \tan\left(d x\right) \tan\left(c\right)^{4} + 480 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{4} + 48 \, a b^{3} \tan\left(c\right)^{5} + 90 \, a^{2} b^{2} \tan\left(d x\right)^{4} - 15 \, b^{4} \tan\left(d x\right)^{4} - 1440 \, a^{3} b d x \tan\left(d x\right) \tan\left(c\right) + 1440 \, a b^{3} d x \tan\left(d x\right) \tan\left(c\right) - 120 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right) + 1080 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) - 180 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right) + 210 \, a^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 2070 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 495 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 120 \, a^{4} \tan\left(d x\right) \tan\left(c\right)^{3} + 1080 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} - 180 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{3} + 90 \, a^{2} b^{2} \tan\left(c\right)^{4} - 15 \, b^{4} \tan\left(c\right)^{4} + 80 \, a^{3} b \tan\left(d x\right)^{3} - 80 \, a b^{3} \tan\left(d x\right)^{3} - 180 \, a^{4} \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) \tan\left(c\right) + 1080 \, a^{2} b^{2} \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) \tan\left(c\right) - 180 \, b^{4} \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) \tan\left(c\right) + 1440 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right) - 1440 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right) + 1440 \, a^{3} b \tan\left(d x\right) \tan\left(c\right)^{2} - 1440 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{2} + 80 \, a^{3} b \tan\left(c\right)^{3} - 80 \, a b^{3} \tan\left(c\right)^{3} + 240 \, a^{3} b d x - 240 \, a b^{3} d x + 30 \, a^{4} \tan\left(d x\right)^{2} - 180 \, a^{2} b^{2} \tan\left(d x\right)^{2} + 30 \, b^{4} \tan\left(d x\right)^{2} - 120 \, a^{4} \tan\left(d x\right) \tan\left(c\right) + 1260 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right) - 270 \, b^{4} \tan\left(d x\right) \tan\left(c\right) + 30 \, a^{4} \tan\left(c\right)^{2} - 180 \, a^{2} b^{2} \tan\left(c\right)^{2} + 30 \, b^{4} \tan\left(c\right)^{2} + 30 \, a^{4} \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) - 180 \, a^{2} b^{2} \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) + 30 \, b^{4} \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) - 240 \, a^{3} b \tan\left(d x\right) + 240 \, a b^{3} \tan\left(d x\right) - 240 \, a^{3} b \tan\left(c\right) + 240 \, a b^{3} \tan\left(c\right) + 30 \, a^{4} - 270 \, a^{2} b^{2} + 55 \, b^{4}}{60 \, {\left(d \tan\left(d x\right)^{6} \tan\left(c\right)^{6} - 6 \, d \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 15 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 20 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 15 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 6 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"1/60*(240*a^3*b*d*x*tan(d*x)^6*tan(c)^6 - 240*a*b^3*d*x*tan(d*x)^6*tan(c)^6 + 30*a^4*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)^6*tan(c)^6 - 180*a^2*b^2*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)^6*tan(c)^6 + 30*b^4*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)^6*tan(c)^6 - 1440*a^3*b*d*x*tan(d*x)^5*tan(c)^5 + 1440*a*b^3*d*x*tan(d*x)^5*tan(c)^5 + 30*a^4*tan(d*x)^6*tan(c)^6 - 270*a^2*b^2*tan(d*x)^6*tan(c)^6 + 55*b^4*tan(d*x)^6*tan(c)^6 - 180*a^4*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)^5*tan(c)^5 + 1080*a^2*b^2*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)^5*tan(c)^5 - 180*b^4*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)^5*tan(c)^5 + 240*a^3*b*tan(d*x)^6*tan(c)^5 - 240*a*b^3*tan(d*x)^6*tan(c)^5 + 240*a^3*b*tan(d*x)^5*tan(c)^6 - 240*a*b^3*tan(d*x)^5*tan(c)^6 + 3600*a^3*b*d*x*tan(d*x)^4*tan(c)^4 - 3600*a*b^3*d*x*tan(d*x)^4*tan(c)^4 + 30*a^4*tan(d*x)^6*tan(c)^4 - 180*a^2*b^2*tan(d*x)^6*tan(c)^4 + 30*b^4*tan(d*x)^6*tan(c)^4 - 120*a^4*tan(d*x)^5*tan(c)^5 + 1260*a^2*b^2*tan(d*x)^5*tan(c)^5 - 270*b^4*tan(d*x)^5*tan(c)^5 + 30*a^4*tan(d*x)^4*tan(c)^6 - 180*a^2*b^2*tan(d*x)^4*tan(c)^6 + 30*b^4*tan(d*x)^4*tan(c)^6 - 80*a^3*b*tan(d*x)^6*tan(c)^3 + 80*a*b^3*tan(d*x)^6*tan(c)^3 + 450*a^4*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)^4*tan(c)^4 - 2700*a^2*b^2*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)^4*tan(c)^4 + 450*b^4*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)^4*tan(c)^4 - 1440*a^3*b*tan(d*x)^5*tan(c)^4 + 1440*a*b^3*tan(d*x)^5*tan(c)^4 - 1440*a^3*b*tan(d*x)^4*tan(c)^5 + 1440*a*b^3*tan(d*x)^4*tan(c)^5 - 80*a^3*b*tan(d*x)^3*tan(c)^6 + 80*a*b^3*tan(d*x)^3*tan(c)^6 + 90*a^2*b^2*tan(d*x)^6*tan(c)^2 - 15*b^4*tan(d*x)^6*tan(c)^2 - 4800*a^3*b*d*x*tan(d*x)^3*tan(c)^3 + 4800*a*b^3*d*x*tan(d*x)^3*tan(c)^3 - 120*a^4*tan(d*x)^5*tan(c)^3 + 1080*a^2*b^2*tan(d*x)^5*tan(c)^3 - 180*b^4*tan(d*x)^5*tan(c)^3 + 210*a^4*tan(d*x)^4*tan(c)^4 - 2070*a^2*b^2*tan(d*x)^4*tan(c)^4 + 495*b^4*tan(d*x)^4*tan(c)^4 - 120*a^4*tan(d*x)^3*tan(c)^5 + 1080*a^2*b^2*tan(d*x)^3*tan(c)^5 - 180*b^4*tan(d*x)^3*tan(c)^5 + 90*a^2*b^2*tan(d*x)^2*tan(c)^6 - 15*b^4*tan(d*x)^2*tan(c)^6 - 48*a*b^3*tan(d*x)^6*tan(c) + 240*a^3*b*tan(d*x)^5*tan(c)^2 - 480*a*b^3*tan(d*x)^5*tan(c)^2 - 600*a^4*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)^3*tan(c)^3 + 3600*a^2*b^2*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)^3*tan(c)^3 - 600*b^4*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)^3*tan(c)^3 + 3120*a^3*b*tan(d*x)^4*tan(c)^3 - 3600*a*b^3*tan(d*x)^4*tan(c)^3 + 3120*a^3*b*tan(d*x)^3*tan(c)^4 - 3600*a*b^3*tan(d*x)^3*tan(c)^4 + 240*a^3*b*tan(d*x)^2*tan(c)^5 - 480*a*b^3*tan(d*x)^2*tan(c)^5 - 48*a*b^3*tan(d*x)*tan(c)^6 + 10*b^4*tan(d*x)^6 - 180*a^2*b^2*tan(d*x)^5*tan(c) + 90*b^4*tan(d*x)^5*tan(c) + 3600*a^3*b*d*x*tan(d*x)^2*tan(c)^2 - 3600*a*b^3*d*x*tan(d*x)^2*tan(c)^2 + 180*a^4*tan(d*x)^4*tan(c)^2 - 1800*a^2*b^2*tan(d*x)^4*tan(c)^2 + 450*b^4*tan(d*x)^4*tan(c)^2 - 240*a^4*tan(d*x)^3*tan(c)^3 + 2160*a^2*b^2*tan(d*x)^3*tan(c)^3 - 360*b^4*tan(d*x)^3*tan(c)^3 + 180*a^4*tan(d*x)^2*tan(c)^4 - 1800*a^2*b^2*tan(d*x)^2*tan(c)^4 + 450*b^4*tan(d*x)^2*tan(c)^4 - 180*a^2*b^2*tan(d*x)*tan(c)^5 + 90*b^4*tan(d*x)*tan(c)^5 + 10*b^4*tan(c)^6 + 48*a*b^3*tan(d*x)^5 - 240*a^3*b*tan(d*x)^4*tan(c) + 480*a*b^3*tan(d*x)^4*tan(c) + 450*a^4*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 - 2700*a^2*b^2*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 + 450*b^4*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 - 3120*a^3*b*tan(d*x)^3*tan(c)^2 + 3600*a*b^3*tan(d*x)^3*tan(c)^2 - 3120*a^3*b*tan(d*x)^2*tan(c)^3 + 3600*a*b^3*tan(d*x)^2*tan(c)^3 - 240*a^3*b*tan(d*x)*tan(c)^4 + 480*a*b^3*tan(d*x)*tan(c)^4 + 48*a*b^3*tan(c)^5 + 90*a^2*b^2*tan(d*x)^4 - 15*b^4*tan(d*x)^4 - 1440*a^3*b*d*x*tan(d*x)*tan(c) + 1440*a*b^3*d*x*tan(d*x)*tan(c) - 120*a^4*tan(d*x)^3*tan(c) + 1080*a^2*b^2*tan(d*x)^3*tan(c) - 180*b^4*tan(d*x)^3*tan(c) + 210*a^4*tan(d*x)^2*tan(c)^2 - 2070*a^2*b^2*tan(d*x)^2*tan(c)^2 + 495*b^4*tan(d*x)^2*tan(c)^2 - 120*a^4*tan(d*x)*tan(c)^3 + 1080*a^2*b^2*tan(d*x)*tan(c)^3 - 180*b^4*tan(d*x)*tan(c)^3 + 90*a^2*b^2*tan(c)^4 - 15*b^4*tan(c)^4 + 80*a^3*b*tan(d*x)^3 - 80*a*b^3*tan(d*x)^3 - 180*a^4*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)*tan(c) + 1080*a^2*b^2*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)*tan(c) - 180*b^4*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)*tan(c) + 1440*a^3*b*tan(d*x)^2*tan(c) - 1440*a*b^3*tan(d*x)^2*tan(c) + 1440*a^3*b*tan(d*x)*tan(c)^2 - 1440*a*b^3*tan(d*x)*tan(c)^2 + 80*a^3*b*tan(c)^3 - 80*a*b^3*tan(c)^3 + 240*a^3*b*d*x - 240*a*b^3*d*x + 30*a^4*tan(d*x)^2 - 180*a^2*b^2*tan(d*x)^2 + 30*b^4*tan(d*x)^2 - 120*a^4*tan(d*x)*tan(c) + 1260*a^2*b^2*tan(d*x)*tan(c) - 270*b^4*tan(d*x)*tan(c) + 30*a^4*tan(c)^2 - 180*a^2*b^2*tan(c)^2 + 30*b^4*tan(c)^2 + 30*a^4*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)) - 180*a^2*b^2*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)) + 30*b^4*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)) - 240*a^3*b*tan(d*x) + 240*a*b^3*tan(d*x) - 240*a^3*b*tan(c) + 240*a*b^3*tan(c) + 30*a^4 - 270*a^2*b^2 + 55*b^4)/(d*tan(d*x)^6*tan(c)^6 - 6*d*tan(d*x)^5*tan(c)^5 + 15*d*tan(d*x)^4*tan(c)^4 - 20*d*tan(d*x)^3*tan(c)^3 + 15*d*tan(d*x)^2*tan(c)^2 - 6*d*tan(d*x)*tan(c) + d)","B",0
446,1,2281,0,34.214224," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{15 \, a^{4} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 90 \, a^{2} b^{2} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 15 \, b^{4} d x \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 30 \, a^{3} b \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)^{5} \tan\left(c\right)^{5} + 30 \, a 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)^{5} \tan\left(c\right)^{5} - 75 \, a^{4} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 450 \, a^{2} b^{2} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 75 \, b^{4} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 30 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 45 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{5} + 150 \, a^{3} b \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)^{4} \tan\left(c\right)^{4} - 150 \, a 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)^{4} \tan\left(c\right)^{4} + 15 \, a^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} - 90 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 15 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{4} + 15 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} - 90 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 15 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{5} + 150 \, a^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 900 \, a^{2} b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 150 \, b^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 30 \, a^{3} b \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 30 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right)^{3} + 90 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 165 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 30 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 30 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{5} + 30 \, a^{2} b^{2} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} - 5 \, b^{4} \tan\left(d x\right)^{5} \tan\left(c\right)^{2} - 300 \, a^{3} b \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)^{3} \tan\left(c\right)^{3} + 300 \, a 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)^{3} \tan\left(c\right)^{3} - 60 \, a^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 450 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 75 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 60 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 450 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 75 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 30 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} - 5 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{5} - 15 \, a b^{3} \tan\left(d x\right)^{5} \tan\left(c\right) - 150 \, a^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 900 \, a^{2} b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 150 \, b^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 90 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 150 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} - 120 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 180 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 90 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 150 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} - 15 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{5} + 3 \, b^{4} \tan\left(d x\right)^{5} - 60 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right) + 25 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right) + 300 \, a^{3} b \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} - 300 \, a 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} + 90 \, a^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 720 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 150 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 90 \, a^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 720 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 150 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} - 60 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{4} + 25 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{4} + 3 \, b^{4} \tan\left(c\right)^{5} + 15 \, a b^{3} \tan\left(d x\right)^{4} + 75 \, a^{4} d x \tan\left(d x\right) \tan\left(c\right) - 450 \, a^{2} b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 75 \, b^{4} d x \tan\left(d x\right) \tan\left(c\right) - 90 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right) + 150 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right) + 120 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 180 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 90 \, a^{3} b \tan\left(d x\right) \tan\left(c\right)^{3} + 150 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{3} + 15 \, a b^{3} \tan\left(c\right)^{4} + 30 \, a^{2} b^{2} \tan\left(d x\right)^{3} - 5 \, b^{4} \tan\left(d x\right)^{3} - 150 \, a^{3} b \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) \tan\left(c\right) + 150 \, a 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) \tan\left(c\right) - 60 \, a^{4} \tan\left(d x\right)^{2} \tan\left(c\right) + 450 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 75 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right) - 60 \, a^{4} \tan\left(d x\right) \tan\left(c\right)^{2} + 450 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 75 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{2} + 30 \, a^{2} b^{2} \tan\left(c\right)^{3} - 5 \, b^{4} \tan\left(c\right)^{3} - 15 \, a^{4} d x + 90 \, a^{2} b^{2} d x - 15 \, b^{4} d x + 30 \, a^{3} b \tan\left(d x\right)^{2} - 30 \, a b^{3} \tan\left(d x\right)^{2} - 90 \, a^{3} b \tan\left(d x\right) \tan\left(c\right) + 165 \, a b^{3} \tan\left(d x\right) \tan\left(c\right) + 30 \, a^{3} b \tan\left(c\right)^{2} - 30 \, a b^{3} \tan\left(c\right)^{2} + 30 \, a^{3} b \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) - 30 \, a 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) + 15 \, a^{4} \tan\left(d x\right) - 90 \, a^{2} b^{2} \tan\left(d x\right) + 15 \, b^{4} \tan\left(d x\right) + 15 \, a^{4} \tan\left(c\right) - 90 \, a^{2} b^{2} \tan\left(c\right) + 15 \, b^{4} \tan\left(c\right) + 30 \, a^{3} b - 45 \, a b^{3}}{15 \, {\left(d \tan\left(d x\right)^{5} \tan\left(c\right)^{5} - 5 \, d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 10 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 10 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 5 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"-1/15*(15*a^4*d*x*tan(d*x)^5*tan(c)^5 - 90*a^2*b^2*d*x*tan(d*x)^5*tan(c)^5 + 15*b^4*d*x*tan(d*x)^5*tan(c)^5 - 30*a^3*b*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)^5*tan(c)^5 + 30*a*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)^5*tan(c)^5 - 75*a^4*d*x*tan(d*x)^4*tan(c)^4 + 450*a^2*b^2*d*x*tan(d*x)^4*tan(c)^4 - 75*b^4*d*x*tan(d*x)^4*tan(c)^4 - 30*a^3*b*tan(d*x)^5*tan(c)^5 + 45*a*b^3*tan(d*x)^5*tan(c)^5 + 150*a^3*b*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)^4*tan(c)^4 - 150*a*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)^4*tan(c)^4 + 15*a^4*tan(d*x)^5*tan(c)^4 - 90*a^2*b^2*tan(d*x)^5*tan(c)^4 + 15*b^4*tan(d*x)^5*tan(c)^4 + 15*a^4*tan(d*x)^4*tan(c)^5 - 90*a^2*b^2*tan(d*x)^4*tan(c)^5 + 15*b^4*tan(d*x)^4*tan(c)^5 + 150*a^4*d*x*tan(d*x)^3*tan(c)^3 - 900*a^2*b^2*d*x*tan(d*x)^3*tan(c)^3 + 150*b^4*d*x*tan(d*x)^3*tan(c)^3 - 30*a^3*b*tan(d*x)^5*tan(c)^3 + 30*a*b^3*tan(d*x)^5*tan(c)^3 + 90*a^3*b*tan(d*x)^4*tan(c)^4 - 165*a*b^3*tan(d*x)^4*tan(c)^4 - 30*a^3*b*tan(d*x)^3*tan(c)^5 + 30*a*b^3*tan(d*x)^3*tan(c)^5 + 30*a^2*b^2*tan(d*x)^5*tan(c)^2 - 5*b^4*tan(d*x)^5*tan(c)^2 - 300*a^3*b*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)^3*tan(c)^3 + 300*a*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)^3*tan(c)^3 - 60*a^4*tan(d*x)^4*tan(c)^3 + 450*a^2*b^2*tan(d*x)^4*tan(c)^3 - 75*b^4*tan(d*x)^4*tan(c)^3 - 60*a^4*tan(d*x)^3*tan(c)^4 + 450*a^2*b^2*tan(d*x)^3*tan(c)^4 - 75*b^4*tan(d*x)^3*tan(c)^4 + 30*a^2*b^2*tan(d*x)^2*tan(c)^5 - 5*b^4*tan(d*x)^2*tan(c)^5 - 15*a*b^3*tan(d*x)^5*tan(c) - 150*a^4*d*x*tan(d*x)^2*tan(c)^2 + 900*a^2*b^2*d*x*tan(d*x)^2*tan(c)^2 - 150*b^4*d*x*tan(d*x)^2*tan(c)^2 + 90*a^3*b*tan(d*x)^4*tan(c)^2 - 150*a*b^3*tan(d*x)^4*tan(c)^2 - 120*a^3*b*tan(d*x)^3*tan(c)^3 + 180*a*b^3*tan(d*x)^3*tan(c)^3 + 90*a^3*b*tan(d*x)^2*tan(c)^4 - 150*a*b^3*tan(d*x)^2*tan(c)^4 - 15*a*b^3*tan(d*x)*tan(c)^5 + 3*b^4*tan(d*x)^5 - 60*a^2*b^2*tan(d*x)^4*tan(c) + 25*b^4*tan(d*x)^4*tan(c) + 300*a^3*b*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 - 300*a*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 + 90*a^4*tan(d*x)^3*tan(c)^2 - 720*a^2*b^2*tan(d*x)^3*tan(c)^2 + 150*b^4*tan(d*x)^3*tan(c)^2 + 90*a^4*tan(d*x)^2*tan(c)^3 - 720*a^2*b^2*tan(d*x)^2*tan(c)^3 + 150*b^4*tan(d*x)^2*tan(c)^3 - 60*a^2*b^2*tan(d*x)*tan(c)^4 + 25*b^4*tan(d*x)*tan(c)^4 + 3*b^4*tan(c)^5 + 15*a*b^3*tan(d*x)^4 + 75*a^4*d*x*tan(d*x)*tan(c) - 450*a^2*b^2*d*x*tan(d*x)*tan(c) + 75*b^4*d*x*tan(d*x)*tan(c) - 90*a^3*b*tan(d*x)^3*tan(c) + 150*a*b^3*tan(d*x)^3*tan(c) + 120*a^3*b*tan(d*x)^2*tan(c)^2 - 180*a*b^3*tan(d*x)^2*tan(c)^2 - 90*a^3*b*tan(d*x)*tan(c)^3 + 150*a*b^3*tan(d*x)*tan(c)^3 + 15*a*b^3*tan(c)^4 + 30*a^2*b^2*tan(d*x)^3 - 5*b^4*tan(d*x)^3 - 150*a^3*b*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)*tan(c) + 150*a*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)*tan(c) - 60*a^4*tan(d*x)^2*tan(c) + 450*a^2*b^2*tan(d*x)^2*tan(c) - 75*b^4*tan(d*x)^2*tan(c) - 60*a^4*tan(d*x)*tan(c)^2 + 450*a^2*b^2*tan(d*x)*tan(c)^2 - 75*b^4*tan(d*x)*tan(c)^2 + 30*a^2*b^2*tan(c)^3 - 5*b^4*tan(c)^3 - 15*a^4*d*x + 90*a^2*b^2*d*x - 15*b^4*d*x + 30*a^3*b*tan(d*x)^2 - 30*a*b^3*tan(d*x)^2 - 90*a^3*b*tan(d*x)*tan(c) + 165*a*b^3*tan(d*x)*tan(c) + 30*a^3*b*tan(c)^2 - 30*a*b^3*tan(c)^2 + 30*a^3*b*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)) - 30*a*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)) + 15*a^4*tan(d*x) - 90*a^2*b^2*tan(d*x) + 15*b^4*tan(d*x) + 15*a^4*tan(c) - 90*a^2*b^2*tan(c) + 15*b^4*tan(c) + 30*a^3*b - 45*a*b^3)/(d*tan(d*x)^5*tan(c)^5 - 5*d*tan(d*x)^4*tan(c)^4 + 10*d*tan(d*x)^3*tan(c)^3 - 10*d*tan(d*x)^2*tan(c)^2 + 5*d*tan(d*x)*tan(c) - d)","B",0
447,1,1886,0,10.717859," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{48 \, a^{3} b d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 48 \, a b^{3} d x \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 6 \, a^{4} \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)^{4} \tan\left(c\right)^{4} - 36 \, a^{2} b^{2} \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)^{4} \tan\left(c\right)^{4} + 6 \, b^{4} \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)^{4} \tan\left(c\right)^{4} - 192 \, a^{3} b d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 192 \, a b^{3} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 36 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} + 9 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 24 \, a^{4} \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)^{3} \tan\left(c\right)^{3} + 144 \, a^{2} b^{2} \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)^{3} \tan\left(c\right)^{3} - 24 \, b^{4} \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)^{3} \tan\left(c\right)^{3} + 48 \, a^{3} b \tan\left(d x\right)^{4} \tan\left(c\right)^{3} - 48 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right)^{3} + 48 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{4} - 48 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{4} + 288 \, a^{3} b d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 288 \, a b^{3} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 36 \, a^{2} b^{2} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 6 \, b^{4} \tan\left(d x\right)^{4} \tan\left(c\right)^{2} + 72 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 24 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 36 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 6 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{4} + 16 \, a b^{3} \tan\left(d x\right)^{4} \tan\left(c\right) + 36 \, a^{4} \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} - 216 \, a^{2} b^{2} \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} + 36 \, b^{4} \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} - 144 \, a^{3} b \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 192 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 144 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 192 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 16 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{4} - 3 \, b^{4} \tan\left(d x\right)^{4} - 192 \, a^{3} b d x \tan\left(d x\right) \tan\left(c\right) + 192 \, a b^{3} d x \tan\left(d x\right) \tan\left(c\right) + 72 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right) - 24 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right) - 72 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 12 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 72 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{3} - 24 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{3} - 3 \, b^{4} \tan\left(c\right)^{4} - 16 \, a b^{3} \tan\left(d x\right)^{3} - 24 \, a^{4} \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) \tan\left(c\right) + 144 \, a^{2} b^{2} \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) \tan\left(c\right) - 24 \, b^{4} \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) \tan\left(c\right) + 144 \, a^{3} b \tan\left(d x\right)^{2} \tan\left(c\right) - 192 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right) + 144 \, a^{3} b \tan\left(d x\right) \tan\left(c\right)^{2} - 192 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{2} - 16 \, a b^{3} \tan\left(c\right)^{3} + 48 \, a^{3} b d x - 48 \, a b^{3} d x - 36 \, a^{2} b^{2} \tan\left(d x\right)^{2} + 6 \, b^{4} \tan\left(d x\right)^{2} + 72 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right) - 24 \, b^{4} \tan\left(d x\right) \tan\left(c\right) - 36 \, a^{2} b^{2} \tan\left(c\right)^{2} + 6 \, b^{4} \tan\left(c\right)^{2} + 6 \, a^{4} \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) - 36 \, a^{2} b^{2} \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) + 6 \, b^{4} \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) - 48 \, a^{3} b \tan\left(d x\right) + 48 \, a b^{3} \tan\left(d x\right) - 48 \, a^{3} b \tan\left(c\right) + 48 \, a b^{3} \tan\left(c\right) - 36 \, a^{2} b^{2} + 9 \, b^{4}}{12 \, {\left(d \tan\left(d x\right)^{4} \tan\left(c\right)^{4} - 4 \, d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 6 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 4 \, d \tan\left(d x\right) \tan\left(c\right) + d\right)}}"," ",0,"-1/12*(48*a^3*b*d*x*tan(d*x)^4*tan(c)^4 - 48*a*b^3*d*x*tan(d*x)^4*tan(c)^4 + 6*a^4*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)^4*tan(c)^4 - 36*a^2*b^2*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)^4*tan(c)^4 + 6*b^4*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)^4*tan(c)^4 - 192*a^3*b*d*x*tan(d*x)^3*tan(c)^3 + 192*a*b^3*d*x*tan(d*x)^3*tan(c)^3 - 36*a^2*b^2*tan(d*x)^4*tan(c)^4 + 9*b^4*tan(d*x)^4*tan(c)^4 - 24*a^4*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)^3*tan(c)^3 + 144*a^2*b^2*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)^3*tan(c)^3 - 24*b^4*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)^3*tan(c)^3 + 48*a^3*b*tan(d*x)^4*tan(c)^3 - 48*a*b^3*tan(d*x)^4*tan(c)^3 + 48*a^3*b*tan(d*x)^3*tan(c)^4 - 48*a*b^3*tan(d*x)^3*tan(c)^4 + 288*a^3*b*d*x*tan(d*x)^2*tan(c)^2 - 288*a*b^3*d*x*tan(d*x)^2*tan(c)^2 - 36*a^2*b^2*tan(d*x)^4*tan(c)^2 + 6*b^4*tan(d*x)^4*tan(c)^2 + 72*a^2*b^2*tan(d*x)^3*tan(c)^3 - 24*b^4*tan(d*x)^3*tan(c)^3 - 36*a^2*b^2*tan(d*x)^2*tan(c)^4 + 6*b^4*tan(d*x)^2*tan(c)^4 + 16*a*b^3*tan(d*x)^4*tan(c) + 36*a^4*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 - 216*a^2*b^2*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 + 36*b^4*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 - 144*a^3*b*tan(d*x)^3*tan(c)^2 + 192*a*b^3*tan(d*x)^3*tan(c)^2 - 144*a^3*b*tan(d*x)^2*tan(c)^3 + 192*a*b^3*tan(d*x)^2*tan(c)^3 + 16*a*b^3*tan(d*x)*tan(c)^4 - 3*b^4*tan(d*x)^4 - 192*a^3*b*d*x*tan(d*x)*tan(c) + 192*a*b^3*d*x*tan(d*x)*tan(c) + 72*a^2*b^2*tan(d*x)^3*tan(c) - 24*b^4*tan(d*x)^3*tan(c) - 72*a^2*b^2*tan(d*x)^2*tan(c)^2 + 12*b^4*tan(d*x)^2*tan(c)^2 + 72*a^2*b^2*tan(d*x)*tan(c)^3 - 24*b^4*tan(d*x)*tan(c)^3 - 3*b^4*tan(c)^4 - 16*a*b^3*tan(d*x)^3 - 24*a^4*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)*tan(c) + 144*a^2*b^2*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)*tan(c) - 24*b^4*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)*tan(c) + 144*a^3*b*tan(d*x)^2*tan(c) - 192*a*b^3*tan(d*x)^2*tan(c) + 144*a^3*b*tan(d*x)*tan(c)^2 - 192*a*b^3*tan(d*x)*tan(c)^2 - 16*a*b^3*tan(c)^3 + 48*a^3*b*d*x - 48*a*b^3*d*x - 36*a^2*b^2*tan(d*x)^2 + 6*b^4*tan(d*x)^2 + 72*a^2*b^2*tan(d*x)*tan(c) - 24*b^4*tan(d*x)*tan(c) - 36*a^2*b^2*tan(c)^2 + 6*b^4*tan(c)^2 + 6*a^4*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)) - 36*a^2*b^2*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)) + 6*b^4*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)) - 48*a^3*b*tan(d*x) + 48*a*b^3*tan(d*x) - 48*a^3*b*tan(c) + 48*a*b^3*tan(c) - 36*a^2*b^2 + 9*b^4)/(d*tan(d*x)^4*tan(c)^4 - 4*d*tan(d*x)^3*tan(c)^3 + 6*d*tan(d*x)^2*tan(c)^2 - 4*d*tan(d*x)*tan(c) + d)","B",0
448,1,1071,0,3.330603," ","integrate((a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 18 \, a^{2} b^{2} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 3 \, b^{4} d x \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 6 \, a^{3} b \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)^{3} \tan\left(c\right)^{3} + 6 \, a 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)^{3} \tan\left(c\right)^{3} - 9 \, a^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 54 \, a^{2} b^{2} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} - 9 \, b^{4} d x \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right)^{3} + 18 \, a^{3} b \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} - 18 \, a 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} - 18 \, a^{2} b^{2} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} + 3 \, b^{4} \tan\left(d x\right)^{3} \tan\left(c\right)^{2} - 18 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 3 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right)^{3} + 9 \, a^{4} d x \tan\left(d x\right) \tan\left(c\right) - 54 \, a^{2} b^{2} d x \tan\left(d x\right) \tan\left(c\right) + 9 \, b^{4} d x \tan\left(d x\right) \tan\left(c\right) + 6 \, a b^{3} \tan\left(d x\right)^{3} \tan\left(c\right) - 6 \, a b^{3} \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 6 \, a b^{3} \tan\left(d x\right) \tan\left(c\right)^{3} - b^{4} \tan\left(d x\right)^{3} - 18 \, a^{3} b \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) \tan\left(c\right) + 18 \, a 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) \tan\left(c\right) + 36 \, a^{2} b^{2} \tan\left(d x\right)^{2} \tan\left(c\right) - 9 \, b^{4} \tan\left(d x\right)^{2} \tan\left(c\right) + 36 \, a^{2} b^{2} \tan\left(d x\right) \tan\left(c\right)^{2} - 9 \, b^{4} \tan\left(d x\right) \tan\left(c\right)^{2} - b^{4} \tan\left(c\right)^{3} - 3 \, a^{4} d x + 18 \, a^{2} b^{2} d x - 3 \, b^{4} d x - 6 \, a b^{3} \tan\left(d x\right)^{2} + 6 \, a b^{3} \tan\left(d x\right) \tan\left(c\right) - 6 \, a b^{3} \tan\left(c\right)^{2} + 6 \, a^{3} b \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) - 6 \, a 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) - 18 \, a^{2} b^{2} \tan\left(d x\right) + 3 \, b^{4} \tan\left(d x\right) - 18 \, a^{2} b^{2} \tan\left(c\right) + 3 \, b^{4} \tan\left(c\right) - 6 \, a b^{3}}{3 \, {\left(d \tan\left(d x\right)^{3} \tan\left(c\right)^{3} - 3 \, d \tan\left(d x\right)^{2} \tan\left(c\right)^{2} + 3 \, d \tan\left(d x\right) \tan\left(c\right) - d\right)}}"," ",0,"1/3*(3*a^4*d*x*tan(d*x)^3*tan(c)^3 - 18*a^2*b^2*d*x*tan(d*x)^3*tan(c)^3 + 3*b^4*d*x*tan(d*x)^3*tan(c)^3 - 6*a^3*b*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)^3*tan(c)^3 + 6*a*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)^3*tan(c)^3 - 9*a^4*d*x*tan(d*x)^2*tan(c)^2 + 54*a^2*b^2*d*x*tan(d*x)^2*tan(c)^2 - 9*b^4*d*x*tan(d*x)^2*tan(c)^2 + 6*a*b^3*tan(d*x)^3*tan(c)^3 + 18*a^3*b*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 - 18*a*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 - 18*a^2*b^2*tan(d*x)^3*tan(c)^2 + 3*b^4*tan(d*x)^3*tan(c)^2 - 18*a^2*b^2*tan(d*x)^2*tan(c)^3 + 3*b^4*tan(d*x)^2*tan(c)^3 + 9*a^4*d*x*tan(d*x)*tan(c) - 54*a^2*b^2*d*x*tan(d*x)*tan(c) + 9*b^4*d*x*tan(d*x)*tan(c) + 6*a*b^3*tan(d*x)^3*tan(c) - 6*a*b^3*tan(d*x)^2*tan(c)^2 + 6*a*b^3*tan(d*x)*tan(c)^3 - b^4*tan(d*x)^3 - 18*a^3*b*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)*tan(c) + 18*a*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)*tan(c) + 36*a^2*b^2*tan(d*x)^2*tan(c) - 9*b^4*tan(d*x)^2*tan(c) + 36*a^2*b^2*tan(d*x)*tan(c)^2 - 9*b^4*tan(d*x)*tan(c)^2 - b^4*tan(c)^3 - 3*a^4*d*x + 18*a^2*b^2*d*x - 3*b^4*d*x - 6*a*b^3*tan(d*x)^2 + 6*a*b^3*tan(d*x)*tan(c) - 6*a*b^3*tan(c)^2 + 6*a^3*b*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)) - 6*a*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)) - 18*a^2*b^2*tan(d*x) + 3*b^4*tan(d*x) - 18*a^2*b^2*tan(c) + 3*b^4*tan(c) - 6*a*b^3)/(d*tan(d*x)^3*tan(c)^3 - 3*d*tan(d*x)^2*tan(c)^2 + 3*d*tan(d*x)*tan(c) - d)","B",0
449,1,90,0,5.383788," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{b^{4} \tan\left(d x + c\right)^{2} + 2 \, a^{4} \log\left({\left| \tan\left(d x + c\right) \right|}\right) + 8 \, a b^{3} \tan\left(d x + c\right) + 8 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(b^4*tan(d*x + c)^2 + 2*a^4*log(abs(tan(d*x + c))) + 8*a*b^3*tan(d*x + c) + 8*(a^3*b - a*b^3)*(d*x + c) - (a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2 + 1))/d","A",0
450,1,102,0,5.571697," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{4 \, a^{3} b \log\left({\left| \tan\left(d x + c\right) \right|}\right) + b^{4} \tan\left(d x + c\right) - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} - 2 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - \frac{4 \, a^{3} b \tan\left(d x + c\right) + a^{4}}{\tan\left(d x + c\right)}}{d}"," ",0,"(4*a^3*b*log(abs(tan(d*x + c))) + b^4*tan(d*x + c) - (a^4 - 6*a^2*b^2 + b^4)*(d*x + c) - 2*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1) - (4*a^3*b*tan(d*x + c) + a^4)/tan(d*x + c))/d","A",0
451,1,132,0,8.403423," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{8 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right) - \frac{3 \, a^{4} \tan\left(d x + c\right)^{2} - 18 \, a^{2} b^{2} \tan\left(d x + c\right)^{2} - 8 \, a^{3} b \tan\left(d x + c\right) - a^{4}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(8*(a^3*b - a*b^3)*(d*x + c) - (a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2 + 1) + 2*(a^4 - 6*a^2*b^2)*log(abs(tan(d*x + c))) - (3*a^4*tan(d*x + c)^2 - 18*a^2*b^2*tan(d*x + c)^2 - 8*a^3*b*tan(d*x + c) - a^4)/tan(d*x + c)^2)/d","A",0
452,1,246,0,7.092012," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 12 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 24 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} + 96 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 96 \, {\left(a^{3} b - a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{176 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 176 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 15 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 72 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 12 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3}}}{24 \, d}"," ",0,"1/24*(a^4*tan(1/2*d*x + 1/2*c)^3 - 12*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 15*a^4*tan(1/2*d*x + 1/2*c) + 72*a^2*b^2*tan(1/2*d*x + 1/2*c) + 24*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c) + 96*(a^3*b - a*b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 96*(a^3*b - a*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) + (176*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 176*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 15*a^4*tan(1/2*d*x + 1/2*c)^2 - 72*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 12*a^3*b*tan(1/2*d*x + 1/2*c) - a^4)/tan(1/2*d*x + 1/2*c)^3)/d","B",0
453,1,335,0,7.956957," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 32 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 480 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 768 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} + 192 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) - 192 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) + \frac{400 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 2400 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 400 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 480 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 36 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 144 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 32 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4}}}{192 \, d}"," ",0,"-1/192*(3*a^4*tan(1/2*d*x + 1/2*c)^4 - 32*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 36*a^4*tan(1/2*d*x + 1/2*c)^2 + 144*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 480*a^3*b*tan(1/2*d*x + 1/2*c) - 384*a*b^3*tan(1/2*d*x + 1/2*c) - 768*(a^3*b - a*b^3)*(d*x + c) + 192*(a^4 - 6*a^2*b^2 + b^4)*log(tan(1/2*d*x + 1/2*c)^2 + 1) - 192*(a^4 - 6*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c))) + (400*a^4*tan(1/2*d*x + 1/2*c)^4 - 2400*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 400*b^4*tan(1/2*d*x + 1/2*c)^4 - 480*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 384*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 36*a^4*tan(1/2*d*x + 1/2*c)^2 + 144*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 32*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/tan(1/2*d*x + 1/2*c)^4)/d","B",0
454,1,416,0,15.108909," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{3 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 30 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 35 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 120 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 360 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 330 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 1800 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 480 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} - 1920 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 1920 \, {\left(a^{3} b - a b^{3}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{4384 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 4384 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 330 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 1800 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 360 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 240 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 35 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 120 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 30 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 3 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5}}}{480 \, d}"," ",0,"1/480*(3*a^4*tan(1/2*d*x + 1/2*c)^5 - 30*a^3*b*tan(1/2*d*x + 1/2*c)^4 - 35*a^4*tan(1/2*d*x + 1/2*c)^3 + 120*a^2*b^2*tan(1/2*d*x + 1/2*c)^3 + 360*a^3*b*tan(1/2*d*x + 1/2*c)^2 - 240*a*b^3*tan(1/2*d*x + 1/2*c)^2 + 330*a^4*tan(1/2*d*x + 1/2*c) - 1800*a^2*b^2*tan(1/2*d*x + 1/2*c) + 240*b^4*tan(1/2*d*x + 1/2*c) - 480*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c) - 1920*(a^3*b - a*b^3)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 1920*(a^3*b - a*b^3)*log(abs(tan(1/2*d*x + 1/2*c))) - (4384*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 4384*a*b^3*tan(1/2*d*x + 1/2*c)^5 + 330*a^4*tan(1/2*d*x + 1/2*c)^4 - 1800*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 240*b^4*tan(1/2*d*x + 1/2*c)^4 - 360*a^3*b*tan(1/2*d*x + 1/2*c)^3 + 240*a*b^3*tan(1/2*d*x + 1/2*c)^3 - 35*a^4*tan(1/2*d*x + 1/2*c)^2 + 120*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 30*a^3*b*tan(1/2*d*x + 1/2*c) + 3*a^4)/tan(1/2*d*x + 1/2*c)^5)/d","B",0
455,1,506,0,14.551538," ","integrate(cot(d*x+c)^7*(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{5 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 48 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 60 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 435 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2160 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 5280 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4800 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 7680 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} - 1920 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 1\right) + 1920 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left({\left| \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \right|}\right) - \frac{4704 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 28224 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} + 4704 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6} - 5280 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} + 4800 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{5} - 435 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 2160 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} - 240 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{4} + 560 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} - 320 \, a b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{3} + 60 \, a^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 180 \, a^{2} b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, a^{3} b \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 5 \, a^{4}}{\tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*(5*a^4*tan(1/2*d*x + 1/2*c)^6 - 48*a^3*b*tan(1/2*d*x + 1/2*c)^5 - 60*a^4*tan(1/2*d*x + 1/2*c)^4 + 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 + 560*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 320*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 435*a^4*tan(1/2*d*x + 1/2*c)^2 - 2160*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 + 240*b^4*tan(1/2*d*x + 1/2*c)^2 - 5280*a^3*b*tan(1/2*d*x + 1/2*c) + 4800*a*b^3*tan(1/2*d*x + 1/2*c) + 7680*(a^3*b - a*b^3)*(d*x + c) - 1920*(a^4 - 6*a^2*b^2 + b^4)*log(tan(1/2*d*x + 1/2*c)^2 + 1) + 1920*(a^4 - 6*a^2*b^2 + b^4)*log(abs(tan(1/2*d*x + 1/2*c))) - (4704*a^4*tan(1/2*d*x + 1/2*c)^6 - 28224*a^2*b^2*tan(1/2*d*x + 1/2*c)^6 + 4704*b^4*tan(1/2*d*x + 1/2*c)^6 - 5280*a^3*b*tan(1/2*d*x + 1/2*c)^5 + 4800*a*b^3*tan(1/2*d*x + 1/2*c)^5 - 435*a^4*tan(1/2*d*x + 1/2*c)^4 + 2160*a^2*b^2*tan(1/2*d*x + 1/2*c)^4 - 240*b^4*tan(1/2*d*x + 1/2*c)^4 + 560*a^3*b*tan(1/2*d*x + 1/2*c)^3 - 320*a*b^3*tan(1/2*d*x + 1/2*c)^3 + 60*a^4*tan(1/2*d*x + 1/2*c)^2 - 180*a^2*b^2*tan(1/2*d*x + 1/2*c)^2 - 48*a^3*b*tan(1/2*d*x + 1/2*c) - 5*a^4)/tan(1/2*d*x + 1/2*c)^6)/d","B",0
456,1,158,0,17.070846," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{12 \, a^{6} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b^{5} + b^{7}} - \frac{12 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} + \frac{6 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \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} - 6 \, b^{3} \tan\left(d x + c\right)^{2} - 12 \, a^{3} \tan\left(d x + c\right) + 12 \, a b^{2} \tan\left(d x + c\right)}{b^{4}}}{12 \, d}"," ",0,"1/12*(12*a^6*log(abs(b*tan(d*x + c) + a))/(a^2*b^5 + b^7) - 12*(d*x + c)*a/(a^2 + b^2) + 6*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + (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 - 6*b^3*tan(d*x + c)^2 - 12*a^3*tan(d*x + c) + 12*a*b^2*tan(d*x + c))/b^4)/d","A",0
457,1,129,0,7.408446," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{6 \, a^{5} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b^{4} + b^{6}} - \frac{6 \, {\left(d x + c\right)} b}{a^{2} + b^{2}} - \frac{3 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, b^{2} \tan\left(d x + c\right)^{3} - 3 \, a b \tan\left(d x + c\right)^{2} + 6 \, a^{2} \tan\left(d x + c\right) - 6 \, b^{2} \tan\left(d x + c\right)}{b^{3}}}{6 \, d}"," ",0,"-1/6*(6*a^5*log(abs(b*tan(d*x + c) + a))/(a^2*b^4 + b^6) - 6*(d*x + c)*b/(a^2 + b^2) - 3*a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - (2*b^2*tan(d*x + c)^3 - 3*a*b*tan(d*x + c)^2 + 6*a^2*tan(d*x + c) - 6*b^2*tan(d*x + c))/b^3)/d","A",0
458,1,100,0,3.893664," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a^{4} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b^{3} + b^{5}} + \frac{2 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{b \tan\left(d x + c\right)^{2} - 2 \, a \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*a^4*log(abs(b*tan(d*x + c) + a))/(a^2*b^3 + b^5) + 2*(d*x + c)*a/(a^2 + b^2) - b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + (b*tan(d*x + c)^2 - 2*a*tan(d*x + c))/b^2)/d","A",0
459,1,86,0,3.217786," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, a^{3} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(d x + c\right)} b}{a^{2} + b^{2}} + \frac{a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, \tan\left(d x + c\right)}{b}}{2 \, d}"," ",0,"-1/2*(2*a^3*log(abs(b*tan(d*x + c) + a))/(a^2*b^2 + b^4) + 2*(d*x + c)*b/(a^2 + b^2) + a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*tan(d*x + c)/b)/d","A",0
460,1,73,0,1.085370," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, a^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b + b^{3}} - \frac{2 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} + \frac{b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*a^2*log(abs(b*tan(d*x + c) + a))/(a^2*b + b^3) - 2*(d*x + c)*a/(a^2 + b^2) + b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
461,1,73,0,0.679167," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, a b \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b + b^{3}} - \frac{2 \, {\left(d x + c\right)} b}{a^{2} + b^{2}} - \frac{a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*b*log(abs(b*tan(d*x + c) + a))/(a^2*b + b^3) - 2*(d*x + c)*b/(a^2 + b^2) - a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
462,1,74,0,0.405247," ","integrate(1/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{2} b + b^{3}} + \frac{2 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} - \frac{b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*b^2*log(abs(b*tan(d*x + c) + a))/(a^2*b + b^3) + 2*(d*x + c)*a/(a^2 + b^2) - b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
463,1,88,0,0.813083," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{3} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{3} b + a b^{3}} + \frac{2 \, {\left(d x + c\right)} b}{a^{2} + b^{2}} + \frac{a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a}}{2 \, d}"," ",0,"-1/2*(2*b^3*log(abs(b*tan(d*x + c) + a))/(a^3*b + a*b^3) + 2*(d*x + c)*b/(a^2 + b^2) + a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*log(abs(tan(d*x + c)))/a)/d","A",0
464,1,116,0,1.085539," ","integrate(cot(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 + a^{2} b^{3}} - \frac{2 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} + \frac{b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{2}} + \frac{2 \, {\left(b \tan\left(d x + c\right) - a\right)}}{a^{2} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*b^4*log(abs(b*tan(d*x + c) + a))/(a^4*b + a^2*b^3) - 2*(d*x + c)*a/(a^2 + b^2) + b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*b*log(abs(tan(d*x + c)))/a^2 + 2*(b*tan(d*x + c) - a)/(a^2*tan(d*x + c)))/d","A",0
465,1,155,0,1.316601," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""giac"")","-\frac{\frac{2 \, b^{5} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{5} b + a^{3} b^{3}} - \frac{2 \, {\left(d x + c\right)} b}{a^{2} + b^{2}} - \frac{a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}} - \frac{3 \, a^{2} \tan\left(d x + c\right)^{2} - 3 \, b^{2} \tan\left(d x + c\right)^{2} + 2 \, a b \tan\left(d x + c\right) - a^{2}}{a^{3} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*b^5*log(abs(b*tan(d*x + c) + a))/(a^5*b + a^3*b^3) - 2*(d*x + c)*b/(a^2 + b^2) - a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(a^2 - b^2)*log(abs(tan(d*x + c)))/a^3 - (3*a^2*tan(d*x + c)^2 - 3*b^2*tan(d*x + c)^2 + 2*a*b*tan(d*x + c) - a^2)/(a^3*tan(d*x + c)^2))/d","A",0
466,1,187,0,1.510556," ","integrate(cot(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\frac{\frac{6 \, b^{6} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + a^{4} b^{3}} + \frac{6 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} - \frac{3 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{6 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{11 \, a^{2} b \tan\left(d x + c\right)^{3} - 11 \, b^{3} \tan\left(d x + c\right)^{3} - 6 \, a^{3} \tan\left(d x + c\right)^{2} + 6 \, a b^{2} \tan\left(d x + c\right)^{2} - 3 \, a^{2} b \tan\left(d x + c\right) + 2 \, a^{3}}{a^{4} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*b^6*log(abs(b*tan(d*x + c) + a))/(a^6*b + a^4*b^3) + 6*(d*x + c)*a/(a^2 + b^2) - 3*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 6*(a^2*b - b^3)*log(abs(tan(d*x + c)))/a^4 - (11*a^2*b*tan(d*x + c)^3 - 11*b^3*tan(d*x + c)^3 - 6*a^3*tan(d*x + c)^2 + 6*a*b^2*tan(d*x + c)^2 - 3*a^2*b*tan(d*x + c) + 2*a^3)/(a^4*tan(d*x + c)^3))/d","A",0
467,1,251,0,22.240598," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{3 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{3 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{6 \, {\left(2 \, a^{7} + 3 \, a^{5} b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}} + \frac{3 \, {\left(4 \, a^{7} b \tan\left(d x + c\right) + 6 \, a^{5} b^{3} \tan\left(d x + c\right) + 3 \, a^{8} + 5 \, a^{6} b^{2}\right)}}{{\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} + \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) - 3 \, b^{4} \tan\left(d x + c\right)}{b^{6}}}{3 \, d}"," ",0,"1/3*(3*a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 3*(a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 6*(2*a^7 + 3*a^5*b^2)*log(abs(b*tan(d*x + c) + a))/(a^4*b^5 + 2*a^2*b^7 + b^9) + 3*(4*a^7*b*tan(d*x + c) + 6*a^5*b^3*tan(d*x + c) + 3*a^8 + 5*a^6*b^2)/((a^4*b^5 + 2*a^2*b^7 + b^9)*(b*tan(d*x + c) + a)) + (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) - 3*b^4*tan(d*x + c))/b^6)/d","A",0
468,1,221,0,7.906598," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(3 \, a^{6} + 5 \, a^{4} b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}} - \frac{2 \, {\left(3 \, a^{6} b \tan\left(d x + c\right) + 5 \, a^{4} b^{3} \tan\left(d x + c\right) + 2 \, a^{7} + 4 \, a^{5} b^{2}\right)}}{{\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} + \frac{b^{2} \tan\left(d x + c\right)^{2} - 4 \, a b \tan\left(d x + c\right)}{b^{4}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(3*a^6 + 5*a^4*b^2)*log(abs(b*tan(d*x + c) + a))/(a^4*b^4 + 2*a^2*b^6 + b^8) - 2*(3*a^6*b*tan(d*x + c) + 5*a^4*b^3*tan(d*x + c) + 2*a^7 + 4*a^5*b^2)/((a^4*b^4 + 2*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)) + (b^2*tan(d*x + c)^2 - 4*a*b*tan(d*x + c))/b^4)/d","A",0
469,1,201,0,3.939962," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(a^{5} + 2 \, a^{3} b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} - \frac{2 \, a^{5} b \tan\left(d x + c\right) + 4 \, a^{3} b^{3} \tan\left(d x + c\right) + a^{6} + 3 \, a^{4} b^{2}}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} - \frac{\tan\left(d x + c\right)}{b^{2}}}{d}"," ",0,"-(a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(a^5 + 2*a^3*b^2)*log(abs(b*tan(d*x + c) + a))/(a^4*b^3 + 2*a^2*b^5 + b^7) - (2*a^5*b*tan(d*x + c) + 4*a^3*b^3*tan(d*x + c) + a^6 + 3*a^4*b^2)/((a^4*b^3 + 2*a^2*b^5 + b^7)*(b*tan(d*x + c) + a)) - tan(d*x + c)/b^2)/d","A",0
470,1,181,0,3.036219," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(a^{4} \tan\left(d x + c\right) + 3 \, a^{2} b^{2} \tan\left(d x + c\right) + 2 \, a^{3} b\right)}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"-1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(a^4 + 3*a^2*b^2)*log(abs(b*tan(d*x + c) + a))/(a^4*b^2 + 2*a^2*b^4 + b^6) + 2*(a^4*tan(d*x + c) + 3*a^2*b^2*tan(d*x + c) + 2*a^3*b)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(d*x + c) + a)))/d","A",0
471,1,165,0,1.416850," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, a b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, a b^{3} \tan\left(d x + c\right) - a^{4} + a^{2} b^{2}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{d}"," ",0,"-(2*a*b^2*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (2*a*b^3*tan(d*x + c) - a^4 + a^2*b^2)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(d*x + c) + a)))/d","A",0
472,1,173,0,1.432404," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(a^{2} b - b^{3}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} + \frac{2 \, {\left(a^{2} b \tan\left(d x + c\right) - b^{3} \tan\left(d x + c\right) + 2 \, a^{3}\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(a^2*b - b^3)*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) + 2*(a^2*b*tan(d*x + c) - b^3*tan(d*x + c) + 2*a^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c) + a)))/d","B",0
473,1,159,0,0.486602," ","integrate(1/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{2 \, a b^{2} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, a b^{2} \tan\left(d x + c\right) + 3 \, a^{2} b + b^{3}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}}}{d}"," ",0,"(2*a*b^2*log(abs(b*tan(d*x + c) + a))/(a^4*b + 2*a^2*b^3 + b^5) - a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - (2*a*b^2*tan(d*x + c) + 3*a^2*b + b^3)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(d*x + c) + a)))/d","A",0
474,1,206,0,1.477770," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(3 \, a^{2} b^{3} + b^{5}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}} - \frac{2 \, {\left(3 \, a^{2} b^{3} \tan\left(d x + c\right) + b^{5} \tan\left(d x + c\right) + 4 \, a^{3} b^{2} + 2 \, a b^{4}\right)}}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} - \frac{2 \, \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{2}}}{2 \, d}"," ",0,"-1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(3*a^2*b^3 + b^5)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 2*a^4*b^3 + a^2*b^5) - 2*(3*a^2*b^3*tan(d*x + c) + b^5*tan(d*x + c) + 4*a^3*b^2 + 2*a*b^4)/((a^6 + 2*a^4*b^2 + a^2*b^4)*(b*tan(d*x + c) + a)) - 2*log(abs(tan(d*x + c)))/a^2)/d","A",0
475,1,235,0,2.842745," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a^{2} - b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, a^{2} b^{4} + b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}} + \frac{a^{3} b^{2} \tan\left(d x + c\right)^{2} - 3 \, a^{2} b^{3} \tan\left(d x + c\right) - 2 \, b^{5} \tan\left(d x + c\right) - a^{5} - 2 \, a^{3} b^{2} - a b^{4}}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} {\left(b \tan\left(d x + c\right)^{2} + a \tan\left(d x + c\right)\right)}} - \frac{2 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}}}{d}"," ",0,"(a*b*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^2 - b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*a^2*b^4 + b^6)*log(abs(b*tan(d*x + c) + a))/(a^7*b + 2*a^5*b^3 + a^3*b^5) + (a^3*b^2*tan(d*x + c)^2 - 3*a^2*b^3*tan(d*x + c) - 2*b^5*tan(d*x + c) - a^5 - 2*a^3*b^2 - a*b^4)/((a^6 + 2*a^4*b^2 + a^2*b^4)*(b*tan(d*x + c)^2 + a*tan(d*x + c))) - 2*b*log(abs(tan(d*x + c)))/a^3)/d","A",0
476,1,272,0,2.183456," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(5 \, a^{2} b^{5} + 3 \, b^{7}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}} + \frac{2 \, {\left(5 \, a^{2} b^{5} \tan\left(d x + c\right) + 3 \, b^{7} \tan\left(d x + c\right) + 6 \, a^{3} b^{4} + 4 \, a b^{6}\right)}}{{\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} {\left(b \tan\left(d x + c\right) + a\right)}} - \frac{2 \, {\left(a^{2} - 3 \, b^{2}\right)} \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}} + \frac{3 \, a^{2} \tan\left(d x + c\right)^{2} - 9 \, b^{2} \tan\left(d x + c\right)^{2} + 4 \, a b \tan\left(d x + c\right) - a^{2}}{a^{4} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(5*a^2*b^5 + 3*b^7)*log(abs(b*tan(d*x + c) + a))/(a^8*b + 2*a^6*b^3 + a^4*b^5) + 2*(5*a^2*b^5*tan(d*x + c) + 3*b^7*tan(d*x + c) + 6*a^3*b^4 + 4*a*b^6)/((a^8 + 2*a^6*b^2 + a^4*b^4)*(b*tan(d*x + c) + a)) - 2*(a^2 - 3*b^2)*log(abs(tan(d*x + c)))/a^4 + (3*a^2*tan(d*x + c)^2 - 9*b^2*tan(d*x + c)^2 + 4*a*b*tan(d*x + c) - a^2)/(a^4*tan(d*x + c)^2))/d","A",0
477,1,345,0,24.827371," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \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{2 \, {\left(6 \, a^{8} + 17 \, a^{6} b^{2} + 15 \, a^{4} b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}} + \frac{18 \, a^{8} b^{2} \tan\left(d x + c\right)^{2} + 51 \, a^{6} b^{4} \tan\left(d x + c\right)^{2} + 45 \, a^{4} b^{6} \tan\left(d x + c\right)^{2} + 28 \, a^{9} b \tan\left(d x + c\right) + 82 \, a^{7} b^{3} \tan\left(d x + c\right) + 78 \, a^{5} b^{5} \tan\left(d x + c\right) + 11 \, a^{10} + 33 \, a^{8} b^{2} + 34 \, a^{6} b^{4}}{{\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}} - \frac{b^{3} \tan\left(d x + c\right)^{2} - 6 \, a b^{2} \tan\left(d x + c\right)}{b^{6}}}{2 \, d}"," ",0,"-1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(6*a^8 + 17*a^6*b^2 + 15*a^4*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11) + (18*a^8*b^2*tan(d*x + c)^2 + 51*a^6*b^4*tan(d*x + c)^2 + 45*a^4*b^6*tan(d*x + c)^2 + 28*a^9*b*tan(d*x + c) + 82*a^7*b^3*tan(d*x + c) + 78*a^5*b^5*tan(d*x + c) + 11*a^10 + 33*a^8*b^2 + 34*a^6*b^4)/((a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*(b*tan(d*x + c) + a)^2) - (b^3*tan(d*x + c)^2 - 6*a*b^2*tan(d*x + c))/b^6)/d","A",0
478,1,325,0,7.941932," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \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{2 \, {\left(3 \, a^{7} + 9 \, a^{5} b^{2} + 10 \, a^{3} b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}} + \frac{9 \, a^{7} b^{2} \tan\left(d x + c\right)^{2} + 27 \, a^{5} b^{4} \tan\left(d x + c\right)^{2} + 30 \, a^{3} b^{6} \tan\left(d x + c\right)^{2} + 12 \, a^{8} b \tan\left(d x + c\right) + 38 \, a^{6} b^{3} \tan\left(d x + c\right) + 50 \, a^{4} b^{5} \tan\left(d x + c\right) + 4 \, a^{9} + 13 \, a^{7} b^{2} + 21 \, a^{5} b^{4}}{{\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}} + \frac{2 \, \tan\left(d x + c\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*(2*(3*a^2*b - b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(3*a^7 + 9*a^5*b^2 + 10*a^3*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + (9*a^7*b^2*tan(d*x + c)^2 + 27*a^5*b^4*tan(d*x + c)^2 + 30*a^3*b^6*tan(d*x + c)^2 + 12*a^8*b*tan(d*x + c) + 38*a^6*b^3*tan(d*x + c) + 50*a^4*b^5*tan(d*x + c) + 4*a^9 + 13*a^7*b^2 + 21*a^5*b^4)/((a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*(b*tan(d*x + c) + a)^2) + 2*tan(d*x + c)/b^3)/d","A",0
479,1,304,0,4.086566," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \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{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}} - \frac{3 \, a^{6} b \tan\left(d x + c\right)^{2} + 9 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} + 18 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} + 2 \, a^{7} \tan\left(d x + c\right) + 6 \, a^{5} b^{2} \tan\left(d x + c\right) + 28 \, a^{3} b^{4} \tan\left(d x + c\right) - a^{6} b + 11 \, a^{4} b^{3}}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(a^6 + 3*a^4*b^2 + 6*a^2*b^4)*log(abs(b*tan(d*x + c) + a))/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) - (3*a^6*b*tan(d*x + c)^2 + 9*a^4*b^3*tan(d*x + c)^2 + 18*a^2*b^5*tan(d*x + c)^2 + 2*a^7*tan(d*x + c) + 6*a^5*b^2*tan(d*x + c) + 28*a^3*b^4*tan(d*x + c) - a^6*b + 11*a^4*b^3)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^2))/d","A",0
480,1,282,0,2.727765," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \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{2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} \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{3 \, a^{3} b^{4} \tan\left(d x + c\right)^{2} - 9 \, a b^{6} \tan\left(d x + c\right)^{2} + 2 \, a^{6} b \tan\left(d x + c\right) + 14 \, a^{4} b^{3} \tan\left(d x + c\right) - 12 \, a^{2} b^{5} \tan\left(d x + c\right) + a^{7} + 9 \, a^{5} b^{2} - 4 \, a^{3} b^{4}}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(3*a^2*b - b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(a^3*b - 3*a*b^3)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + (3*a^3*b^4*tan(d*x + c)^2 - 9*a*b^6*tan(d*x + c)^2 + 2*a^6*b*tan(d*x + c) + 14*a^4*b^3*tan(d*x + c) - 12*a^2*b^5*tan(d*x + c) + a^7 + 9*a^5*b^2 - 4*a^3*b^4)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(d*x + c) + a)^2))/d","A",0
481,1,263,0,1.883866," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \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{2 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \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{9 \, a^{2} b^{4} \tan\left(d x + c\right)^{2} - 3 \, b^{6} \tan\left(d x + c\right)^{2} + 22 \, a^{3} b^{3} \tan\left(d x + c\right) - 2 \, a b^{5} \tan\left(d x + c\right) - a^{6} + 11 \, a^{4} b^{2}}{{\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"-1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*a^2*b^2 - 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) - (9*a^2*b^4*tan(d*x + c)^2 - 3*b^6*tan(d*x + c)^2 + 22*a^3*b^3*tan(d*x + c) - 2*a*b^5*tan(d*x + c) - a^6 + 11*a^4*b^2)/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*(b*tan(d*x + c) + a)^2))/d","B",0
482,1,275,0,1.119664," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \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{2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} \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{3 \, a^{3} b^{2} \tan\left(d x + c\right)^{2} - 9 \, a b^{4} \tan\left(d x + c\right)^{2} + 8 \, a^{4} b \tan\left(d x + c\right) - 18 \, a^{2} b^{3} \tan\left(d x + c\right) - 2 \, b^{5} \tan\left(d x + c\right) + 6 \, a^{5} - 7 \, a^{3} b^{2} - a b^{4}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(3*a^2*b - b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(a^3*b - 3*a*b^3)*log(abs(b*tan(d*x + c) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) + (3*a^3*b^2*tan(d*x + c)^2 - 9*a*b^4*tan(d*x + c)^2 + 8*a^4*b*tan(d*x + c) - 18*a^2*b^3*tan(d*x + c) - 2*b^5*tan(d*x + c) + 6*a^5 - 7*a^3*b^2 - a*b^4)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(b*tan(d*x + c) + a)^2))/d","B",0
483,1,265,0,0.590017," ","integrate(1/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \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{2 \, {\left(3 \, a^{2} b^{2} - b^{4}\right)} \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{9 \, a^{2} b^{3} \tan\left(d x + c\right)^{2} - 3 \, b^{5} \tan\left(d x + c\right)^{2} + 22 \, a^{3} b^{2} \tan\left(d x + c\right) - 2 \, a b^{4} \tan\left(d x + c\right) + 14 \, a^{4} b + 3 \, a^{2} b^{3} + b^{5}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*a^2*b^2 - 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) - (9*a^2*b^3*tan(d*x + c)^2 - 3*b^5*tan(d*x + c)^2 + 22*a^3*b^2*tan(d*x + c) - 2*a*b^4*tan(d*x + c) + 14*a^4*b + 3*a^2*b^3 + b^5)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(b*tan(d*x + c) + a)^2))/d","B",0
484,1,328,0,2.514006," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{3} - 3 \, a b^{2}\right)} \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{2 \, {\left(6 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}} - \frac{18 \, a^{4} b^{4} \tan\left(d x + c\right)^{2} + 9 \, a^{2} b^{6} \tan\left(d x + c\right)^{2} + 3 \, b^{8} \tan\left(d x + c\right)^{2} + 42 \, a^{5} b^{3} \tan\left(d x + c\right) + 26 \, a^{3} b^{5} \tan\left(d x + c\right) + 8 \, a b^{7} \tan\left(d x + c\right) + 25 \, a^{6} b^{2} + 19 \, a^{4} b^{4} + 6 \, a^{2} b^{6}}{{\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}} - \frac{2 \, \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*(2*(3*a^2*b - b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(6*a^4*b^3 + 3*a^2*b^5 + b^7)*log(abs(b*tan(d*x + c) + a))/(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7) - (18*a^4*b^4*tan(d*x + c)^2 + 9*a^2*b^6*tan(d*x + c)^2 + 3*b^8*tan(d*x + c)^2 + 42*a^5*b^3*tan(d*x + c) + 26*a^3*b^5*tan(d*x + c) + 8*a*b^7*tan(d*x + c) + 25*a^6*b^2 + 19*a^4*b^4 + 6*a^2*b^6)/((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*(b*tan(d*x + c) + a)^2) - 2*log(abs(tan(d*x + c)))/a^3)/d","A",0
485,1,357,0,3.726738," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b - b^{3}\right)} \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{2 \, {\left(10 \, a^{4} b^{4} + 9 \, a^{2} b^{6} + 3 \, b^{8}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{10} b + 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} + a^{4} b^{7}} + \frac{30 \, a^{4} b^{5} \tan\left(d x + c\right)^{2} + 27 \, a^{2} b^{7} \tan\left(d x + c\right)^{2} + 9 \, b^{9} \tan\left(d x + c\right)^{2} + 68 \, a^{5} b^{4} \tan\left(d x + c\right) + 66 \, a^{3} b^{6} \tan\left(d x + c\right) + 22 \, a b^{8} \tan\left(d x + c\right) + 39 \, a^{6} b^{3} + 41 \, a^{4} b^{5} + 14 \, a^{2} b^{7}}{{\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2}} + \frac{6 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}} - \frac{2 \, {\left(3 \, b \tan\left(d x + c\right) - a\right)}}{a^{4} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(10*a^4*b^4 + 9*a^2*b^6 + 3*b^8)*log(abs(b*tan(d*x + c) + a))/(a^10*b + 3*a^8*b^3 + 3*a^6*b^5 + a^4*b^7) + (30*a^4*b^5*tan(d*x + c)^2 + 27*a^2*b^7*tan(d*x + c)^2 + 9*b^9*tan(d*x + c)^2 + 68*a^5*b^4*tan(d*x + c) + 66*a^3*b^6*tan(d*x + c) + 22*a*b^8*tan(d*x + c) + 39*a^6*b^3 + 41*a^4*b^5 + 14*a^2*b^7)/((a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*(b*tan(d*x + c) + a)^2) + 6*b*log(abs(tan(d*x + c)))/a^4 - 2*(3*b*tan(d*x + c) - a)/(a^4*tan(d*x + c)))/d","A",0
486,1,472,0,22.973401," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 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{6 \, {\left(a^{3} b - a b^{3}\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{12 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 5 \, a^{3} b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b^{5} + 4 \, a^{6} b^{7} + 6 \, a^{4} b^{9} + 4 \, a^{2} b^{11} + b^{13}} - \frac{22 \, a^{9} b^{3} \tan\left(d x + c\right)^{3} + 88 \, a^{7} b^{5} \tan\left(d x + c\right)^{3} + 132 \, a^{5} b^{7} \tan\left(d x + c\right)^{3} + 110 \, a^{3} b^{9} \tan\left(d x + c\right)^{3} + 48 \, a^{10} b^{2} \tan\left(d x + c\right)^{2} + 195 \, a^{8} b^{4} \tan\left(d x + c\right)^{2} + 300 \, a^{6} b^{6} \tan\left(d x + c\right)^{2} + 285 \, a^{4} b^{8} \tan\left(d x + c\right)^{2} + 36 \, a^{11} b \tan\left(d x + c\right) + 147 \, a^{9} b^{3} \tan\left(d x + c\right) + 228 \, a^{7} b^{5} \tan\left(d x + c\right) + 249 \, a^{5} b^{7} \tan\left(d x + c\right) + 9 \, a^{12} + 37 \, a^{10} b^{2} + 57 \, a^{8} b^{4} + 73 \, a^{6} b^{6}}{{\left(a^{8} b^{5} + 4 \, a^{6} b^{7} + 6 \, a^{4} b^{9} + 4 \, a^{2} b^{11} + b^{13}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}} - \frac{3 \, \tan\left(d x + c\right)}{b^{4}}}{3 \, d}"," ",0,"-1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*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) + 12*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 5*a^3*b^6)*log(abs(b*tan(d*x + c) + a))/(a^8*b^5 + 4*a^6*b^7 + 6*a^4*b^9 + 4*a^2*b^11 + b^13) - (22*a^9*b^3*tan(d*x + c)^3 + 88*a^7*b^5*tan(d*x + c)^3 + 132*a^5*b^7*tan(d*x + c)^3 + 110*a^3*b^9*tan(d*x + c)^3 + 48*a^10*b^2*tan(d*x + c)^2 + 195*a^8*b^4*tan(d*x + c)^2 + 300*a^6*b^6*tan(d*x + c)^2 + 285*a^4*b^8*tan(d*x + c)^2 + 36*a^11*b*tan(d*x + c) + 147*a^9*b^3*tan(d*x + c) + 228*a^7*b^5*tan(d*x + c) + 249*a^5*b^7*tan(d*x + c) + 9*a^12 + 37*a^10*b^2 + 57*a^8*b^4 + 73*a^6*b^6)/((a^8*b^5 + 4*a^6*b^7 + 6*a^4*b^9 + 4*a^2*b^11 + b^13)*(b*tan(d*x + c) + a)^3) - 3*tan(d*x + c)/b^4)/d","A",0
487,1,451,0,9.799234," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{3} b - a b^{3}\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{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\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{6 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + 10 \, a^{2} b^{6}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}} - \frac{11 \, a^{8} b^{2} \tan\left(d x + c\right)^{3} + 44 \, a^{6} b^{4} \tan\left(d x + c\right)^{3} + 55 \, a^{4} b^{6} \tan\left(d x + c\right)^{3} + 110 \, a^{2} b^{8} \tan\left(d x + c\right)^{3} + 15 \, a^{9} b \tan\left(d x + c\right)^{2} + 60 \, a^{7} b^{3} \tan\left(d x + c\right)^{2} + 51 \, a^{5} b^{5} \tan\left(d x + c\right)^{2} + 270 \, a^{3} b^{7} \tan\left(d x + c\right)^{2} + 6 \, a^{10} \tan\left(d x + c\right) + 21 \, a^{8} b^{2} \tan\left(d x + c\right) - 24 \, a^{6} b^{4} \tan\left(d x + c\right) + 225 \, a^{4} b^{6} \tan\left(d x + c\right) - a^{9} b - 26 \, a^{7} b^{3} + 63 \, a^{5} b^{5}}{{\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{6 \, d}"," ",0,"1/6*(24*(a^3*b - a*b^3)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(a^4 - 6*a^2*b^2 + b^4)*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) + 6*(a^8 + 4*a^6*b^2 + 5*a^4*b^4 + 10*a^2*b^6)*log(abs(b*tan(d*x + c) + a))/(a^8*b^4 + 4*a^6*b^6 + 6*a^4*b^8 + 4*a^2*b^10 + b^12) - (11*a^8*b^2*tan(d*x + c)^3 + 44*a^6*b^4*tan(d*x + c)^3 + 55*a^4*b^6*tan(d*x + c)^3 + 110*a^2*b^8*tan(d*x + c)^3 + 15*a^9*b*tan(d*x + c)^2 + 60*a^7*b^3*tan(d*x + c)^2 + 51*a^5*b^5*tan(d*x + c)^2 + 270*a^3*b^7*tan(d*x + c)^2 + 6*a^10*tan(d*x + c) + 21*a^8*b^2*tan(d*x + c) - 24*a^6*b^4*tan(d*x + c) + 225*a^4*b^6*tan(d*x + c) - a^9*b - 26*a^7*b^3 + 63*a^5*b^5)/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*(b*tan(d*x + c) + a)^3))/d","A",0
488,1,409,0,5.674607," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 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{6 \, {\left(a^{3} b - a b^{3}\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{12 \, {\left(a^{3} b^{2} - a b^{4}\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{22 \, a^{3} b^{7} \tan\left(d x + c\right)^{3} - 22 \, a b^{9} \tan\left(d x + c\right)^{3} + 3 \, a^{8} b^{2} \tan\left(d x + c\right)^{2} + 12 \, a^{6} b^{4} \tan\left(d x + c\right)^{2} + 93 \, a^{4} b^{6} \tan\left(d x + c\right)^{2} - 48 \, a^{2} b^{8} \tan\left(d x + c\right)^{2} + 3 \, a^{9} b \tan\left(d x + c\right) + 12 \, a^{7} b^{3} \tan\left(d x + c\right) + 105 \, a^{5} b^{5} \tan\left(d x + c\right) - 36 \, a^{3} b^{7} \tan\left(d x + c\right) + a^{10} + 3 \, a^{8} b^{2} + 37 \, a^{6} b^{4} - 9 \, a^{4} b^{6}}{{\left(a^{8} b^{3} + 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} + 4 \, a^{2} b^{9} + b^{11}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*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) + 12*(a^3*b^2 - a*b^4)*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) - (22*a^3*b^7*tan(d*x + c)^3 - 22*a*b^9*tan(d*x + c)^3 + 3*a^8*b^2*tan(d*x + c)^2 + 12*a^6*b^4*tan(d*x + c)^2 + 93*a^4*b^6*tan(d*x + c)^2 - 48*a^2*b^8*tan(d*x + c)^2 + 3*a^9*b*tan(d*x + c) + 12*a^7*b^3*tan(d*x + c) + 105*a^5*b^5*tan(d*x + c) - 36*a^3*b^7*tan(d*x + c) + a^10 + 3*a^8*b^2 + 37*a^6*b^4 - 9*a^4*b^6)/((a^8*b^3 + 4*a^6*b^5 + 6*a^4*b^7 + 4*a^2*b^9 + b^11)*(b*tan(d*x + c) + a)^3))/d","B",0
489,1,400,0,3.370342," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(a^{3} b - a b^{3}\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{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\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{6 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + b^{5}\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{11 \, a^{4} b^{5} \tan\left(d x + c\right)^{3} - 66 \, a^{2} b^{7} \tan\left(d x + c\right)^{3} + 11 \, b^{9} \tan\left(d x + c\right)^{3} + 39 \, a^{5} b^{4} \tan\left(d x + c\right)^{2} - 210 \, a^{3} b^{6} \tan\left(d x + c\right)^{2} + 15 \, a b^{8} \tan\left(d x + c\right)^{2} + 3 \, a^{8} b \tan\left(d x + c\right) + 60 \, a^{6} b^{3} \tan\left(d x + c\right) - 201 \, a^{4} b^{5} \tan\left(d x + c\right) + 6 \, a^{2} b^{7} \tan\left(d x + c\right) + a^{9} + 26 \, a^{7} b^{2} - 63 \, a^{5} b^{4}}{{\left(a^{8} b^{2} + 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{6 \, d}"," ",0,"-1/6*(24*(a^3*b - a*b^3)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(a^4 - 6*a^2*b^2 + b^4)*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) - 6*(a^4*b - 6*a^2*b^3 + b^5)*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) + (11*a^4*b^5*tan(d*x + c)^3 - 66*a^2*b^7*tan(d*x + c)^3 + 11*b^9*tan(d*x + c)^3 + 39*a^5*b^4*tan(d*x + c)^2 - 210*a^3*b^6*tan(d*x + c)^2 + 15*a*b^8*tan(d*x + c)^2 + 3*a^8*b*tan(d*x + c) + 60*a^6*b^3*tan(d*x + c) - 201*a^4*b^5*tan(d*x + c) + 6*a^2*b^7*tan(d*x + c) + a^9 + 26*a^7*b^2 - 63*a^5*b^4)/((a^8*b^2 + 4*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*(b*tan(d*x + c) + a)^3))/d","B",0
490,1,376,0,5.071827," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 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{6 \, {\left(a^{3} b - a b^{3}\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{12 \, {\left(a^{3} b^{2} - a b^{4}\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{22 \, a^{3} b^{5} \tan\left(d x + c\right)^{3} - 22 \, a b^{7} \tan\left(d x + c\right)^{3} + 75 \, a^{4} b^{4} \tan\left(d x + c\right)^{2} - 60 \, a^{2} b^{6} \tan\left(d x + c\right)^{2} - 3 \, b^{8} \tan\left(d x + c\right)^{2} + 87 \, a^{5} b^{3} \tan\left(d x + c\right) - 48 \, a^{3} b^{5} \tan\left(d x + c\right) - 3 \, a b^{7} \tan\left(d x + c\right) - a^{8} + 31 \, a^{6} b^{2} - 13 \, a^{4} b^{4} - a^{2} b^{6}}{{\left(a^{8} b + 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}}}{3 \, d}"," ",0,"-1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*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) + 12*(a^3*b^2 - a*b^4)*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) - (22*a^3*b^5*tan(d*x + c)^3 - 22*a*b^7*tan(d*x + c)^3 + 75*a^4*b^4*tan(d*x + c)^2 - 60*a^2*b^6*tan(d*x + c)^2 - 3*b^8*tan(d*x + c)^2 + 87*a^5*b^3*tan(d*x + c) - 48*a^3*b^5*tan(d*x + c) - 3*a*b^7*tan(d*x + c) - a^8 + 31*a^6*b^2 - 13*a^4*b^4 - a^2*b^6)/((a^8*b + 4*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*(b*tan(d*x + c) + a)^3))/d","B",0
491,1,401,0,2.000160," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{24 \, {\left(a^{3} b - a b^{3}\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{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\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{6 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + b^{5}\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{11 \, a^{4} b^{3} \tan\left(d x + c\right)^{3} - 66 \, a^{2} b^{5} \tan\left(d x + c\right)^{3} + 11 \, b^{7} \tan\left(d x + c\right)^{3} + 39 \, a^{5} b^{2} \tan\left(d x + c\right)^{2} - 210 \, a^{3} b^{4} \tan\left(d x + c\right)^{2} + 15 \, a b^{6} \tan\left(d x + c\right)^{2} + 48 \, a^{6} b \tan\left(d x + c\right) - 219 \, a^{4} b^{3} \tan\left(d x + c\right) - 6 \, a^{2} b^{5} \tan\left(d x + c\right) - 3 \, b^{7} \tan\left(d x + c\right) + 22 \, a^{7} - 69 \, a^{5} b^{2} - 4 \, a^{3} b^{4} - a b^{6}}{{\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)}^{3}}}{6 \, d}"," ",0,"1/6*(24*(a^3*b - a*b^3)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(a^4 - 6*a^2*b^2 + b^4)*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) - 6*(a^4*b - 6*a^2*b^3 + b^5)*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) + (11*a^4*b^3*tan(d*x + c)^3 - 66*a^2*b^5*tan(d*x + c)^3 + 11*b^7*tan(d*x + c)^3 + 39*a^5*b^2*tan(d*x + c)^2 - 210*a^3*b^4*tan(d*x + c)^2 + 15*a*b^6*tan(d*x + c)^2 + 48*a^6*b*tan(d*x + c) - 219*a^4*b^3*tan(d*x + c) - 6*a^2*b^5*tan(d*x + c) - 3*b^7*tan(d*x + c) + 22*a^7 - 69*a^5*b^2 - 4*a^3*b^4 - a*b^6)/((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)^3))/d","B",0
492,1,370,0,1.007157," ","integrate(1/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 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{6 \, {\left(a^{3} b - a b^{3}\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{12 \, {\left(a^{3} b^{2} - a b^{4}\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{22 \, a^{3} b^{4} \tan\left(d x + c\right)^{3} - 22 \, a b^{6} \tan\left(d x + c\right)^{3} + 75 \, a^{4} b^{3} \tan\left(d x + c\right)^{2} - 60 \, a^{2} b^{5} \tan\left(d x + c\right)^{2} - 3 \, b^{7} \tan\left(d x + c\right)^{2} + 87 \, a^{5} b^{2} \tan\left(d x + c\right) - 48 \, a^{3} b^{4} \tan\left(d x + c\right) - 3 \, a b^{6} \tan\left(d x + c\right) + 35 \, a^{6} b - 7 \, a^{4} b^{3} + 3 \, 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)}^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*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) + 12*(a^3*b^2 - a*b^4)*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) - (22*a^3*b^4*tan(d*x + c)^3 - 22*a*b^6*tan(d*x + c)^3 + 75*a^4*b^3*tan(d*x + c)^2 - 60*a^2*b^5*tan(d*x + c)^2 - 3*b^7*tan(d*x + c)^2 + 87*a^5*b^2*tan(d*x + c) - 48*a^3*b^4*tan(d*x + c) - 3*a*b^6*tan(d*x + c) + 35*a^6*b - 7*a^4*b^3 + 3*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)^3))/d","B",0
493,1,476,0,3.352821," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{24 \, {\left(a^{3} b - a b^{3}\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{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\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{6 \, {\left(10 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{12} b + 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} + 4 \, a^{6} b^{7} + a^{4} b^{9}} - \frac{110 \, a^{6} b^{5} \tan\left(d x + c\right)^{3} + 55 \, a^{4} b^{7} \tan\left(d x + c\right)^{3} + 44 \, a^{2} b^{9} \tan\left(d x + c\right)^{3} + 11 \, b^{11} \tan\left(d x + c\right)^{3} + 366 \, a^{7} b^{4} \tan\left(d x + c\right)^{2} + 219 \, a^{5} b^{6} \tan\left(d x + c\right)^{2} + 156 \, a^{3} b^{8} \tan\left(d x + c\right)^{2} + 39 \, a b^{10} \tan\left(d x + c\right)^{2} + 411 \, a^{8} b^{3} \tan\left(d x + c\right) + 294 \, a^{6} b^{5} \tan\left(d x + c\right) + 195 \, a^{4} b^{7} \tan\left(d x + c\right) + 48 \, a^{2} b^{9} \tan\left(d x + c\right) + 157 \, a^{9} b^{2} + 136 \, a^{7} b^{4} + 89 \, a^{5} b^{6} + 22 \, a^{3} b^{8}}{{\left(a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}} - \frac{6 \, \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{4}}}{6 \, d}"," ",0,"-1/6*(24*(a^3*b - a*b^3)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 3*(a^4 - 6*a^2*b^2 + b^4)*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) + 6*(10*a^6*b^3 + 5*a^4*b^5 + 4*a^2*b^7 + b^9)*log(abs(b*tan(d*x + c) + a))/(a^12*b + 4*a^10*b^3 + 6*a^8*b^5 + 4*a^6*b^7 + a^4*b^9) - (110*a^6*b^5*tan(d*x + c)^3 + 55*a^4*b^7*tan(d*x + c)^3 + 44*a^2*b^9*tan(d*x + c)^3 + 11*b^11*tan(d*x + c)^3 + 366*a^7*b^4*tan(d*x + c)^2 + 219*a^5*b^6*tan(d*x + c)^2 + 156*a^3*b^8*tan(d*x + c)^2 + 39*a*b^10*tan(d*x + c)^2 + 411*a^8*b^3*tan(d*x + c) + 294*a^6*b^5*tan(d*x + c) + 195*a^4*b^7*tan(d*x + c) + 48*a^2*b^9*tan(d*x + c) + 157*a^9*b^2 + 136*a^7*b^4 + 89*a^5*b^6 + 22*a^3*b^8)/((a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*b^8)*(b*tan(d*x + c) + a)^3) - 6*log(abs(tan(d*x + c)))/a^4)/d","B",0
494,1,502,0,3.463058," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 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{6 \, {\left(a^{3} b - a b^{3}\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{12 \, {\left(5 \, a^{6} b^{4} + 6 \, a^{4} b^{6} + 4 \, a^{2} b^{8} + b^{10}\right)} \log\left({\left| b \tan\left(d x + c\right) + a \right|}\right)}{a^{13} b + 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} + 4 \, a^{7} b^{7} + a^{5} b^{9}} + \frac{110 \, a^{6} b^{6} \tan\left(d x + c\right)^{3} + 132 \, a^{4} b^{8} \tan\left(d x + c\right)^{3} + 88 \, a^{2} b^{10} \tan\left(d x + c\right)^{3} + 22 \, b^{12} \tan\left(d x + c\right)^{3} + 360 \, a^{7} b^{5} \tan\left(d x + c\right)^{2} + 453 \, a^{5} b^{7} \tan\left(d x + c\right)^{2} + 300 \, a^{3} b^{9} \tan\left(d x + c\right)^{2} + 75 \, a b^{11} \tan\left(d x + c\right)^{2} + 396 \, a^{8} b^{4} \tan\left(d x + c\right) + 525 \, a^{6} b^{6} \tan\left(d x + c\right) + 348 \, a^{4} b^{8} \tan\left(d x + c\right) + 87 \, a^{2} b^{10} \tan\left(d x + c\right) + 147 \, a^{9} b^{3} + 207 \, a^{7} b^{5} + 139 \, a^{5} b^{7} + 35 \, a^{3} b^{9}}{{\left(a^{13} + 4 \, a^{11} b^{2} + 6 \, a^{9} b^{4} + 4 \, a^{7} b^{6} + a^{5} b^{8}\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3}} + \frac{12 \, b \log\left({\left| \tan\left(d x + c\right) \right|}\right)}{a^{5}} - \frac{3 \, {\left(4 \, b \tan\left(d x + c\right) - a\right)}}{a^{5} \tan\left(d x + c\right)}}{3 \, d}"," ",0,"-1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(a^3*b - a*b^3)*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) - 12*(5*a^6*b^4 + 6*a^4*b^6 + 4*a^2*b^8 + b^10)*log(abs(b*tan(d*x + c) + a))/(a^13*b + 4*a^11*b^3 + 6*a^9*b^5 + 4*a^7*b^7 + a^5*b^9) + (110*a^6*b^6*tan(d*x + c)^3 + 132*a^4*b^8*tan(d*x + c)^3 + 88*a^2*b^10*tan(d*x + c)^3 + 22*b^12*tan(d*x + c)^3 + 360*a^7*b^5*tan(d*x + c)^2 + 453*a^5*b^7*tan(d*x + c)^2 + 300*a^3*b^9*tan(d*x + c)^2 + 75*a*b^11*tan(d*x + c)^2 + 396*a^8*b^4*tan(d*x + c) + 525*a^6*b^6*tan(d*x + c) + 348*a^4*b^8*tan(d*x + c) + 87*a^2*b^10*tan(d*x + c) + 147*a^9*b^3 + 207*a^7*b^5 + 139*a^5*b^7 + 35*a^3*b^9)/((a^13 + 4*a^11*b^2 + 6*a^9*b^4 + 4*a^7*b^6 + a^5*b^8)*(b*tan(d*x + c) + a)^3) + 12*b*log(abs(tan(d*x + c)))/a^5 - 3*(4*b*tan(d*x + c) - a)/(a^5*tan(d*x + c)))/d","A",0
495,1,40,0,0.933215," ","integrate(1/(3+5*tan(d*x+c)),x, algorithm=""giac"")","\frac{6 \, d x + 6 \, c - 5 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 10 \, \log\left({\left| 5 \, \tan\left(d x + c\right) + 3 \right|}\right)}{68 \, d}"," ",0,"1/68*(6*d*x + 6*c - 5*log(tan(d*x + c)^2 + 1) + 10*log(abs(5*tan(d*x + c) + 3)))/d","A",0
496,1,64,0,0.473196," ","integrate(1/(3+5*tan(d*x+c))^2,x, algorithm=""giac"")","-\frac{16 \, d x + 16 \, c + \frac{10 \, {\left(15 \, \tan\left(d x + c\right) + 26\right)}}{5 \, \tan\left(d x + c\right) + 3} + 15 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 30 \, \log\left({\left| 5 \, \tan\left(d x + c\right) + 3 \right|}\right)}{1156 \, d}"," ",0,"-1/1156*(16*d*x + 16*c + 10*(15*tan(d*x + c) + 26)/(5*tan(d*x + c) + 3) + 15*log(tan(d*x + c)^2 + 1) - 30*log(abs(5*tan(d*x + c) + 3)))/d","A",0
497,1,74,0,0.551933," ","integrate(1/(3+5*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{198 \, d x + 198 \, c + \frac{5 \, {\left(75 \, \tan\left(d x + c\right)^{2} + 1110 \, \tan\left(d x + c\right) + 1217\right)}}{{\left(5 \, \tan\left(d x + c\right) + 3\right)}^{2}} + 5 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 10 \, \log\left({\left| 5 \, \tan\left(d x + c\right) + 3 \right|}\right)}{39304 \, d}"," ",0,"-1/39304*(198*d*x + 198*c + 5*(75*tan(d*x + c)^2 + 1110*tan(d*x + c) + 1217)/(5*tan(d*x + c) + 3)^2 + 5*log(tan(d*x + c)^2 + 1) - 10*log(abs(5*tan(d*x + c) + 3)))/d","A",0
498,1,84,0,0.695475," ","integrate(1/(3+5*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{483 \, d x + 483 \, c - \frac{25 \, {\left(6600 \, \tan\left(d x + c\right)^{3} + 11625 \, \tan\left(d x + c\right)^{2} + 4221 \, \tan\left(d x + c\right) - 2192\right)}}{{\left(5 \, \tan\left(d x + c\right) + 3\right)}^{3}} - 360 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 720 \, \log\left({\left| 5 \, \tan\left(d x + c\right) + 3 \right|}\right)}{1002252 \, d}"," ",0,"-1/1002252*(483*d*x + 483*c - 25*(6600*tan(d*x + c)^3 + 11625*tan(d*x + c)^2 + 4221*tan(d*x + c) - 2192)/(5*tan(d*x + c) + 3)^3 - 360*log(tan(d*x + c)^2 + 1) + 720*log(abs(5*tan(d*x + c) + 3)))/d","A",0
499,1,40,0,0.410720," ","integrate(1/(5+3*tan(d*x+c)),x, algorithm=""giac"")","\frac{10 \, d x + 10 \, c - 3 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, \log\left({\left| 3 \, \tan\left(d x + c\right) + 5 \right|}\right)}{68 \, d}"," ",0,"1/68*(10*d*x + 10*c - 3*log(tan(d*x + c)^2 + 1) + 6*log(abs(3*tan(d*x + c) + 5)))/d","A",0
500,1,64,0,0.509485," ","integrate(1/(5+3*tan(d*x+c))^2,x, algorithm=""giac"")","\frac{16 \, d x + 16 \, c - \frac{18 \, {\left(5 \, \tan\left(d x + c\right) + 14\right)}}{3 \, \tan\left(d x + c\right) + 5} - 15 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 30 \, \log\left({\left| 3 \, \tan\left(d x + c\right) + 5 \right|}\right)}{1156 \, d}"," ",0,"1/1156*(16*d*x + 16*c - 18*(5*tan(d*x + c) + 14)/(3*tan(d*x + c) + 5) - 15*log(tan(d*x + c)^2 + 1) + 30*log(abs(3*tan(d*x + c) + 5)))/d","A",0
501,1,74,0,0.606947," ","integrate(1/(5+3*tan(d*x+c))^3,x, algorithm=""giac"")","-\frac{10 \, d x + 10 \, c + \frac{3 \, {\left(891 \, \tan\left(d x + c\right)^{2} + 3990 \, \tan\left(d x + c\right) + 4753\right)}}{{\left(3 \, \tan\left(d x + c\right) + 5\right)}^{2}} + 99 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 198 \, \log\left({\left| 3 \, \tan\left(d x + c\right) + 5 \right|}\right)}{39304 \, d}"," ",0,"-1/39304*(10*d*x + 10*c + 3*(891*tan(d*x + c)^2 + 3990*tan(d*x + c) + 4753)/(3*tan(d*x + c) + 5)^2 + 99*log(tan(d*x + c)^2 + 1) - 198*log(abs(3*tan(d*x + c) + 5)))/d","A",0
502,1,83,0,0.725377," ","integrate(1/(5+3*tan(d*x+c))^4,x, algorithm=""giac"")","-\frac{161 \, d x + 161 \, c + \frac{11880 \, \tan\left(d x + c\right)^{3} + 74547 \, \tan\left(d x + c\right)^{2} + 162495 \, \tan\left(d x + c\right) + 128576}{{\left(3 \, \tan\left(d x + c\right) + 5\right)}^{3}} + 120 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 240 \, \log\left({\left| 3 \, \tan\left(d x + c\right) + 5 \right|}\right)}{334084 \, d}"," ",0,"-1/334084*(161*d*x + 161*c + (11880*tan(d*x + c)^3 + 74547*tan(d*x + c)^2 + 162495*tan(d*x + c) + 128576)/(3*tan(d*x + c) + 5)^3 + 120*log(tan(d*x + c)^2 + 1) - 240*log(abs(3*tan(d*x + c) + 5)))/d","A",0
503,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
513,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
514,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
522,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
523,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
526,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,-1,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,-1,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
533,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
534,-1,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
535,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
536,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-1,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,-1,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
547,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
556,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
557,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/sqrt(tan(d*x + c)), x)","F",0
559,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/tan(d*x + c)^(3/2), x)","F",0
560,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/tan(d*x + c)^(5/2), x)","F",0
561,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/tan(d*x + c)^(7/2), x)","F",0
562,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/sqrt(tan(d*x + c)), x)","F",0
566,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/tan(d*x + c)^(3/2), x)","F",0
567,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/tan(d*x + c)^(5/2), x)","F",0
568,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/tan(d*x + c)^(7/2), x)","F",0
569,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/sqrt(tan(d*x + c)), x)","F",0
573,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/tan(d*x + c)^(3/2), x)","F",0
574,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/tan(d*x + c)^(5/2), x)","F",0
575,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/tan(d*x + c)^(7/2), x)","F",0
576,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\tan\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/tan(d*x + c)^(9/2), x)","F",0
577,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(11/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\tan\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/tan(d*x + c)^(11/2), x)","F",0
578,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/sqrt(tan(d*x + c)), x)","F",0
579,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/(-tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\sqrt{-\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/sqrt(-tan(d*x + c)), x)","F",0
580,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\sqrt{e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/sqrt(e*tan(d*x + c)), x)","F",0
581,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/(-e*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\sqrt{-e \tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/sqrt(-e*tan(d*x + c)), x)","F",0
582,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(b*tan(d*x + c) + a), x)","F",0
587,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*sqrt(tan(d*x + c))), x)","F",0
588,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*tan(d*x + c)^(3/2)), x)","F",0
589,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*tan(d*x + c)^(5/2)), x)","F",0
590,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*tan(d*x + c)^(7/2)), x)","F",0
591,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
592,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*sqrt(tan(d*x + c))), x)","F",0
597,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*tan(d*x + c)^(3/2)), x)","F",0
598,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*tan(d*x + c)^(5/2)), x)","F",0
599,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(11/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*sqrt(tan(d*x + c))), x)","F",0
606,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*tan(d*x + c)^(3/2)), x)","F",0
607,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*tan(d*x + c)^(5/2)), x)","F",0
608,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
609,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
626,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
627,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
628,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
629,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
636,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
637,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
647,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
655,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, \tan\left(d x + c\right) + 2} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*tan(d*x + c) + 2)*sqrt(tan(d*x + c))), x)","F",0
656,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, \tan\left(d x + c\right) - 2} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(3*tan(d*x + c) - 2)*sqrt(tan(d*x + c))), x)","F",0
657,0,0,0,0.000000," ","integrate(1/(2-3*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, \tan\left(d x + c\right) + 2} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*tan(d*x + c) + 2)*sqrt(tan(d*x + c))), x)","F",0
658,0,0,0,0.000000," ","integrate(1/(-2-3*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-3 \, \tan\left(d x + c\right) - 2} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-3*tan(d*x + c) - 2)*sqrt(tan(d*x + c))), x)","F",0
659,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, \tan\left(d x + c\right) + 3} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*tan(d*x + c) + 3)*sqrt(tan(d*x + c))), x)","F",0
660,0,0,0,0.000000," ","integrate(1/(3-2*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, \tan\left(d x + c\right) + 3} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*tan(d*x + c) + 3)*sqrt(tan(d*x + c))), x)","F",0
661,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, \tan\left(d x + c\right) - 3} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(2*tan(d*x + c) - 3)*sqrt(tan(d*x + c))), x)","F",0
662,0,0,0,0.000000," ","integrate(1/(-3-2*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-2 \, \tan\left(d x + c\right) - 3} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(-2*tan(d*x + c) - 3)*sqrt(tan(d*x + c))), x)","F",0
663,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
665,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(2-3*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
666,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-2-3*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
667,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
668,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(3-2*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
669,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
670,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-3-2*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
671,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{3}}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/3)/(b*tan(d*x + c) + a), x)","F",0
672,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\tan\left(d x + c\right)^{\frac{1}{3}}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(tan(d*x + c)^(1/3)/(b*tan(d*x + c) + a), x)","F",0
673,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*tan(d*x + c)^(1/3)), x)","F",0
674,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*tan(d*x + c)^(5/3)), x)","F",0
675,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
680,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
681,-1,0,0,0.000000," ","integrate(tan(f*x+e)^4*(c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
682,-1,0,0,0.000000," ","integrate(tan(f*x+e)^3*(c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
683,0,0,0,0.000000," ","integrate(tan(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
684,1,18,0,13.786663," ","integrate(tan(f*x+e)*(c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\frac{3 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}}}{f}"," ",0,"3*(d*tan(f*x + e) + c)^(1/3)/f","A",0
685,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
686,0,0,0,0.000000," ","integrate(cot(f*x+e)*(c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}} \cot\left(f x + e\right)\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3)*cot(f*x + e), x)","F",0
687,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x, algorithm=""giac"")","\mathit{undef}"," ",0,"undef","F",0
688,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/3),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/3), x)","F",0
689,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(4/3), x)","F",0
690,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(2/3),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(2/3), x)","F",0
691,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(1/3), x)","F",0
692,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(-1/3), x)","F",0
693,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(2/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(-2/3), x)","F",0
694,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(4/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(-4/3), x)","F",0
695,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(5/3),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(-5/3), x)","F",0
696,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^4,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{4} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^4*(d*tan(f*x + e))^n, x)","F",0
697,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*(d*tan(f*x + e))^n, x)","F",0
698,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*tan(f*x + e))^n, x)","F",0
699,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*(d*tan(f*x + e))^n, x)","F",0
700,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(b*tan(f*x + e) + a), x)","F",0
701,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \tan\left(f x + e\right)\right)^{n}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*tan(f*x + e))^n/(b*tan(f*x + e) + a)^2, x)","F",0
702,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
703,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
704,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{m} \left(d \tan\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m*(d*tan(f*x + e))^n, x)","F",0
707,0,0,0,0.000000," ","integrate(tan(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} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
708,0,0,0,0.000000," ","integrate(tan(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} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
709,0,0,0,0.000000," ","integrate(tan(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} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
710,0,0,0,0.000000," ","integrate(tan(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} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*tan(d*x + c), x)","F",0
711,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n, x)","F",0
712,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cot(d*x + c), x)","F",0
713,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
714,0,0,0,0.000000," ","integrate(cot(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} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
715,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
717,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n/tan(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
718,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n/tan(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n/tan(d*x + c)^(3/2), x)","F",0
719,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*cot(d*x + c)^(5/2), x)","F",0
720,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*cot(d*x + c)^(3/2), x)","F",0
721,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)*sqrt(cot(d*x + c)), x)","F",0
722,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/sqrt(cot(d*x + c)), x)","F",0
723,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(d x + c\right) + a}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)/cot(d*x + c)^(3/2), x)","F",0
724,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*cot(d*x + c)^(7/2), x)","F",0
725,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*cot(d*x + c)^(5/2), x)","F",0
726,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*cot(d*x + c)^(3/2), x)","F",0
727,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2*sqrt(cot(d*x + c)), x)","F",0
728,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/sqrt(cot(d*x + c)), x)","F",0
729,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^2/cot(d*x + c)^(3/2), x)","F",0
730,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3*cot(d*x + c)^(7/2), x)","F",0
731,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3*cot(d*x + c)^(5/2), x)","F",0
732,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3*cot(d*x + c)^(3/2), x)","F",0
733,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3*sqrt(cot(d*x + c)), x)","F",0
734,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^3/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^3/sqrt(cot(d*x + c)), x)","F",0
735,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(I*a*tan(d*x + c) + a), x)","F",0
736,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{i \, a \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(I*a*tan(d*x + c) + a), x)","F",0
737,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)*sqrt(cot(d*x + c))), x)","F",0
738,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)*cot(d*x + c)^(3/2)), x)","F",0
739,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""giac"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> An error occurred running a Giac command:INPUT:sage2OUTPUT: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)Not invertible Error: Bad Argument ValueUnable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*t_nostep+c))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of sin(d*t_nostep+c) were not checkedEvaluation time: 2.39integrate((a*tan(d*x+c)*i+a)^-1*(sqrt(cos(d*x+c)/sin(d*x+c)))^-1*(cos(d*x+c)/sin(d*x+c))^-2,x)","F(-2)",0
740,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(I*a*tan(d*x + c) + a)^2, x)","F",0
741,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(I*a*tan(d*x + c) + a)^2, x)","F",0
742,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*sqrt(cot(d*x + c))), x)","F",0
743,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*cot(d*x + c)^(3/2)), x)","F",0
744,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*cot(d*x + c)^(5/2)), x)","F",0
745,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^2*cot(d*x + c)^(7/2)), x)","F",0
746,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(I*a*tan(d*x + c) + a)^3, x)","F",0
747,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^3*sqrt(cot(d*x + c))), x)","F",0
748,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^3*cot(d*x + c)^(3/2)), x)","F",0
749,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^3*cot(d*x + c)^(5/2)), x)","F",0
750,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^3*cot(d*x + c)^(7/2)), x)","F",0
751,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^(7/2), x)","F",0
752,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^(5/2), x)","F",0
753,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^(3/2), x)","F",0
754,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*sqrt(cot(d*x + c)), x)","F",0
755,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/sqrt(cot(d*x + c)), x)","F",0
756,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/cot(d*x + c)^(3/2), x)","F",0
757,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(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}} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(7/2), x)","F",0
758,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(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}} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(5/2), x)","F",0
759,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(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}} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(3/2), x)","F",0
760,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(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}} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c)), x)","F",0
761,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(3/2)/sqrt(cot(d*x + c)), x)","F",0
762,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(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}} \cot\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(9/2), x)","F",0
763,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(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}} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(7/2), x)","F",0
764,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(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}} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(5/2), x)","F",0
765,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(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}} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(3/2), x)","F",0
766,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(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}} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)*sqrt(cot(d*x + c)), x)","F",0
767,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^(5/2)/sqrt(cot(d*x + c)), x)","F",0
768,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
769,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/sqrt(I*a*tan(d*x + c) + a), x)","F",0
770,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/sqrt(I*a*tan(d*x + c) + a), x)","F",0
771,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*sqrt(cot(d*x + c))), x)","F",0
772,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^(3/2)), x)","F",0
773,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(d*x + c) + a)*cot(d*x + c)^(5/2)), x)","F",0
774,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
775,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
776,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(I*a*tan(d*x + c) + a)^(3/2), x)","F",0
777,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c))), x)","F",0
778,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(3/2)), x)","F",0
779,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(5/2)), x)","F",0
780,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(7/2)), x)","F",0
781,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
782,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
783,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(I*a*tan(d*x + c) + a)^(5/2), x)","F",0
784,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*sqrt(cot(d*x + c))), x)","F",0
785,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(3/2)), x)","F",0
786,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(5/2)), x)","F",0
787,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(7/2)), x)","F",0
788,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} \left(d \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(d*cot(f*x + e))^n, x)","F",0
789,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} \left(d \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(d*cot(f*x + e))^n, x)","F",0
790,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)} \left(d \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)*(d*cot(f*x + e))^n, x)","F",0
791,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \cot\left(f x + e\right)\right)^{n}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n/(I*a*tan(f*x + e) + a), x)","F",0
792,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \cot\left(f x + e\right)\right)^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n/(I*a*tan(f*x + e) + a)^2, x)","F",0
793,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""giac"")","\int \left(d \cot\left(f x + e\right)\right)^{n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*(I*a*tan(f*x + e) + a)^m, x)","F",0
794,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*cot(d*x + c)^(3/2), x)","F",0
795,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
796,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/sqrt(cot(d*x + c)), x)","F",0
797,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(d*x + c) + a)^n/cot(d*x + c)^(3/2), x)","F",0
798,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)*cot(d*x + c)^(7/2), x)","F",0
799,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)*cot(d*x + c)^(5/2), x)","F",0
800,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)*cot(d*x + c)^(3/2), x)","F",0
801,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)*sqrt(cot(d*x + c)), x)","F",0
802,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/sqrt(cot(d*x + c)), x)","F",0
803,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/cot(d*x + c)^(3/2), x)","F",0
804,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{b \tan\left(d x + c\right) + a}{\cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)/cot(d*x + c)^(5/2), x)","F",0
805,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*cot(d*x + c)^(9/2), x)","F",0
806,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*cot(d*x + c)^(7/2), x)","F",0
807,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*cot(d*x + c)^(5/2), x)","F",0
808,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*cot(d*x + c)^(3/2), x)","F",0
809,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{2} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2*sqrt(cot(d*x + c)), x)","F",0
810,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/sqrt(cot(d*x + c)), x)","F",0
811,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/cot(d*x + c)^(3/2), x)","F",0
812,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}{\cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^2/cot(d*x + c)^(5/2), x)","F",0
813,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*cot(d*x + c)^(9/2), x)","F",0
814,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*cot(d*x + c)^(7/2), x)","F",0
815,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*cot(d*x + c)^(5/2), x)","F",0
816,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*cot(d*x + c)^(3/2), x)","F",0
817,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{3} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3*sqrt(cot(d*x + c)), x)","F",0
818,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/sqrt(cot(d*x + c)), x)","F",0
819,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^3/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^3/cot(d*x + c)^(3/2), x)","F",0
820,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a), x)","F",0
821,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a), x)","F",0
822,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(b*tan(d*x + c) + a), x)","F",0
823,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*sqrt(cot(d*x + c))), x)","F",0
824,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*cot(d*x + c)^(3/2)), x)","F",0
825,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)*cot(d*x + c)^(5/2)), x)","F",0
826,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^2, x)","F",0
827,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^2, x)","F",0
828,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^2, x)","F",0
829,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*sqrt(cot(d*x + c))), x)","F",0
830,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*cot(d*x + c)^(3/2)), x)","F",0
831,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*cot(d*x + c)^(5/2)), x)","F",0
832,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{2} \cot\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^2*cot(d*x + c)^(7/2)), x)","F",0
833,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^3, x)","F",0
834,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^3, x)","F",0
835,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^3, x)","F",0
836,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*sqrt(cot(d*x + c))), x)","F",0
837,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*cot(d*x + c)^(3/2)), x)","F",0
838,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*cot(d*x + c)^(5/2)), x)","F",0
839,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{3} \cot\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^3*cot(d*x + c)^(7/2)), x)","F",0
840,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
843,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
845,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
846,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
863,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
869,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:Warning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*x+c))]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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)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)Unable to check sign: (2*pi/t_nostep/2)>(-2*pi/t_nostep/2)Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d]=[-33,-35]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d]=[-95,41]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedDiscontinuities at zeroes of sin(d*x+c) were not checkedEvaluation time: 52.03Done","F(-2)",0
875,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),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/x/2)>(-2*pi/x/2)Unable to check sign: (2*pi/x/2)>(-2*pi/x/2)Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d]=[-59,63]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d]=[74,98]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*t_nostep+c))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of sin(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep),abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedEvaluation time: 47.13Done","F(-2)",0
878,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),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/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)Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d]=[-59,63]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [d]=[74,98]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(sin(d*t_nostep+c))]Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Unable to check sign: (4*pi/t_nostep/2)>(-4*pi/t_nostep/2)Discontinuities at zeroes of sin(d*t_nostep+c) were not checkedWarning, integration of abs or sign assumes constant sign by intervals (correct if the argument is real):Check [abs(t_nostep),abs(t_nostep^2-1)]Discontinuities at zeroes of t_nostep^2-1 were not checkedEvaluation time: 41.96Done","F(-2)",0
879,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(d \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*(d*cot(f*x + e))^n, x)","F",0
881,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(d \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*cot(f*x + e))^n, x)","F",0
882,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(d \cot\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*(d*cot(f*x + e))^n, x)","F",0
883,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(d \cot\left(f x + e\right)\right)^{n}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n/(b*tan(f*x + e) + a), x)","F",0
884,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(d \cot\left(f x + e\right)\right)^{n}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n/(b*tan(f*x + e) + a)^2, x)","F",0
885,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^m,x, algorithm=""giac"")","\int \left(d \cot\left(f x + e\right)\right)^{n} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*cot(f*x + e))^n*(b*tan(f*x + e) + a)^m, x)","F",0
886,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*cot(d*x + c)^(3/2), x)","F",0
887,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{n} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
888,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n/cot(d*x+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n/sqrt(cot(d*x + c)), x)","F",0
889,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n/cot(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{n}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^n/cot(d*x + c)^(3/2), x)","F",0
890,1,83,0,0.804902," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\frac{24 i \, a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} + 24 i \, a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{3} c}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(24*I*a^3*c*e^(4*I*f*x + 4*I*e) + 24*I*a^3*c*e^(2*I*f*x + 2*I*e) + 8*I*a^3*c)/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
891,1,53,0,0.783318," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\frac{4 i \, a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} + 2 i \, a^{2} c}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"(4*I*a^2*c*e^(2*I*f*x + 2*I*e) + 2*I*a^2*c)/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
892,1,13,0,0.413608," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\frac{a c \tan\left(f x + e\right)}{f}"," ",0,"a*c*tan(f*x + e)/f","A",0
893,1,33,0,0.609492," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{a f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{2}}"," ",0,"-2*c*tan(1/2*f*x + 1/2*e)/(a*f*(tan(1/2*f*x + 1/2*e) - I)^2)","A",0
894,1,65,0,0.730062," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - i \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{a^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{4}}"," ",0,"-2*(c*tan(1/2*f*x + 1/2*e)^3 - I*c*tan(1/2*f*x + 1/2*e)^2 - c*tan(1/2*f*x + 1/2*e))/(a^2*f*(tan(1/2*f*x + 1/2*e) - I)^4)","B",0
895,1,96,0,1.114932," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 6 i \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 10 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 i \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{6}}"," ",0,"-2/3*(3*c*tan(1/2*f*x + 1/2*e)^5 - 6*I*c*tan(1/2*f*x + 1/2*e)^4 - 10*c*tan(1/2*f*x + 1/2*e)^3 + 6*I*c*tan(1/2*f*x + 1/2*e)^2 + 3*c*tan(1/2*f*x + 1/2*e))/(a^3*f*(tan(1/2*f*x + 1/2*e) - I)^6)","B",0
896,1,133,0,1.290795," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{80 i \, a^{4} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 80 i \, a^{4} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 40 i \, a^{4} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{4} c^{2}}{5 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/5*(80*I*a^4*c^2*e^(6*I*f*x + 6*I*e) + 80*I*a^4*c^2*e^(4*I*f*x + 4*I*e) + 40*I*a^4*c^2*e^(2*I*f*x + 2*I*e) + 8*I*a^4*c^2)/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","B",0
897,1,102,0,1.118482," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{24 i \, a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 16 i \, a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{3} c^{2}}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(24*I*a^3*c^2*e^(4*I*f*x + 4*I*e) + 16*I*a^3*c^2*e^(2*I*f*x + 2*I*e) + 4*I*a^3*c^2)/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","A",0
898,1,166,0,0.927366," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{3 \, a^{2} c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 3 \, a^{2} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + a^{2} c^{2} \tan\left(f x\right)^{3} - 3 \, a^{2} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 3 \, a^{2} c^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + a^{2} c^{2} \tan\left(e\right)^{3} + 3 \, a^{2} c^{2} \tan\left(f x\right) + 3 \, a^{2} c^{2} \tan\left(e\right)}{3 \, {\left(f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"-1/3*(3*a^2*c^2*tan(f*x)^3*tan(e)^2 + 3*a^2*c^2*tan(f*x)^2*tan(e)^3 + a^2*c^2*tan(f*x)^3 - 3*a^2*c^2*tan(f*x)^2*tan(e) - 3*a^2*c^2*tan(f*x)*tan(e)^2 + a^2*c^2*tan(e)^3 + 3*a^2*c^2*tan(f*x) + 3*a^2*c^2*tan(e))/(f*tan(f*x)^3*tan(e)^3 - 3*f*tan(f*x)^2*tan(e)^2 + 3*f*tan(f*x)*tan(e) - f)","B",0
899,1,35,0,0.856960," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{2 i \, a c^{2}}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"2*I*a*c^2/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","A",0
900,1,125,0,0.871072," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{i \, c^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{a} - \frac{2 i \, c^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}{a} + \frac{i \, c^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{a} + \frac{3 i \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 10 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 i \, c^{2}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{2}}}{f}"," ",0,"-(I*c^2*log(tan(1/2*f*x + 1/2*e) + 1)/a - 2*I*c^2*log(tan(1/2*f*x + 1/2*e) - I)/a + I*c^2*log(tan(1/2*f*x + 1/2*e) - 1)/a + (3*I*c^2*tan(1/2*f*x + 1/2*e)^2 + 10*c^2*tan(1/2*f*x + 1/2*e) - 3*I*c^2)/(a*(tan(1/2*f*x + 1/2*e) - I)^2))/f","B",0
901,1,54,0,1.217583," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{a^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{4}}"," ",0,"-2*(c^2*tan(1/2*f*x + 1/2*e)^3 - c^2*tan(1/2*f*x + 1/2*e))/(a^2*f*(tan(1/2*f*x + 1/2*e) - I)^4)","B",0
902,1,106,0,1.334285," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 3 i \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 8 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 i \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{6}}"," ",0,"-2/3*(3*c^2*tan(1/2*f*x + 1/2*e)^5 - 3*I*c^2*tan(1/2*f*x + 1/2*e)^4 - 8*c^2*tan(1/2*f*x + 1/2*e)^3 + 3*I*c^2*tan(1/2*f*x + 1/2*e)^2 + 3*c^2*tan(1/2*f*x + 1/2*e))/(a^3*f*(tan(1/2*f*x + 1/2*e) - I)^6)","B",0
903,1,140,0,1.621409," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 6 i \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 17 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 16 i \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 17 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 i \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, a^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{8}}"," ",0,"-2/3*(3*c^2*tan(1/2*f*x + 1/2*e)^7 - 6*I*c^2*tan(1/2*f*x + 1/2*e)^6 - 17*c^2*tan(1/2*f*x + 1/2*e)^5 + 16*I*c^2*tan(1/2*f*x + 1/2*e)^4 + 17*c^2*tan(1/2*f*x + 1/2*e)^3 - 6*I*c^2*tan(1/2*f*x + 1/2*e)^2 - 3*c^2*tan(1/2*f*x + 1/2*e))/(a^4*f*(tan(1/2*f*x + 1/2*e) - I)^8)","B",0
904,1,177,0,1.944426," ","integrate((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{4480 i \, a^{5} c^{3} e^{\left(8 i \, f x + 8 i \, e\right)} + 4480 i \, a^{5} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 2688 i \, a^{5} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 896 i \, a^{5} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 128 i \, a^{5} c^{3}}{105 \, {\left(f e^{\left(14 i \, f x + 14 i \, e\right)} + 7 \, f e^{\left(12 i \, f x + 12 i \, e\right)} + 21 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 35 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 35 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 21 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 7 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/105*(4480*I*a^5*c^3*e^(8*I*f*x + 8*I*e) + 4480*I*a^5*c^3*e^(6*I*f*x + 6*I*e) + 2688*I*a^5*c^3*e^(4*I*f*x + 4*I*e) + 896*I*a^5*c^3*e^(2*I*f*x + 2*I*e) + 128*I*a^5*c^3)/(f*e^(14*I*f*x + 14*I*e) + 7*f*e^(12*I*f*x + 12*I*e) + 21*f*e^(10*I*f*x + 10*I*e) + 35*f*e^(8*I*f*x + 8*I*e) + 35*f*e^(6*I*f*x + 6*I*e) + 21*f*e^(4*I*f*x + 4*I*e) + 7*f*e^(2*I*f*x + 2*I*e) + f)","B",0
905,1,146,0,1.461369," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{320 i \, a^{4} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} + 240 i \, a^{4} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, a^{4} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{4} c^{3}}{15 \, {\left(f e^{\left(12 i \, f x + 12 i \, e\right)} + 6 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 15 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 20 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 15 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 6 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(320*I*a^4*c^3*e^(6*I*f*x + 6*I*e) + 240*I*a^4*c^3*e^(4*I*f*x + 4*I*e) + 96*I*a^4*c^3*e^(2*I*f*x + 2*I*e) + 16*I*a^4*c^3)/(f*e^(12*I*f*x + 12*I*e) + 6*f*e^(10*I*f*x + 10*I*e) + 15*f*e^(8*I*f*x + 8*I*e) + 20*f*e^(6*I*f*x + 6*I*e) + 15*f*e^(4*I*f*x + 4*I*e) + 6*f*e^(2*I*f*x + 2*I*e) + f)","A",0
906,1,371,0,5.069873," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{15 \, a^{3} c^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} + 15 \, a^{3} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} + 10 \, a^{3} c^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{2} - 30 \, a^{3} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 30 \, a^{3} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 10 \, a^{3} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{5} + 3 \, a^{3} c^{3} \tan\left(f x\right)^{5} - 5 \, a^{3} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right) + 60 \, a^{3} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 60 \, a^{3} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 5 \, a^{3} c^{3} \tan\left(f x\right) \tan\left(e\right)^{4} + 3 \, a^{3} c^{3} \tan\left(e\right)^{5} + 10 \, a^{3} c^{3} \tan\left(f x\right)^{3} - 30 \, a^{3} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right) - 30 \, a^{3} c^{3} \tan\left(f x\right) \tan\left(e\right)^{2} + 10 \, a^{3} c^{3} \tan\left(e\right)^{3} + 15 \, a^{3} c^{3} \tan\left(f x\right) + 15 \, a^{3} c^{3} \tan\left(e\right)}{15 \, {\left(f \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 5 \, f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 10 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 10 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 5 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"-1/15*(15*a^3*c^3*tan(f*x)^5*tan(e)^4 + 15*a^3*c^3*tan(f*x)^4*tan(e)^5 + 10*a^3*c^3*tan(f*x)^5*tan(e)^2 - 30*a^3*c^3*tan(f*x)^4*tan(e)^3 - 30*a^3*c^3*tan(f*x)^3*tan(e)^4 + 10*a^3*c^3*tan(f*x)^2*tan(e)^5 + 3*a^3*c^3*tan(f*x)^5 - 5*a^3*c^3*tan(f*x)^4*tan(e) + 60*a^3*c^3*tan(f*x)^3*tan(e)^2 + 60*a^3*c^3*tan(f*x)^2*tan(e)^3 - 5*a^3*c^3*tan(f*x)*tan(e)^4 + 3*a^3*c^3*tan(e)^5 + 10*a^3*c^3*tan(f*x)^3 - 30*a^3*c^3*tan(f*x)^2*tan(e) - 30*a^3*c^3*tan(f*x)*tan(e)^2 + 10*a^3*c^3*tan(e)^3 + 15*a^3*c^3*tan(f*x) + 15*a^3*c^3*tan(e))/(f*tan(f*x)^5*tan(e)^5 - 5*f*tan(f*x)^4*tan(e)^4 + 10*f*tan(f*x)^3*tan(e)^3 - 10*f*tan(f*x)^2*tan(e)^2 + 5*f*tan(f*x)*tan(e) - f)","B",0
907,1,84,0,0.994291," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{16 i \, a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a^{2} c^{3}}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(16*I*a^2*c^3*e^(2*I*f*x + 2*I*e) + 4*I*a^2*c^3)/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","A",0
908,1,48,0,0.967725," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{8 i \, a c^{3}}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"8/3*I*a*c^3/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
909,1,183,0,1.097082," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(-\frac{2 i \, c^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{a} + \frac{4 i \, c^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}{a} - \frac{2 i \, c^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{a} + \frac{2 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 i \, c^{3}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} a} + \frac{-6 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 16 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 i \, c^{3}}{a {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{2}}\right)}}{f}"," ",0,"2*(-2*I*c^3*log(tan(1/2*f*x + 1/2*e) + 1)/a + 4*I*c^3*log(tan(1/2*f*x + 1/2*e) - I)/a - 2*I*c^3*log(tan(1/2*f*x + 1/2*e) - 1)/a + (2*I*c^3*tan(1/2*f*x + 1/2*e)^2 - c^3*tan(1/2*f*x + 1/2*e) - 2*I*c^3)/((tan(1/2*f*x + 1/2*e)^2 - 1)*a) + (-6*I*c^3*tan(1/2*f*x + 1/2*e)^2 - 16*c^3*tan(1/2*f*x + 1/2*e) + 6*I*c^3)/(a*(tan(1/2*f*x + 1/2*e) - I)^2))/f","B",0
910,1,159,0,1.319907," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{-\frac{6 i \, c^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{a^{2}} + \frac{12 i \, c^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}{a^{2}} - \frac{6 i \, c^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{a^{2}} + \frac{-25 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 100 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 198 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 100 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 25 i \, c^{3}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{4}}}{6 \, f}"," ",0,"-1/6*(-6*I*c^3*log(tan(1/2*f*x + 1/2*e) + 1)/a^2 + 12*I*c^3*log(tan(1/2*f*x + 1/2*e) - I)/a^2 - 6*I*c^3*log(tan(1/2*f*x + 1/2*e) - 1)/a^2 + (-25*I*c^3*tan(1/2*f*x + 1/2*e)^4 - 100*c^3*tan(1/2*f*x + 1/2*e)^3 + 198*I*c^3*tan(1/2*f*x + 1/2*e)^2 + 100*c^3*tan(1/2*f*x + 1/2*e) - 25*I*c^3)/(a^2*(tan(1/2*f*x + 1/2*e) - I)^4))/f","B",0
911,1,72,0,1.547455," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 10 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, a^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{6}}"," ",0,"-2/3*(3*c^3*tan(1/2*f*x + 1/2*e)^5 - 10*c^3*tan(1/2*f*x + 1/2*e)^3 + 3*c^3*tan(1/2*f*x + 1/2*e))/(a^3*f*(tan(1/2*f*x + 1/2*e) - I)^6)","A",0
912,1,140,0,1.948727," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 3 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 17 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 10 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 17 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, a^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{8}}"," ",0,"-2/3*(3*c^3*tan(1/2*f*x + 1/2*e)^7 - 3*I*c^3*tan(1/2*f*x + 1/2*e)^6 - 17*c^3*tan(1/2*f*x + 1/2*e)^5 + 10*I*c^3*tan(1/2*f*x + 1/2*e)^4 + 17*c^3*tan(1/2*f*x + 1/2*e)^3 - 3*I*c^3*tan(1/2*f*x + 1/2*e)^2 - 3*c^3*tan(1/2*f*x + 1/2*e))/(a^4*f*(tan(1/2*f*x + 1/2*e) - I)^8)","A",0
913,1,174,0,2.730648," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(15 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} - 30 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 140 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 170 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 282 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 170 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 140 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 30 i \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 15 \, c^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{15 \, a^{5} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{10}}"," ",0,"-2/15*(15*c^3*tan(1/2*f*x + 1/2*e)^9 - 30*I*c^3*tan(1/2*f*x + 1/2*e)^8 - 140*c^3*tan(1/2*f*x + 1/2*e)^7 + 170*I*c^3*tan(1/2*f*x + 1/2*e)^6 + 282*c^3*tan(1/2*f*x + 1/2*e)^5 - 170*I*c^3*tan(1/2*f*x + 1/2*e)^4 - 140*c^3*tan(1/2*f*x + 1/2*e)^3 + 30*I*c^3*tan(1/2*f*x + 1/2*e)^2 + 15*c^3*tan(1/2*f*x + 1/2*e))/(a^5*f*(tan(1/2*f*x + 1/2*e) - I)^10)","B",0
914,1,190,0,2.089203," ","integrate((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","\frac{2240 i \, a^{5} c^{4} e^{\left(8 i \, f x + 8 i \, e\right)} + 1792 i \, a^{5} c^{4} e^{\left(6 i \, f x + 6 i \, e\right)} + 896 i \, a^{5} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 256 i \, a^{5} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 32 i \, a^{5} c^{4}}{35 \, {\left(f e^{\left(16 i \, f x + 16 i \, e\right)} + 8 \, f e^{\left(14 i \, f x + 14 i \, e\right)} + 28 \, f e^{\left(12 i \, f x + 12 i \, e\right)} + 56 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 70 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 56 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 28 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 8 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/35*(2240*I*a^5*c^4*e^(8*I*f*x + 8*I*e) + 1792*I*a^5*c^4*e^(6*I*f*x + 6*I*e) + 896*I*a^5*c^4*e^(4*I*f*x + 4*I*e) + 256*I*a^5*c^4*e^(2*I*f*x + 2*I*e) + 32*I*a^5*c^4)/(f*e^(16*I*f*x + 16*I*e) + 8*f*e^(14*I*f*x + 14*I*e) + 28*f*e^(12*I*f*x + 12*I*e) + 56*f*e^(10*I*f*x + 10*I*e) + 70*f*e^(8*I*f*x + 8*I*e) + 56*f*e^(6*I*f*x + 6*I*e) + 28*f*e^(4*I*f*x + 4*I*e) + 8*f*e^(2*I*f*x + 2*I*e) + f)","B",0
915,1,650,0,25.026308," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{35 \, a^{4} c^{4} \tan\left(f x\right)^{7} \tan\left(e\right)^{6} + 35 \, a^{4} c^{4} \tan\left(f x\right)^{6} \tan\left(e\right)^{7} + 35 \, a^{4} c^{4} \tan\left(f x\right)^{7} \tan\left(e\right)^{4} - 105 \, a^{4} c^{4} \tan\left(f x\right)^{6} \tan\left(e\right)^{5} - 105 \, a^{4} c^{4} \tan\left(f x\right)^{5} \tan\left(e\right)^{6} + 35 \, a^{4} c^{4} \tan\left(f x\right)^{4} \tan\left(e\right)^{7} + 21 \, a^{4} c^{4} \tan\left(f x\right)^{7} \tan\left(e\right)^{2} - 35 \, a^{4} c^{4} \tan\left(f x\right)^{6} \tan\left(e\right)^{3} + 315 \, a^{4} c^{4} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} + 315 \, a^{4} c^{4} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} - 35 \, a^{4} c^{4} \tan\left(f x\right)^{3} \tan\left(e\right)^{6} + 21 \, a^{4} c^{4} \tan\left(f x\right)^{2} \tan\left(e\right)^{7} + 5 \, a^{4} c^{4} \tan\left(f x\right)^{7} - 7 \, a^{4} c^{4} \tan\left(f x\right)^{6} \tan\left(e\right) + 105 \, a^{4} c^{4} \tan\left(f x\right)^{5} \tan\left(e\right)^{2} - 315 \, a^{4} c^{4} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 315 \, a^{4} c^{4} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 105 \, a^{4} c^{4} \tan\left(f x\right)^{2} \tan\left(e\right)^{5} - 7 \, a^{4} c^{4} \tan\left(f x\right) \tan\left(e\right)^{6} + 5 \, a^{4} c^{4} \tan\left(e\right)^{7} + 21 \, a^{4} c^{4} \tan\left(f x\right)^{5} - 35 \, a^{4} c^{4} \tan\left(f x\right)^{4} \tan\left(e\right) + 315 \, a^{4} c^{4} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 315 \, a^{4} c^{4} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 35 \, a^{4} c^{4} \tan\left(f x\right) \tan\left(e\right)^{4} + 21 \, a^{4} c^{4} \tan\left(e\right)^{5} + 35 \, a^{4} c^{4} \tan\left(f x\right)^{3} - 105 \, a^{4} c^{4} \tan\left(f x\right)^{2} \tan\left(e\right) - 105 \, a^{4} c^{4} \tan\left(f x\right) \tan\left(e\right)^{2} + 35 \, a^{4} c^{4} \tan\left(e\right)^{3} + 35 \, a^{4} c^{4} \tan\left(f x\right) + 35 \, a^{4} c^{4} \tan\left(e\right)}{35 \, {\left(f \tan\left(f x\right)^{7} \tan\left(e\right)^{7} - 7 \, f \tan\left(f x\right)^{6} \tan\left(e\right)^{6} + 21 \, f \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 35 \, f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 35 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 21 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 7 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"-1/35*(35*a^4*c^4*tan(f*x)^7*tan(e)^6 + 35*a^4*c^4*tan(f*x)^6*tan(e)^7 + 35*a^4*c^4*tan(f*x)^7*tan(e)^4 - 105*a^4*c^4*tan(f*x)^6*tan(e)^5 - 105*a^4*c^4*tan(f*x)^5*tan(e)^6 + 35*a^4*c^4*tan(f*x)^4*tan(e)^7 + 21*a^4*c^4*tan(f*x)^7*tan(e)^2 - 35*a^4*c^4*tan(f*x)^6*tan(e)^3 + 315*a^4*c^4*tan(f*x)^5*tan(e)^4 + 315*a^4*c^4*tan(f*x)^4*tan(e)^5 - 35*a^4*c^4*tan(f*x)^3*tan(e)^6 + 21*a^4*c^4*tan(f*x)^2*tan(e)^7 + 5*a^4*c^4*tan(f*x)^7 - 7*a^4*c^4*tan(f*x)^6*tan(e) + 105*a^4*c^4*tan(f*x)^5*tan(e)^2 - 315*a^4*c^4*tan(f*x)^4*tan(e)^3 - 315*a^4*c^4*tan(f*x)^3*tan(e)^4 + 105*a^4*c^4*tan(f*x)^2*tan(e)^5 - 7*a^4*c^4*tan(f*x)*tan(e)^6 + 5*a^4*c^4*tan(e)^7 + 21*a^4*c^4*tan(f*x)^5 - 35*a^4*c^4*tan(f*x)^4*tan(e) + 315*a^4*c^4*tan(f*x)^3*tan(e)^2 + 315*a^4*c^4*tan(f*x)^2*tan(e)^3 - 35*a^4*c^4*tan(f*x)*tan(e)^4 + 21*a^4*c^4*tan(e)^5 + 35*a^4*c^4*tan(f*x)^3 - 105*a^4*c^4*tan(f*x)^2*tan(e) - 105*a^4*c^4*tan(f*x)*tan(e)^2 + 35*a^4*c^4*tan(e)^3 + 35*a^4*c^4*tan(f*x) + 35*a^4*c^4*tan(e))/(f*tan(f*x)^7*tan(e)^7 - 7*f*tan(f*x)^6*tan(e)^6 + 21*f*tan(f*x)^5*tan(e)^5 - 35*f*tan(f*x)^4*tan(e)^4 + 35*f*tan(f*x)^3*tan(e)^3 - 21*f*tan(f*x)^2*tan(e)^2 + 7*f*tan(f*x)*tan(e) - f)","B",0
916,1,128,0,1.490959," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","\frac{240 i \, a^{3} c^{4} e^{\left(4 i \, f x + 4 i \, e\right)} + 96 i \, a^{3} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 16 i \, a^{3} c^{4}}{15 \, {\left(f e^{\left(12 i \, f x + 12 i \, e\right)} + 6 \, f e^{\left(10 i \, f x + 10 i \, e\right)} + 15 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 20 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 15 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 6 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(240*I*a^3*c^4*e^(4*I*f*x + 4*I*e) + 96*I*a^3*c^4*e^(2*I*f*x + 2*I*e) + 16*I*a^3*c^4)/(f*e^(12*I*f*x + 12*I*e) + 6*f*e^(10*I*f*x + 10*I*e) + 15*f*e^(8*I*f*x + 8*I*e) + 20*f*e^(6*I*f*x + 6*I*e) + 15*f*e^(4*I*f*x + 4*I*e) + 6*f*e^(2*I*f*x + 2*I*e) + f)","A",0
917,1,97,0,1.354009," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","\frac{40 i \, a^{2} c^{4} e^{\left(2 i \, f x + 2 i \, e\right)} + 8 i \, a^{2} c^{4}}{5 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/5*(40*I*a^2*c^4*e^(2*I*f*x + 2*I*e) + 8*I*a^2*c^4)/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","B",0
918,1,61,0,1.161289," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","\frac{4 i \, a c^{4}}{f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"4*I*a*c^4/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
919,1,200,0,1.285680," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(-\frac{6 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{a} + \frac{12 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}{a} - \frac{6 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{a} - \frac{13 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 9 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 24 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 9 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 13 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{2} a}\right)}}{f}"," ",0,"2*(-6*I*c^4*log(tan(1/2*f*x + 1/2*e) + 1)/a + 12*I*c^4*log(tan(1/2*f*x + 1/2*e) - I)/a - 6*I*c^4*log(tan(1/2*f*x + 1/2*e) - 1)/a - (13*c^4*tan(1/2*f*x + 1/2*e)^5 - 9*I*c^4*tan(1/2*f*x + 1/2*e)^4 - 24*c^4*tan(1/2*f*x + 1/2*e)^3 + 9*I*c^4*tan(1/2*f*x + 1/2*e)^2 + 13*c^4*tan(1/2*f*x + 1/2*e))/((tan(1/2*f*x + 1/2*e)^3 - I*tan(1/2*f*x + 1/2*e)^2 - tan(1/2*f*x + 1/2*e) + I)^2*a))/f","B",0
920,1,217,0,1.509978," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{-\frac{6 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{a^{2}} + \frac{12 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}{a^{2}} - \frac{6 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{a^{2}} - \frac{2 \, {\left(-3 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 i \, c^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} a^{2}} + \frac{-25 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 108 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 182 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 108 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 25 i \, c^{4}}{a^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{4}}}{f}"," ",0,"-(-6*I*c^4*log(tan(1/2*f*x + 1/2*e) + 1)/a^2 + 12*I*c^4*log(tan(1/2*f*x + 1/2*e) - I)/a^2 - 6*I*c^4*log(tan(1/2*f*x + 1/2*e) - 1)/a^2 - 2*(-3*I*c^4*tan(1/2*f*x + 1/2*e)^2 + c^4*tan(1/2*f*x + 1/2*e) + 3*I*c^4)/((tan(1/2*f*x + 1/2*e)^2 - 1)*a^2) + (-25*I*c^4*tan(1/2*f*x + 1/2*e)^4 - 108*c^4*tan(1/2*f*x + 1/2*e)^3 + 182*I*c^4*tan(1/2*f*x + 1/2*e)^2 + 108*c^4*tan(1/2*f*x + 1/2*e) - 25*I*c^4)/(a^2*(tan(1/2*f*x + 1/2*e) - I)^4))/f","B",0
921,1,193,0,2.395852," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{30 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{a^{3}} - \frac{60 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}{a^{3}} + \frac{30 i \, c^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{a^{3}} + \frac{147 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 1002 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 2445 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 3820 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 2445 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1002 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 147 i \, c^{4}}{a^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{6}}}{30 \, f}"," ",0,"-1/30*(30*I*c^4*log(tan(1/2*f*x + 1/2*e) + 1)/a^3 - 60*I*c^4*log(tan(1/2*f*x + 1/2*e) - I)/a^3 + 30*I*c^4*log(tan(1/2*f*x + 1/2*e) - 1)/a^3 + (147*I*c^4*tan(1/2*f*x + 1/2*e)^6 + 1002*c^4*tan(1/2*f*x + 1/2*e)^5 - 2445*I*c^4*tan(1/2*f*x + 1/2*e)^4 - 3820*c^4*tan(1/2*f*x + 1/2*e)^3 + 2445*I*c^4*tan(1/2*f*x + 1/2*e)^2 + 1002*c^4*tan(1/2*f*x + 1/2*e) - 147*I*c^4)/(a^3*(tan(1/2*f*x + 1/2*e) - I)^6))/f","A",0
922,1,88,0,2.469605," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 7 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 7 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{a^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{8}}"," ",0,"-2*(c^4*tan(1/2*f*x + 1/2*e)^7 - 7*c^4*tan(1/2*f*x + 1/2*e)^5 + 7*c^4*tan(1/2*f*x + 1/2*e)^3 - c^4*tan(1/2*f*x + 1/2*e))/(a^4*f*(tan(1/2*f*x + 1/2*e) - I)^8)","B",0
923,1,174,0,2.987928," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^5,x, algorithm=""giac"")","-\frac{2 \, {\left(5 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{9} - 5 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 50 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 35 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 98 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 35 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 50 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 5 i \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 5 \, c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{5 \, a^{5} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{10}}"," ",0,"-2/5*(5*c^4*tan(1/2*f*x + 1/2*e)^9 - 5*I*c^4*tan(1/2*f*x + 1/2*e)^8 - 50*c^4*tan(1/2*f*x + 1/2*e)^7 + 35*I*c^4*tan(1/2*f*x + 1/2*e)^6 + 98*c^4*tan(1/2*f*x + 1/2*e)^5 - 35*I*c^4*tan(1/2*f*x + 1/2*e)^4 - 50*c^4*tan(1/2*f*x + 1/2*e)^3 + 5*I*c^4*tan(1/2*f*x + 1/2*e)^2 + 5*c^4*tan(1/2*f*x + 1/2*e))/(a^5*f*(tan(1/2*f*x + 1/2*e) - I)^10)","B",0
924,1,200,0,1.144318," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{6 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c} - \frac{12 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c} + \frac{6 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c} - \frac{13 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 9 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 24 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 9 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 13 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i\right)}^{2} c}\right)}}{f}"," ",0,"2*(6*I*a^4*log(tan(1/2*f*x + 1/2*e) + 1)/c - 12*I*a^4*log(tan(1/2*f*x + 1/2*e) + I)/c + 6*I*a^4*log(tan(1/2*f*x + 1/2*e) - 1)/c - (13*a^4*tan(1/2*f*x + 1/2*e)^5 + 9*I*a^4*tan(1/2*f*x + 1/2*e)^4 - 24*a^4*tan(1/2*f*x + 1/2*e)^3 - 9*I*a^4*tan(1/2*f*x + 1/2*e)^2 + 13*a^4*tan(1/2*f*x + 1/2*e))/((tan(1/2*f*x + 1/2*e)^3 + I*tan(1/2*f*x + 1/2*e)^2 - tan(1/2*f*x + 1/2*e) - I)^2*c))/f","B",0
925,1,183,0,1.034943," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c} - \frac{4 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c} + \frac{2 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c} + \frac{-2 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 i \, a^{3}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} c} + \frac{6 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 16 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 6 i \, a^{3}}{c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{2}}\right)}}{f}"," ",0,"2*(2*I*a^3*log(tan(1/2*f*x + 1/2*e) + 1)/c - 4*I*a^3*log(tan(1/2*f*x + 1/2*e) + I)/c + 2*I*a^3*log(tan(1/2*f*x + 1/2*e) - 1)/c + (-2*I*a^3*tan(1/2*f*x + 1/2*e)^2 - a^3*tan(1/2*f*x + 1/2*e) + 2*I*a^3)/((tan(1/2*f*x + 1/2*e)^2 - 1)*c) + (6*I*a^3*tan(1/2*f*x + 1/2*e)^2 - 16*a^3*tan(1/2*f*x + 1/2*e) - 6*I*a^3)/(c*(tan(1/2*f*x + 1/2*e) + I)^2))/f","B",0
926,1,125,0,0.666549," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","-\frac{-\frac{i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c} + \frac{2 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c} - \frac{i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c} + \frac{-3 i \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 10 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 i \, a^{2}}{c {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{2}}}{f}"," ",0,"-(-I*a^2*log(tan(1/2*f*x + 1/2*e) + 1)/c + 2*I*a^2*log(tan(1/2*f*x + 1/2*e) + I)/c - I*a^2*log(tan(1/2*f*x + 1/2*e) - 1)/c + (-3*I*a^2*tan(1/2*f*x + 1/2*e)^2 + 10*a^2*tan(1/2*f*x + 1/2*e) + 3*I*a^2)/(c*(tan(1/2*f*x + 1/2*e) + I)^2))/f","B",0
927,1,33,0,0.576099," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)}{c f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{2}}"," ",0,"-2*a*tan(1/2*f*x + 1/2*e)/(c*f*(tan(1/2*f*x + 1/2*e) + I)^2)","A",0
928,1,46,0,0.717514," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{f x + e}{a c} + \frac{\tan\left(f x + e\right)}{{\left(\tan\left(f x + e\right)^{2} + 1\right)} a c}}{2 \, f}"," ",0,"1/2*((f*x + e)/(a*c) + tan(f*x + e)/((tan(f*x + e)^2 + 1)*a*c))/f","A",0
929,1,118,0,0.970691," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{6 i \, \log\left(i \, \tan\left(f x + e\right) + 1\right)}{a^{2} c} - \frac{6 i \, \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a^{2} c} + \frac{2 \, {\left(3 \, \tan\left(f x + e\right) + 5 i\right)}}{a^{2} c {\left(-i \, \tan\left(f x + e\right) + 1\right)}} + \frac{-9 i \, \tan\left(f x + e\right)^{2} - 26 \, \tan\left(f x + e\right) + 21 i}{a^{2} c {\left(\tan\left(f x + e\right) - i\right)}^{2}}}{32 \, f}"," ",0,"-1/32*(6*I*log(I*tan(f*x + e) + 1)/(a^2*c) - 6*I*log(I*tan(f*x + e) - 1)/(a^2*c) + 2*(3*tan(f*x + e) + 5*I)/(a^2*c*(-I*tan(f*x + e) + 1)) + (-9*I*tan(f*x + e)^2 - 26*tan(f*x + e) + 21*I)/(a^2*c*(tan(f*x + e) - I)^2))/f","A",0
930,1,123,0,1.029254," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","-\frac{-\frac{6 i \, \log\left(\tan\left(f x + e\right) + i\right)}{a^{3} c} + \frac{6 i \, \log\left(\tan\left(f x + e\right) - i\right)}{a^{3} c} + \frac{3 \, {\left(2 i \, \tan\left(f x + e\right) - 3\right)}}{a^{3} c {\left(\tan\left(f x + e\right) + i\right)}} + \frac{-11 i \, \tan\left(f x + e\right)^{3} - 42 \, \tan\left(f x + e\right)^{2} + 57 i \, \tan\left(f x + e\right) + 30}{a^{3} c {\left(\tan\left(f x + e\right) - i\right)}^{3}}}{48 \, f}"," ",0,"-1/48*(-6*I*log(tan(f*x + e) + I)/(a^3*c) + 6*I*log(tan(f*x + e) - I)/(a^3*c) + 3*(2*I*tan(f*x + e) - 3)/(a^3*c*(tan(f*x + e) + I)) + (-11*I*tan(f*x + e)^3 - 42*tan(f*x + e)^2 + 57*I*tan(f*x + e) + 30)/(a^3*c*(tan(f*x + e) - I)^3))/f","A",0
931,1,217,0,1.585576," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{6 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{2}} - \frac{12 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{2}} + \frac{6 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{2}} - \frac{2 \, {\left(3 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 3 i \, a^{4}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} c^{2}} + \frac{25 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 108 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 182 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 108 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 25 i \, a^{4}}{c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{4}}}{f}"," ",0,"-(6*I*a^4*log(tan(1/2*f*x + 1/2*e) + 1)/c^2 - 12*I*a^4*log(tan(1/2*f*x + 1/2*e) + I)/c^2 + 6*I*a^4*log(tan(1/2*f*x + 1/2*e) - 1)/c^2 - 2*(3*I*a^4*tan(1/2*f*x + 1/2*e)^2 + a^4*tan(1/2*f*x + 1/2*e) - 3*I*a^4)/((tan(1/2*f*x + 1/2*e)^2 - 1)*c^2) + (25*I*a^4*tan(1/2*f*x + 1/2*e)^4 - 108*a^4*tan(1/2*f*x + 1/2*e)^3 - 182*I*a^4*tan(1/2*f*x + 1/2*e)^2 + 108*a^4*tan(1/2*f*x + 1/2*e) + 25*I*a^4)/(c^2*(tan(1/2*f*x + 1/2*e) + I)^4))/f","B",0
932,1,159,0,1.119475," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{6 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{2}} - \frac{12 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{2}} + \frac{6 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{2}} + \frac{25 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 100 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 198 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 100 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 25 i \, a^{3}}{c^{2} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{4}}}{6 \, f}"," ",0,"-1/6*(6*I*a^3*log(tan(1/2*f*x + 1/2*e) + 1)/c^2 - 12*I*a^3*log(tan(1/2*f*x + 1/2*e) + I)/c^2 + 6*I*a^3*log(tan(1/2*f*x + 1/2*e) - 1)/c^2 + (25*I*a^3*tan(1/2*f*x + 1/2*e)^4 - 100*a^3*tan(1/2*f*x + 1/2*e)^3 - 198*I*a^3*tan(1/2*f*x + 1/2*e)^2 + 100*a^3*tan(1/2*f*x + 1/2*e) + 25*I*a^3)/(c^2*(tan(1/2*f*x + 1/2*e) + I)^4))/f","B",0
933,1,54,0,0.881125," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{c^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{4}}"," ",0,"-2*(a^2*tan(1/2*f*x + 1/2*e)^3 - a^2*tan(1/2*f*x + 1/2*e))/(c^2*f*(tan(1/2*f*x + 1/2*e) + I)^4)","B",0
934,1,65,0,0.714110," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + i \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{c^{2} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{4}}"," ",0,"-2*(a*tan(1/2*f*x + 1/2*e)^3 + I*a*tan(1/2*f*x + 1/2*e)^2 - a*tan(1/2*f*x + 1/2*e))/(c^2*f*(tan(1/2*f*x + 1/2*e) + I)^4)","B",0
935,1,118,0,0.651784," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{-\frac{6 i \, \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{a c^{2}} + \frac{6 i \, \log\left(-i \, \tan\left(f x + e\right) - 1\right)}{a c^{2}} + \frac{2 \, {\left(3 \, \tan\left(f x + e\right) - 5 i\right)}}{a c^{2} {\left(i \, \tan\left(f x + e\right) + 1\right)}} + \frac{9 i \, \tan\left(f x + e\right)^{2} - 26 \, \tan\left(f x + e\right) - 21 i}{a c^{2} {\left(\tan\left(f x + e\right) + i\right)}^{2}}}{32 \, f}"," ",0,"-1/32*(-6*I*log(-I*tan(f*x + e) + 1)/(a*c^2) + 6*I*log(-I*tan(f*x + e) - 1)/(a*c^2) + 2*(3*tan(f*x + e) - 5*I)/(a*c^2*(I*tan(f*x + e) + 1)) + (9*I*tan(f*x + e)^2 - 26*tan(f*x + e) - 21*I)/(a*c^2*(tan(f*x + e) + I)^2))/f","A",0
936,1,61,0,0.842467," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{3 \, {\left(f x + e\right)}}{a^{2} c^{2}} + \frac{3 \, \tan\left(f x + e\right)^{3} + 5 \, \tan\left(f x + e\right)}{{\left(\tan\left(f x + e\right)^{2} + 1\right)}^{2} a^{2} c^{2}}}{8 \, f}"," ",0,"1/8*(3*(f*x + e)/(a^2*c^2) + (3*tan(f*x + e)^3 + 5*tan(f*x + e))/((tan(f*x + e)^2 + 1)^2*a^2*c^2))/f","A",0
937,1,137,0,1.290647," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{-\frac{30 i \, \log\left(\tan\left(f x + e\right) + i\right)}{a^{3} c^{2}} + \frac{30 i \, \log\left(\tan\left(f x + e\right) - i\right)}{a^{3} c^{2}} + \frac{3 \, {\left(-15 i \, \tan\left(f x + e\right)^{2} + 38 \, \tan\left(f x + e\right) + 25 i\right)}}{a^{3} c^{2} {\left(-i \, \tan\left(f x + e\right) + 1\right)}^{2}} - \frac{55 i \, \tan\left(f x + e\right)^{3} + 201 \, \tan\left(f x + e\right)^{2} - 255 i \, \tan\left(f x + e\right) - 117}{a^{3} c^{2} {\left(\tan\left(f x + e\right) - i\right)}^{3}}}{192 \, f}"," ",0,"-1/192*(-30*I*log(tan(f*x + e) + I)/(a^3*c^2) + 30*I*log(tan(f*x + e) - I)/(a^3*c^2) + 3*(-15*I*tan(f*x + e)^2 + 38*tan(f*x + e) + 25*I)/(a^3*c^2*(-I*tan(f*x + e) + 1)^2) - (55*I*tan(f*x + e)^3 + 201*tan(f*x + e)^2 - 255*I*tan(f*x + e) - 117)/(a^3*c^2*(tan(f*x + e) - I)^3))/f","A",0
938,1,286,0,2.327372," ","integrate((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(-\frac{60 i \, a^{6} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{3}} + \frac{120 i \, a^{6} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{3}} - \frac{60 i \, a^{6} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{3}} - \frac{3 \, {\left(-30 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 9 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 61 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 9 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 30 i \, a^{6}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)}^{2} c^{3}} + \frac{-294 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 1860 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 4842 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 6680 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4842 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1860 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 294 i \, a^{6}}{c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{6}}\right)}}{3 \, f}"," ",0,"-2/3*(-60*I*a^6*log(tan(1/2*f*x + 1/2*e) + 1)/c^3 + 120*I*a^6*log(tan(1/2*f*x + 1/2*e) + I)/c^3 - 60*I*a^6*log(tan(1/2*f*x + 1/2*e) - 1)/c^3 - 3*(-30*I*a^6*tan(1/2*f*x + 1/2*e)^4 - 9*a^6*tan(1/2*f*x + 1/2*e)^3 + 61*I*a^6*tan(1/2*f*x + 1/2*e)^2 + 9*a^6*tan(1/2*f*x + 1/2*e) - 30*I*a^6)/((tan(1/2*f*x + 1/2*e)^2 - 1)^2*c^3) + (-294*I*a^6*tan(1/2*f*x + 1/2*e)^6 + 1860*a^6*tan(1/2*f*x + 1/2*e)^5 + 4842*I*a^6*tan(1/2*f*x + 1/2*e)^4 - 6680*a^6*tan(1/2*f*x + 1/2*e)^3 - 4842*I*a^6*tan(1/2*f*x + 1/2*e)^2 + 1860*a^6*tan(1/2*f*x + 1/2*e) + 294*I*a^6)/(c^3*(tan(1/2*f*x + 1/2*e) + I)^6))/f","B",0
939,1,252,0,1.995140," ","integrate((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(-\frac{60 i \, a^{5} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{3}} + \frac{120 i \, a^{5} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{3}} - \frac{60 i \, a^{5} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{3}} - \frac{15 \, {\left(-4 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 i \, a^{5}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} c^{3}} + \frac{-294 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 1884 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 4890 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 6920 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4890 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1884 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 294 i \, a^{5}}{c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{6}}\right)}}{15 \, f}"," ",0,"-2/15*(-60*I*a^5*log(tan(1/2*f*x + 1/2*e) + 1)/c^3 + 120*I*a^5*log(tan(1/2*f*x + 1/2*e) + I)/c^3 - 60*I*a^5*log(tan(1/2*f*x + 1/2*e) - 1)/c^3 - 15*(-4*I*a^5*tan(1/2*f*x + 1/2*e)^2 - a^5*tan(1/2*f*x + 1/2*e) + 4*I*a^5)/((tan(1/2*f*x + 1/2*e)^2 - 1)*c^3) + (-294*I*a^5*tan(1/2*f*x + 1/2*e)^6 + 1884*a^5*tan(1/2*f*x + 1/2*e)^5 + 4890*I*a^5*tan(1/2*f*x + 1/2*e)^4 - 6920*a^5*tan(1/2*f*x + 1/2*e)^3 - 4890*I*a^5*tan(1/2*f*x + 1/2*e)^2 + 1884*a^5*tan(1/2*f*x + 1/2*e) + 294*I*a^5)/(c^3*(tan(1/2*f*x + 1/2*e) + I)^6))/f","B",0
940,1,193,0,1.796832," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{-\frac{30 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{3}} + \frac{60 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{3}} - \frac{30 i \, a^{4} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{3}} + \frac{-147 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 1002 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 2445 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 3820 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2445 i \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 1002 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 147 i \, a^{4}}{c^{3} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{6}}}{30 \, f}"," ",0,"-1/30*(-30*I*a^4*log(tan(1/2*f*x + 1/2*e) + 1)/c^3 + 60*I*a^4*log(tan(1/2*f*x + 1/2*e) + I)/c^3 - 30*I*a^4*log(tan(1/2*f*x + 1/2*e) - 1)/c^3 + (-147*I*a^4*tan(1/2*f*x + 1/2*e)^6 + 1002*a^4*tan(1/2*f*x + 1/2*e)^5 + 2445*I*a^4*tan(1/2*f*x + 1/2*e)^4 - 3820*a^4*tan(1/2*f*x + 1/2*e)^3 - 2445*I*a^4*tan(1/2*f*x + 1/2*e)^2 + 1002*a^4*tan(1/2*f*x + 1/2*e) + 147*I*a^4)/(c^3*(tan(1/2*f*x + 1/2*e) + I)^6))/f","A",0
941,1,72,0,1.647443," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 10 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, c^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{6}}"," ",0,"-2/3*(3*a^3*tan(1/2*f*x + 1/2*e)^5 - 10*a^3*tan(1/2*f*x + 1/2*e)^3 + 3*a^3*tan(1/2*f*x + 1/2*e))/(c^3*f*(tan(1/2*f*x + 1/2*e) + I)^6)","A",0
942,1,106,0,1.237070," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 3 i \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 8 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 i \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, c^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{6}}"," ",0,"-2/3*(3*a^2*tan(1/2*f*x + 1/2*e)^5 + 3*I*a^2*tan(1/2*f*x + 1/2*e)^4 - 8*a^2*tan(1/2*f*x + 1/2*e)^3 - 3*I*a^2*tan(1/2*f*x + 1/2*e)^2 + 3*a^2*tan(1/2*f*x + 1/2*e))/(c^3*f*(tan(1/2*f*x + 1/2*e) + I)^6)","B",0
943,1,96,0,1.078136," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 6 i \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 10 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 i \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, c^{3} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{6}}"," ",0,"-2/3*(3*a*tan(1/2*f*x + 1/2*e)^5 + 6*I*a*tan(1/2*f*x + 1/2*e)^4 - 10*a*tan(1/2*f*x + 1/2*e)^3 - 6*I*a*tan(1/2*f*x + 1/2*e)^2 + 3*a*tan(1/2*f*x + 1/2*e))/(c^3*f*(tan(1/2*f*x + 1/2*e) + I)^6)","B",0
944,1,123,0,0.960615," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{-\frac{6 i \, \log\left(\tan\left(f x + e\right) + i\right)}{a c^{3}} + \frac{6 i \, \log\left(\tan\left(f x + e\right) - i\right)}{a c^{3}} + \frac{3 \, {\left(-2 i \, \tan\left(f x + e\right) - 3\right)}}{a c^{3} {\left(\tan\left(f x + e\right) - i\right)}} + \frac{11 i \, \tan\left(f x + e\right)^{3} - 42 \, \tan\left(f x + e\right)^{2} - 57 i \, \tan\left(f x + e\right) + 30}{a c^{3} {\left(\tan\left(f x + e\right) + i\right)}^{3}}}{48 \, f}"," ",0,"-1/48*(-6*I*log(tan(f*x + e) + I)/(a*c^3) + 6*I*log(tan(f*x + e) - I)/(a*c^3) + 3*(-2*I*tan(f*x + e) - 3)/(a*c^3*(tan(f*x + e) - I)) + (11*I*tan(f*x + e)^3 - 42*tan(f*x + e)^2 - 57*I*tan(f*x + e) + 30)/(a*c^3*(tan(f*x + e) + I)^3))/f","A",0
945,1,137,0,1.462841," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{-\frac{30 i \, \log\left(\tan\left(f x + e\right) + i\right)}{a^{2} c^{3}} + \frac{30 i \, \log\left(\tan\left(f x + e\right) - i\right)}{a^{2} c^{3}} + \frac{3 \, {\left(15 i \, \tan\left(f x + e\right)^{2} + 38 \, \tan\left(f x + e\right) - 25 i\right)}}{a^{2} c^{3} {\left(i \, \tan\left(f x + e\right) + 1\right)}^{2}} - \frac{-55 i \, \tan\left(f x + e\right)^{3} + 201 \, \tan\left(f x + e\right)^{2} + 255 i \, \tan\left(f x + e\right) - 117}{a^{2} c^{3} {\left(\tan\left(f x + e\right) + i\right)}^{3}}}{192 \, f}"," ",0,"-1/192*(-30*I*log(tan(f*x + e) + I)/(a^2*c^3) + 30*I*log(tan(f*x + e) - I)/(a^2*c^3) + 3*(15*I*tan(f*x + e)^2 + 38*tan(f*x + e) - 25*I)/(a^2*c^3*(I*tan(f*x + e) + 1)^2) - (-55*I*tan(f*x + e)^3 + 201*tan(f*x + e)^2 + 255*I*tan(f*x + e) - 117)/(a^2*c^3*(tan(f*x + e) + I)^3))/f","A",0
946,1,72,0,1.302060," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{15 \, {\left(f x + e\right)}}{a^{3} c^{3}} + \frac{15 \, \tan\left(f x + e\right)^{5} + 40 \, \tan\left(f x + e\right)^{3} + 33 \, \tan\left(f x + e\right)}{{\left(\tan\left(f x + e\right)^{2} + 1\right)}^{3} a^{3} c^{3}}}{48 \, f}"," ",0,"1/48*(15*(f*x + e)/(a^3*c^3) + (15*tan(f*x + e)^5 + 40*tan(f*x + e)^3 + 33*tan(f*x + e))/((tan(f*x + e)^2 + 1)^3*a^3*c^3))/f","A",0
947,1,285,0,3.644946," ","integrate((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{420 i \, a^{6} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{4}} - \frac{840 i \, a^{6} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{4}} + \frac{420 i \, a^{6} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{4}} - \frac{84 \, {\left(5 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 5 i \, a^{6}\right)}}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} c^{4}} + \frac{2283 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 18936 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 69300 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 141512 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 183106 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 141512 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 69300 i \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18936 \, a^{6} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2283 i \, a^{6}}{c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{8}}}{42 \, f}"," ",0,"-1/42*(420*I*a^6*log(tan(1/2*f*x + 1/2*e) + 1)/c^4 - 840*I*a^6*log(tan(1/2*f*x + 1/2*e) + I)/c^4 + 420*I*a^6*log(tan(1/2*f*x + 1/2*e) - 1)/c^4 - 84*(5*I*a^6*tan(1/2*f*x + 1/2*e)^2 + a^6*tan(1/2*f*x + 1/2*e) - 5*I*a^6)/((tan(1/2*f*x + 1/2*e)^2 - 1)*c^4) + (2283*I*a^6*tan(1/2*f*x + 1/2*e)^8 - 18936*a^6*tan(1/2*f*x + 1/2*e)^7 - 69300*I*a^6*tan(1/2*f*x + 1/2*e)^6 + 141512*a^6*tan(1/2*f*x + 1/2*e)^5 + 183106*I*a^6*tan(1/2*f*x + 1/2*e)^4 - 141512*a^6*tan(1/2*f*x + 1/2*e)^3 - 69300*I*a^6*tan(1/2*f*x + 1/2*e)^2 + 18936*a^6*tan(1/2*f*x + 1/2*e) + 2283*I*a^6)/(c^4*(tan(1/2*f*x + 1/2*e) + I)^8))/f","B",0
948,1,227,0,2.761882," ","integrate((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{420 i \, a^{5} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{c^{4}} - \frac{840 i \, a^{5} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c^{4}} + \frac{420 i \, a^{5} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{c^{4}} + \frac{2283 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{8} - 18264 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 70644 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} + 136808 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 191170 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 136808 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 70644 i \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 18264 \, a^{5} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2283 i \, a^{5}}{c^{4} {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{8}}}{420 \, f}"," ",0,"-1/420*(420*I*a^5*log(tan(1/2*f*x + 1/2*e) + 1)/c^4 - 840*I*a^5*log(tan(1/2*f*x + 1/2*e) + I)/c^4 + 420*I*a^5*log(tan(1/2*f*x + 1/2*e) - 1)/c^4 + (2283*I*a^5*tan(1/2*f*x + 1/2*e)^8 - 18264*a^5*tan(1/2*f*x + 1/2*e)^7 - 70644*I*a^5*tan(1/2*f*x + 1/2*e)^6 + 136808*a^5*tan(1/2*f*x + 1/2*e)^5 + 191170*I*a^5*tan(1/2*f*x + 1/2*e)^4 - 136808*a^5*tan(1/2*f*x + 1/2*e)^3 - 70644*I*a^5*tan(1/2*f*x + 1/2*e)^2 + 18264*a^5*tan(1/2*f*x + 1/2*e) + 2283*I*a^5)/(c^4*(tan(1/2*f*x + 1/2*e) + I)^8))/f","A",0
949,1,88,0,2.309397," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} - 7 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} + 7 \, a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - a^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{8}}"," ",0,"-2*(a^4*tan(1/2*f*x + 1/2*e)^7 - 7*a^4*tan(1/2*f*x + 1/2*e)^5 + 7*a^4*tan(1/2*f*x + 1/2*e)^3 - a^4*tan(1/2*f*x + 1/2*e))/(c^4*f*(tan(1/2*f*x + 1/2*e) + I)^8)","B",0
950,1,140,0,2.167560," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 3 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 17 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 10 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 17 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 i \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, a^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{8}}"," ",0,"-2/3*(3*a^3*tan(1/2*f*x + 1/2*e)^7 + 3*I*a^3*tan(1/2*f*x + 1/2*e)^6 - 17*a^3*tan(1/2*f*x + 1/2*e)^5 - 10*I*a^3*tan(1/2*f*x + 1/2*e)^4 + 17*a^3*tan(1/2*f*x + 1/2*e)^3 + 3*I*a^3*tan(1/2*f*x + 1/2*e)^2 - 3*a^3*tan(1/2*f*x + 1/2*e))/(c^4*f*(tan(1/2*f*x + 1/2*e) + I)^8)","A",0
951,1,140,0,1.904054," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(3 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 6 i \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 17 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 16 i \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 17 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 6 i \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 \, a^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{3 \, c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{8}}"," ",0,"-2/3*(3*a^2*tan(1/2*f*x + 1/2*e)^7 + 6*I*a^2*tan(1/2*f*x + 1/2*e)^6 - 17*a^2*tan(1/2*f*x + 1/2*e)^5 - 16*I*a^2*tan(1/2*f*x + 1/2*e)^4 + 17*a^2*tan(1/2*f*x + 1/2*e)^3 + 6*I*a^2*tan(1/2*f*x + 1/2*e)^2 - 3*a^2*tan(1/2*f*x + 1/2*e))/(c^4*f*(tan(1/2*f*x + 1/2*e) + I)^8)","B",0
952,1,125,0,1.620140," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{2 \, {\left(a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{7} + 3 i \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{6} - 7 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{5} - 8 i \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} + 7 \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} + 3 i \, a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - a \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)\right)}}{c^{4} f {\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}^{8}}"," ",0,"-2*(a*tan(1/2*f*x + 1/2*e)^7 + 3*I*a*tan(1/2*f*x + 1/2*e)^6 - 7*a*tan(1/2*f*x + 1/2*e)^5 - 8*I*a*tan(1/2*f*x + 1/2*e)^4 + 7*a*tan(1/2*f*x + 1/2*e)^3 + 3*I*a*tan(1/2*f*x + 1/2*e)^2 - a*tan(1/2*f*x + 1/2*e))/(c^4*f*(tan(1/2*f*x + 1/2*e) + I)^8)","B",0
953,1,140,0,1.193419," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{60 i \, \log\left(i \, \tan\left(f x + e\right) + 1\right)}{a c^{4}} - \frac{60 i \, \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a c^{4}} - \frac{12 \, {\left(5 \, \tan\left(f x + e\right) - 7 i\right)}}{a c^{4} {\left(-i \, \tan\left(f x + e\right) - 1\right)}} + \frac{125 i \, \tan\left(f x + e\right)^{4} - 596 \, \tan\left(f x + e\right)^{3} - 1110 i \, \tan\left(f x + e\right)^{2} + 996 \, \tan\left(f x + e\right) + 405 i}{a c^{4} {\left(\tan\left(f x + e\right) + i\right)}^{4}}}{768 \, f}"," ",0,"-1/768*(60*I*log(I*tan(f*x + e) + 1)/(a*c^4) - 60*I*log(I*tan(f*x + e) - 1)/(a*c^4) - 12*(5*tan(f*x + e) - 7*I)/(a*c^4*(-I*tan(f*x + e) - 1)) + (125*I*tan(f*x + e)^4 - 596*tan(f*x + e)^3 - 1110*I*tan(f*x + e)^2 + 996*tan(f*x + e) + 405*I)/(a*c^4*(tan(f*x + e) + I)^4))/f","A",0
954,1,149,0,1.202735," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{-\frac{60 i \, \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{a^{2} c^{4}} + \frac{60 i \, \log\left(-i \, \tan\left(f x + e\right) - 1\right)}{a^{2} c^{4}} + \frac{2 \, {\left(-45 i \, \tan\left(f x + e\right)^{2} - 110 \, \tan\left(f x + e\right) + 69 i\right)}}{a^{2} c^{4} {\left(\tan\left(f x + e\right) - i\right)}^{2}} + \frac{125 i \, \tan\left(f x + e\right)^{4} - 580 \, \tan\left(f x + e\right)^{3} - 1038 i \, \tan\left(f x + e\right)^{2} + 868 \, \tan\left(f x + e\right) + 301 i}{a^{2} c^{4} {\left(\tan\left(f x + e\right) + i\right)}^{4}}}{512 \, f}"," ",0,"-1/512*(-60*I*log(-I*tan(f*x + e) + 1)/(a^2*c^4) + 60*I*log(-I*tan(f*x + e) - 1)/(a^2*c^4) + 2*(-45*I*tan(f*x + e)^2 - 110*tan(f*x + e) + 69*I)/(a^2*c^4*(tan(f*x + e) - I)^2) + (125*I*tan(f*x + e)^4 - 580*tan(f*x + e)^3 - 1038*I*tan(f*x + e)^2 + 868*tan(f*x + e) + 301*I)/(a^2*c^4*(tan(f*x + e) + I)^4))/f","A",0
955,1,160,0,1.944831," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","-\frac{\frac{420 i \, \log\left(\tan\left(f x + e\right) - i\right)}{a^{3} c^{4}} - \frac{420 i \, \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a^{3} c^{4}} - \frac{2 \, {\left(385 \, \tan\left(f x + e\right)^{3} - 1335 i \, \tan\left(f x + e\right)^{2} - 1575 \, \tan\left(f x + e\right) + 641 i\right)}}{a^{3} c^{4} {\left(i \, \tan\left(f x + e\right) + 1\right)}^{3}} + \frac{875 i \, \tan\left(f x + e\right)^{4} - 3980 \, \tan\left(f x + e\right)^{3} - 6930 i \, \tan\left(f x + e\right)^{2} + 5548 \, \tan\left(f x + e\right) + 1771 i}{a^{3} c^{4} {\left(\tan\left(f x + e\right) + i\right)}^{4}}}{3072 \, f}"," ",0,"-1/3072*(420*I*log(tan(f*x + e) - I)/(a^3*c^4) - 420*I*log(I*tan(f*x + e) - 1)/(a^3*c^4) - 2*(385*tan(f*x + e)^3 - 1335*I*tan(f*x + e)^2 - 1575*tan(f*x + e) + 641*I)/(a^3*c^4*(I*tan(f*x + e) + 1)^3) + (875*I*tan(f*x + e)^4 - 3980*tan(f*x + e)^3 - 6930*I*tan(f*x + e)^2 + 5548*tan(f*x + e) + 1771*I)/(a^3*c^4*(tan(f*x + e) + I)^4))/f","A",0
956,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} \sqrt{-i \, c \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*sqrt(-I*c*tan(f*x + e) + c), x)","F",0
957,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} \sqrt{-i \, c \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*sqrt(-I*c*tan(f*x + e) + c), x)","F",0
958,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),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)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)2*a*i/f*exp(1/2*ln((-i)*c*tan(f*x+exp(1))+c))","F(-2)",0
959,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/(I*a*tan(f*x + e) + a), x)","F",0
960,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/(I*a*tan(f*x + e) + a)^2, x)","F",0
961,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/(I*a*tan(f*x + e) + a)^3, x)","F",0
962,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
963,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
964,1,20,0,0.498300," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a}{3 \, f}"," ",0,"2/3*I*(-I*c*tan(f*x + e) + c)^(3/2)*a/f","A",0
965,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a), x)","F",0
966,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a)^2, x)","F",0
967,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a)^3, x)","F",0
968,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
969,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
970,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)*(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
971,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a), x)","F",0
972,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^2, x)","F",0
973,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^3, x)","F",0
974,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
975,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
976,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
977,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
978,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^2*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
979,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^3*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
980,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
981,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
982,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
983,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
984,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^2*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
985,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^3*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
986,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
987,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
988,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{i \, a \tan\left(f x + e\right) + a}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
989,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
990,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^2*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
991,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^3*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
992,1,325,0,3.144777," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{15 \, {\left(a^{3} c - a^{2} c\right)} \sqrt{-a c} e^{\left(9 i \, f x + 9 i \, e\right)} + 74 \, {\left(a^{3} c - a^{2} c\right)} \sqrt{-a c} e^{\left(7 i \, f x + 7 i \, e\right)} + 132 \, {\left(a^{3} c - a^{2} c\right)} \sqrt{-a c} e^{\left(5 i \, f x + 5 i \, e\right)} + 102 \, {\left(a^{3} c - a^{2} c\right)} \sqrt{-a c} e^{\left(3 i \, f x + 3 i \, e\right)} + 29 \, {\left(a^{3} c - a^{2} c\right)} \sqrt{-a c} e^{\left(i \, f x + i \, e\right)}}{4 \, {\left({\left(a - 1\right)} c f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, {\left(a - 1\right)} c f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, {\left(a - 1\right)} c f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, {\left(a - 1\right)} c f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, {\left(a - 1\right)} c f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a - 1\right)} c f\right)}} - \frac{i \, {\left(12 \, a^{\frac{5}{2}} \sqrt{c} \arctan\left(e^{\left(i \, f x + i \, e\right)}\right) - \frac{5 \, a^{\frac{5}{2}} \sqrt{c} e^{\left(3 i \, f x + 3 i \, e\right)} + 7 \, a^{\frac{5}{2}} \sqrt{c} e^{\left(i \, f x + i \, e\right)}}{{\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}^{2}}\right)}}{4 \, f}"," ",0,"1/4*(15*(a^3*c - a^2*c)*sqrt(-a*c)*e^(9*I*f*x + 9*I*e) + 74*(a^3*c - a^2*c)*sqrt(-a*c)*e^(7*I*f*x + 7*I*e) + 132*(a^3*c - a^2*c)*sqrt(-a*c)*e^(5*I*f*x + 5*I*e) + 102*(a^3*c - a^2*c)*sqrt(-a*c)*e^(3*I*f*x + 3*I*e) + 29*(a^3*c - a^2*c)*sqrt(-a*c)*e^(I*f*x + I*e))/((a - 1)*c*f*e^(10*I*f*x + 10*I*e) + 5*(a - 1)*c*f*e^(8*I*f*x + 8*I*e) + 10*(a - 1)*c*f*e^(6*I*f*x + 6*I*e) + 10*(a - 1)*c*f*e^(4*I*f*x + 4*I*e) + 5*(a - 1)*c*f*e^(2*I*f*x + 2*I*e) + (a - 1)*c*f) - 1/4*I*(12*a^(5/2)*sqrt(c)*arctan(e^(I*f*x + I*e)) - (5*a^(5/2)*sqrt(c)*e^(3*I*f*x + 3*I*e) + 7*a^(5/2)*sqrt(c)*e^(I*f*x + I*e))/(e^(2*I*f*x + 2*I*e) + 1)^2)/f","B",0
993,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-i \, c \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(3/2)*sqrt(-I*c*tan(f*x + e) + c), x)","F",0
994,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(f x + e\right) + a} \sqrt{-i \, c \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)*sqrt(-I*c*tan(f*x + e) + c), x)","F",0
995,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{i \, a \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/sqrt(I*a*tan(f*x + e) + a), x)","F",0
996,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/(I*a*tan(f*x + e) + a)^(3/2), x)","F",0
997,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/(I*a*tan(f*x + e) + a)^(5/2), x)","F",0
998,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{\sqrt{-i \, c \tan\left(f x + e\right) + c}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)/(I*a*tan(f*x + e) + a)^(7/2), x)","F",0
999,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1000,1,307,0,40.945017," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{7 \, {\left({\left(a^{2} c - a c\right)} \sqrt{-a c} e^{\left(9 i \, f x + 9 i \, e\right)} + 6 \, {\left(a^{2} c - a c\right)} \sqrt{-a c} e^{\left(7 i \, f x + 7 i \, e\right)} + 12 \, {\left(a^{2} c - a c\right)} \sqrt{-a c} e^{\left(5 i \, f x + 5 i \, e\right)} + 10 \, {\left(a^{2} c - a c\right)} \sqrt{-a c} e^{\left(3 i \, f x + 3 i \, e\right)} + 3 \, {\left(a^{2} c - a c\right)} \sqrt{-a c} e^{\left(i \, f x + i \, e\right)}\right)}}{4 \, {\left({\left(a - 1\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, {\left(a - 1\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, {\left(a - 1\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, {\left(a - 1\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, {\left(a - 1\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a - 1\right)} f\right)}} - \frac{i \, {\left(4 \, a^{\frac{3}{2}} c^{\frac{3}{2}} \arctan\left(e^{\left(i \, f x + i \, e\right)}\right) - \frac{3 \, a^{\frac{3}{2}} c^{\frac{3}{2}} e^{\left(3 i \, f x + 3 i \, e\right)} + a^{\frac{3}{2}} c^{\frac{3}{2}} e^{\left(i \, f x + i \, e\right)}}{{\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}^{2}}\right)}}{4 \, f}"," ",0,"-7/4*((a^2*c - a*c)*sqrt(-a*c)*e^(9*I*f*x + 9*I*e) + 6*(a^2*c - a*c)*sqrt(-a*c)*e^(7*I*f*x + 7*I*e) + 12*(a^2*c - a*c)*sqrt(-a*c)*e^(5*I*f*x + 5*I*e) + 10*(a^2*c - a*c)*sqrt(-a*c)*e^(3*I*f*x + 3*I*e) + 3*(a^2*c - a*c)*sqrt(-a*c)*e^(I*f*x + I*e))/((a - 1)*f*e^(10*I*f*x + 10*I*e) + 5*(a - 1)*f*e^(8*I*f*x + 8*I*e) + 10*(a - 1)*f*e^(6*I*f*x + 6*I*e) + 10*(a - 1)*f*e^(4*I*f*x + 4*I*e) + 5*(a - 1)*f*e^(2*I*f*x + 2*I*e) + (a - 1)*f) - 1/4*I*(4*a^(3/2)*c^(3/2)*arctan(e^(I*f*x + I*e)) - (3*a^(3/2)*c^(3/2)*e^(3*I*f*x + 3*I*e) + a^(3/2)*c^(3/2)*e^(I*f*x + I*e))/(e^(2*I*f*x + 2*I*e) + 1)^2)/f","B",0
1001,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \sqrt{i \, a \tan\left(f x + e\right) + a} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)*(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1002,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{i \, a \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/sqrt(I*a*tan(f*x + e) + a), x)","F",0
1003,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a)^(3/2), x)","F",0
1004,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a)^(5/2), x)","F",0
1005,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a)^(7/2), x)","F",0
1006,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)/(I*a*tan(f*x + e) + a)^(9/2), x)","F",0
1007,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1008,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1009,1,313,0,15.905484," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{11 \, {\left(a c^{2} - c^{2}\right)} \sqrt{-a c} e^{\left(9 i \, f x + 9 i \, e\right)} + 50 \, {\left(a c^{2} - c^{2}\right)} \sqrt{-a c} e^{\left(7 i \, f x + 7 i \, e\right)} + 84 \, {\left(a c^{2} - c^{2}\right)} \sqrt{-a c} e^{\left(5 i \, f x + 5 i \, e\right)} + 62 \, {\left(a c^{2} - c^{2}\right)} \sqrt{-a c} e^{\left(3 i \, f x + 3 i \, e\right)} + 17 \, {\left(a c^{2} - c^{2}\right)} \sqrt{-a c} e^{\left(i \, f x + i \, e\right)}}{4 \, {\left({\left(a - 1\right)} f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, {\left(a - 1\right)} f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, {\left(a - 1\right)} f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, {\left(a - 1\right)} f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, {\left(a - 1\right)} f e^{\left(2 i \, f x + 2 i \, e\right)} + {\left(a - 1\right)} f\right)}} - \frac{i \, {\left(32 \, \sqrt{a} c^{\frac{5}{2}} \arctan\left(e^{\left(i \, f x + i \, e\right)}\right) + \frac{11 \, \sqrt{a} c^{\frac{5}{2}} e^{\left(3 i \, f x + 3 i \, e\right)} + 9 \, \sqrt{a} c^{\frac{5}{2}} e^{\left(i \, f x + i \, e\right)}}{{\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right)}^{2}}\right)}}{4 \, f}"," ",0,"-1/4*(11*(a*c^2 - c^2)*sqrt(-a*c)*e^(9*I*f*x + 9*I*e) + 50*(a*c^2 - c^2)*sqrt(-a*c)*e^(7*I*f*x + 7*I*e) + 84*(a*c^2 - c^2)*sqrt(-a*c)*e^(5*I*f*x + 5*I*e) + 62*(a*c^2 - c^2)*sqrt(-a*c)*e^(3*I*f*x + 3*I*e) + 17*(a*c^2 - c^2)*sqrt(-a*c)*e^(I*f*x + I*e))/((a - 1)*f*e^(10*I*f*x + 10*I*e) + 5*(a - 1)*f*e^(8*I*f*x + 8*I*e) + 10*(a - 1)*f*e^(6*I*f*x + 6*I*e) + 10*(a - 1)*f*e^(4*I*f*x + 4*I*e) + 5*(a - 1)*f*e^(2*I*f*x + 2*I*e) + (a - 1)*f) - 1/4*I*(32*sqrt(a)*c^(5/2)*arctan(e^(I*f*x + I*e)) + (11*sqrt(a)*c^(5/2)*e^(3*I*f*x + 3*I*e) + 9*sqrt(a)*c^(5/2)*e^(I*f*x + I*e))/(e^(2*I*f*x + 2*I*e) + 1)^2)/f","B",0
1010,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{i \, a \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/sqrt(I*a*tan(f*x + e) + a), x)","F",0
1011,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^(3/2), x)","F",0
1012,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^(5/2), x)","F",0
1013,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^(7/2), x)","F",0
1014,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(9/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^(9/2), x)","F",0
1015,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(11/2),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)/(I*a*tan(f*x + e) + a)^(11/2), x)","F",0
1016,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(7/2)/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
1017,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(5/2)/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
1018,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(3/2)/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
1019,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(f x + e\right) + a}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
1020,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(f x + e\right) + a} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(f*x + e) + a)*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
1021,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(3/2)*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
1022,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(5/2)*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
1023,0,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}} \sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(7/2)*sqrt(-I*c*tan(f*x + e) + c)), x)","F",0
1024,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{9}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(9/2)/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1025,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(7/2)/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1026,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(5/2)/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1027,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(3/2)/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1028,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(f x + e\right) + a}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1029,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(f x + e\right) + a} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(f*x + e) + a)*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
1030,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(3/2)*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
1031,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(5/2)*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
1032,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(7/2)*(-I*c*tan(f*x + e) + c)^(3/2)), x)","F",0
1033,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(11/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{11}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(11/2)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1034,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{9}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(9/2)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1035,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(7/2)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1036,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(5/2)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1037,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^(3/2)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1038,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{\sqrt{i \, a \tan\left(f x + e\right) + a}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1039,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{i \, a \tan\left(f x + e\right) + a} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(f*x + e) + a)*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
1040,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(3/2)*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
1041,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(5/2)*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
1042,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{1}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((I*a*tan(f*x + e) + a)^(7/2)*(-I*c*tan(f*x + e) + c)^(5/2)), x)","F",0
1043,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{4} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^4*(-I*c*tan(f*x + e) + c)^n, x)","F",0
1044,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(-I*c*tan(f*x + e) + c)^n, x)","F",0
1045,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(-I*c*tan(f*x + e) + c)^n, x)","F",0
1046,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,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)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)a*i/f/n*exp(n*ln((-i)*c*tan(f*x+exp(1))+c))","F(-2)",0
1047,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^n/(I*a*tan(f*x + e) + a), x)","F",0
1048,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^n/(I*a*tan(f*x + e) + a)^2, x)","F",0
1049,0,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^n/(I*a*tan(f*x + e) + a)^3, x)","F",0
1050,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m} {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m*(-I*c*tan(f*x + e) + c)^n, x)","F",0
1051,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","\int {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^4*(I*a*tan(f*x + e) + a)^m, x)","F",0
1052,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^3*(I*a*tan(f*x + e) + a)^m, x)","F",0
1053,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^2*(I*a*tan(f*x + e) + a)^m, x)","F",0
1054,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e)),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)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)c*(-i)/f/m*exp(m*ln(i*a*tan(f*x+exp(1))+a))","F(-2)",0
1055,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{-i \, c \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(-I*c*tan(f*x + e) + c), x)","F",0
1056,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(-I*c*tan(f*x + e) + c)^2, x)","F",0
1057,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(-I*c*tan(f*x + e) + c)^3, x)","F",0
1058,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^4,x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(-I*c*tan(f*x + e) + c)^4, x)","F",0
1059,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(5/2)*(I*a*tan(f*x + e) + a)^m, x)","F",0
1060,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((-I*c*tan(f*x + e) + c)^(3/2)*(I*a*tan(f*x + e) + a)^m, x)","F",0
1061,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(-I*c*tan(f*x + e) + c)*(I*a*tan(f*x + e) + a)^m, x)","F",0
1062,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/sqrt(-I*c*tan(f*x + e) + c), x)","F",0
1063,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(-I*c*tan(f*x + e) + c)^(3/2), x)","F",0
1064,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(-I*c*tan(f*x + e) + c)^(5/2), x)","F",0
1065,1,333,0,0.656129," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{-12 i \, a^{3} c e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 12 \, a^{3} d e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 i \, a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 \, a^{3} d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 i \, a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 24 i \, a^{3} c e^{\left(4 i \, f x + 4 i \, e\right)} - 48 \, a^{3} d e^{\left(4 i \, f x + 4 i \, e\right)} - 42 i \, a^{3} c e^{\left(2 i \, f x + 2 i \, e\right)} - 66 \, a^{3} d e^{\left(2 i \, f x + 2 i \, e\right)} - 12 i \, a^{3} c \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 12 \, a^{3} d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 i \, a^{3} c - 26 \, a^{3} d}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-12*I*a^3*c*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 12*a^3*d*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*I*a^3*c*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*a^3*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*I*a^3*c*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*a^3*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 24*I*a^3*c*e^(4*I*f*x + 4*I*e) - 48*a^3*d*e^(4*I*f*x + 4*I*e) - 42*I*a^3*c*e^(2*I*f*x + 2*I*e) - 66*a^3*d*e^(2*I*f*x + 2*I*e) - 12*I*a^3*c*log(e^(2*I*f*x + 2*I*e) + 1) - 12*a^3*d*log(e^(2*I*f*x + 2*I*e) + 1) - 18*I*a^3*c - 26*a^3*d)/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1066,1,229,0,0.981288," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{-2 i \, a^{2} c e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 \, a^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 4 i \, a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 4 \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 i \, a^{2} c e^{\left(2 i \, f x + 2 i \, e\right)} - 6 \, a^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} - 2 i \, a^{2} c \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 \, a^{2} d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 i \, a^{2} c - 4 \, a^{2} d}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"(-2*I*a^2*c*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 2*a^2*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 4*I*a^2*c*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 4*a^2*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 2*I*a^2*c*e^(2*I*f*x + 2*I*e) - 6*a^2*d*e^(2*I*f*x + 2*I*e) - 2*I*a^2*c*log(e^(2*I*f*x + 2*I*e) + 1) - 2*a^2*d*log(e^(2*I*f*x + 2*I*e) + 1) - 2*I*a^2*c - 4*a^2*d)/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1067,1,110,0,0.347165," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{-i \, a c e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - a d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - i \, a c \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - a d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 \, a d}{f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"(-I*a*c*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - a*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - I*a*c*log(e^(2*I*f*x + 2*I*e) + 1) - a*d*log(e^(2*I*f*x + 2*I*e) + 1) - 2*a*d)/(f*e^(2*I*f*x + 2*I*e) + f)","B",0
1068,1,90,0,0.994376," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left(i \, c + d\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a} + \frac{{\left(-i \, c - d\right)} \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{a} + \frac{-i \, c \tan\left(f x + e\right) - d \tan\left(f x + e\right) - 3 \, c - i \, d}{a {\left(\tan\left(f x + e\right) - i\right)}}}{4 \, f}"," ",0,"-1/4*((I*c + d)*log(tan(f*x + e) - I)/a + (-I*c - d)*log(-I*tan(f*x + e) + 1)/a + (-I*c*tan(f*x + e) - d*tan(f*x + e) - 3*c - I*d)/(a*(tan(f*x + e) - I)))/f","B",0
1069,1,117,0,0.747534," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(-i \, c - d\right)} \log\left(\tan\left(f x + e\right) + i\right)}{a^{2}} - \frac{2 \, {\left(-i \, c - d\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a^{2}} - \frac{3 i \, c \tan\left(f x + e\right)^{2} + 3 \, d \tan\left(f x + e\right)^{2} + 10 \, c \tan\left(f x + e\right) - 10 i \, d \tan\left(f x + e\right) - 11 i \, c - 3 \, d}{a^{2} {\left(\tan\left(f x + e\right) - i\right)}^{2}}}{16 \, f}"," ",0,"-1/16*(2*(-I*c - d)*log(tan(f*x + e) + I)/a^2 - 2*(-I*c - d)*log(tan(f*x + e) - I)/a^2 - (3*I*c*tan(f*x + e)^2 + 3*d*tan(f*x + e)^2 + 10*c*tan(f*x + e) - 10*I*d*tan(f*x + e) - 11*I*c - 3*d)/(a^2*(tan(f*x + e) - I)^2))/f","A",0
1070,1,140,0,0.823669," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(i \, c + d\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a^{3}} + \frac{6 \, {\left(-i \, c - d\right)} \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a^{3}} + \frac{-11 i \, c \tan\left(f x + e\right)^{3} - 11 \, d \tan\left(f x + e\right)^{3} - 45 \, c \tan\left(f x + e\right)^{2} + 45 i \, d \tan\left(f x + e\right)^{2} + 69 i \, c \tan\left(f x + e\right) + 69 \, d \tan\left(f x + e\right) + 51 \, c - 19 i \, d}{a^{3} {\left(\tan\left(f x + e\right) - i\right)}^{3}}}{96 \, f}"," ",0,"-1/96*(6*(I*c + d)*log(tan(f*x + e) - I)/a^3 + 6*(-I*c - d)*log(I*tan(f*x + e) - 1)/a^3 + (-11*I*c*tan(f*x + e)^3 - 11*d*tan(f*x + e)^3 - 45*c*tan(f*x + e)^2 + 45*I*d*tan(f*x + e)^2 + 69*I*c*tan(f*x + e) + 69*d*tan(f*x + e) + 51*c - 19*I*d)/(a^3*(tan(f*x + e) - I)^3))/f","A",0
1071,1,670,0,1.545046," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{-12 i \, a^{3} c^{2} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 24 \, a^{3} c d e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 12 i \, a^{3} d^{2} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 48 i \, a^{3} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 96 \, a^{3} c d e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 48 i \, a^{3} d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 72 i \, a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 144 \, a^{3} c d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 72 i \, a^{3} d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 48 i \, a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 96 \, a^{3} c d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 48 i \, a^{3} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 24 i \, a^{3} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 96 \, a^{3} c d e^{\left(6 i \, f x + 6 i \, e\right)} + 72 i \, a^{3} d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} - 66 i \, a^{3} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 228 \, a^{3} c d e^{\left(4 i \, f x + 4 i \, e\right)} + 138 i \, a^{3} d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 60 i \, a^{3} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 184 \, a^{3} c d e^{\left(2 i \, f x + 2 i \, e\right)} + 108 i \, a^{3} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 12 i \, a^{3} c^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 24 \, a^{3} c d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 12 i \, a^{3} d^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 i \, a^{3} c^{2} - 52 \, a^{3} c d + 30 i \, a^{3} d^{2}}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-12*I*a^3*c^2*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 24*a^3*c*d*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 12*I*a^3*d^2*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 48*I*a^3*c^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 96*a^3*c*d*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 48*I*a^3*d^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 72*I*a^3*c^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 144*a^3*c*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 72*I*a^3*d^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 48*I*a^3*c^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 96*a^3*c*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 48*I*a^3*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 24*I*a^3*c^2*e^(6*I*f*x + 6*I*e) - 96*a^3*c*d*e^(6*I*f*x + 6*I*e) + 72*I*a^3*d^2*e^(6*I*f*x + 6*I*e) - 66*I*a^3*c^2*e^(4*I*f*x + 4*I*e) - 228*a^3*c*d*e^(4*I*f*x + 4*I*e) + 138*I*a^3*d^2*e^(4*I*f*x + 4*I*e) - 60*I*a^3*c^2*e^(2*I*f*x + 2*I*e) - 184*a^3*c*d*e^(2*I*f*x + 2*I*e) + 108*I*a^3*d^2*e^(2*I*f*x + 2*I*e) - 12*I*a^3*c^2*log(e^(2*I*f*x + 2*I*e) + 1) - 24*a^3*c*d*log(e^(2*I*f*x + 2*I*e) + 1) + 12*I*a^3*d^2*log(e^(2*I*f*x + 2*I*e) + 1) - 18*I*a^3*c^2 - 52*a^3*c*d + 30*I*a^3*d^2)/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1072,1,512,0,0.894689," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{-6 i \, a^{2} c^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 12 \, a^{2} c d e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 6 i \, a^{2} d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 i \, a^{2} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 \, a^{2} c d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 18 i \, a^{2} d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 i \, a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 \, a^{2} c d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 18 i \, a^{2} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 6 i \, a^{2} c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 36 \, a^{2} c d e^{\left(4 i \, f x + 4 i \, e\right)} + 30 i \, a^{2} d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} - 12 i \, a^{2} c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 60 \, a^{2} c d e^{\left(2 i \, f x + 2 i \, e\right)} + 36 i \, a^{2} d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - 6 i \, a^{2} c^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 12 \, a^{2} c d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 6 i \, a^{2} d^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 6 i \, a^{2} c^{2} - 24 \, a^{2} c d + 14 i \, a^{2} d^{2}}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-6*I*a^2*c^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 12*a^2*c*d*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 6*I*a^2*d^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 18*I*a^2*c^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*a^2*c*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 18*I*a^2*d^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 18*I*a^2*c^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*a^2*c*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 18*I*a^2*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 6*I*a^2*c^2*e^(4*I*f*x + 4*I*e) - 36*a^2*c*d*e^(4*I*f*x + 4*I*e) + 30*I*a^2*d^2*e^(4*I*f*x + 4*I*e) - 12*I*a^2*c^2*e^(2*I*f*x + 2*I*e) - 60*a^2*c*d*e^(2*I*f*x + 2*I*e) + 36*I*a^2*d^2*e^(2*I*f*x + 2*I*e) - 6*I*a^2*c^2*log(e^(2*I*f*x + 2*I*e) + 1) - 12*a^2*c*d*log(e^(2*I*f*x + 2*I*e) + 1) + 6*I*a^2*d^2*log(e^(2*I*f*x + 2*I*e) + 1) - 6*I*a^2*c^2 - 24*a^2*c*d + 14*I*a^2*d^2)/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1073,1,301,0,1.568993," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{-i \, a c^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 \, a c d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + i \, a d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 i \, a c^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 4 \, a c d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 2 i \, a d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 4 \, a c d e^{\left(2 i \, f x + 2 i \, e\right)} + 4 i \, a d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} - i \, a c^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 2 \, a c d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + i \, a d^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 4 \, a c d + 2 i \, a d^{2}}{f e^{\left(4 i \, f x + 4 i \, e\right)} + 2 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f}"," ",0,"(-I*a*c^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 2*a*c*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + I*a*d^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 2*I*a*c^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 4*a*c*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 2*I*a*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 4*a*c*d*e^(2*I*f*x + 2*I*e) + 4*I*a*d^2*e^(2*I*f*x + 2*I*e) - I*a*c^2*log(e^(2*I*f*x + 2*I*e) + 1) - 2*a*c*d*log(e^(2*I*f*x + 2*I*e) + 1) + I*a*d^2*log(e^(2*I*f*x + 2*I*e) + 1) - 4*a*c*d + 2*I*a*d^2)/(f*e^(4*I*f*x + 4*I*e) + 2*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1074,1,131,0,0.972320," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{{\left(i \, c^{2} + 2 \, c d + 3 i \, d^{2}\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a} + \frac{{\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a} + \frac{-i \, c^{2} \tan\left(f x + e\right) - 2 \, c d \tan\left(f x + e\right) - 3 i \, d^{2} \tan\left(f x + e\right) - 3 \, c^{2} - 2 i \, c d - d^{2}}{a {\left(\tan\left(f x + e\right) - i\right)}}}{4 \, f}"," ",0,"-1/4*((I*c^2 + 2*c*d + 3*I*d^2)*log(tan(f*x + e) - I)/a + (-I*c^2 - 2*c*d + I*d^2)*log(I*tan(f*x + e) - 1)/a + (-I*c^2*tan(f*x + e) - 2*c*d*tan(f*x + e) - 3*I*d^2*tan(f*x + e) - 3*c^2 - 2*I*c*d - d^2)/(a*(tan(f*x + e) - I)))/f","B",0
1075,1,176,0,0.694907," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{a^{2}} + \frac{2 \, {\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} \log\left(-i \, \tan\left(f x + e\right) - 1\right)}{a^{2}} + \frac{-3 i \, c^{2} \tan\left(f x + e\right)^{2} - 6 \, c d \tan\left(f x + e\right)^{2} + 3 i \, d^{2} \tan\left(f x + e\right)^{2} - 10 \, c^{2} \tan\left(f x + e\right) + 20 i \, c d \tan\left(f x + e\right) - 6 \, d^{2} \tan\left(f x + e\right) + 11 i \, c^{2} + 6 \, c d + 5 i \, d^{2}}{a^{2} {\left(\tan\left(f x + e\right) - i\right)}^{2}}}{16 \, f}"," ",0,"-1/16*(2*(-I*c^2 - 2*c*d + I*d^2)*log(-I*tan(f*x + e) + 1)/a^2 + 2*(I*c^2 + 2*c*d - I*d^2)*log(-I*tan(f*x + e) - 1)/a^2 + (-3*I*c^2*tan(f*x + e)^2 - 6*c*d*tan(f*x + e)^2 + 3*I*d^2*tan(f*x + e)^2 - 10*c^2*tan(f*x + e) + 20*I*c*d*tan(f*x + e) - 6*d^2*tan(f*x + e) + 11*I*c^2 + 6*c*d + 5*I*d^2)/(a^2*(tan(f*x + e) - I)^2))/f","B",0
1076,1,215,0,1.250341," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a^{3}} + \frac{6 \, {\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a^{3}} + \frac{-11 i \, c^{2} \tan\left(f x + e\right)^{3} - 22 \, c d \tan\left(f x + e\right)^{3} + 11 i \, d^{2} \tan\left(f x + e\right)^{3} - 45 \, c^{2} \tan\left(f x + e\right)^{2} + 90 i \, c d \tan\left(f x + e\right)^{2} + 45 \, d^{2} \tan\left(f x + e\right)^{2} + 69 i \, c^{2} \tan\left(f x + e\right) + 138 \, c d \tan\left(f x + e\right) - 21 i \, d^{2} \tan\left(f x + e\right) + 51 \, c^{2} - 38 i \, c d - 3 \, d^{2}}{a^{3} {\left(\tan\left(f x + e\right) - i\right)}^{3}}}{96 \, f}"," ",0,"-1/96*(6*(I*c^2 + 2*c*d - I*d^2)*log(tan(f*x + e) - I)/a^3 + 6*(-I*c^2 - 2*c*d + I*d^2)*log(I*tan(f*x + e) - 1)/a^3 + (-11*I*c^2*tan(f*x + e)^3 - 22*c*d*tan(f*x + e)^3 + 11*I*d^2*tan(f*x + e)^3 - 45*c^2*tan(f*x + e)^2 + 90*I*c*d*tan(f*x + e)^2 + 45*d^2*tan(f*x + e)^2 + 69*I*c^2*tan(f*x + e) + 138*c*d*tan(f*x + e) - 21*I*d^2*tan(f*x + e) + 51*c^2 - 38*I*c*d - 3*d^2)/(a^3*(tan(f*x + e) - I)^3))/f","B",0
1077,1,1117,0,6.003429," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{-60 i \, a^{3} c^{3} e^{\left(10 i \, f x + 10 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 180 \, a^{3} c^{2} d e^{\left(10 i \, f x + 10 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 180 i \, a^{3} c d^{2} e^{\left(10 i \, f x + 10 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 60 \, a^{3} d^{3} e^{\left(10 i \, f x + 10 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 300 i \, a^{3} c^{3} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 900 \, a^{3} c^{2} d e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 900 i \, a^{3} c d^{2} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 300 \, a^{3} d^{3} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 600 i \, a^{3} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 1800 \, a^{3} c^{2} d e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 1800 i \, a^{3} c d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 600 \, a^{3} d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 600 i \, a^{3} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 1800 \, a^{3} c^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 1800 i \, a^{3} c d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 600 \, a^{3} d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 300 i \, a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 900 \, a^{3} c^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 900 i \, a^{3} c d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 300 \, a^{3} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 120 i \, a^{3} c^{3} e^{\left(8 i \, f x + 8 i \, e\right)} - 720 \, a^{3} c^{2} d e^{\left(8 i \, f x + 8 i \, e\right)} + 1080 i \, a^{3} c d^{2} e^{\left(8 i \, f x + 8 i \, e\right)} + 480 \, a^{3} d^{3} e^{\left(8 i \, f x + 8 i \, e\right)} - 450 i \, a^{3} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 2430 \, a^{3} c^{2} d e^{\left(6 i \, f x + 6 i \, e\right)} + 3150 i \, a^{3} c d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 1170 \, a^{3} d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 630 i \, a^{3} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 3090 \, a^{3} c^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} + 3690 i \, a^{3} c d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 1390 \, a^{3} d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 390 i \, a^{3} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 1770 \, a^{3} c^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + 2070 i \, a^{3} c d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 770 \, a^{3} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 60 i \, a^{3} c^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 180 \, a^{3} c^{2} d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 180 i \, a^{3} c d^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 60 \, a^{3} d^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 90 i \, a^{3} c^{3} - 390 \, a^{3} c^{2} d + 450 i \, a^{3} c d^{2} + 166 \, a^{3} d^{3}}{15 \, {\left(f e^{\left(10 i \, f x + 10 i \, e\right)} + 5 \, f e^{\left(8 i \, f x + 8 i \, e\right)} + 10 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 10 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 5 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/15*(-60*I*a^3*c^3*e^(10*I*f*x + 10*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 180*a^3*c^2*d*e^(10*I*f*x + 10*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 180*I*a^3*c*d^2*e^(10*I*f*x + 10*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 60*a^3*d^3*e^(10*I*f*x + 10*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 300*I*a^3*c^3*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 900*a^3*c^2*d*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 900*I*a^3*c*d^2*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 300*a^3*d^3*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 600*I*a^3*c^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 1800*a^3*c^2*d*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 1800*I*a^3*c*d^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 600*a^3*d^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 600*I*a^3*c^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 1800*a^3*c^2*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 1800*I*a^3*c*d^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 600*a^3*d^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 300*I*a^3*c^3*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 900*a^3*c^2*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 900*I*a^3*c*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 300*a^3*d^3*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 120*I*a^3*c^3*e^(8*I*f*x + 8*I*e) - 720*a^3*c^2*d*e^(8*I*f*x + 8*I*e) + 1080*I*a^3*c*d^2*e^(8*I*f*x + 8*I*e) + 480*a^3*d^3*e^(8*I*f*x + 8*I*e) - 450*I*a^3*c^3*e^(6*I*f*x + 6*I*e) - 2430*a^3*c^2*d*e^(6*I*f*x + 6*I*e) + 3150*I*a^3*c*d^2*e^(6*I*f*x + 6*I*e) + 1170*a^3*d^3*e^(6*I*f*x + 6*I*e) - 630*I*a^3*c^3*e^(4*I*f*x + 4*I*e) - 3090*a^3*c^2*d*e^(4*I*f*x + 4*I*e) + 3690*I*a^3*c*d^2*e^(4*I*f*x + 4*I*e) + 1390*a^3*d^3*e^(4*I*f*x + 4*I*e) - 390*I*a^3*c^3*e^(2*I*f*x + 2*I*e) - 1770*a^3*c^2*d*e^(2*I*f*x + 2*I*e) + 2070*I*a^3*c*d^2*e^(2*I*f*x + 2*I*e) + 770*a^3*d^3*e^(2*I*f*x + 2*I*e) - 60*I*a^3*c^3*log(e^(2*I*f*x + 2*I*e) + 1) - 180*a^3*c^2*d*log(e^(2*I*f*x + 2*I*e) + 1) + 180*I*a^3*c*d^2*log(e^(2*I*f*x + 2*I*e) + 1) + 60*a^3*d^3*log(e^(2*I*f*x + 2*I*e) + 1) - 90*I*a^3*c^3 - 390*a^3*c^2*d + 450*I*a^3*c*d^2 + 166*a^3*d^3)/(f*e^(10*I*f*x + 10*I*e) + 5*f*e^(8*I*f*x + 8*I*e) + 10*f*e^(6*I*f*x + 6*I*e) + 10*f*e^(4*I*f*x + 4*I*e) + 5*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1078,1,904,0,2.580282," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{-6 i \, a^{2} c^{3} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 \, a^{2} c^{2} d e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 18 i \, a^{2} c d^{2} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 6 \, a^{2} d^{3} e^{\left(8 i \, f x + 8 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 24 i \, a^{2} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 72 \, a^{2} c^{2} d e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 72 i \, a^{2} c d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 24 \, a^{2} d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 36 i \, a^{2} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 108 \, a^{2} c^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 108 i \, a^{2} c d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 36 \, a^{2} d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 24 i \, a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 72 \, a^{2} c^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 72 i \, a^{2} c d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 24 \, a^{2} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 6 i \, a^{2} c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 54 \, a^{2} c^{2} d e^{\left(6 i \, f x + 6 i \, e\right)} + 90 i \, a^{2} c d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} + 42 \, a^{2} d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} - 18 i \, a^{2} c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 144 \, a^{2} c^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} + 198 i \, a^{2} c d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 72 \, a^{2} d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 18 i \, a^{2} c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 126 \, a^{2} c^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + 150 i \, a^{2} c d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 58 \, a^{2} d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 6 i \, a^{2} c^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 \, a^{2} c^{2} d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 18 i \, a^{2} c d^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 6 \, a^{2} d^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 6 i \, a^{2} c^{3} - 36 \, a^{2} c^{2} d + 42 i \, a^{2} c d^{2} + 16 \, a^{2} d^{3}}{3 \, {\left(f e^{\left(8 i \, f x + 8 i \, e\right)} + 4 \, f e^{\left(6 i \, f x + 6 i \, e\right)} + 6 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 4 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-6*I*a^2*c^3*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 18*a^2*c^2*d*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 18*I*a^2*c*d^2*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 6*a^2*d^3*e^(8*I*f*x + 8*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 24*I*a^2*c^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 72*a^2*c^2*d*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 72*I*a^2*c*d^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 24*a^2*d^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 36*I*a^2*c^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 108*a^2*c^2*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 108*I*a^2*c*d^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 36*a^2*d^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 24*I*a^2*c^3*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 72*a^2*c^2*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 72*I*a^2*c*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 24*a^2*d^3*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 6*I*a^2*c^3*e^(6*I*f*x + 6*I*e) - 54*a^2*c^2*d*e^(6*I*f*x + 6*I*e) + 90*I*a^2*c*d^2*e^(6*I*f*x + 6*I*e) + 42*a^2*d^3*e^(6*I*f*x + 6*I*e) - 18*I*a^2*c^3*e^(4*I*f*x + 4*I*e) - 144*a^2*c^2*d*e^(4*I*f*x + 4*I*e) + 198*I*a^2*c*d^2*e^(4*I*f*x + 4*I*e) + 72*a^2*d^3*e^(4*I*f*x + 4*I*e) - 18*I*a^2*c^3*e^(2*I*f*x + 2*I*e) - 126*a^2*c^2*d*e^(2*I*f*x + 2*I*e) + 150*I*a^2*c*d^2*e^(2*I*f*x + 2*I*e) + 58*a^2*d^3*e^(2*I*f*x + 2*I*e) - 6*I*a^2*c^3*log(e^(2*I*f*x + 2*I*e) + 1) - 18*a^2*c^2*d*log(e^(2*I*f*x + 2*I*e) + 1) + 18*I*a^2*c*d^2*log(e^(2*I*f*x + 2*I*e) + 1) + 6*a^2*d^3*log(e^(2*I*f*x + 2*I*e) + 1) - 6*I*a^2*c^3 - 36*a^2*c^2*d + 42*I*a^2*c*d^2 + 16*a^2*d^3)/(f*e^(8*I*f*x + 8*I*e) + 4*f*e^(6*I*f*x + 6*I*e) + 6*f*e^(4*I*f*x + 4*I*e) + 4*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1079,1,597,0,3.000586," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{-3 i \, a c^{3} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 9 \, a c^{2} d e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 9 i \, a c d^{2} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 3 \, a d^{3} e^{\left(6 i \, f x + 6 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 9 i \, a c^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 27 \, a c^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 27 i \, a c d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 9 \, a d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 9 i \, a c^{3} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 27 \, a c^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 27 i \, a c d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 9 \, a d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 \, a c^{2} d e^{\left(4 i \, f x + 4 i \, e\right)} + 36 i \, a c d^{2} e^{\left(4 i \, f x + 4 i \, e\right)} + 18 \, a d^{3} e^{\left(4 i \, f x + 4 i \, e\right)} - 36 \, a c^{2} d e^{\left(2 i \, f x + 2 i \, e\right)} + 54 i \, a c d^{2} e^{\left(2 i \, f x + 2 i \, e\right)} + 18 \, a d^{3} e^{\left(2 i \, f x + 2 i \, e\right)} - 3 i \, a c^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 9 \, a c^{2} d \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 9 i \, a c d^{2} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) + 3 \, a d^{3} \log\left(e^{\left(2 i \, f x + 2 i \, e\right)} + 1\right) - 18 \, a c^{2} d + 18 i \, a c d^{2} + 8 \, a d^{3}}{3 \, {\left(f e^{\left(6 i \, f x + 6 i \, e\right)} + 3 \, f e^{\left(4 i \, f x + 4 i \, e\right)} + 3 \, f e^{\left(2 i \, f x + 2 i \, e\right)} + f\right)}}"," ",0,"1/3*(-3*I*a*c^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 9*a*c^2*d*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 9*I*a*c*d^2*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 3*a*d^3*e^(6*I*f*x + 6*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 9*I*a*c^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 27*a*c^2*d*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 27*I*a*c*d^2*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 9*a*d^3*e^(4*I*f*x + 4*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 9*I*a*c^3*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 27*a*c^2*d*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 27*I*a*c*d^2*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) + 9*a*d^3*e^(2*I*f*x + 2*I*e)*log(e^(2*I*f*x + 2*I*e) + 1) - 18*a*c^2*d*e^(4*I*f*x + 4*I*e) + 36*I*a*c*d^2*e^(4*I*f*x + 4*I*e) + 18*a*d^3*e^(4*I*f*x + 4*I*e) - 36*a*c^2*d*e^(2*I*f*x + 2*I*e) + 54*I*a*c*d^2*e^(2*I*f*x + 2*I*e) + 18*a*d^3*e^(2*I*f*x + 2*I*e) - 3*I*a*c^3*log(e^(2*I*f*x + 2*I*e) + 1) - 9*a*c^2*d*log(e^(2*I*f*x + 2*I*e) + 1) + 9*I*a*c*d^2*log(e^(2*I*f*x + 2*I*e) + 1) + 3*a*d^3*log(e^(2*I*f*x + 2*I*e) + 1) - 18*a*c^2*d + 18*I*a*c*d^2 + 8*a*d^3)/(f*e^(6*I*f*x + 6*I*e) + 3*f*e^(4*I*f*x + 4*I*e) + 3*f*e^(2*I*f*x + 2*I*e) + f)","B",0
1080,1,186,0,0.946661," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{4 i \, d^{3} \tan\left(f x + e\right)}{a} - \frac{{\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} \log\left(\tan\left(f x + e\right) + i\right)}{a} + \frac{{\left(i \, c^{3} + 3 \, c^{2} d + 9 i \, c d^{2} - 5 \, d^{3}\right)} \log\left(-i \, \tan\left(f x + e\right) - 1\right)}{a} + \frac{-i \, c^{3} \tan\left(f x + e\right) - 3 \, c^{2} d \tan\left(f x + e\right) - 9 i \, c d^{2} \tan\left(f x + e\right) + 5 \, d^{3} \tan\left(f x + e\right) - 3 \, c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} - 3 i \, d^{3}}{a {\left(\tan\left(f x + e\right) - i\right)}}}{4 \, f}"," ",0,"-1/4*(4*I*d^3*tan(f*x + e)/a - (I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*log(tan(f*x + e) + I)/a + (I*c^3 + 3*c^2*d + 9*I*c*d^2 - 5*d^3)*log(-I*tan(f*x + e) - 1)/a + (-I*c^3*tan(f*x + e) - 3*c^2*d*tan(f*x + e) - 9*I*c*d^2*tan(f*x + e) + 5*d^3*tan(f*x + e) - 3*c^3 - 3*I*c^2*d - 3*c*d^2 - 3*I*d^3)/(a*(tan(f*x + e) - I)))/f","A",0
1081,1,226,0,1.135430," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\frac{2 \, {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} \log\left(\tan\left(f x + e\right) + i\right)}{a^{2}} + \frac{2 \, {\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} + 7 \, d^{3}\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a^{2}} + \frac{-3 i \, c^{3} \tan\left(f x + e\right)^{2} - 9 \, c^{2} d \tan\left(f x + e\right)^{2} + 9 i \, c d^{2} \tan\left(f x + e\right)^{2} - 21 \, d^{3} \tan\left(f x + e\right)^{2} - 10 \, c^{3} \tan\left(f x + e\right) + 30 i \, c^{2} d \tan\left(f x + e\right) - 18 \, c d^{2} \tan\left(f x + e\right) + 22 i \, d^{3} \tan\left(f x + e\right) + 11 i \, c^{3} + 9 \, c^{2} d + 15 i \, c d^{2} + 5 \, d^{3}}{a^{2} {\left(\tan\left(f x + e\right) - i\right)}^{2}}}{16 \, f}"," ",0,"-1/16*(2*(-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*log(tan(f*x + e) + I)/a^2 + 2*(I*c^3 + 3*c^2*d - 3*I*c*d^2 + 7*d^3)*log(tan(f*x + e) - I)/a^2 + (-3*I*c^3*tan(f*x + e)^2 - 9*c^2*d*tan(f*x + e)^2 + 9*I*c*d^2*tan(f*x + e)^2 - 21*d^3*tan(f*x + e)^2 - 10*c^3*tan(f*x + e) + 30*I*c^2*d*tan(f*x + e) - 18*c*d^2*tan(f*x + e) + 22*I*d^3*tan(f*x + e) + 11*I*c^3 + 9*c^2*d + 15*I*c*d^2 + 5*d^3)/(a^2*(tan(f*x + e) - I)^2))/f","A",0
1082,1,286,0,1.477670," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{\frac{6 \, {\left(i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}\right)} \log\left(\tan\left(f x + e\right) - i\right)}{a^{3}} + \frac{6 \, {\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} \log\left(i \, \tan\left(f x + e\right) - 1\right)}{a^{3}} + \frac{-11 i \, c^{3} \tan\left(f x + e\right)^{3} - 33 \, c^{2} d \tan\left(f x + e\right)^{3} + 33 i \, c d^{2} \tan\left(f x + e\right)^{3} + 11 \, d^{3} \tan\left(f x + e\right)^{3} - 45 \, c^{3} \tan\left(f x + e\right)^{2} + 135 i \, c^{2} d \tan\left(f x + e\right)^{2} + 135 \, c d^{2} \tan\left(f x + e\right)^{2} + 51 i \, d^{3} \tan\left(f x + e\right)^{2} + 69 i \, c^{3} \tan\left(f x + e\right) + 207 \, c^{2} d \tan\left(f x + e\right) - 63 i \, c d^{2} \tan\left(f x + e\right) + 75 \, d^{3} \tan\left(f x + e\right) + 51 \, c^{3} - 57 i \, c^{2} d - 9 \, c d^{2} - 29 i \, d^{3}}{a^{3} {\left(\tan\left(f x + e\right) - i\right)}^{3}}}{96 \, f}"," ",0,"-1/96*(6*(I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3)*log(tan(f*x + e) - I)/a^3 + 6*(-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*log(I*tan(f*x + e) - 1)/a^3 + (-11*I*c^3*tan(f*x + e)^3 - 33*c^2*d*tan(f*x + e)^3 + 33*I*c*d^2*tan(f*x + e)^3 + 11*d^3*tan(f*x + e)^3 - 45*c^3*tan(f*x + e)^2 + 135*I*c^2*d*tan(f*x + e)^2 + 135*c*d^2*tan(f*x + e)^2 + 51*I*d^3*tan(f*x + e)^2 + 69*I*c^3*tan(f*x + e) + 207*c^2*d*tan(f*x + e) - 63*I*c*d^2*tan(f*x + e) + 75*d^3*tan(f*x + e) + 51*c^3 - 57*I*c^2*d - 9*c*d^2 - 29*I*d^3)/(a^3*(tan(f*x + e) - I)^3))/f","B",0
1083,1,247,0,0.997775," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""giac"")","-\frac{-\frac{8 i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c - i \, d} + \frac{{\left(-i \, a^{3} c^{2} + 2 \, a^{3} c d + i \, a^{3} d^{2}\right)} \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{c d^{2} - i \, d^{3}} - \frac{{\left(-i \, a^{3} c + 3 \, a^{3} d\right)} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{d^{2}} + \frac{{\left(i \, a^{3} c - 3 \, a^{3} d\right)} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{d^{2}} + \frac{-i \, a^{3} c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 \, a^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 i \, a^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i \, a^{3} c - 3 \, a^{3} d}{{\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 1\right)} d^{2}}}{f}"," ",0,"-(-8*I*a^3*log(tan(1/2*f*x + 1/2*e) + I)/(c - I*d) + (-I*a^3*c^2 + 2*a^3*c*d + I*a^3*d^2)*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(c*d^2 - I*d^3) - (-I*a^3*c + 3*a^3*d)*log(tan(1/2*f*x + 1/2*e) + 1)/d^2 + (I*a^3*c - 3*a^3*d)*log(tan(1/2*f*x + 1/2*e) - 1)/d^2 + (-I*a^3*c*tan(1/2*f*x + 1/2*e)^2 + 3*a^3*d*tan(1/2*f*x + 1/2*e)^2 - 2*I*a^3*d*tan(1/2*f*x + 1/2*e) + I*a^3*c - 3*a^3*d)/((tan(1/2*f*x + 1/2*e)^2 - 1)*d^2))/f","B",0
1084,1,127,0,2.015851," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{a^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{d} + \frac{4 i \, a^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c - i \, d} + \frac{a^{2} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{d} - \frac{{\left(a^{2} c + i \, a^{2} d\right)} \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{c d - i \, d^{2}}}{f}"," ",0,"(a^2*log(tan(1/2*f*x + 1/2*e) + 1)/d + 4*I*a^2*log(tan(1/2*f*x + 1/2*e) + I)/(c - I*d) + a^2*log(tan(1/2*f*x + 1/2*e) - 1)/d - (a^2*c + I*a^2*d)*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(c*d - I*d^2))/f","A",0
1085,1,73,0,1.432429," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(-\frac{i \, a \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{2 \, c - 2 i \, d} + \frac{i \, a \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{c - i \, d}\right)}}{f}"," ",0,"2*(-I*a*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(2*c - 2*I*d) + I*a*log(tan(1/2*f*x + 1/2*e) + I)/(c - I*d))/f","A",0
1086,1,180,0,0.416232," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""giac"")","-\frac{-\frac{8 i \, d^{3} \log\left(-i \, d \tan\left(f x + e\right) - i \, c\right)}{2 \, a c^{3} d + 2 i \, a c^{2} d^{2} + 2 \, a c d^{3} + 2 i \, a d^{4}} - \frac{{\left(-i \, c + 3 \, d\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{a c^{2} + 2 i \, a c d - a d^{2}} - \frac{8 \, \log\left(\tan\left(f x + e\right) + i\right)}{-8 i \, a c - 8 \, a d} - \frac{i \, c \tan\left(f x + e\right) - 3 \, d \tan\left(f x + e\right) + 3 \, c + 5 i \, d}{{\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} {\left(\tan\left(f x + e\right) - i\right)}}}{4 \, f}"," ",0,"-1/4*(-8*I*d^3*log(-I*d*tan(f*x + e) - I*c)/(2*a*c^3*d + 2*I*a*c^2*d^2 + 2*a*c*d^3 + 2*I*a*d^4) - (-I*c + 3*d)*log(I*tan(f*x + e) + 1)/(a*c^2 + 2*I*a*c*d - a*d^2) - 8*log(tan(f*x + e) + I)/(-8*I*a*c - 8*a*d) - (I*c*tan(f*x + e) - 3*d*tan(f*x + e) + 3*c + 5*I*d)/((a*c^2 + 2*I*a*c*d - a*d^2)*(tan(f*x + e) - I)))/f","A",0
1087,1,296,0,1.474736," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{d^{4} \log\left(-i \, d \tan\left(f x + e\right) - i \, c\right)}{2 \, a^{2} c^{4} d + 4 i \, a^{2} c^{3} d^{2} + 4 i \, a^{2} c d^{4} - 2 \, a^{2} d^{5}} + \frac{{\left(c^{2} + 4 i \, c d - 7 \, d^{2}\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{-16 i \, a^{2} c^{3} + 48 \, a^{2} c^{2} d + 48 i \, a^{2} c d^{2} - 16 \, a^{2} d^{3}} - \frac{\log\left(\tan\left(f x + e\right) + i\right)}{-16 i \, a^{2} c - 16 \, a^{2} d} - \frac{3 \, c^{2} \tan\left(f x + e\right)^{2} + 12 i \, c d \tan\left(f x + e\right)^{2} - 21 \, d^{2} \tan\left(f x + e\right)^{2} - 10 i \, c^{2} \tan\left(f x + e\right) + 40 \, c d \tan\left(f x + e\right) + 54 i \, d^{2} \tan\left(f x + e\right) - 11 \, c^{2} - 36 i \, c d + 37 \, d^{2}}{{\left(-32 i \, a^{2} c^{3} + 96 \, a^{2} c^{2} d + 96 i \, a^{2} c d^{2} - 32 \, a^{2} d^{3}\right)} {\left(\tan\left(f x + e\right) - i\right)}^{2}}\right)}}{f}"," ",0,"-2*(d^4*log(-I*d*tan(f*x + e) - I*c)/(2*a^2*c^4*d + 4*I*a^2*c^3*d^2 + 4*I*a^2*c*d^4 - 2*a^2*d^5) + (c^2 + 4*I*c*d - 7*d^2)*log(I*tan(f*x + e) + 1)/(-16*I*a^2*c^3 + 48*a^2*c^2*d + 48*I*a^2*c*d^2 - 16*a^2*d^3) - log(tan(f*x + e) + I)/(-16*I*a^2*c - 16*a^2*d) - (3*c^2*tan(f*x + e)^2 + 12*I*c*d*tan(f*x + e)^2 - 21*d^2*tan(f*x + e)^2 - 10*I*c^2*tan(f*x + e) + 40*c*d*tan(f*x + e) + 54*I*d^2*tan(f*x + e) - 11*c^2 - 36*I*c*d + 37*d^2)/((-32*I*a^2*c^3 + 96*a^2*c^2*d + 96*I*a^2*c*d^2 - 32*a^2*d^3)*(tan(f*x + e) - I)^2))/f","B",0
1088,1,447,0,0.853230," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(-\frac{i \, d^{5} \log\left(-i \, d \tan\left(f x + e\right) - i \, c\right)}{2 \, a^{3} c^{5} d + 6 i \, a^{3} c^{4} d^{2} - 4 \, a^{3} c^{3} d^{3} + 4 i \, a^{3} c^{2} d^{4} - 6 \, a^{3} c d^{5} - 2 i \, a^{3} d^{6}} + \frac{{\left(-i \, c^{3} + 5 \, c^{2} d + 11 i \, c d^{2} - 15 \, d^{3}\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{32 \, a^{3} c^{4} + 128 i \, a^{3} c^{3} d - 192 \, a^{3} c^{2} d^{2} - 128 i \, a^{3} c d^{3} + 32 \, a^{3} d^{4}} + \frac{\log\left(\tan\left(f x + e\right) + i\right)}{-32 i \, a^{3} c - 32 \, a^{3} d} + \frac{11 i \, c^{3} \tan\left(f x + e\right)^{3} - 55 \, c^{2} d \tan\left(f x + e\right)^{3} - 121 i \, c d^{2} \tan\left(f x + e\right)^{3} + 165 \, d^{3} \tan\left(f x + e\right)^{3} + 45 \, c^{3} \tan\left(f x + e\right)^{2} + 225 i \, c^{2} d \tan\left(f x + e\right)^{2} - 495 \, c d^{2} \tan\left(f x + e\right)^{2} - 579 i \, d^{3} \tan\left(f x + e\right)^{2} - 69 i \, c^{3} \tan\left(f x + e\right) + 345 \, c^{2} d \tan\left(f x + e\right) + 711 i \, c d^{2} \tan\left(f x + e\right) - 699 \, d^{3} \tan\left(f x + e\right) - 51 \, c^{3} - 223 i \, c^{2} d + 385 \, c d^{2} + 301 i \, d^{3}}{{\left(192 \, a^{3} c^{4} + 768 i \, a^{3} c^{3} d - 1152 \, a^{3} c^{2} d^{2} - 768 i \, a^{3} c d^{3} + 192 \, a^{3} d^{4}\right)} {\left(\tan\left(f x + e\right) - i\right)}^{3}}\right)}}{f}"," ",0,"2*(-I*d^5*log(-I*d*tan(f*x + e) - I*c)/(2*a^3*c^5*d + 6*I*a^3*c^4*d^2 - 4*a^3*c^3*d^3 + 4*I*a^3*c^2*d^4 - 6*a^3*c*d^5 - 2*I*a^3*d^6) + (-I*c^3 + 5*c^2*d + 11*I*c*d^2 - 15*d^3)*log(I*tan(f*x + e) + 1)/(32*a^3*c^4 + 128*I*a^3*c^3*d - 192*a^3*c^2*d^2 - 128*I*a^3*c*d^3 + 32*a^3*d^4) + log(tan(f*x + e) + I)/(-32*I*a^3*c - 32*a^3*d) + (11*I*c^3*tan(f*x + e)^3 - 55*c^2*d*tan(f*x + e)^3 - 121*I*c*d^2*tan(f*x + e)^3 + 165*d^3*tan(f*x + e)^3 + 45*c^3*tan(f*x + e)^2 + 225*I*c^2*d*tan(f*x + e)^2 - 495*c*d^2*tan(f*x + e)^2 - 579*I*d^3*tan(f*x + e)^2 - 69*I*c^3*tan(f*x + e) + 345*c^2*d*tan(f*x + e) + 711*I*c*d^2*tan(f*x + e) - 699*d^3*tan(f*x + e) - 51*c^3 - 223*I*c^2*d + 385*c*d^2 + 301*I*d^3)/((192*a^3*c^4 + 768*I*a^3*c^3*d - 1152*a^3*c^2*d^2 - 768*I*a^3*c*d^3 + 192*a^3*d^4)*(tan(f*x + e) - I)^3))/f","B",0
1089,1,392,0,0.794650," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{8 \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i\right)}{-i \, c^{2} - 2 \, c d + i \, d^{2}} + \frac{i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{d^{2}} + \frac{i \, a^{3} \log\left(\tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 1\right)}{d^{2}} + \frac{2 \, {\left(-i \, a^{3} c^{2} - 2 \, a^{3} c d - 3 i \, a^{3} d^{2}\right)} \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{2 \, c^{2} d^{2} - 4 i \, c d^{3} - 2 \, d^{4}} - \frac{2 \, {\left(-i \, a^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, a^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 3 i \, a^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 i \, a^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 8 i \, a^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + i \, a^{3} c^{4} + 2 \, a^{3} c^{3} d + 3 i \, a^{3} c^{2} d^{2}\right)}}{{\left(2 \, c^{3} d^{2} - 4 i \, c^{2} d^{3} - 2 \, c d^{4}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}}}{f}"," ",0,"(8*a^3*log(tan(1/2*f*x + 1/2*e) + I)/(-I*c^2 - 2*c*d + I*d^2) + I*a^3*log(tan(1/2*f*x + 1/2*e) + 1)/d^2 + I*a^3*log(tan(1/2*f*x + 1/2*e) - 1)/d^2 + 2*(-I*a^3*c^2 - 2*a^3*c*d - 3*I*a^3*d^2)*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(2*c^2*d^2 - 4*I*c*d^3 - 2*d^4) - 2*(-I*a^3*c^4*tan(1/2*f*x + 1/2*e)^2 - 2*a^3*c^3*d*tan(1/2*f*x + 1/2*e)^2 - 3*I*a^3*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 4*I*a^3*c^3*d*tan(1/2*f*x + 1/2*e) + 2*a^3*c^2*d^2*tan(1/2*f*x + 1/2*e) + 8*I*a^3*c*d^3*tan(1/2*f*x + 1/2*e) - 2*a^3*d^4*tan(1/2*f*x + 1/2*e) + I*a^3*c^4 + 2*a^3*c^3*d + 3*I*a^3*c^2*d^2)/((2*c^3*d^2 - 4*I*c^2*d^3 - 2*c*d^4)*(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)))/f","B",0
1090,1,232,0,0.974611," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{a^{2} \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{i \, c^{2} + 2 \, c d - i \, d^{2}} + \frac{2 \, a^{2} \log\left(-i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{-i \, c^{2} - 2 \, c d + i \, d^{2}} - \frac{a^{2} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - i \, a^{2} c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - 2 \, a^{2} c d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - i \, a^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a^{2} c^{2}}{{\left(i \, c^{3} + 2 \, c^{2} d - i \, c d^{2}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}}\right)}}{f}"," ",0,"2*(a^2*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(I*c^2 + 2*c*d - I*d^2) + 2*a^2*log(-I*tan(1/2*f*x + 1/2*e) + 1)/(-I*c^2 - 2*c*d + I*d^2) - (a^2*c^2*tan(1/2*f*x + 1/2*e)^2 - I*a^2*c^2*tan(1/2*f*x + 1/2*e) - 2*a^2*c*d*tan(1/2*f*x + 1/2*e) - I*a^2*d^2*tan(1/2*f*x + 1/2*e) - a^2*c^2)/((I*c^3 + 2*c^2*d - I*c*d^2)*(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)))/f","B",0
1091,1,186,0,0.512040," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{a \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{2 i \, c^{2} + 4 \, c d - 2 i \, d^{2}} + \frac{a \log\left(-i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{-i \, c^{2} - 2 \, c d + i \, d^{2}} - \frac{a c^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 i \, a d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - a c^{2}}{{\left(2 i \, c^{3} + 4 \, c^{2} d - 2 i \, c d^{2}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}}\right)}}{f}"," ",0,"2*(a*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(2*I*c^2 + 4*c*d - 2*I*d^2) + a*log(-I*tan(1/2*f*x + 1/2*e) + 1)/(-I*c^2 - 2*c*d + I*d^2) - (a*c^2*tan(1/2*f*x + 1/2*e)^2 - 2*I*a*d^2*tan(1/2*f*x + 1/2*e) - a*c^2)/((2*I*c^3 + 4*c^2*d - 2*I*c*d^2)*(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)))/f","B",0
1092,1,343,0,0.590964," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{16 \, {\left(3 \, c d^{3} - i \, d^{4}\right)} \log\left(i \, d \tan\left(f x + e\right) + i \, c\right)}{-2 i \, a c^{5} d + 2 \, a c^{4} d^{2} - 4 i \, a c^{3} d^{3} + 4 \, a c^{2} d^{4} - 2 i \, a c d^{5} + 2 \, a d^{6}} - \frac{16 \, {\left(i \, c - 5 \, d\right)} \log\left(\tan\left(f x + e\right) - i\right)}{8 \, a c^{3} + 24 i \, a c^{2} d - 24 \, a c d^{2} - 8 i \, a d^{3}} - \frac{16 \, \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{8 i \, a c^{2} + 16 \, a c d - 8 i \, a d^{2}} + \frac{i \, c^{2} d \tan\left(f x + e\right)^{2} - 2 \, c d^{2} \tan\left(f x + e\right)^{2} - i \, d^{3} \tan\left(f x + e\right)^{2} + i \, c^{3} \tan\left(f x + e\right) + 3 \, c^{2} d \tan\left(f x + e\right) - 15 i \, c d^{2} \tan\left(f x + e\right) - 13 \, d^{3} \tan\left(f x + e\right) + 5 \, c^{3} - 6 i \, c^{2} d - 13 \, c d^{2} + 8 i \, d^{3}}{{\left(a c^{4} + 2 \, a c^{2} d^{2} + a d^{4}\right)} {\left(d \tan\left(f x + e\right)^{2} + c \tan\left(f x + e\right) - i \, d \tan\left(f x + e\right) - i \, c\right)}}}{8 \, f}"," ",0,"1/8*(16*(3*c*d^3 - I*d^4)*log(I*d*tan(f*x + e) + I*c)/(-2*I*a*c^5*d + 2*a*c^4*d^2 - 4*I*a*c^3*d^3 + 4*a*c^2*d^4 - 2*I*a*c*d^5 + 2*a*d^6) - 16*(I*c - 5*d)*log(tan(f*x + e) - I)/(8*a*c^3 + 24*I*a*c^2*d - 24*a*c*d^2 - 8*I*a*d^3) - 16*log(-I*tan(f*x + e) + 1)/(8*I*a*c^2 + 16*a*c*d - 8*I*a*d^2) + (I*c^2*d*tan(f*x + e)^2 - 2*c*d^2*tan(f*x + e)^2 - I*d^3*tan(f*x + e)^2 + I*c^3*tan(f*x + e) + 3*c^2*d*tan(f*x + e) - 15*I*c*d^2*tan(f*x + e) - 13*d^3*tan(f*x + e) + 5*c^3 - 6*I*c^2*d - 13*c*d^2 + 8*I*d^3)/((a*c^4 + 2*a*c^2*d^2 + a*d^4)*(d*tan(f*x + e)^2 + c*tan(f*x + e) - I*d*tan(f*x + e) - I*c)))/f","A",0
1093,1,495,0,0.844650," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(2 \, c d^{4} - i \, d^{5}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{a^{2} c^{6} d + 2 i \, a^{2} c^{5} d^{2} + a^{2} c^{4} d^{3} + 4 i \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} + 2 i \, a^{2} c d^{6} - a^{2} d^{7}} - \frac{{\left(c^{2} + 6 i \, c d - 17 \, d^{2}\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{16 i \, a^{2} c^{4} - 64 \, a^{2} c^{3} d - 96 i \, a^{2} c^{2} d^{2} + 64 \, a^{2} c d^{3} + 16 i \, a^{2} d^{4}} + \frac{\log\left(-i \, \tan\left(f x + e\right) + 1\right)}{16 i \, a^{2} c^{2} + 32 \, a^{2} c d - 16 i \, a^{2} d^{2}} - \frac{4 \, c d^{4} \tan\left(f x + e\right) - 2 i \, d^{5} \tan\left(f x + e\right) + 5 \, c^{2} d^{3} - 2 i \, c d^{4} + d^{5}}{{\left(2 \, a^{2} c^{6} + 4 i \, a^{2} c^{5} d + 2 \, a^{2} c^{4} d^{2} + 8 i \, a^{2} c^{3} d^{3} - 2 \, a^{2} c^{2} d^{4} + 4 i \, a^{2} c d^{5} - 2 \, a^{2} d^{6}\right)} {\left(d \tan\left(f x + e\right) + c\right)}} + \frac{3 \, c^{2} \tan\left(f x + e\right)^{2} + 18 i \, c d \tan\left(f x + e\right)^{2} - 51 \, d^{2} \tan\left(f x + e\right)^{2} - 10 i \, c^{2} \tan\left(f x + e\right) + 60 \, c d \tan\left(f x + e\right) + 122 i \, d^{2} \tan\left(f x + e\right) - 11 \, c^{2} - 50 i \, c d + 75 \, d^{2}}{{\left(32 i \, a^{2} c^{4} - 128 \, a^{2} c^{3} d - 192 i \, a^{2} c^{2} d^{2} + 128 \, a^{2} c d^{3} + 32 i \, a^{2} d^{4}\right)} {\left(\tan\left(f x + e\right) - i\right)}^{2}}\right)}}{f}"," ",0,"-2*((2*c*d^4 - I*d^5)*log(d*tan(f*x + e) + c)/(a^2*c^6*d + 2*I*a^2*c^5*d^2 + a^2*c^4*d^3 + 4*I*a^2*c^3*d^4 - a^2*c^2*d^5 + 2*I*a^2*c*d^6 - a^2*d^7) - (c^2 + 6*I*c*d - 17*d^2)*log(I*tan(f*x + e) + 1)/(16*I*a^2*c^4 - 64*a^2*c^3*d - 96*I*a^2*c^2*d^2 + 64*a^2*c*d^3 + 16*I*a^2*d^4) + log(-I*tan(f*x + e) + 1)/(16*I*a^2*c^2 + 32*a^2*c*d - 16*I*a^2*d^2) - (4*c*d^4*tan(f*x + e) - 2*I*d^5*tan(f*x + e) + 5*c^2*d^3 - 2*I*c*d^4 + d^5)/((2*a^2*c^6 + 4*I*a^2*c^5*d + 2*a^2*c^4*d^2 + 8*I*a^2*c^3*d^3 - 2*a^2*c^2*d^4 + 4*I*a^2*c*d^5 - 2*a^2*d^6)*(d*tan(f*x + e) + c)) + (3*c^2*tan(f*x + e)^2 + 18*I*c*d*tan(f*x + e)^2 - 51*d^2*tan(f*x + e)^2 - 10*I*c^2*tan(f*x + e) + 60*c*d*tan(f*x + e) + 122*I*d^2*tan(f*x + e) - 11*c^2 - 50*I*c*d + 75*d^2)/((32*I*a^2*c^4 - 128*a^2*c^3*d - 192*I*a^2*c^2*d^2 + 128*a^2*c*d^3 + 32*I*a^2*d^4)*(tan(f*x + e) - I)^2))/f","B",0
1094,1,648,0,1.232065," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(5 \, c d^{5} - 3 i \, d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{-2 i \, a^{3} c^{7} d + 6 \, a^{3} c^{6} d^{2} + 2 i \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} + 10 i \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 6 i \, a^{3} c d^{7} - 2 \, a^{3} d^{8}} - \frac{{\left(c^{3} + 7 i \, c^{2} d - 23 \, c d^{2} - 49 i \, d^{3}\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{32 i \, a^{3} c^{5} - 160 \, a^{3} c^{4} d - 320 i \, a^{3} c^{3} d^{2} + 320 \, a^{3} c^{2} d^{3} + 160 i \, a^{3} c d^{4} - 32 \, a^{3} d^{5}} - \frac{\log\left(-i \, \tan\left(f x + e\right) + 1\right)}{-32 i \, a^{3} c^{2} - 64 \, a^{3} c d + 32 i \, a^{3} d^{2}} - \frac{5 \, c d^{5} \tan\left(f x + e\right) - 3 i \, d^{6} \tan\left(f x + e\right) + 6 \, c^{2} d^{4} - 3 i \, c d^{5} + d^{6}}{{\left(-2 i \, a^{3} c^{7} + 6 \, a^{3} c^{6} d + 2 i \, a^{3} c^{5} d^{2} + 10 \, a^{3} c^{4} d^{3} + 10 i \, a^{3} c^{3} d^{4} + 2 \, a^{3} c^{2} d^{5} + 6 i \, a^{3} c d^{6} - 2 \, a^{3} d^{7}\right)} {\left(d \tan\left(f x + e\right) + c\right)}} + \frac{11 \, c^{3} \tan\left(f x + e\right)^{3} + 77 i \, c^{2} d \tan\left(f x + e\right)^{3} - 253 \, c d^{2} \tan\left(f x + e\right)^{3} - 539 i \, d^{3} \tan\left(f x + e\right)^{3} - 45 i \, c^{3} \tan\left(f x + e\right)^{2} + 315 \, c^{2} d \tan\left(f x + e\right)^{2} + 1035 i \, c d^{2} \tan\left(f x + e\right)^{2} - 1821 \, d^{3} \tan\left(f x + e\right)^{2} - 69 \, c^{3} \tan\left(f x + e\right) - 483 i \, c^{2} d \tan\left(f x + e\right) + 1443 \, c d^{2} \tan\left(f x + e\right) + 2085 i \, d^{3} \tan\left(f x + e\right) + 51 i \, c^{3} - 293 \, c^{2} d - 709 i \, c d^{2} + 819 \, d^{3}}{{\left(192 i \, a^{3} c^{5} - 960 \, a^{3} c^{4} d - 1920 i \, a^{3} c^{3} d^{2} + 1920 \, a^{3} c^{2} d^{3} + 960 i \, a^{3} c d^{4} - 192 \, a^{3} d^{5}\right)} {\left(\tan\left(f x + e\right) - i\right)}^{3}}\right)}}{f}"," ",0,"-2*((5*c*d^5 - 3*I*d^6)*log(d*tan(f*x + e) + c)/(-2*I*a^3*c^7*d + 6*a^3*c^6*d^2 + 2*I*a^3*c^5*d^3 + 10*a^3*c^4*d^4 + 10*I*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 6*I*a^3*c*d^7 - 2*a^3*d^8) - (c^3 + 7*I*c^2*d - 23*c*d^2 - 49*I*d^3)*log(I*tan(f*x + e) + 1)/(32*I*a^3*c^5 - 160*a^3*c^4*d - 320*I*a^3*c^3*d^2 + 320*a^3*c^2*d^3 + 160*I*a^3*c*d^4 - 32*a^3*d^5) - log(-I*tan(f*x + e) + 1)/(-32*I*a^3*c^2 - 64*a^3*c*d + 32*I*a^3*d^2) - (5*c*d^5*tan(f*x + e) - 3*I*d^6*tan(f*x + e) + 6*c^2*d^4 - 3*I*c*d^5 + d^6)/((-2*I*a^3*c^7 + 6*a^3*c^6*d + 2*I*a^3*c^5*d^2 + 10*a^3*c^4*d^3 + 10*I*a^3*c^3*d^4 + 2*a^3*c^2*d^5 + 6*I*a^3*c*d^6 - 2*a^3*d^7)*(d*tan(f*x + e) + c)) + (11*c^3*tan(f*x + e)^3 + 77*I*c^2*d*tan(f*x + e)^3 - 253*c*d^2*tan(f*x + e)^3 - 539*I*d^3*tan(f*x + e)^3 - 45*I*c^3*tan(f*x + e)^2 + 315*c^2*d*tan(f*x + e)^2 + 1035*I*c*d^2*tan(f*x + e)^2 - 1821*d^3*tan(f*x + e)^2 - 69*c^3*tan(f*x + e) - 483*I*c^2*d*tan(f*x + e) + 1443*c*d^2*tan(f*x + e) + 2085*I*d^3*tan(f*x + e) + 51*I*c^3 - 293*c^2*d - 709*I*c*d^2 + 819*d^3)/((192*I*a^3*c^5 - 960*a^3*c^4*d - 1920*I*a^3*c^3*d^2 + 1920*a^3*c^2*d^3 + 960*I*a^3*c*d^4 - 192*a^3*d^5)*(tan(f*x + e) - I)^3))/f","B",0
1095,1,470,0,1.123776," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{2 \, a^{3} \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}} - \frac{4 \, a^{3} \log\left(-i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}} + \frac{3 \, a^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 3 i \, a^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 13 \, a^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 3 i \, a^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - a^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 7 \, a^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 i \, a^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 12 \, a^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 i \, a^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + a^{3} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 3 i \, a^{3} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 13 \, a^{3} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 i \, a^{3} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + a^{3} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a^{3} c^{4}}{{\left(-i \, c^{5} - 3 \, c^{4} d + 3 i \, c^{3} d^{2} + c^{2} d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}^{2}}\right)}}{f}"," ",0,"2*(2*a^3*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3) - 4*a^3*log(-I*tan(1/2*f*x + 1/2*e) + 1)/(I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3) + (3*a^3*c^4*tan(1/2*f*x + 1/2*e)^4 - 3*I*a^3*c^4*tan(1/2*f*x + 1/2*e)^3 - 13*a^3*c^3*d*tan(1/2*f*x + 1/2*e)^3 - 3*I*a^3*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 - a^3*c*d^3*tan(1/2*f*x + 1/2*e)^3 - 7*a^3*c^4*tan(1/2*f*x + 1/2*e)^2 + 6*I*a^3*c^3*d*tan(1/2*f*x + 1/2*e)^2 + 12*a^3*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 6*I*a^3*c*d^3*tan(1/2*f*x + 1/2*e)^2 + a^3*d^4*tan(1/2*f*x + 1/2*e)^2 + 3*I*a^3*c^4*tan(1/2*f*x + 1/2*e) + 13*a^3*c^3*d*tan(1/2*f*x + 1/2*e) + 3*I*a^3*c^2*d^2*tan(1/2*f*x + 1/2*e) + a^3*c*d^3*tan(1/2*f*x + 1/2*e) + 3*a^3*c^4)/((-I*c^5 - 3*c^4*d + 3*I*c^3*d^2 + c^2*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)^2))/f","B",0
1096,1,472,0,0.936894," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{a^{2} \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}} - \frac{2 \, a^{2} \log\left(-i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}} + \frac{3 \, a^{2} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 2 i \, a^{2} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 10 \, a^{2} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 i \, a^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 2 \, a^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a^{2} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 i \, a^{2} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 6 \, a^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 10 i \, a^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 2 i \, a^{2} c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 10 \, a^{2} c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 6 i \, a^{2} c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 2 \, a^{2} c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a^{2} c^{4}}{{\left(-2 i \, c^{5} - 6 \, c^{4} d + 6 i \, c^{3} d^{2} + 2 \, c^{2} d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}^{2}}\right)}}{f}"," ",0,"2*(a^2*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3) - 2*a^2*log(-I*tan(1/2*f*x + 1/2*e) + 1)/(I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3) + (3*a^2*c^4*tan(1/2*f*x + 1/2*e)^4 - 2*I*a^2*c^4*tan(1/2*f*x + 1/2*e)^3 - 10*a^2*c^3*d*tan(1/2*f*x + 1/2*e)^3 - 6*I*a^2*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 - 2*a^2*c*d^3*tan(1/2*f*x + 1/2*e)^3 - 6*a^2*c^4*tan(1/2*f*x + 1/2*e)^2 + 2*I*a^2*c^3*d*tan(1/2*f*x + 1/2*e)^2 + 6*a^2*c^2*d^2*tan(1/2*f*x + 1/2*e)^2 + 10*I*a^2*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 2*a^2*d^4*tan(1/2*f*x + 1/2*e)^2 + 2*I*a^2*c^4*tan(1/2*f*x + 1/2*e) + 10*a^2*c^3*d*tan(1/2*f*x + 1/2*e) + 6*I*a^2*c^2*d^2*tan(1/2*f*x + 1/2*e) + 2*a^2*c*d^3*tan(1/2*f*x + 1/2*e) + 3*a^2*c^4)/((-2*I*c^5 - 6*c^4*d + 6*I*c^3*d^2 + 2*c^2*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)^2))/f","B",0
1097,1,364,0,0.830537," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{2 \, {\left(\frac{a \log\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}{2 i \, c^{3} + 6 \, c^{2} d - 6 i \, c d^{2} - 2 \, d^{3}} - \frac{a \log\left(-i \, \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 1\right)}{i \, c^{3} + 3 \, c^{2} d - 3 i \, c d^{2} - d^{3}} + \frac{3 \, a c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{4} - 4 \, a c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 12 i \, a c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 4 \, a c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{3} - 6 \, a c^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 16 i \, a c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a d^{4} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} + 4 \, a c^{3} d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 12 i \, a c^{2} d^{2} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 4 \, a c d^{3} \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) + 3 \, a c^{4}}{{\left(-4 i \, c^{5} - 12 \, c^{4} d + 12 i \, c^{3} d^{2} + 4 \, c^{2} d^{3}\right)} {\left(c \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right)^{2} - 2 \, d \tan\left(\frac{1}{2} \, f x + \frac{1}{2} \, e\right) - c\right)}^{2}}\right)}}{f}"," ",0,"2*(a*log(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)/(2*I*c^3 + 6*c^2*d - 6*I*c*d^2 - 2*d^3) - a*log(-I*tan(1/2*f*x + 1/2*e) + 1)/(I*c^3 + 3*c^2*d - 3*I*c*d^2 - d^3) + (3*a*c^4*tan(1/2*f*x + 1/2*e)^4 - 4*a*c^3*d*tan(1/2*f*x + 1/2*e)^3 - 12*I*a*c^2*d^2*tan(1/2*f*x + 1/2*e)^3 - 4*a*c*d^3*tan(1/2*f*x + 1/2*e)^3 - 6*a*c^4*tan(1/2*f*x + 1/2*e)^2 + 16*I*a*c*d^3*tan(1/2*f*x + 1/2*e)^2 + 4*a*d^4*tan(1/2*f*x + 1/2*e)^2 + 4*a*c^3*d*tan(1/2*f*x + 1/2*e) + 12*I*a*c^2*d^2*tan(1/2*f*x + 1/2*e) + 4*a*c*d^3*tan(1/2*f*x + 1/2*e) + 3*a*c^4)/((-4*I*c^5 - 12*c^4*d + 12*I*c^3*d^2 + 4*c^2*d^3)*(c*tan(1/2*f*x + 1/2*e)^2 - 2*d*tan(1/2*f*x + 1/2*e) - c)^2))/f","B",0
1098,1,500,0,0.982833," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(3 \, c^{2} d^{3} - 2 i \, c d^{4} - d^{5}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{i \, a c^{7} d - a c^{6} d^{2} + 3 i \, a c^{5} d^{3} - 3 \, a c^{4} d^{4} + 3 i \, a c^{3} d^{5} - 3 \, a c^{2} d^{6} + i \, a c d^{7} - a d^{8}} + \frac{{\left(i \, c - 7 \, d\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{8 \, a c^{4} + 32 i \, a c^{3} d - 48 \, a c^{2} d^{2} - 32 i \, a c d^{3} + 8 \, a d^{4}} - \frac{i \, \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{8 \, a c^{3} - 24 i \, a c^{2} d - 24 \, a c d^{2} + 8 i \, a d^{3}} + \frac{-i \, c \tan\left(f x + e\right) + 7 \, d \tan\left(f x + e\right) - 3 \, c - 9 i \, d}{{\left(8 \, a c^{4} + 32 i \, a c^{3} d - 48 \, a c^{2} d^{2} - 32 i \, a c d^{3} + 8 \, a d^{4}\right)} {\left(\tan\left(f x + e\right) - i\right)}} - \frac{18 \, c^{2} d^{4} \tan\left(f x + e\right)^{2} - 12 i \, c d^{5} \tan\left(f x + e\right)^{2} - 6 \, d^{6} \tan\left(f x + e\right)^{2} + 42 \, c^{3} d^{3} \tan\left(f x + e\right) - 26 i \, c^{2} d^{4} \tan\left(f x + e\right) - 6 \, c d^{5} \tan\left(f x + e\right) - 2 i \, d^{6} \tan\left(f x + e\right) + 25 \, c^{4} d^{2} - 14 i \, c^{3} d^{3} + 2 \, c^{2} d^{4} - 2 i \, c d^{5} + d^{6}}{{\left(4 i \, a c^{7} - 4 \, a c^{6} d + 12 i \, a c^{5} d^{2} - 12 \, a c^{4} d^{3} + 12 i \, a c^{3} d^{4} - 12 \, a c^{2} d^{5} + 4 i \, a c d^{6} - 4 \, a d^{7}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}\right)}}{f}"," ",0,"-2*((3*c^2*d^3 - 2*I*c*d^4 - d^5)*log(d*tan(f*x + e) + c)/(I*a*c^7*d - a*c^6*d^2 + 3*I*a*c^5*d^3 - 3*a*c^4*d^4 + 3*I*a*c^3*d^5 - 3*a*c^2*d^6 + I*a*c*d^7 - a*d^8) + (I*c - 7*d)*log(I*tan(f*x + e) + 1)/(8*a*c^4 + 32*I*a*c^3*d - 48*a*c^2*d^2 - 32*I*a*c*d^3 + 8*a*d^4) - I*log(-I*tan(f*x + e) + 1)/(8*a*c^3 - 24*I*a*c^2*d - 24*a*c*d^2 + 8*I*a*d^3) + (-I*c*tan(f*x + e) + 7*d*tan(f*x + e) - 3*c - 9*I*d)/((8*a*c^4 + 32*I*a*c^3*d - 48*a*c^2*d^2 - 32*I*a*c*d^3 + 8*a*d^4)*(tan(f*x + e) - I)) - (18*c^2*d^4*tan(f*x + e)^2 - 12*I*c*d^5*tan(f*x + e)^2 - 6*d^6*tan(f*x + e)^2 + 42*c^3*d^3*tan(f*x + e) - 26*I*c^2*d^4*tan(f*x + e) - 6*c*d^5*tan(f*x + e) - 2*I*d^6*tan(f*x + e) + 25*c^4*d^2 - 14*I*c^3*d^3 + 2*c^2*d^4 - 2*I*c*d^5 + d^6)/((4*I*a*c^7 - 4*a*c^6*d + 12*I*a*c^5*d^2 - 12*a*c^4*d^3 + 12*I*a*c^3*d^4 - 12*a*c^2*d^5 + 4*I*a*c*d^6 - 4*a*d^7)*(d*tan(f*x + e) + c)^2))/f","B",0
1099,1,805,0,1.350613," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(5 \, c^{2} d^{4} - 5 i \, c d^{5} - 2 \, d^{6}\right)} \log\left(i \, d \tan\left(f x + e\right) + i \, c\right)}{a^{2} c^{8} d + 2 i \, a^{2} c^{7} d^{2} + 2 \, a^{2} c^{6} d^{3} + 6 i \, a^{2} c^{5} d^{4} + 6 i \, a^{2} c^{3} d^{6} - 2 \, a^{2} c^{2} d^{7} + 2 i \, a^{2} c d^{8} - a^{2} d^{9}} + \frac{{\left(i \, c^{2} - 8 \, c d - 31 i \, d^{2}\right)} \log\left(\tan\left(f x + e\right) - i\right)}{16 \, a^{2} c^{5} + 80 i \, a^{2} c^{4} d - 160 \, a^{2} c^{3} d^{2} - 160 i \, a^{2} c^{2} d^{3} + 80 \, a^{2} c d^{4} + 16 i \, a^{2} d^{5}} + \frac{\log\left(-i \, \tan\left(f x + e\right) + 1\right)}{16 i \, a^{2} c^{3} + 48 \, a^{2} c^{2} d - 48 i \, a^{2} c d^{2} - 16 \, a^{2} d^{3}} - \frac{3 \, c^{4} d^{2} \tan\left(f x + e\right)^{4} + 12 i \, c^{3} d^{3} \tan\left(f x + e\right)^{4} - 18 \, c^{2} d^{4} \tan\left(f x + e\right)^{4} - 12 i \, c d^{5} \tan\left(f x + e\right)^{4} + 3 \, d^{6} \tan\left(f x + e\right)^{4} + 6 \, c^{5} d \tan\left(f x + e\right)^{3} + 10 i \, c^{4} d^{2} \tan\left(f x + e\right)^{3} + 20 \, c^{3} d^{3} \tan\left(f x + e\right)^{3} - 260 i \, c^{2} d^{4} \tan\left(f x + e\right)^{3} - 370 \, c d^{5} \tan\left(f x + e\right)^{3} + 114 i \, d^{6} \tan\left(f x + e\right)^{3} + 3 \, c^{6} \tan\left(f x + e\right)^{2} - 16 i \, c^{5} d \tan\left(f x + e\right)^{2} + 75 \, c^{4} d^{2} \tan\left(f x + e\right)^{2} - 400 i \, c^{3} d^{3} \tan\left(f x + e\right)^{2} - 955 \, c^{2} d^{4} \tan\left(f x + e\right)^{2} + 720 i \, c d^{5} \tan\left(f x + e\right)^{2} + 173 \, d^{6} \tan\left(f x + e\right)^{2} - 14 i \, c^{6} \tan\left(f x + e\right) + 18 \, c^{5} d \tan\left(f x + e\right) - 164 i \, c^{4} d^{2} \tan\left(f x + e\right) - 724 \, c^{3} d^{3} \tan\left(f x + e\right) + 970 i \, c^{2} d^{4} \tan\left(f x + e\right) + 410 \, c d^{5} \tan\left(f x + e\right) - 32 i \, d^{6} \tan\left(f x + e\right) - 19 \, c^{6} - 28 i \, c^{5} d - 126 \, c^{4} d^{2} + 332 i \, c^{3} d^{3} + 269 \, c^{2} d^{4} - 48 i \, c d^{5} + 16 \, d^{6}}{{\left(-64 i \, a^{2} c^{7} + 64 \, a^{2} c^{6} d - 192 i \, a^{2} c^{5} d^{2} + 192 \, a^{2} c^{4} d^{3} - 192 i \, a^{2} c^{3} d^{4} + 192 \, a^{2} c^{2} d^{5} - 64 i \, a^{2} c d^{6} + 64 \, a^{2} d^{7}\right)} {\left(d \tan\left(f x + e\right)^{2} + c \tan\left(f x + e\right) - i \, d \tan\left(f x + e\right) - i \, c\right)}^{2}}\right)}}{f}"," ",0,"-2*((5*c^2*d^4 - 5*I*c*d^5 - 2*d^6)*log(I*d*tan(f*x + e) + I*c)/(a^2*c^8*d + 2*I*a^2*c^7*d^2 + 2*a^2*c^6*d^3 + 6*I*a^2*c^5*d^4 + 6*I*a^2*c^3*d^6 - 2*a^2*c^2*d^7 + 2*I*a^2*c*d^8 - a^2*d^9) + (I*c^2 - 8*c*d - 31*I*d^2)*log(tan(f*x + e) - I)/(16*a^2*c^5 + 80*I*a^2*c^4*d - 160*a^2*c^3*d^2 - 160*I*a^2*c^2*d^3 + 80*a^2*c*d^4 + 16*I*a^2*d^5) + log(-I*tan(f*x + e) + 1)/(16*I*a^2*c^3 + 48*a^2*c^2*d - 48*I*a^2*c*d^2 - 16*a^2*d^3) - (3*c^4*d^2*tan(f*x + e)^4 + 12*I*c^3*d^3*tan(f*x + e)^4 - 18*c^2*d^4*tan(f*x + e)^4 - 12*I*c*d^5*tan(f*x + e)^4 + 3*d^6*tan(f*x + e)^4 + 6*c^5*d*tan(f*x + e)^3 + 10*I*c^4*d^2*tan(f*x + e)^3 + 20*c^3*d^3*tan(f*x + e)^3 - 260*I*c^2*d^4*tan(f*x + e)^3 - 370*c*d^5*tan(f*x + e)^3 + 114*I*d^6*tan(f*x + e)^3 + 3*c^6*tan(f*x + e)^2 - 16*I*c^5*d*tan(f*x + e)^2 + 75*c^4*d^2*tan(f*x + e)^2 - 400*I*c^3*d^3*tan(f*x + e)^2 - 955*c^2*d^4*tan(f*x + e)^2 + 720*I*c*d^5*tan(f*x + e)^2 + 173*d^6*tan(f*x + e)^2 - 14*I*c^6*tan(f*x + e) + 18*c^5*d*tan(f*x + e) - 164*I*c^4*d^2*tan(f*x + e) - 724*c^3*d^3*tan(f*x + e) + 970*I*c^2*d^4*tan(f*x + e) + 410*c*d^5*tan(f*x + e) - 32*I*d^6*tan(f*x + e) - 19*c^6 - 28*I*c^5*d - 126*c^4*d^2 + 332*I*c^3*d^3 + 269*c^2*d^4 - 48*I*c*d^5 + 16*d^6)/((-64*I*a^2*c^7 + 64*a^2*c^6*d - 192*I*a^2*c^5*d^2 + 192*a^2*c^4*d^3 - 192*I*a^2*c^3*d^4 + 192*a^2*c^2*d^5 - 64*I*a^2*c*d^6 + 64*a^2*d^7)*(d*tan(f*x + e)^2 + c*tan(f*x + e) - I*d*tan(f*x + e) - I*c)^2))/f","B",0
1100,1,784,0,1.742470," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(\frac{{\left(15 \, c^{2} d^{5} - 18 i \, c d^{6} - 7 \, d^{7}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{-2 i \, a^{3} c^{9} d + 6 \, a^{3} c^{8} d^{2} + 16 \, a^{3} c^{6} d^{4} + 12 i \, a^{3} c^{5} d^{5} + 12 \, a^{3} c^{4} d^{6} + 16 i \, a^{3} c^{3} d^{7} + 6 i \, a^{3} c d^{9} - 2 \, a^{3} d^{10}} - \frac{{\left(-i \, c^{3} + 9 \, c^{2} d + 39 i \, c d^{2} - 111 \, d^{3}\right)} \log\left(i \, \tan\left(f x + e\right) + 1\right)}{32 \, a^{3} c^{6} + 192 i \, a^{3} c^{5} d - 480 \, a^{3} c^{4} d^{2} - 640 i \, a^{3} c^{3} d^{3} + 480 \, a^{3} c^{2} d^{4} + 192 i \, a^{3} c d^{5} - 32 \, a^{3} d^{6}} - \frac{i \, \log\left(-i \, \tan\left(f x + e\right) + 1\right)}{32 \, a^{3} c^{3} - 96 i \, a^{3} c^{2} d - 96 \, a^{3} c d^{2} + 32 i \, a^{3} d^{3}} - \frac{45 \, c^{2} d^{6} \tan\left(f x + e\right)^{2} - 54 i \, c d^{7} \tan\left(f x + e\right)^{2} - 21 \, d^{8} \tan\left(f x + e\right)^{2} + 100 \, c^{3} d^{5} \tan\left(f x + e\right) - 114 i \, c^{2} d^{6} \tan\left(f x + e\right) - 32 \, c d^{7} \tan\left(f x + e\right) - 6 i \, d^{8} \tan\left(f x + e\right) + 56 \, c^{4} d^{4} - 60 i \, c^{3} d^{5} - 9 \, c^{2} d^{6} - 6 i \, c d^{7} + d^{8}}{{\left(-4 i \, a^{3} c^{9} + 12 \, a^{3} c^{8} d + 32 \, a^{3} c^{6} d^{3} + 24 i \, a^{3} c^{5} d^{4} + 24 \, a^{3} c^{4} d^{5} + 32 i \, a^{3} c^{3} d^{6} + 12 i \, a^{3} c d^{8} - 4 \, a^{3} d^{9}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}} - \frac{11 i \, c^{3} \tan\left(f x + e\right)^{3} - 99 \, c^{2} d \tan\left(f x + e\right)^{3} - 429 i \, c d^{2} \tan\left(f x + e\right)^{3} + 1221 \, d^{3} \tan\left(f x + e\right)^{3} + 45 \, c^{3} \tan\left(f x + e\right)^{2} + 405 i \, c^{2} d \tan\left(f x + e\right)^{2} - 1755 \, c d^{2} \tan\left(f x + e\right)^{2} - 4035 i \, d^{3} \tan\left(f x + e\right)^{2} - 69 i \, c^{3} \tan\left(f x + e\right) + 621 \, c^{2} d \tan\left(f x + e\right) + 2403 i \, c d^{2} \tan\left(f x + e\right) - 4491 \, d^{3} \tan\left(f x + e\right) - 51 \, c^{3} - 363 i \, c^{2} d + 1125 \, c d^{2} + 1693 i \, d^{3}}{{\left(192 \, a^{3} c^{6} + 1152 i \, a^{3} c^{5} d - 2880 \, a^{3} c^{4} d^{2} - 3840 i \, a^{3} c^{3} d^{3} + 2880 \, a^{3} c^{2} d^{4} + 1152 i \, a^{3} c d^{5} - 192 \, a^{3} d^{6}\right)} {\left(\tan\left(f x + e\right) - i\right)}^{3}}\right)}}{f}"," ",0,"-2*((15*c^2*d^5 - 18*I*c*d^6 - 7*d^7)*log(d*tan(f*x + e) + c)/(-2*I*a^3*c^9*d + 6*a^3*c^8*d^2 + 16*a^3*c^6*d^4 + 12*I*a^3*c^5*d^5 + 12*a^3*c^4*d^6 + 16*I*a^3*c^3*d^7 + 6*I*a^3*c*d^9 - 2*a^3*d^10) - (-I*c^3 + 9*c^2*d + 39*I*c*d^2 - 111*d^3)*log(I*tan(f*x + e) + 1)/(32*a^3*c^6 + 192*I*a^3*c^5*d - 480*a^3*c^4*d^2 - 640*I*a^3*c^3*d^3 + 480*a^3*c^2*d^4 + 192*I*a^3*c*d^5 - 32*a^3*d^6) - I*log(-I*tan(f*x + e) + 1)/(32*a^3*c^3 - 96*I*a^3*c^2*d - 96*a^3*c*d^2 + 32*I*a^3*d^3) - (45*c^2*d^6*tan(f*x + e)^2 - 54*I*c*d^7*tan(f*x + e)^2 - 21*d^8*tan(f*x + e)^2 + 100*c^3*d^5*tan(f*x + e) - 114*I*c^2*d^6*tan(f*x + e) - 32*c*d^7*tan(f*x + e) - 6*I*d^8*tan(f*x + e) + 56*c^4*d^4 - 60*I*c^3*d^5 - 9*c^2*d^6 - 6*I*c*d^7 + d^8)/((-4*I*a^3*c^9 + 12*a^3*c^8*d + 32*a^3*c^6*d^3 + 24*I*a^3*c^5*d^4 + 24*a^3*c^4*d^5 + 32*I*a^3*c^3*d^6 + 12*I*a^3*c*d^8 - 4*a^3*d^9)*(d*tan(f*x + e) + c)^2) - (11*I*c^3*tan(f*x + e)^3 - 99*c^2*d*tan(f*x + e)^3 - 429*I*c*d^2*tan(f*x + e)^3 + 1221*d^3*tan(f*x + e)^3 + 45*c^3*tan(f*x + e)^2 + 405*I*c^2*d*tan(f*x + e)^2 - 1755*c*d^2*tan(f*x + e)^2 - 4035*I*d^3*tan(f*x + e)^2 - 69*I*c^3*tan(f*x + e) + 621*c^2*d*tan(f*x + e) + 2403*I*c*d^2*tan(f*x + e) - 4491*d^3*tan(f*x + e) - 51*c^3 - 363*I*c^2*d + 1125*c*d^2 + 1693*I*d^3)/((192*a^3*c^6 + 1152*I*a^3*c^5*d - 2880*a^3*c^4*d^2 - 3840*I*a^3*c^3*d^3 + 2880*a^3*c^2*d^4 + 1152*I*a^3*c*d^5 - 192*a^3*d^6)*(tan(f*x + e) - I)^3))/f","B",0
1101,1,277,0,0.748885," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{32 \, {\left(-i \, a^{3} c - a^{3} d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} d^{8} f^{4} - 10 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} c d^{8} f^{4} + 30 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} d^{9} f^{4} - 120 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} d^{10} f^{4}}{15 \, d^{10} f^{5}}"," ",0,"-32*(-I*a^3*c - a^3*d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/15*(6*I*(d*tan(f*x + e) + c)^(5/2)*a^3*d^8*f^4 - 10*I*(d*tan(f*x + e) + c)^(3/2)*a^3*c*d^8*f^4 + 30*(d*tan(f*x + e) + c)^(3/2)*a^3*d^9*f^4 - 120*I*sqrt(d*tan(f*x + e) + c)*a^3*d^10*f^4)/(d^10*f^5)","B",0
1102,1,228,0,0.674925," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{16 \, {\left(-i \, a^{2} c - a^{2} d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} d^{2} f^{2} - 12 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{2} d^{3} f^{2}}{3 \, d^{3} f^{3}}"," ",0,"-16*(-I*a^2*c - a^2*d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/3*(2*(d*tan(f*x + e) + c)^(3/2)*a^2*d^2*f^2 - 12*I*sqrt(d*tan(f*x + e) + c)*a^2*d^3*f^2)/(d^3*f^3)","B",0
1103,1,185,0,0.415213," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 i \, \sqrt{d \tan\left(f x + e\right) + c} a}{f} + \frac{8 \, {\left(i \, a c + a d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"2*I*sqrt(d*tan(f*x + e) + c)*a/f + 8*(I*a*c + a*d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1104,1,358,0,0.506778," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{\sqrt{2} c \arctan\left(\frac{16 i \, \sqrt{d \tan\left(f x + e\right) + c} c + 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c + i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{2 \, a \sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{\sqrt{d \tan\left(f x + e\right) + c} d}{2 \, {\left(d \tan\left(f x + e\right) - i \, d\right)} a f} + \frac{2 \, {\left(i \, c + d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{a \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"1/2*sqrt(2)*c*arctan(1/8*(16*I*sqrt(d*tan(f*x + e) + c)*c + 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c + I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(a*sqrt(c + sqrt(c^2 + d^2))*f*(I*d/(c + sqrt(c^2 + d^2)) + 1)) + 1/2*sqrt(d*tan(f*x + e) + c)*d/((d*tan(f*x + e) - I*d)*a*f) + 2*(I*c + d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1105,1,469,0,0.604740," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c^{2} + 2 i \, c d + d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-4 i \, a^{2} c f + 4 \, a^{2} d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d - 2 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d + i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{2} - 5 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{2} + 3 \, \sqrt{d \tan\left(f x + e\right) + c} d^{3}}{8 \, {\left(a^{2} c f + i \, a^{2} d f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2}} + \frac{\sqrt{2} {\left(c - i \, d\right)} \arctan\left(\frac{-16 i \, \sqrt{d \tan\left(f x + e\right) + c} c - 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c - i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{4 \, a^{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"-2*(2*c^2 + 2*I*c*d + d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-4*I*a^2*c*f + 4*a^2*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/8*(2*(d*tan(f*x + e) + c)^(3/2)*c*d - 2*sqrt(d*tan(f*x + e) + c)*c^2*d + I*(d*tan(f*x + e) + c)^(3/2)*d^2 - 5*I*sqrt(d*tan(f*x + e) + c)*c*d^2 + 3*sqrt(d*tan(f*x + e) + c)*d^3)/((a^2*c*f + I*a^2*d*f)*(d*tan(f*x + e) - I*d)^2) + 1/4*sqrt(2)*(c - I*d)*arctan(1/8*(-16*I*sqrt(d*tan(f*x + e) + c)*c - 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c - I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(a^2*sqrt(c + sqrt(c^2 + d^2))*f*(-I*d/(c + sqrt(c^2 + d^2)) + 1))","B",0
1106,1,633,0,0.849524," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{2 \, {\left(2 \, c^{3} + 4 i \, c^{2} d - c d^{2} + 2 i \, d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(8 i \, a^{3} c^{2} f - 16 \, a^{3} c d f - 8 i \, a^{3} d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{6 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} d - 12 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} d + 6 \, \sqrt{d \tan\left(f x + e\right) + c} c^{4} d + 9 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c d^{2} - 36 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} d^{2} + 27 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{3} d^{2} + 28 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d^{3} - 48 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d^{3} + 4 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{4} - 39 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{4} + 12 \, \sqrt{d \tan\left(f x + e\right) + c} d^{5}}{{\left(48 \, a^{3} c^{2} f + 96 i \, a^{3} c d f - 48 \, a^{3} d^{2} f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{3}} - \frac{{\left(-i \, c - d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, a^{3} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"2*(2*c^3 + 4*I*c^2*d - c*d^2 + 2*I*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((8*I*a^3*c^2*f - 16*a^3*c*d*f - 8*I*a^3*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + (6*(d*tan(f*x + e) + c)^(5/2)*c^2*d - 12*(d*tan(f*x + e) + c)^(3/2)*c^3*d + 6*sqrt(d*tan(f*x + e) + c)*c^4*d + 9*I*(d*tan(f*x + e) + c)^(5/2)*c*d^2 - 36*I*(d*tan(f*x + e) + c)^(3/2)*c^2*d^2 + 27*I*sqrt(d*tan(f*x + e) + c)*c^3*d^2 + 28*(d*tan(f*x + e) + c)^(3/2)*c*d^3 - 48*sqrt(d*tan(f*x + e) + c)*c^2*d^3 + 4*I*(d*tan(f*x + e) + c)^(3/2)*d^4 - 39*I*sqrt(d*tan(f*x + e) + c)*c*d^4 + 12*sqrt(d*tan(f*x + e) + c)*d^5)/((48*a^3*c^2*f + 96*I*a^3*c*d*f - 48*a^3*d^2*f)*(d*tan(f*x + e) - I*d)^3) - 1/2*(-I*c - d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^3*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1107,1,337,0,1.549522," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(16 i \, a^{3} c^{2} + 32 \, a^{3} c d - 16 i \, a^{3} d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{30 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} d^{12} f^{6} - 42 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} c d^{12} f^{6} + 126 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} d^{13} f^{6} - 280 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} d^{14} f^{6} - 840 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} c d^{14} f^{6} - 840 \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} d^{15} f^{6}}{105 \, d^{14} f^{7}}"," ",0,"2*(16*I*a^3*c^2 + 32*a^3*c*d - 16*I*a^3*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/105*(30*I*(d*tan(f*x + e) + c)^(7/2)*a^3*d^12*f^6 - 42*I*(d*tan(f*x + e) + c)^(5/2)*a^3*c*d^12*f^6 + 126*(d*tan(f*x + e) + c)^(5/2)*a^3*d^13*f^6 - 280*I*(d*tan(f*x + e) + c)^(3/2)*a^3*d^14*f^6 - 840*I*sqrt(d*tan(f*x + e) + c)*a^3*c*d^14*f^6 - 840*sqrt(d*tan(f*x + e) + c)*a^3*d^15*f^6)/(d^14*f^7)","B",0
1108,1,288,0,1.161261," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(8 i \, a^{2} c^{2} + 16 \, a^{2} c d - 8 i \, a^{2} d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{6 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} d^{4} f^{4} - 20 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} d^{5} f^{4} - 60 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{2} c d^{5} f^{4} - 60 \, \sqrt{d \tan\left(f x + e\right) + c} a^{2} d^{6} f^{4}}{15 \, d^{5} f^{5}}"," ",0,"2*(8*I*a^2*c^2 + 16*a^2*c*d - 8*I*a^2*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/15*(6*(d*tan(f*x + e) + c)^(5/2)*a^2*d^4*f^4 - 20*I*(d*tan(f*x + e) + c)^(3/2)*a^2*d^5*f^4 - 60*I*sqrt(d*tan(f*x + e) + c)*a^2*c*d^5*f^4 - 60*sqrt(d*tan(f*x + e) + c)*a^2*d^6*f^4)/(d^5*f^5)","B",0
1109,1,241,0,0.478749," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, {\left(4 i \, a c^{2} + 8 \, a c d - 4 i \, a d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{-2 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a f^{2} - 6 i \, \sqrt{d \tan\left(f x + e\right) + c} a c f^{2} - 6 \, \sqrt{d \tan\left(f x + e\right) + c} a d f^{2}}{3 \, f^{3}}"," ",0,"2*(4*I*a*c^2 + 8*a*c*d - 4*I*a*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/3*(-2*I*(d*tan(f*x + e) + c)^(3/2)*a*f^2 - 6*I*sqrt(d*tan(f*x + e) + c)*a*c*f^2 - 6*sqrt(d*tan(f*x + e) + c)*a*d*f^2)/f^3","B",0
1110,1,409,0,0.756730," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, {\left(-i \, c^{2} - c d - 2 i \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{a \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(i \, c^{2} + 2 \, c d - i \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{a \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{\sqrt{d \tan\left(f x + e\right) + c} c d + i \, \sqrt{d \tan\left(f x + e\right) + c} d^{2}}{2 \, {\left(d \tan\left(f x + e\right) - i \, d\right)} a f}"," ",0,"2*(-I*c^2 - c*d - 2*I*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(I*c^2 + 2*c*d - I*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/2*(sqrt(d*tan(f*x + e) + c)*c*d + I*sqrt(d*tan(f*x + e) + c)*d^2)/((d*tan(f*x + e) - I*d)*a*f)","B",0
1111,1,458,0,0.866265," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(c^{2} - 2 i \, c d - d^{2}\right)} \arctan\left(\frac{16 i \, \sqrt{d \tan\left(f x + e\right) + c} c + 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c - i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{4 \, a^{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{{\left(2 i \, c^{2} + 2 \, c d + i \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, a^{2} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d - 2 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d - 3 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{2} - i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{2} - \sqrt{d \tan\left(f x + e\right) + c} d^{3}}{8 \, {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}"," ",0,"-1/4*sqrt(2)*(c^2 - 2*I*c*d - d^2)*arctan(1/8*(16*I*sqrt(d*tan(f*x + e) + c)*c + 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c - I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(a^2*sqrt(c + sqrt(c^2 + d^2))*f*(-I*d/(c + sqrt(c^2 + d^2)) + 1)) - 1/2*(2*I*c^2 + 2*c*d + I*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^2*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/8*(2*(d*tan(f*x + e) + c)^(3/2)*c*d - 2*sqrt(d*tan(f*x + e) + c)*c^2*d - 3*I*(d*tan(f*x + e) + c)^(3/2)*d^2 - I*sqrt(d*tan(f*x + e) + c)*c*d^2 - sqrt(d*tan(f*x + e) + c)*d^3)/((d*tan(f*x + e) - I*d)^2*a^2*f)","B",0
1112,1,624,0,0.992627," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{2 \, {\left(2 \, c^{3} + 3 \, c d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-8 i \, a^{3} c f + 8 \, a^{3} d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{-6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} d + 12 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} d - 6 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{4} d - 3 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c d^{2} - 12 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} d^{2} + 15 \, \sqrt{d \tan\left(f x + e\right) + c} c^{3} d^{2} - 6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} d^{3} + 20 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d^{3} + 6 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d^{3} - 20 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{4} + 9 \, \sqrt{d \tan\left(f x + e\right) + c} c d^{4} + 6 i \, \sqrt{d \tan\left(f x + e\right) + c} d^{5}}{{\left(-48 i \, a^{3} c f + 48 \, a^{3} d f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{3}} - \frac{{\left(-i \, c^{2} - 2 \, c d + i \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, a^{3} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"-2*(2*c^3 + 3*c*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-8*I*a^3*c*f + 8*a^3*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + (-6*I*(d*tan(f*x + e) + c)^(5/2)*c^2*d + 12*I*(d*tan(f*x + e) + c)^(3/2)*c^3*d - 6*I*sqrt(d*tan(f*x + e) + c)*c^4*d - 3*(d*tan(f*x + e) + c)^(5/2)*c*d^2 - 12*(d*tan(f*x + e) + c)^(3/2)*c^2*d^2 + 15*sqrt(d*tan(f*x + e) + c)*c^3*d^2 - 6*I*(d*tan(f*x + e) + c)^(5/2)*d^3 + 20*I*(d*tan(f*x + e) + c)^(3/2)*c*d^3 + 6*I*sqrt(d*tan(f*x + e) + c)*c^2*d^3 - 20*(d*tan(f*x + e) + c)^(3/2)*d^4 + 9*sqrt(d*tan(f*x + e) + c)*c*d^4 + 6*I*sqrt(d*tan(f*x + e) + c)*d^5)/((-48*I*a^3*c*f + 48*a^3*d*f)*(d*tan(f*x + e) - I*d)^3) - 1/2*(-I*c^2 - 2*c*d + I*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^3*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1113,1,424,0,2.582744," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(16 i \, a^{3} c^{3} + 48 \, a^{3} c^{2} d - 48 i \, a^{3} c d^{2} - 16 \, a^{3} d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{70 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} a^{3} d^{16} f^{8} - 90 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} c d^{16} f^{8} + 270 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} d^{17} f^{8} - 504 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} d^{18} f^{8} - 840 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} c d^{18} f^{8} - 2520 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} c^{2} d^{18} f^{8} - 840 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} d^{19} f^{8} - 5040 \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} c d^{19} f^{8} + 2520 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} d^{20} f^{8}}{315 \, d^{18} f^{9}}"," ",0,"2*(16*I*a^3*c^3 + 48*a^3*c^2*d - 48*I*a^3*c*d^2 - 16*a^3*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/315*(70*I*(d*tan(f*x + e) + c)^(9/2)*a^3*d^16*f^8 - 90*I*(d*tan(f*x + e) + c)^(7/2)*a^3*c*d^16*f^8 + 270*(d*tan(f*x + e) + c)^(7/2)*a^3*d^17*f^8 - 504*I*(d*tan(f*x + e) + c)^(5/2)*a^3*d^18*f^8 - 840*I*(d*tan(f*x + e) + c)^(3/2)*a^3*c*d^18*f^8 - 2520*I*sqrt(d*tan(f*x + e) + c)*a^3*c^2*d^18*f^8 - 840*(d*tan(f*x + e) + c)^(3/2)*a^3*d^19*f^8 - 5040*sqrt(d*tan(f*x + e) + c)*a^3*c*d^19*f^8 + 2520*I*sqrt(d*tan(f*x + e) + c)*a^3*d^20*f^8)/(d^18*f^9)","B",0
1114,1,375,0,2.023319," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{2 \, {\left(8 i \, a^{2} c^{3} + 24 \, a^{2} c^{2} d - 24 i \, a^{2} c d^{2} - 8 \, a^{2} d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{30 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{2} d^{6} f^{6} - 84 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} d^{7} f^{6} - 140 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} c d^{7} f^{6} - 420 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{2} c^{2} d^{7} f^{6} - 140 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} d^{8} f^{6} - 840 \, \sqrt{d \tan\left(f x + e\right) + c} a^{2} c d^{8} f^{6} + 420 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{2} d^{9} f^{6}}{105 \, d^{7} f^{7}}"," ",0,"2*(8*I*a^2*c^3 + 24*a^2*c^2*d - 24*I*a^2*c*d^2 - 8*a^2*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/105*(30*(d*tan(f*x + e) + c)^(7/2)*a^2*d^6*f^6 - 84*I*(d*tan(f*x + e) + c)^(5/2)*a^2*d^7*f^6 - 140*I*(d*tan(f*x + e) + c)^(3/2)*a^2*c*d^7*f^6 - 420*I*sqrt(d*tan(f*x + e) + c)*a^2*c^2*d^7*f^6 - 140*(d*tan(f*x + e) + c)^(3/2)*a^2*d^8*f^6 - 840*sqrt(d*tan(f*x + e) + c)*a^2*c*d^8*f^6 + 420*I*sqrt(d*tan(f*x + e) + c)*a^2*d^9*f^6)/(d^7*f^7)","B",0
1115,1,315,0,0.906940," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{2 \, {\left(-4 i \, a c^{3} - 12 \, a c^{2} d + 12 i \, a c d^{2} + 4 \, a d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{-6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a f^{4} - 10 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a c f^{4} - 30 i \, \sqrt{d \tan\left(f x + e\right) + c} a c^{2} f^{4} - 10 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a d f^{4} - 60 \, \sqrt{d \tan\left(f x + e\right) + c} a c d f^{4} + 30 i \, \sqrt{d \tan\left(f x + e\right) + c} a d^{2} f^{4}}{15 \, f^{5}}"," ",0,"-2*(-4*I*a*c^3 - 12*a*c^2*d + 12*I*a*c*d^2 + 4*a*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/15*(-6*I*(d*tan(f*x + e) + c)^(5/2)*a*f^4 - 10*I*(d*tan(f*x + e) + c)^(3/2)*a*c*f^4 - 30*I*sqrt(d*tan(f*x + e) + c)*a*c^2*f^4 - 10*(d*tan(f*x + e) + c)^(3/2)*a*d*f^4 - 60*sqrt(d*tan(f*x + e) + c)*a*c*d*f^4 + 30*I*sqrt(d*tan(f*x + e) + c)*a*d^2*f^4)/f^5","B",0
1116,1,462,0,0.860766," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","-\frac{2 i \, \sqrt{d \tan\left(f x + e\right) + c} d^{2}}{a f} + \frac{\sqrt{2} {\left(c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}\right)} \arctan\left(\frac{-16 i \, \sqrt{d \tan\left(f x + e\right) + c} c - 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c - i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{2 \, a \sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(-i \, c^{3} - 2 \, c^{2} d - 7 i \, c d^{2} + 4 \, d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{a \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{\sqrt{d \tan\left(f x + e\right) + c} c^{2} d + 2 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{2} - \sqrt{d \tan\left(f x + e\right) + c} d^{3}}{2 \, {\left(d \tan\left(f x + e\right) - i \, d\right)} a f}"," ",0,"-2*I*sqrt(d*tan(f*x + e) + c)*d^2/(a*f) + 1/2*sqrt(2)*(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)*arctan(1/8*(-16*I*sqrt(d*tan(f*x + e) + c)*c - 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c - I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(a*sqrt(c + sqrt(c^2 + d^2))*f*(-I*d/(c + sqrt(c^2 + d^2)) + 1)) + 2*(-I*c^3 - 2*c^2*d - 7*I*c*d^2 + 4*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/2*(sqrt(d*tan(f*x + e) + c)*c^2*d + 2*I*sqrt(d*tan(f*x + e) + c)*c*d^2 - sqrt(d*tan(f*x + e) + c)*d^3)/((d*tan(f*x + e) - I*d)*a*f)","B",0
1117,1,516,0,1.208704," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(c^{3} - 3 i \, c^{2} d - 3 \, c d^{2} + i \, d^{3}\right)} \arctan\left(\frac{-16 i \, \sqrt{d \tan\left(f x + e\right) + c} c - 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c - i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{4 \, a^{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{{\left(2 i \, c^{3} + 4 \, c^{2} d - i \, c d^{2} + 7 \, d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, a^{2} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} d - 2 \, \sqrt{d \tan\left(f x + e\right) + c} c^{3} d - 5 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d^{2} + i \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d^{2} + 7 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{3} - 8 \, \sqrt{d \tan\left(f x + e\right) + c} c d^{3} - 5 i \, \sqrt{d \tan\left(f x + e\right) + c} d^{4}}{8 \, {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2} a^{2} f}"," ",0,"1/4*sqrt(2)*(c^3 - 3*I*c^2*d - 3*c*d^2 + I*d^3)*arctan(1/8*(-16*I*sqrt(d*tan(f*x + e) + c)*c - 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c - I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(a^2*sqrt(c + sqrt(c^2 + d^2))*f*(-I*d/(c + sqrt(c^2 + d^2)) + 1)) - 1/2*(2*I*c^3 + 4*c^2*d - I*c*d^2 + 7*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^2*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/8*(2*(d*tan(f*x + e) + c)^(3/2)*c^2*d - 2*sqrt(d*tan(f*x + e) + c)*c^3*d - 5*I*(d*tan(f*x + e) + c)^(3/2)*c*d^2 + I*sqrt(d*tan(f*x + e) + c)*c^2*d^2 + 7*(d*tan(f*x + e) + c)^(3/2)*d^3 - 8*sqrt(d*tan(f*x + e) + c)*c*d^3 - 5*I*sqrt(d*tan(f*x + e) + c)*d^4)/((d*tan(f*x + e) - I*d)^2*a^2*f)","B",0
1118,1,602,0,1.384920," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{{\left(2 i \, c^{3} + 4 \, c^{2} d - i \, c d^{2} + 2 \, d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{4 \, a^{3} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{{\left(-i \, c^{3} - 3 \, c^{2} d + 3 i \, c d^{2} + d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, a^{3} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{6 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} d - 12 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} d + 6 \, \sqrt{d \tan\left(f x + e\right) + c} c^{4} d - 15 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c d^{2} + 12 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} d^{2} + 3 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{3} d^{2} - 12 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} d^{3} - 20 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d^{3} + 12 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d^{3} + 4 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{4} + 9 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{4}}{48 \, {\left(d \tan\left(f x + e\right) - i \, d\right)}^{3} a^{3} f}"," ",0,"-1/4*(2*I*c^3 + 4*c^2*d - I*c*d^2 + 2*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^3*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/2*(-I*c^3 - 3*c^2*d + 3*I*c*d^2 + d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^3*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/48*(6*(d*tan(f*x + e) + c)^(5/2)*c^2*d - 12*(d*tan(f*x + e) + c)^(3/2)*c^3*d + 6*sqrt(d*tan(f*x + e) + c)*c^4*d - 15*I*(d*tan(f*x + e) + c)^(5/2)*c*d^2 + 12*I*(d*tan(f*x + e) + c)^(3/2)*c^2*d^2 + 3*I*sqrt(d*tan(f*x + e) + c)*c^3*d^2 - 12*(d*tan(f*x + e) + c)^(5/2)*d^3 - 20*(d*tan(f*x + e) + c)^(3/2)*c*d^3 + 12*sqrt(d*tan(f*x + e) + c)*c^2*d^3 + 4*I*(d*tan(f*x + e) + c)^(3/2)*d^4 + 9*I*sqrt(d*tan(f*x + e) + c)*c*d^4)/((d*tan(f*x + e) - I*d)^3*a^3*f)","B",0
1119,1,243,0,0.942166," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{32 i \, a^{3} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{2 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} d^{4} f^{2} - 6 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} c d^{4} f^{2} + 18 \, \sqrt{d \tan\left(f x + e\right) + c} a^{3} d^{5} f^{2}}{3 \, d^{6} f^{3}}"," ",0,"32*I*a^3*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 1/3*(2*I*(d*tan(f*x + e) + c)^(3/2)*a^3*d^4*f^2 - 6*I*sqrt(d*tan(f*x + e) + c)*a^3*c*d^4*f^2 + 18*sqrt(d*tan(f*x + e) + c)*a^3*d^5*f^2)/(d^6*f^3)","B",0
1120,1,185,0,0.702675," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","-\frac{2 \, \sqrt{d \tan\left(f x + e\right) + c} a^{2}}{d f} + \frac{16 i \, a^{2} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{\sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"-2*sqrt(d*tan(f*x + e) + c)*a^2/(d*f) + 16*I*a^2*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1121,1,152,0,0.513778," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} a \arctan\left(\frac{-16 i \, \sqrt{d \tan\left(f x + e\right) + c} c - 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c - i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{\sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"2*sqrt(2)*a*arctan(1/8*(-16*I*sqrt(d*tan(f*x + e) + c)*c - 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c - I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(sqrt(c + sqrt(c^2 + d^2))*f*(-I*d/(c + sqrt(c^2 + d^2)) + 1))","B",0
1122,1,376,0,0.745462," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\frac{\sqrt{d \tan\left(f x + e\right) + c} d}{2 \, {\left(a c f + i \, a d f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}} + \frac{4 \, {\left(c + 2 i \, d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(2 i \, a c f - 2 \, a d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{a \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"1/2*sqrt(d*tan(f*x + e) + c)*d/((a*c*f + I*a*d*f)*(d*tan(f*x + e) - I*d)) + 4*(c + 2*I*d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((2*I*a*c*f - 2*a*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1123,1,491,0,0.853325," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","-\frac{4 \, {\left(2 \, c^{2} + 6 i \, c d - 7 \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-8 i \, a^{2} c^{2} f + 16 \, a^{2} c d f + 8 i \, a^{2} d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d - 2 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d + 5 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{2} - 9 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{2} + 7 \, \sqrt{d \tan\left(f x + e\right) + c} d^{3}\right)}}{{\left(16 \, a^{2} c^{2} f + 32 i \, a^{2} c d f - 16 \, a^{2} d^{2} f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2}} - \frac{\sqrt{2} \arctan\left(\frac{16 i \, \sqrt{d \tan\left(f x + e\right) + c} c + 16 i \, \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}}{8 \, {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} c - i \, \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} d + \sqrt{2} \sqrt{c^{2} + d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}}\right)}}\right)}{4 \, a^{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c + \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"-4*(2*c^2 + 6*I*c*d - 7*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-8*I*a^2*c^2*f + 16*a^2*c*d*f + 8*I*a^2*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(2*(d*tan(f*x + e) + c)^(3/2)*c*d - 2*sqrt(d*tan(f*x + e) + c)*c^2*d + 5*I*(d*tan(f*x + e) + c)^(3/2)*d^2 - 9*I*sqrt(d*tan(f*x + e) + c)*c*d^2 + 7*sqrt(d*tan(f*x + e) + c)*d^3)/((16*a^2*c^2*f + 32*I*a^2*c*d*f - 16*a^2*d^2*f)*(d*tan(f*x + e) - I*d)^2) - 1/4*sqrt(2)*arctan(1/8*(16*I*sqrt(d*tan(f*x + e) + c)*c + 16*I*sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*c - I*sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*d + sqrt(2)*sqrt(c^2 + d^2)*sqrt(c + sqrt(c^2 + d^2))))/(a^2*sqrt(c + sqrt(c^2 + d^2))*f*(-I*d/(c + sqrt(c^2 + d^2)) + 1))","B",0
1124,1,669,0,1.258831," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","-\frac{4 \, {\left(2 \, c^{3} + 8 i \, c^{2} d - 13 \, c d^{2} - 12 i \, d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-16 i \, a^{3} c^{3} f + 48 \, a^{3} c^{2} d f + 48 i \, a^{3} c d^{2} f - 16 \, a^{3} d^{3} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(-6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} d + 12 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} d - 6 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{4} d + 21 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c d^{2} - 60 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} d^{2} + 39 \, \sqrt{d \tan\left(f x + e\right) + c} c^{3} d^{2} + 30 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} d^{3} - 124 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d^{3} + 114 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d^{3} + 76 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{4} - 135 \, \sqrt{d \tan\left(f x + e\right) + c} c d^{4} - 54 i \, \sqrt{d \tan\left(f x + e\right) + c} d^{5}\right)}}{{\left(-96 i \, a^{3} c^{3} f + 288 \, a^{3} c^{2} d f + 288 i \, a^{3} c d^{2} f - 96 \, a^{3} d^{3} f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{3}} + \frac{i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, a^{3} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} f {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"-4*(2*c^3 + 8*I*c^2*d - 13*c*d^2 - 12*I*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-16*I*a^3*c^3*f + 48*a^3*c^2*d*f + 48*I*a^3*c*d^2*f - 16*a^3*d^3*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(-6*I*(d*tan(f*x + e) + c)^(5/2)*c^2*d + 12*I*(d*tan(f*x + e) + c)^(3/2)*c^3*d - 6*I*sqrt(d*tan(f*x + e) + c)*c^4*d + 21*(d*tan(f*x + e) + c)^(5/2)*c*d^2 - 60*(d*tan(f*x + e) + c)^(3/2)*c^2*d^2 + 39*sqrt(d*tan(f*x + e) + c)*c^3*d^2 + 30*I*(d*tan(f*x + e) + c)^(5/2)*d^3 - 124*I*(d*tan(f*x + e) + c)^(3/2)*c*d^3 + 114*I*sqrt(d*tan(f*x + e) + c)*c^2*d^3 + 76*(d*tan(f*x + e) + c)^(3/2)*d^4 - 135*sqrt(d*tan(f*x + e) + c)*c*d^4 - 54*I*sqrt(d*tan(f*x + e) + c)*d^5)/((-96*I*a^3*c^3*f + 288*a^3*c^2*d*f + 288*I*a^3*c*d^2*f - 96*a^3*d^3*f)*(d*tan(f*x + e) - I*d)^3) + 1/2*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/(a^3*sqrt(-8*c + 8*sqrt(c^2 + d^2))*f*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1125,1,247,0,1.177330," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{32 \, a^{3} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-i \, c f - d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{2 i \, \sqrt{d \tan\left(f x + e\right) + c} a^{3}}{d^{2} f} - \frac{2 i \, a^{3} c^{2} - 4 \, a^{3} c d - 2 i \, a^{3} d^{2}}{{\left(c d^{2} f - i \, d^{3} f\right)} \sqrt{d \tan\left(f x + e\right) + c}}"," ",0,"32*a^3*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-I*c*f - d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) - 2*I*sqrt(d*tan(f*x + e) + c)*a^3/(d^2*f) - (2*I*a^3*c^2 - 4*a^3*c*d - 2*I*a^3*d^2)/((c*d^2*f - I*d^3*f)*sqrt(d*tan(f*x + e) + c))","B",0
1126,1,209,0,0.968046," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{16 \, a^{2} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-i \, c f - d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, a^{2} c + 2 i \, a^{2} d}{{\left(c d f - i \, d^{2} f\right)} \sqrt{d \tan\left(f x + e\right) + c}}"," ",0,"16*a^2*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-I*c*f - d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + (2*a^2*c + 2*I*a^2*d)/((c*d*f - I*d^2*f)*sqrt(d*tan(f*x + e) + c))","B",0
1127,1,192,0,0.764484," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","-2 \, a {\left(\frac{1}{{\left(i \, c f + d f\right)} \sqrt{d \tan\left(f x + e\right) + c}} - \frac{4 i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(c f - i \, d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}\right)}"," ",0,"-2*a*(1/((I*c*f + d*f)*sqrt(d*tan(f*x + e) + c)) - 4*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((c*f - I*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)))","B",0
1128,1,480,0,1.168207," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{4 \, {\left(i \, c - 4 \, d\right)} \arctan\left(-\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(2 \, a c^{2} f + 4 i \, a c d f - 2 \, a d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{2 \, {\left({\left(-i \, d \tan\left(f x + e\right) - i \, c\right)} c d - 5 \, {\left(d \tan\left(f x + e\right) + c\right)} d^{2} + 4 \, c d^{2} + 4 i \, d^{3}\right)}}{{\left(4 \, a c^{3} f + 4 i \, a c^{2} d f + 4 \, a c d^{2} f + 4 i \, a d^{3} f\right)} {\left(i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} - i \, \sqrt{d \tan\left(f x + e\right) + c} c + \sqrt{d \tan\left(f x + e\right) + c} d\right)}} + \frac{2 i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(a c f - i \, a d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"4*(I*c - 4*d)*arctan(-4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((2*a*c^2*f + 4*I*a*c*d*f - 2*a*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) - 2*((-I*d*tan(f*x + e) - I*c)*c*d - 5*(d*tan(f*x + e) + c)*d^2 + 4*c*d^2 + 4*I*d^3)/((4*a*c^3*f + 4*I*a*c^2*d*f + 4*a*c*d^2*f + 4*I*a*d^3*f)*(I*(d*tan(f*x + e) + c)^(3/2) - I*sqrt(d*tan(f*x + e) + c)*c + sqrt(d*tan(f*x + e) + c)*d)) + 2*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((a*c*f - I*a*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1129,1,590,0,1.509648," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, d^{3}}{{\left(a^{2} c^{4} f + 2 i \, a^{2} c^{3} d f + 2 i \, a^{2} c d^{3} f - a^{2} d^{4} f\right)} \sqrt{d \tan\left(f x + e\right) + c}} - \frac{4 \, {\left(2 i \, c^{2} - 10 \, c d - 23 i \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(8 \, a^{2} c^{3} f + 24 i \, a^{2} c^{2} d f - 24 \, a^{2} c d^{2} f - 8 i \, a^{2} d^{3} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} - \frac{4 \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(4 i \, a^{2} c f + 4 \, a^{2} d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d - 2 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d + 9 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{2} - 13 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{2} + 11 \, \sqrt{d \tan\left(f x + e\right) + c} d^{3}\right)}}{{\left(16 \, a^{2} c^{3} f + 48 i \, a^{2} c^{2} d f - 48 \, a^{2} c d^{2} f - 16 i \, a^{2} d^{3} f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2}}"," ",0,"2*d^3/((a^2*c^4*f + 2*I*a^2*c^3*d*f + 2*I*a^2*c*d^3*f - a^2*d^4*f)*sqrt(d*tan(f*x + e) + c)) - 4*(2*I*c^2 - 10*c*d - 23*I*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((8*a^2*c^3*f + 24*I*a^2*c^2*d*f - 24*a^2*c*d^2*f - 8*I*a^2*d^3*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) - 4*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((4*I*a^2*c*f + 4*a^2*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(2*(d*tan(f*x + e) + c)^(3/2)*c*d - 2*sqrt(d*tan(f*x + e) + c)*c^2*d + 9*I*(d*tan(f*x + e) + c)^(3/2)*d^2 - 13*I*sqrt(d*tan(f*x + e) + c)*c*d^2 + 11*sqrt(d*tan(f*x + e) + c)*d^3)/((16*a^2*c^3*f + 48*I*a^2*c^2*d*f - 48*a^2*c*d^2*f - 16*I*a^2*d^3*f)*(d*tan(f*x + e) - I*d)^2)","B",0
1130,1,787,0,2.647828," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{2 \, d^{4}}{{\left(-i \, a^{3} c^{5} f + 3 \, a^{3} c^{4} d f + 2 i \, a^{3} c^{3} d^{2} f + 2 \, a^{3} c^{2} d^{3} f + 3 i \, a^{3} c d^{4} f - a^{3} d^{5} f\right)} \sqrt{d \tan\left(f x + e\right) + c}} - \frac{4 \, {\left(2 i \, c^{3} - 12 \, c^{2} d - 33 i \, c d^{2} + 58 \, d^{3}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(16 \, a^{3} c^{4} f + 64 i \, a^{3} c^{3} d f - 96 \, a^{3} c^{2} d^{2} f - 64 i \, a^{3} c d^{3} f + 16 \, a^{3} d^{4} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{2 \, {\left(a^{3} c f - i \, a^{3} d f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(6 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} d - 12 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} d + 6 \, \sqrt{d \tan\left(f x + e\right) + c} c^{4} d + 33 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c d^{2} - 84 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} d^{2} + 51 i \, \sqrt{d \tan\left(f x + e\right) + c} c^{3} d^{2} - 84 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} d^{3} + 268 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d^{3} - 204 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d^{3} + 196 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{4} - 279 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{4} + 120 \, \sqrt{d \tan\left(f x + e\right) + c} d^{5}\right)}}{{\left(-96 i \, a^{3} c^{4} f + 384 \, a^{3} c^{3} d f + 576 i \, a^{3} c^{2} d^{2} f - 384 \, a^{3} c d^{3} f - 96 i \, a^{3} d^{4} f\right)} {\left(-i \, d \tan\left(f x + e\right) - d\right)}^{3}}"," ",0,"2*d^4/((-I*a^3*c^5*f + 3*a^3*c^4*d*f + 2*I*a^3*c^3*d^2*f + 2*a^3*c^2*d^3*f + 3*I*a^3*c*d^4*f - a^3*d^5*f)*sqrt(d*tan(f*x + e) + c)) - 4*(2*I*c^3 - 12*c^2*d - 33*I*c*d^2 + 58*d^3)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((16*a^3*c^4*f + 64*I*a^3*c^3*d*f - 96*a^3*c^2*d^2*f - 64*I*a^3*c*d^3*f + 16*a^3*d^4*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 1/2*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((a^3*c*f - I*a^3*d*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(6*(d*tan(f*x + e) + c)^(5/2)*c^2*d - 12*(d*tan(f*x + e) + c)^(3/2)*c^3*d + 6*sqrt(d*tan(f*x + e) + c)*c^4*d + 33*I*(d*tan(f*x + e) + c)^(5/2)*c*d^2 - 84*I*(d*tan(f*x + e) + c)^(3/2)*c^2*d^2 + 51*I*sqrt(d*tan(f*x + e) + c)*c^3*d^2 - 84*(d*tan(f*x + e) + c)^(5/2)*d^3 + 268*(d*tan(f*x + e) + c)^(3/2)*c*d^3 - 204*sqrt(d*tan(f*x + e) + c)*c^2*d^3 + 196*I*(d*tan(f*x + e) + c)^(3/2)*d^4 - 279*I*sqrt(d*tan(f*x + e) + c)*c*d^4 + 120*sqrt(d*tan(f*x + e) + c)*d^5)/((-96*I*a^3*c^4*f + 384*a^3*c^3*d*f + 576*I*a^3*c^2*d^2*f - 384*a^3*c*d^3*f - 96*I*a^3*d^4*f)*(-I*d*tan(f*x + e) - d)^3)","B",0
1131,1,312,0,1.870917," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{32 \, a^{3} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-i \, c^{2} f - 2 \, c d f + i \, d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{{\left(6 i \, d \tan\left(f x + e\right) + 6 i \, c\right)} a^{3} c^{2} - 2 i \, a^{3} c^{3} + 12 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{3} c d + 2 \, a^{3} c^{2} d + {\left(18 i \, d \tan\left(f x + e\right) + 18 i \, c\right)} a^{3} d^{2} - 2 i \, a^{3} c d^{2} + 2 \, a^{3} d^{3}}{{\left(3 \, c^{2} d^{2} f - 6 i \, c d^{3} f - 3 \, d^{4} f\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}"," ",0,"32*a^3*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-I*c^2*f - 2*c*d*f + I*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + ((6*I*d*tan(f*x + e) + 6*I*c)*a^3*c^2 - 2*I*a^3*c^3 + 12*(d*tan(f*x + e) + c)*a^3*c*d + 2*a^3*c^2*d + (18*I*d*tan(f*x + e) + 18*I*c)*a^3*d^2 - 2*I*a^3*c*d^2 + 2*a^3*d^3)/((3*c^2*d^2*f - 6*I*c*d^3*f - 3*d^4*f)*(d*tan(f*x + e) + c)^(3/2))","B",0
1132,1,249,0,1.683077," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{16 \, a^{2} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(-i \, c^{2} f - 2 \, c d f + i \, d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 i \, a^{2} c^{2} - 12 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} d + 2 i \, a^{2} d^{2}}{{\left(3 i \, c^{2} d f + 6 \, c d^{2} f - 3 i \, d^{3} f\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}"," ",0,"16*a^2*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((-I*c^2*f - 2*c*d*f + I*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + (2*I*a^2*c^2 - 12*(d*tan(f*x + e) + c)*a^2*d + 2*I*a^2*d^2)/((3*I*c^2*d*f + 6*c*d^2*f - 3*I*d^3*f)*(d*tan(f*x + e) + c)^(3/2))","B",0
1133,1,228,0,1.398559," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-2 \, a {\left(\frac{3 \, d \tan\left(f x + e\right) + 4 \, c - i \, d}{{\left(3 i \, c^{2} f + 6 \, c d f - 3 i \, d^{2} f\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}} - \frac{4 i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(c^{2} f - 2 i \, c d f - d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}\right)}"," ",0,"-2*a*((3*d*tan(f*x + e) + 4*c - I*d)/((3*I*c^2*f + 6*c*d*f - 3*I*d^2*f)*(d*tan(f*x + e) + c)^(3/2)) - 4*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((c^2*f - 2*I*c*d*f - d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)))","B",0
1134,1,549,0,2.098834," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{d \tan\left(f x + e\right) + c} d}{{\left(-4 i \, a c^{3} f + 12 \, a c^{2} d f + 12 i \, a c d^{2} f - 4 \, a d^{3} f\right)} {\left(i \, d \tan\left(f x + e\right) + d\right)}} + \frac{4 \, {\left(-i \, c + 6 \, d\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(2 \, a c^{3} f + 6 i \, a c^{2} d f - 6 \, a c d^{2} f - 2 i \, a d^{3} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(9 \, {\left(d \tan\left(f x + e\right) + c\right)} c d^{2} + c^{2} d^{2} + {\left(-3 i \, d \tan\left(f x + e\right) - 3 i \, c\right)} d^{3} + d^{4}\right)}}{{\left(3 i \, a c^{5} f - 3 \, a c^{4} d f + 6 i \, a c^{3} d^{2} f - 6 \, a c^{2} d^{3} f + 3 i \, a c d^{4} f - 3 \, a d^{5} f\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}} + \frac{4 i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(2 \, a c^{2} f - 4 i \, a c d f - 2 \, a d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}}"," ",0,"2*sqrt(d*tan(f*x + e) + c)*d/((-4*I*a*c^3*f + 12*a*c^2*d*f + 12*I*a*c*d^2*f - 4*a*d^3*f)*(I*d*tan(f*x + e) + d)) + 4*(-I*c + 6*d)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((2*a*c^3*f + 6*I*a*c^2*d*f - 6*a*c*d^2*f - 2*I*a*d^3*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(9*(d*tan(f*x + e) + c)*c*d^2 + c^2*d^2 + (-3*I*d*tan(f*x + e) - 3*I*c)*d^3 + d^4)/((3*I*a*c^5*f - 3*a*c^4*d*f + 6*I*a*c^3*d^2*f - 6*a*c^2*d^3*f + 3*I*a*c*d^4*f - 3*a*d^5*f)*(d*tan(f*x + e) + c)^(3/2)) + 4*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((2*a*c^2*f - 4*I*a*c*d*f - 2*a*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1))","B",0
1135,1,706,0,2.678008," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{4 \, {\left(2 i \, c^{2} - 14 \, c d - 47 i \, d^{2}\right)} \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(8 \, a^{2} c^{4} f + 32 i \, a^{2} c^{3} d f - 48 \, a^{2} c^{2} d^{2} f - 32 i \, a^{2} c d^{3} f + 8 \, a^{2} d^{4} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(12 \, {\left(d \tan\left(f x + e\right) + c\right)} c d^{3} + c^{2} d^{3} + {\left(-6 i \, d \tan\left(f x + e\right) - 6 i \, c\right)} d^{4} + d^{5}\right)}}{{\left(3 \, a^{2} c^{6} f + 6 i \, a^{2} c^{5} d f + 3 \, a^{2} c^{4} d^{2} f + 12 i \, a^{2} c^{3} d^{3} f - 3 \, a^{2} c^{2} d^{4} f + 6 i \, a^{2} c d^{5} f - 3 \, a^{2} d^{6} f\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}} - \frac{4 \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(4 i \, a^{2} c^{2} f + 8 \, a^{2} c d f - 4 i \, a^{2} d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c d - 2 \, \sqrt{d \tan\left(f x + e\right) + c} c^{2} d + 13 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} d^{2} - 17 i \, \sqrt{d \tan\left(f x + e\right) + c} c d^{2} + 15 \, \sqrt{d \tan\left(f x + e\right) + c} d^{3}\right)}}{{\left(16 \, a^{2} c^{4} f + 64 i \, a^{2} c^{3} d f - 96 \, a^{2} c^{2} d^{2} f - 64 i \, a^{2} c d^{3} f + 16 \, a^{2} d^{4} f\right)} {\left(d \tan\left(f x + e\right) - i \, d\right)}^{2}}"," ",0,"-4*(2*I*c^2 - 14*c*d - 47*I*d^2)*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((8*a^2*c^4*f + 32*I*a^2*c^3*d*f - 48*a^2*c^2*d^2*f - 32*I*a^2*c*d^3*f + 8*a^2*d^4*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(12*(d*tan(f*x + e) + c)*c*d^3 + c^2*d^3 + (-6*I*d*tan(f*x + e) - 6*I*c)*d^4 + d^5)/((3*a^2*c^6*f + 6*I*a^2*c^5*d*f + 3*a^2*c^4*d^2*f + 12*I*a^2*c^3*d^3*f - 3*a^2*c^2*d^4*f + 6*I*a^2*c*d^5*f - 3*a^2*d^6*f)*(d*tan(f*x + e) + c)^(3/2)) - 4*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((4*I*a^2*c^2*f + 8*a^2*c*d*f - 4*I*a^2*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(2*(d*tan(f*x + e) + c)^(3/2)*c*d - 2*sqrt(d*tan(f*x + e) + c)*c^2*d + 13*I*(d*tan(f*x + e) + c)^(3/2)*d^2 - 17*I*sqrt(d*tan(f*x + e) + c)*c*d^2 + 15*sqrt(d*tan(f*x + e) + c)*d^3)/((16*a^2*c^4*f + 64*I*a^2*c^3*d*f - 96*a^2*c^2*d^2*f - 64*I*a^2*c*d^3*f + 16*a^2*d^4*f)*(d*tan(f*x + e) - I*d)^2)","B",0
1136,1,1062,0,4.429136," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{4 \, {\left(-2 i \, c^{3} + 16 \, c^{2} d + 61 i \, c d^{2} - 152 \, d^{3}\right)} \arctan\left(-\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} + i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(16 \, a^{3} c^{5} f + 80 i \, a^{3} c^{4} d f - 160 \, a^{3} c^{3} d^{2} f - 160 i \, a^{3} c^{2} d^{3} f + 80 \, a^{3} c d^{4} f + 16 i \, a^{3} d^{5} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{4 i \, \arctan\left(\frac{4 \, {\left(\sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{c^{2} + d^{2}} \sqrt{d \tan\left(f x + e\right) + c}\right)}}{c \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} - i \, \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} d - \sqrt{c^{2} + d^{2}} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}}}\right)}{{\left(8 \, a^{3} c^{2} f - 16 i \, a^{3} c d f - 8 \, a^{3} d^{2} f\right)} \sqrt{-8 \, c + 8 \, \sqrt{c^{2} + d^{2}}} {\left(-\frac{i \, d}{c - \sqrt{c^{2} + d^{2}}} + 1\right)}} + \frac{2 \, {\left(6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{4} c^{4} d - 12 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} c^{5} d + 6 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c^{6} d - 33 \, {\left(d \tan\left(f x + e\right) + c\right)}^{4} c^{3} d^{2} + 84 \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} c^{4} d^{2} - 51 \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c^{5} d^{2} - 78 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{4} c^{2} d^{3} + 256 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} c^{3} d^{3} - 198 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c^{4} d^{3} - 759 \, {\left(d \tan\left(f x + e\right) + c\right)}^{4} c d^{4} + 1856 \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} c^{2} d^{4} - 1446 \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c^{3} d^{4} + 384 \, {\left(d \tan\left(f x + e\right) + c\right)} c^{4} d^{4} + 32 \, c^{5} d^{4} + 450 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{4} d^{5} + 844 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} c d^{5} - 2334 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c^{2} d^{5} + {\left(960 i \, d \tan\left(f x + e\right) + 960 i \, c\right)} c^{3} d^{5} + 96 i \, c^{4} d^{5} + 1196 \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} d^{6} - 243 \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c d^{6} - 576 \, {\left(d \tan\left(f x + e\right) + c\right)} c^{2} d^{6} - 64 \, c^{3} d^{6} - 978 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} d^{7} + {\left(192 i \, d \tan\left(f x + e\right) + 192 i \, c\right)} c d^{7} + 64 i \, c^{2} d^{7} - 192 \, {\left(d \tan\left(f x + e\right) + c\right)} d^{8} - 96 \, c d^{8} - 32 i \, d^{9}\right)}}{{\left(96 \, a^{3} c^{7} f + 288 i \, a^{3} c^{6} d f - 96 \, a^{3} c^{5} d^{2} f + 480 i \, a^{3} c^{4} d^{3} f - 480 \, a^{3} c^{3} d^{4} f + 96 i \, a^{3} c^{2} d^{5} f - 288 \, a^{3} c d^{6} f - 96 i \, a^{3} d^{7} f\right)} {\left(-i \, {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} + i \, \sqrt{d \tan\left(f x + e\right) + c} c - \sqrt{d \tan\left(f x + e\right) + c} d\right)}^{3}}"," ",0,"-4*(-2*I*c^3 + 16*c^2*d + 61*I*c*d^2 - 152*d^3)*arctan(-4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) + I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((16*a^3*c^5*f + 80*I*a^3*c^4*d*f - 160*a^3*c^3*d^2*f - 160*I*a^3*c^2*d^3*f + 80*a^3*c*d^4*f + 16*I*a^3*d^5*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(I*d/(c - sqrt(c^2 + d^2)) + 1)) + 4*I*arctan(4*(sqrt(d*tan(f*x + e) + c)*c - sqrt(c^2 + d^2)*sqrt(d*tan(f*x + e) + c))/(c*sqrt(-8*c + 8*sqrt(c^2 + d^2)) - I*sqrt(-8*c + 8*sqrt(c^2 + d^2))*d - sqrt(c^2 + d^2)*sqrt(-8*c + 8*sqrt(c^2 + d^2))))/((8*a^3*c^2*f - 16*I*a^3*c*d*f - 8*a^3*d^2*f)*sqrt(-8*c + 8*sqrt(c^2 + d^2))*(-I*d/(c - sqrt(c^2 + d^2)) + 1)) + 2*(6*I*(d*tan(f*x + e) + c)^4*c^4*d - 12*I*(d*tan(f*x + e) + c)^3*c^5*d + 6*I*(d*tan(f*x + e) + c)^2*c^6*d - 33*(d*tan(f*x + e) + c)^4*c^3*d^2 + 84*(d*tan(f*x + e) + c)^3*c^4*d^2 - 51*(d*tan(f*x + e) + c)^2*c^5*d^2 - 78*I*(d*tan(f*x + e) + c)^4*c^2*d^3 + 256*I*(d*tan(f*x + e) + c)^3*c^3*d^3 - 198*I*(d*tan(f*x + e) + c)^2*c^4*d^3 - 759*(d*tan(f*x + e) + c)^4*c*d^4 + 1856*(d*tan(f*x + e) + c)^3*c^2*d^4 - 1446*(d*tan(f*x + e) + c)^2*c^3*d^4 + 384*(d*tan(f*x + e) + c)*c^4*d^4 + 32*c^5*d^4 + 450*I*(d*tan(f*x + e) + c)^4*d^5 + 844*I*(d*tan(f*x + e) + c)^3*c*d^5 - 2334*I*(d*tan(f*x + e) + c)^2*c^2*d^5 + (960*I*d*tan(f*x + e) + 960*I*c)*c^3*d^5 + 96*I*c^4*d^5 + 1196*(d*tan(f*x + e) + c)^3*d^6 - 243*(d*tan(f*x + e) + c)^2*c*d^6 - 576*(d*tan(f*x + e) + c)*c^2*d^6 - 64*c^3*d^6 - 978*I*(d*tan(f*x + e) + c)^2*d^7 + (192*I*d*tan(f*x + e) + 192*I*c)*c*d^7 + 64*I*c^2*d^7 - 192*(d*tan(f*x + e) + c)*d^8 - 96*c*d^8 - 32*I*d^9)/((96*a^3*c^7*f + 288*I*a^3*c^6*d*f - 96*a^3*c^5*d^2*f + 480*I*a^3*c^4*d^3*f - 480*a^3*c^3*d^4*f + 96*I*a^3*c^2*d^5*f - 288*a^3*c*d^6*f - 96*I*a^3*d^7*f)*(-I*(d*tan(f*x + e) + c)^(3/2) + I*sqrt(d*tan(f*x + e) + c)*c - sqrt(d*tan(f*x + e) + c)*d)^3)","B",0
1137,1,238,0,1.649840," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c - 2 i \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} d\right)} \sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{4 \, {\left({\left(d \tan\left(f x + e\right) + c\right)} d^{2} - c d^{2} + i \, d^{3}\right)}}"," ",0,"-1/4*(2*(d*tan(f*x + e) + c)^2*a^2 - 2*(d*tan(f*x + e) + c)*a^2*c - 2*I*(d*tan(f*x + e) + c)*a^2*d)*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((d*tan(f*x + e) + c)*d^2 - c*d^2 + I*d^3)","A",0
1138,1,194,0,0.612387," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(d \tan\left(f x + e\right) + c\right)} a {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{2 \, {\left({\left(-i \, d \tan\left(f x + e\right) - i \, c\right)} d + i \, c d + d^{2}\right)}}"," ",0,"1/2*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*(d*tan(f*x + e) + c)*a*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((-I*d*tan(f*x + e) - I*c)*d + I*c*d + d^2)","A",0
1139,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1140,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(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/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)Evaluation time: 0.57Error: Bad Argument Type","F(-2)",0
1141,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),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/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)Evaluation time: 1.18Error: Bad Argument Type","F(-2)",0
1142,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),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/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)Evaluation time: 1.73Error: Bad Argument Type","F(-2)",0
1143,1,242,0,4.248959," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} a^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} c - 2 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d\right)} \sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{4 \, {\left({\left(d \tan\left(f x + e\right) + c\right)} d^{2} - c d^{2} + i \, d^{3}\right)}}"," ",0,"-1/4*(2*(d*tan(f*x + e) + c)^3*a^2 - 2*(d*tan(f*x + e) + c)^2*a^2*c - 2*I*(d*tan(f*x + e) + c)^2*a^2*d)*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((d*tan(f*x + e) + c)*d^2 - c*d^2 + I*d^3)","A",0
1144,1,196,0,1.237721," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(d \tan\left(f x + e\right) + c\right)}^{2} a {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{2 \, {\left({\left(-i \, d \tan\left(f x + e\right) - i \, c\right)} d + i \, c d + d^{2}\right)}}"," ",0,"1/2*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*(d*tan(f*x + e) + c)^2*a*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((-I*d*tan(f*x + e) - I*c)*d + I*c*d + d^2)","A",0
1145,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1146,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(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/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)Evaluation time: 0.85Error: Bad Argument Type","F(-2)",0
1147,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),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/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)Evaluation time: 1.64Error: Bad Argument Type","F(-2)",0
1148,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),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/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)Evaluation time: 2.18Error: Bad Argument Type","F(-2)",0
1149,1,242,0,6.959317," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{4} a^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} a^{2} c - 2 i \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} a^{2} d\right)} \sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{4 \, {\left({\left(d \tan\left(f x + e\right) + c\right)} d^{2} - c d^{2} + i \, d^{3}\right)}}"," ",0,"-1/4*(2*(d*tan(f*x + e) + c)^4*a^2 - 2*(d*tan(f*x + e) + c)^3*a^2*c - 2*I*(d*tan(f*x + e) + c)^3*a^2*d)*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((d*tan(f*x + e) + c)*d^2 - c*d^2 + I*d^3)","A",0
1150,1,196,0,1.973506," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(d \tan\left(f x + e\right) + c\right)}^{3} a {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{2 \, {\left({\left(-i \, d \tan\left(f x + e\right) - i \, c\right)} d + i \, c d + d^{2}\right)}}"," ",0,"1/2*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*(d*tan(f*x + e) + c)^3*a*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((-I*d*tan(f*x + e) - I*c)*d + I*c*d + d^2)","A",0
1151,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1152,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(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/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)Evaluation time: 1.24Error: Bad Argument Type","F(-2)",0
1153,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),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/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)Evaluation time: 2.21Error: Bad Argument Type","F(-2)",0
1154,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),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/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)Evaluation time: 2.81Error: Bad Argument Type","F(-2)",0
1155,1,214,0,2.103541," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} - 2 \, a^{2} c - 2 i \, a^{2} d\right)} \sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{4 \, {\left({\left(d \tan\left(f x + e\right) + c\right)} d^{2} - c d^{2} + i \, d^{3}\right)}}"," ",0,"-1/4*(2*(d*tan(f*x + e) + c)*a^2 - 2*a^2*c - 2*I*a^2*d)*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((d*tan(f*x + e) + c)*d^2 - c*d^2 + I*d^3)","A",0
1156,1,183,0,1.036104," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} a {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{2 \, {\left({\left(-i \, d \tan\left(f x + e\right) - i \, c\right)} d + i \, c d + d^{2}\right)}}"," ",0,"1/2*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*a*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((-I*d*tan(f*x + e) - I*c)*d + I*c*d + d^2)","A",0
1157,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1158,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(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/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)Evaluation time: 0.69Error: Bad Argument Type","F(-2)",0
1159,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),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/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)Evaluation time: 1.51Error: Bad Argument Type","F(-2)",0
1160,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),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/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)Evaluation time: 2.04Error: Bad Argument Type","F(-2)",0
1161,1,240,0,2.719157," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} - 2 \, a^{2} c - 2 i \, a^{2} d\right)} \sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{4 \, {\left({\left(d \tan\left(f x + e\right) + c\right)}^{2} d^{2} - {\left(d \tan\left(f x + e\right) + c\right)} c d^{2} + {\left(i \, d \tan\left(f x + e\right) + i \, c\right)} d^{3}\right)}}"," ",0,"-1/4*(2*(d*tan(f*x + e) + c)*a^2 - 2*a^2*c - 2*I*a^2*d)*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((d*tan(f*x + e) + c)^2*d^2 - (d*tan(f*x + e) + c)*c*d^2 + (I*d*tan(f*x + e) + I*c)*d^3)","A",0
1162,1,208,0,2.559603," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} a {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{2 \, {\left(-i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} d + {\left(i \, d \tan\left(f x + e\right) + i \, c\right)} c d + {\left(d \tan\left(f x + e\right) + c\right)} d^{2}\right)}}"," ",0,"1/2*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*a*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/(-I*(d*tan(f*x + e) + c)^2*d + (I*d*tan(f*x + e) + I*c)*c*d + (d*tan(f*x + e) + c)*d^2)","B",0
1163,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1164,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),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/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)Evaluation time: 1.4Error: Bad Argument Type","F(-2)",0
1165,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),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/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)Evaluation time: 3.08Error: Bad Argument Type","F(-2)",0
1166,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),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/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)Evaluation time: 4.56Error: Bad Argument Type","F(-2)",0
1167,1,242,0,2.683363," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} - 2 \, a^{2} c - 2 i \, a^{2} d\right)} \sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{4 \, {\left({\left(d \tan\left(f x + e\right) + c\right)}^{3} d^{2} - {\left(d \tan\left(f x + e\right) + c\right)}^{2} c d^{2} + i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} d^{3}\right)}}"," ",0,"-1/4*(2*(d*tan(f*x + e) + c)*a^2 - 2*a^2*c - 2*I*a^2*d)*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/((d*tan(f*x + e) + c)^3*d^2 - (d*tan(f*x + e) + c)^2*c*d^2 + I*(d*tan(f*x + e) + c)^2*d^3)","A",0
1168,1,210,0,2.215022," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\frac{\sqrt{2 \, a d^{2} + 2 \, \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} c + c^{2} + d^{2}} a d} a {\left(\frac{i \, {\left(d \tan\left(f x + e\right) + c\right)} a d - i \, a c d}{a d^{2} + \sqrt{{\left(d \tan\left(f x + e\right) + c\right)}^{2} a^{2} d^{2} - 2 \, {\left(d \tan\left(f x + e\right) + c\right)} a^{2} c d^{2} + a^{2} c^{2} d^{2} + a^{2} d^{4}}} + 1\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{2 \, {\left(-i \, {\left(d \tan\left(f x + e\right) + c\right)}^{3} d + i \, {\left(d \tan\left(f x + e\right) + c\right)}^{2} c d + {\left(d \tan\left(f x + e\right) + c\right)}^{2} d^{2}\right)}}"," ",0,"1/2*sqrt(2*a*d^2 + 2*sqrt((d*tan(f*x + e) + c)^2 - 2*(d*tan(f*x + e) + c)*c + c^2 + d^2)*a*d)*a*((I*(d*tan(f*x + e) + c)*a*d - I*a*c*d)/(a*d^2 + sqrt((d*tan(f*x + e) + c)^2*a^2*d^2 - 2*(d*tan(f*x + e) + c)*a^2*c*d^2 + a^2*c^2*d^2 + a^2*d^4)) + 1)*log(abs(d*tan(f*x + e) + c))/(-I*(d*tan(f*x + e) + c)^3*d + I*(d*tan(f*x + e) + c)^2*c*d + (d*tan(f*x + e) + c)^2*d^2)","A",0
1169,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1170,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),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/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)Evaluation time: 2.57Error: Bad Argument Type","F(-2)",0
1171,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),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/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)Evaluation time: 5.89Error: Bad Argument Type","F(-2)",0
1172,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),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/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)Evaluation time: 8.04Error: Bad Argument Type","F(-2)",0
1173,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m*(d*tan(f*x + e) + c)^n, x)","F",0
1174,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(d*tan(f*x + e) + c)^n, x)","F",0
1175,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(d*tan(f*x + e) + c)^n, x)","F",0
1176,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^n, x)","F",0
1177,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d \tan\left(f x + e\right) + c\right)}^{n}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^n/(I*a*tan(f*x + e) + a), x)","F",0
1178,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d \tan\left(f x + e\right) + c\right)}^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^n/(I*a*tan(f*x + e) + a)^2, x)","F",0
1179,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(d \tan\left(f x + e\right) + c\right)}^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^n/(I*a*tan(f*x + e) + a)^3, x)","F",0
1180,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{3} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^3*(I*a*tan(f*x + e) + a)^m, x)","F",0
1181,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{2} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^2*(I*a*tan(f*x + e) + a)^m, x)","F",0
1182,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)*(I*a*tan(f*x + e) + a)^m, x)","F",0
1183,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c), x)","F",0
1184,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^2, x)","F",0
1185,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^3, x)","F",0
1186,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1187,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1188,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1189,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1190,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1191,1,2046,0,2.715086," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{6 \, a^{3} c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, a b^{2} c f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, a^{2} b d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, b^{3} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 9 \, a^{2} b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, b^{3} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, a^{3} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, a b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, a^{3} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 54 \, a b^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 54 \, a^{2} b d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, b^{3} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, b^{3} c \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, a b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 27 \, a^{2} b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, b^{3} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, a^{3} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 27 \, a b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, a b^{2} c \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 18 \, a^{2} b d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 6 \, b^{3} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 18 \, a b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 18 \, a^{2} b d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 6 \, b^{3} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 18 \, a^{3} c f x \tan\left(f x\right) \tan\left(e\right) - 54 \, a b^{2} c f x \tan\left(f x\right) \tan\left(e\right) - 54 \, a^{2} b d f x \tan\left(f x\right) \tan\left(e\right) + 18 \, b^{3} d f x \tan\left(f x\right) \tan\left(e\right) + 3 \, b^{3} c \tan\left(f x\right)^{3} \tan\left(e\right) + 9 \, a b^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) - 3 \, b^{3} c \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, a b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, b^{3} c \tan\left(f x\right) \tan\left(e\right)^{3} + 9 \, a b^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} - 2 \, b^{3} d \tan\left(f x\right)^{3} - 27 \, a^{2} b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, b^{3} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 9 \, a^{3} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 27 \, a b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 36 \, a b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right) + 36 \, a^{2} b d \tan\left(f x\right)^{2} \tan\left(e\right) - 18 \, b^{3} d \tan\left(f x\right)^{2} \tan\left(e\right) + 36 \, a b^{2} c \tan\left(f x\right) \tan\left(e\right)^{2} + 36 \, a^{2} b d \tan\left(f x\right) \tan\left(e\right)^{2} - 18 \, b^{3} d \tan\left(f x\right) \tan\left(e\right)^{2} - 2 \, b^{3} d \tan\left(e\right)^{3} - 6 \, a^{3} c f x + 18 \, a b^{2} c f x + 18 \, a^{2} b d f x - 6 \, b^{3} d f x - 3 \, b^{3} c \tan\left(f x\right)^{2} - 9 \, a b^{2} d \tan\left(f x\right)^{2} + 3 \, b^{3} c \tan\left(f x\right) \tan\left(e\right) + 9 \, a b^{2} d \tan\left(f x\right) \tan\left(e\right) - 3 \, b^{3} c \tan\left(e\right)^{2} - 9 \, a b^{2} d \tan\left(e\right)^{2} + 9 \, a^{2} b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, b^{3} c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 3 \, a^{3} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 9 \, a b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 18 \, a b^{2} c \tan\left(f x\right) - 18 \, a^{2} b d \tan\left(f x\right) + 6 \, b^{3} d \tan\left(f x\right) - 18 \, a b^{2} c \tan\left(e\right) - 18 \, a^{2} b d \tan\left(e\right) + 6 \, b^{3} d \tan\left(e\right) - 3 \, b^{3} c - 9 \, a b^{2} d}{6 \, {\left(f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/6*(6*a^3*c*f*x*tan(f*x)^3*tan(e)^3 - 18*a*b^2*c*f*x*tan(f*x)^3*tan(e)^3 - 18*a^2*b*d*f*x*tan(f*x)^3*tan(e)^3 + 6*b^3*d*f*x*tan(f*x)^3*tan(e)^3 - 9*a^2*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*b^3*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 3*a^3*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 9*a*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 18*a^3*c*f*x*tan(f*x)^2*tan(e)^2 + 54*a*b^2*c*f*x*tan(f*x)^2*tan(e)^2 + 54*a^2*b*d*f*x*tan(f*x)^2*tan(e)^2 - 18*b^3*d*f*x*tan(f*x)^2*tan(e)^2 + 3*b^3*c*tan(f*x)^3*tan(e)^3 + 9*a*b^2*d*tan(f*x)^3*tan(e)^3 + 27*a^2*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*b^3*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 9*a^3*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 27*a*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 18*a*b^2*c*tan(f*x)^3*tan(e)^2 - 18*a^2*b*d*tan(f*x)^3*tan(e)^2 + 6*b^3*d*tan(f*x)^3*tan(e)^2 - 18*a*b^2*c*tan(f*x)^2*tan(e)^3 - 18*a^2*b*d*tan(f*x)^2*tan(e)^3 + 6*b^3*d*tan(f*x)^2*tan(e)^3 + 18*a^3*c*f*x*tan(f*x)*tan(e) - 54*a*b^2*c*f*x*tan(f*x)*tan(e) - 54*a^2*b*d*f*x*tan(f*x)*tan(e) + 18*b^3*d*f*x*tan(f*x)*tan(e) + 3*b^3*c*tan(f*x)^3*tan(e) + 9*a*b^2*d*tan(f*x)^3*tan(e) - 3*b^3*c*tan(f*x)^2*tan(e)^2 - 9*a*b^2*d*tan(f*x)^2*tan(e)^2 + 3*b^3*c*tan(f*x)*tan(e)^3 + 9*a*b^2*d*tan(f*x)*tan(e)^3 - 2*b^3*d*tan(f*x)^3 - 27*a^2*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*b^3*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 9*a^3*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 27*a*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 36*a*b^2*c*tan(f*x)^2*tan(e) + 36*a^2*b*d*tan(f*x)^2*tan(e) - 18*b^3*d*tan(f*x)^2*tan(e) + 36*a*b^2*c*tan(f*x)*tan(e)^2 + 36*a^2*b*d*tan(f*x)*tan(e)^2 - 18*b^3*d*tan(f*x)*tan(e)^2 - 2*b^3*d*tan(e)^3 - 6*a^3*c*f*x + 18*a*b^2*c*f*x + 18*a^2*b*d*f*x - 6*b^3*d*f*x - 3*b^3*c*tan(f*x)^2 - 9*a*b^2*d*tan(f*x)^2 + 3*b^3*c*tan(f*x)*tan(e) + 9*a*b^2*d*tan(f*x)*tan(e) - 3*b^3*c*tan(e)^2 - 9*a*b^2*d*tan(e)^2 + 9*a^2*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*b^3*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 3*a^3*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 9*a*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 18*a*b^2*c*tan(f*x) - 18*a^2*b*d*tan(f*x) + 6*b^3*d*tan(f*x) - 18*a*b^2*c*tan(e) - 18*a^2*b*d*tan(e) + 6*b^3*d*tan(e) - 3*b^3*c - 9*a*b^2*d)/(f*tan(f*x)^3*tan(e)^3 - 3*f*tan(f*x)^2*tan(e)^2 + 3*f*tan(f*x)*tan(e) - f)","B",0
1192,1,968,0,1.391016," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, a^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, b^{2} c f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, a b d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} c f x \tan\left(f x\right) \tan\left(e\right) + 4 \, b^{2} c f x \tan\left(f x\right) \tan\left(e\right) + 8 \, a b d f x \tan\left(f x\right) \tan\left(e\right) + b^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 4 \, a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 2 \, a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 2 \, b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 2 \, b^{2} c \tan\left(f x\right)^{2} \tan\left(e\right) - 4 \, a b d \tan\left(f x\right)^{2} \tan\left(e\right) - 2 \, b^{2} c \tan\left(f x\right) \tan\left(e\right)^{2} - 4 \, a b d \tan\left(f x\right) \tan\left(e\right)^{2} + 2 \, a^{2} c f x - 2 \, b^{2} c f x - 4 \, a b d f x + b^{2} d \tan\left(f x\right)^{2} + b^{2} d \tan\left(e\right)^{2} - 2 \, a b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - a^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + b^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 2 \, b^{2} c \tan\left(f x\right) + 4 \, a b d \tan\left(f x\right) + 2 \, b^{2} c \tan\left(e\right) + 4 \, a b d \tan\left(e\right) + b^{2} d}{2 \, {\left(f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/2*(2*a^2*c*f*x*tan(f*x)^2*tan(e)^2 - 2*b^2*c*f*x*tan(f*x)^2*tan(e)^2 - 4*a*b*d*f*x*tan(f*x)^2*tan(e)^2 - 2*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 4*a^2*c*f*x*tan(f*x)*tan(e) + 4*b^2*c*f*x*tan(f*x)*tan(e) + 8*a*b*d*f*x*tan(f*x)*tan(e) + b^2*d*tan(f*x)^2*tan(e)^2 + 4*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 2*a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 2*b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 2*b^2*c*tan(f*x)^2*tan(e) - 4*a*b*d*tan(f*x)^2*tan(e) - 2*b^2*c*tan(f*x)*tan(e)^2 - 4*a*b*d*tan(f*x)*tan(e)^2 + 2*a^2*c*f*x - 2*b^2*c*f*x - 4*a*b*d*f*x + b^2*d*tan(f*x)^2 + b^2*d*tan(e)^2 - 2*a*b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - a^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + b^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 2*b^2*c*tan(f*x) + 4*a*b*d*tan(f*x) + 2*b^2*c*tan(e) + 4*a*b*d*tan(e) + b^2*d)/(f*tan(f*x)^2*tan(e)^2 - 2*f*tan(f*x)*tan(e) + f)","B",0
1193,1,355,0,0.463450," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{2 \, a c f x \tan\left(f x\right) \tan\left(e\right) - 2 \, b d f x \tan\left(f x\right) \tan\left(e\right) - b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 2 \, a c f x + 2 \, b d f x + b c \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + a d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 2 \, b d \tan\left(f x\right) - 2 \, b d \tan\left(e\right)}{2 \, {\left(f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/2*(2*a*c*f*x*tan(f*x)*tan(e) - 2*b*d*f*x*tan(f*x)*tan(e) - b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 2*a*c*f*x + 2*b*d*f*x + b*c*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + a*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 2*b*d*tan(f*x) - 2*b*d*tan(e))/(f*tan(f*x)*tan(e) - f)","B",0
1194,1,98,0,0.575083," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a c + b d\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} - \frac{{\left(b c - a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(b^{2} c - a b d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b + b^{3}}}{2 \, f}"," ",0,"1/2*(2*(a*c + b*d)*(f*x + e)/(a^2 + b^2) - (b*c - a*d)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + 2*(b^2*c - a*b*d)*log(abs(b*tan(f*x + e) + a))/(a^2*b + b^3))/f","A",0
1195,1,241,0,0.747314," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{2} c - b^{2} c + 2 \, a b d\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a b c - a^{2} d + b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, a b^{2} c - a^{2} b d + b^{3} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{2 \, {\left(2 \, a b^{2} c \tan\left(f x + e\right) - a^{2} b d \tan\left(f x + e\right) + b^{3} d \tan\left(f x + e\right) + 3 \, a^{2} b c + b^{3} c - 2 \, a^{3} d\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{2 \, f}"," ",0,"1/2*(2*(a^2*c - b^2*c + 2*a*b*d)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) - (2*a*b*c - a^2*d + b^2*d)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*a*b^2*c - a^2*b*d + b^3*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b + 2*a^2*b^3 + b^5) - 2*(2*a*b^2*c*tan(f*x + e) - a^2*b*d*tan(f*x + e) + b^3*d*tan(f*x + e) + 3*a^2*b*c + b^3*c - 2*a^3*d)/((a^4 + 2*a^2*b^2 + b^4)*(b*tan(f*x + e) + a)))/f","B",0
1196,1,426,0,0.828922," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} c - 3 \, a b^{2} c + 3 \, a^{2} b d - b^{3} d\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b c - b^{3} c - a^{3} d + 3 \, a b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(3 \, a^{2} b^{2} c - b^{4} c - a^{3} b d + 3 \, a b^{3} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{9 \, a^{2} b^{3} c \tan\left(f x + e\right)^{2} - 3 \, b^{5} c \tan\left(f x + e\right)^{2} - 3 \, a^{3} b^{2} d \tan\left(f x + e\right)^{2} + 9 \, a b^{4} d \tan\left(f x + e\right)^{2} + 22 \, a^{3} b^{2} c \tan\left(f x + e\right) - 2 \, a b^{4} c \tan\left(f x + e\right) - 8 \, a^{4} b d \tan\left(f x + e\right) + 18 \, a^{2} b^{3} d \tan\left(f x + e\right) + 2 \, b^{5} d \tan\left(f x + e\right) + 14 \, a^{4} b c + 3 \, a^{2} b^{3} c + b^{5} c - 6 \, a^{5} d + 7 \, a^{3} b^{2} d + a b^{4} d}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^3*c - 3*a*b^2*c + 3*a^2*b*d - b^3*d)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b*c - b^3*c - a^3*d + 3*a*b^2*d)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*a^2*b^2*c - b^4*c - a^3*b*d + 3*a*b^3*d)*log(abs(b*tan(f*x + e) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - (9*a^2*b^3*c*tan(f*x + e)^2 - 3*b^5*c*tan(f*x + e)^2 - 3*a^3*b^2*d*tan(f*x + e)^2 + 9*a*b^4*d*tan(f*x + e)^2 + 22*a^3*b^2*c*tan(f*x + e) - 2*a*b^4*c*tan(f*x + e) - 8*a^4*b*d*tan(f*x + e) + 18*a^2*b^3*d*tan(f*x + e) + 2*b^5*d*tan(f*x + e) + 14*a^4*b*c + 3*a^2*b^3*c + b^5*c - 6*a^5*d + 7*a^3*b^2*d + a*b^4*d)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*(b*tan(f*x + e) + a)^2))/f","B",0
1197,1,4557,0,8.690918," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{12 \, a^{3} c^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 36 \, a b^{2} c^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 72 \, a^{2} b c d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, b^{3} c d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, a^{3} d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, a b^{2} d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 18 \, a^{2} b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, b^{3} c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, a^{3} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, a b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 18 \, a^{2} b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, b^{3} d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 48 \, a^{3} c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 144 \, a b^{2} c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 288 \, a^{2} b c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 96 \, b^{3} c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, a^{3} d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 144 \, a b^{2} d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, b^{3} c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, a b^{2} c d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 18 \, a^{2} b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 9 \, b^{3} d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 72 \, a^{2} b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, b^{3} c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, a^{3} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 144 \, a b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 72 \, a^{2} b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, b^{3} d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 36 \, a b^{2} c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 72 \, a^{2} b c d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 24 \, b^{3} c d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, a^{3} d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 36 \, a b^{2} d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 36 \, a b^{2} c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 72 \, a^{2} b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 24 \, b^{3} c d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 12 \, a^{3} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 36 \, a b^{2} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 72 \, a^{3} c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 216 \, a b^{2} c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 432 \, a^{2} b c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 144 \, b^{3} c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, a^{3} d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 216 \, a b^{2} d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 6 \, b^{3} c^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 36 \, a b^{2} c d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 18 \, a^{2} b d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 6 \, b^{3} d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 12 \, b^{3} c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 72 \, a b^{2} c d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 36 \, a^{2} b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, b^{3} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, b^{3} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 36 \, a b^{2} c d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 18 \, a^{2} b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 6 \, b^{3} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 8 \, b^{3} c d \tan\left(f x\right)^{4} \tan\left(e\right) - 12 \, a b^{2} d^{2} \tan\left(f x\right)^{4} \tan\left(e\right) - 108 \, a^{2} b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, b^{3} c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, a^{3} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 216 \, a b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 108 \, a^{2} b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, b^{3} d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 108 \, a b^{2} c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 216 \, a^{2} b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 96 \, b^{3} c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, a^{3} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 144 \, a b^{2} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 108 \, a b^{2} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 216 \, a^{2} b c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 96 \, b^{3} c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 36 \, a^{3} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 144 \, a b^{2} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 8 \, b^{3} c d \tan\left(f x\right) \tan\left(e\right)^{4} - 12 \, a b^{2} d^{2} \tan\left(f x\right) \tan\left(e\right)^{4} + 3 \, b^{3} d^{2} \tan\left(f x\right)^{4} - 48 \, a^{3} c^{2} f x \tan\left(f x\right) \tan\left(e\right) + 144 \, a b^{2} c^{2} f x \tan\left(f x\right) \tan\left(e\right) + 288 \, a^{2} b c d f x \tan\left(f x\right) \tan\left(e\right) - 96 \, b^{3} c d f x \tan\left(f x\right) \tan\left(e\right) + 48 \, a^{3} d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 144 \, a b^{2} d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 12 \, b^{3} c^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 72 \, a b^{2} c d \tan\left(f x\right)^{3} \tan\left(e\right) - 36 \, a^{2} b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) + 24 \, b^{3} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) + 12 \, b^{3} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, a b^{2} c d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, a^{2} b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, b^{3} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, b^{3} c^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 72 \, a b^{2} c d \tan\left(f x\right) \tan\left(e\right)^{3} - 36 \, a^{2} b d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} + 24 \, b^{3} d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, b^{3} d^{2} \tan\left(e\right)^{4} + 8 \, b^{3} c d \tan\left(f x\right)^{3} + 12 \, a b^{2} d^{2} \tan\left(f x\right)^{3} + 72 \, a^{2} b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, b^{3} c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 48 \, a^{3} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 144 \, a b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 72 \, a^{2} b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, b^{3} d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 108 \, a b^{2} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 216 \, a^{2} b c d \tan\left(f x\right)^{2} \tan\left(e\right) + 96 \, b^{3} c d \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, a^{3} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 144 \, a b^{2} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 108 \, a b^{2} c^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 216 \, a^{2} b c d \tan\left(f x\right) \tan\left(e\right)^{2} + 96 \, b^{3} c d \tan\left(f x\right) \tan\left(e\right)^{2} - 36 \, a^{3} d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 144 \, a b^{2} d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 8 \, b^{3} c d \tan\left(e\right)^{3} + 12 \, a b^{2} d^{2} \tan\left(e\right)^{3} + 12 \, a^{3} c^{2} f x - 36 \, a b^{2} c^{2} f x - 72 \, a^{2} b c d f x + 24 \, b^{3} c d f x - 12 \, a^{3} d^{2} f x + 36 \, a b^{2} d^{2} f x + 6 \, b^{3} c^{2} \tan\left(f x\right)^{2} + 36 \, a b^{2} c d \tan\left(f x\right)^{2} + 18 \, a^{2} b d^{2} \tan\left(f x\right)^{2} - 6 \, b^{3} d^{2} \tan\left(f x\right)^{2} - 12 \, b^{3} c^{2} \tan\left(f x\right) \tan\left(e\right) - 72 \, a b^{2} c d \tan\left(f x\right) \tan\left(e\right) - 36 \, a^{2} b d^{2} \tan\left(f x\right) \tan\left(e\right) + 24 \, b^{3} d^{2} \tan\left(f x\right) \tan\left(e\right) + 6 \, b^{3} c^{2} \tan\left(e\right)^{2} + 36 \, a b^{2} c d \tan\left(e\right)^{2} + 18 \, a^{2} b d^{2} \tan\left(e\right)^{2} - 6 \, b^{3} d^{2} \tan\left(e\right)^{2} - 18 \, a^{2} b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, b^{3} c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 12 \, a^{3} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 36 \, a b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 18 \, a^{2} b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, b^{3} d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 36 \, a b^{2} c^{2} \tan\left(f x\right) + 72 \, a^{2} b c d \tan\left(f x\right) - 24 \, b^{3} c d \tan\left(f x\right) + 12 \, a^{3} d^{2} \tan\left(f x\right) - 36 \, a b^{2} d^{2} \tan\left(f x\right) + 36 \, a b^{2} c^{2} \tan\left(e\right) + 72 \, a^{2} b c d \tan\left(e\right) - 24 \, b^{3} c d \tan\left(e\right) + 12 \, a^{3} d^{2} \tan\left(e\right) - 36 \, a b^{2} d^{2} \tan\left(e\right) + 6 \, b^{3} c^{2} + 36 \, a b^{2} c d + 18 \, a^{2} b d^{2} - 9 \, b^{3} d^{2}}{12 \, {\left(f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 4 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/12*(12*a^3*c^2*f*x*tan(f*x)^4*tan(e)^4 - 36*a*b^2*c^2*f*x*tan(f*x)^4*tan(e)^4 - 72*a^2*b*c*d*f*x*tan(f*x)^4*tan(e)^4 + 24*b^3*c*d*f*x*tan(f*x)^4*tan(e)^4 - 12*a^3*d^2*f*x*tan(f*x)^4*tan(e)^4 + 36*a*b^2*d^2*f*x*tan(f*x)^4*tan(e)^4 - 18*a^2*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*b^3*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 12*a^3*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 36*a*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 18*a^2*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*b^3*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 48*a^3*c^2*f*x*tan(f*x)^3*tan(e)^3 + 144*a*b^2*c^2*f*x*tan(f*x)^3*tan(e)^3 + 288*a^2*b*c*d*f*x*tan(f*x)^3*tan(e)^3 - 96*b^3*c*d*f*x*tan(f*x)^3*tan(e)^3 + 48*a^3*d^2*f*x*tan(f*x)^3*tan(e)^3 - 144*a*b^2*d^2*f*x*tan(f*x)^3*tan(e)^3 + 6*b^3*c^2*tan(f*x)^4*tan(e)^4 + 36*a*b^2*c*d*tan(f*x)^4*tan(e)^4 + 18*a^2*b*d^2*tan(f*x)^4*tan(e)^4 - 9*b^3*d^2*tan(f*x)^4*tan(e)^4 + 72*a^2*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*b^3*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 48*a^3*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 144*a*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 72*a^2*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*b^3*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 36*a*b^2*c^2*tan(f*x)^4*tan(e)^3 - 72*a^2*b*c*d*tan(f*x)^4*tan(e)^3 + 24*b^3*c*d*tan(f*x)^4*tan(e)^3 - 12*a^3*d^2*tan(f*x)^4*tan(e)^3 + 36*a*b^2*d^2*tan(f*x)^4*tan(e)^3 - 36*a*b^2*c^2*tan(f*x)^3*tan(e)^4 - 72*a^2*b*c*d*tan(f*x)^3*tan(e)^4 + 24*b^3*c*d*tan(f*x)^3*tan(e)^4 - 12*a^3*d^2*tan(f*x)^3*tan(e)^4 + 36*a*b^2*d^2*tan(f*x)^3*tan(e)^4 + 72*a^3*c^2*f*x*tan(f*x)^2*tan(e)^2 - 216*a*b^2*c^2*f*x*tan(f*x)^2*tan(e)^2 - 432*a^2*b*c*d*f*x*tan(f*x)^2*tan(e)^2 + 144*b^3*c*d*f*x*tan(f*x)^2*tan(e)^2 - 72*a^3*d^2*f*x*tan(f*x)^2*tan(e)^2 + 216*a*b^2*d^2*f*x*tan(f*x)^2*tan(e)^2 + 6*b^3*c^2*tan(f*x)^4*tan(e)^2 + 36*a*b^2*c*d*tan(f*x)^4*tan(e)^2 + 18*a^2*b*d^2*tan(f*x)^4*tan(e)^2 - 6*b^3*d^2*tan(f*x)^4*tan(e)^2 - 12*b^3*c^2*tan(f*x)^3*tan(e)^3 - 72*a*b^2*c*d*tan(f*x)^3*tan(e)^3 - 36*a^2*b*d^2*tan(f*x)^3*tan(e)^3 + 24*b^3*d^2*tan(f*x)^3*tan(e)^3 + 6*b^3*c^2*tan(f*x)^2*tan(e)^4 + 36*a*b^2*c*d*tan(f*x)^2*tan(e)^4 + 18*a^2*b*d^2*tan(f*x)^2*tan(e)^4 - 6*b^3*d^2*tan(f*x)^2*tan(e)^4 - 8*b^3*c*d*tan(f*x)^4*tan(e) - 12*a*b^2*d^2*tan(f*x)^4*tan(e) - 108*a^2*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*b^3*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 72*a^3*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 216*a*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 108*a^2*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*b^3*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 108*a*b^2*c^2*tan(f*x)^3*tan(e)^2 + 216*a^2*b*c*d*tan(f*x)^3*tan(e)^2 - 96*b^3*c*d*tan(f*x)^3*tan(e)^2 + 36*a^3*d^2*tan(f*x)^3*tan(e)^2 - 144*a*b^2*d^2*tan(f*x)^3*tan(e)^2 + 108*a*b^2*c^2*tan(f*x)^2*tan(e)^3 + 216*a^2*b*c*d*tan(f*x)^2*tan(e)^3 - 96*b^3*c*d*tan(f*x)^2*tan(e)^3 + 36*a^3*d^2*tan(f*x)^2*tan(e)^3 - 144*a*b^2*d^2*tan(f*x)^2*tan(e)^3 - 8*b^3*c*d*tan(f*x)*tan(e)^4 - 12*a*b^2*d^2*tan(f*x)*tan(e)^4 + 3*b^3*d^2*tan(f*x)^4 - 48*a^3*c^2*f*x*tan(f*x)*tan(e) + 144*a*b^2*c^2*f*x*tan(f*x)*tan(e) + 288*a^2*b*c*d*f*x*tan(f*x)*tan(e) - 96*b^3*c*d*f*x*tan(f*x)*tan(e) + 48*a^3*d^2*f*x*tan(f*x)*tan(e) - 144*a*b^2*d^2*f*x*tan(f*x)*tan(e) - 12*b^3*c^2*tan(f*x)^3*tan(e) - 72*a*b^2*c*d*tan(f*x)^3*tan(e) - 36*a^2*b*d^2*tan(f*x)^3*tan(e) + 24*b^3*d^2*tan(f*x)^3*tan(e) + 12*b^3*c^2*tan(f*x)^2*tan(e)^2 + 72*a*b^2*c*d*tan(f*x)^2*tan(e)^2 + 36*a^2*b*d^2*tan(f*x)^2*tan(e)^2 - 12*b^3*d^2*tan(f*x)^2*tan(e)^2 - 12*b^3*c^2*tan(f*x)*tan(e)^3 - 72*a*b^2*c*d*tan(f*x)*tan(e)^3 - 36*a^2*b*d^2*tan(f*x)*tan(e)^3 + 24*b^3*d^2*tan(f*x)*tan(e)^3 + 3*b^3*d^2*tan(e)^4 + 8*b^3*c*d*tan(f*x)^3 + 12*a*b^2*d^2*tan(f*x)^3 + 72*a^2*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*b^3*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 48*a^3*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 144*a*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 72*a^2*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*b^3*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 108*a*b^2*c^2*tan(f*x)^2*tan(e) - 216*a^2*b*c*d*tan(f*x)^2*tan(e) + 96*b^3*c*d*tan(f*x)^2*tan(e) - 36*a^3*d^2*tan(f*x)^2*tan(e) + 144*a*b^2*d^2*tan(f*x)^2*tan(e) - 108*a*b^2*c^2*tan(f*x)*tan(e)^2 - 216*a^2*b*c*d*tan(f*x)*tan(e)^2 + 96*b^3*c*d*tan(f*x)*tan(e)^2 - 36*a^3*d^2*tan(f*x)*tan(e)^2 + 144*a*b^2*d^2*tan(f*x)*tan(e)^2 + 8*b^3*c*d*tan(e)^3 + 12*a*b^2*d^2*tan(e)^3 + 12*a^3*c^2*f*x - 36*a*b^2*c^2*f*x - 72*a^2*b*c*d*f*x + 24*b^3*c*d*f*x - 12*a^3*d^2*f*x + 36*a*b^2*d^2*f*x + 6*b^3*c^2*tan(f*x)^2 + 36*a*b^2*c*d*tan(f*x)^2 + 18*a^2*b*d^2*tan(f*x)^2 - 6*b^3*d^2*tan(f*x)^2 - 12*b^3*c^2*tan(f*x)*tan(e) - 72*a*b^2*c*d*tan(f*x)*tan(e) - 36*a^2*b*d^2*tan(f*x)*tan(e) + 24*b^3*d^2*tan(f*x)*tan(e) + 6*b^3*c^2*tan(e)^2 + 36*a*b^2*c*d*tan(e)^2 + 18*a^2*b*d^2*tan(e)^2 - 6*b^3*d^2*tan(e)^2 - 18*a^2*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*b^3*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 12*a^3*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 36*a*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 18*a^2*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*b^3*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 36*a*b^2*c^2*tan(f*x) + 72*a^2*b*c*d*tan(f*x) - 24*b^3*c*d*tan(f*x) + 12*a^3*d^2*tan(f*x) - 36*a*b^2*d^2*tan(f*x) + 36*a*b^2*c^2*tan(e) + 72*a^2*b*c*d*tan(e) - 24*b^3*c*d*tan(e) + 12*a^3*d^2*tan(e) - 36*a*b^2*d^2*tan(e) + 6*b^3*c^2 + 36*a*b^2*c*d + 18*a^2*b*d^2 - 9*b^3*d^2)/(f*tan(f*x)^4*tan(e)^4 - 4*f*tan(f*x)^3*tan(e)^3 + 6*f*tan(f*x)^2*tan(e)^2 - 4*f*tan(f*x)*tan(e) + f)","B",0
1198,1,2258,0,3.620959," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{3 \, a^{2} c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, b^{2} c^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, a b c d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, a^{2} d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, b^{2} d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, a b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, a^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, a b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 9 \, a^{2} c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, b^{2} c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, a b c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, a^{2} d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, b^{2} d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, b^{2} c d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, a b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, a b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, a^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, a b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 3 \, b^{2} c^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 12 \, a b c d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 3 \, a^{2} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 3 \, b^{2} d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 3 \, b^{2} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 12 \, a b c d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 3 \, a^{2} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 3 \, b^{2} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 9 \, a^{2} c^{2} f x \tan\left(f x\right) \tan\left(e\right) - 9 \, b^{2} c^{2} f x \tan\left(f x\right) \tan\left(e\right) - 36 \, a b c d f x \tan\left(f x\right) \tan\left(e\right) - 9 \, a^{2} d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 9 \, b^{2} d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 3 \, b^{2} c d \tan\left(f x\right)^{3} \tan\left(e\right) + 3 \, a b d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 3 \, b^{2} c d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 3 \, a b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, b^{2} c d \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, a b d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - b^{2} d^{2} \tan\left(f x\right)^{3} - 9 \, a b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 9 \, a^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, a b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 6 \, b^{2} c^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 24 \, a b c d \tan\left(f x\right)^{2} \tan\left(e\right) + 6 \, a^{2} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 9 \, b^{2} d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 6 \, b^{2} c^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 24 \, a b c d \tan\left(f x\right) \tan\left(e\right)^{2} + 6 \, a^{2} d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 9 \, b^{2} d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - b^{2} d^{2} \tan\left(e\right)^{3} - 3 \, a^{2} c^{2} f x + 3 \, b^{2} c^{2} f x + 12 \, a b c d f x + 3 \, a^{2} d^{2} f x - 3 \, b^{2} d^{2} f x - 3 \, b^{2} c d \tan\left(f x\right)^{2} - 3 \, a b d^{2} \tan\left(f x\right)^{2} + 3 \, b^{2} c d \tan\left(f x\right) \tan\left(e\right) + 3 \, a b d^{2} \tan\left(f x\right) \tan\left(e\right) - 3 \, b^{2} c d \tan\left(e\right)^{2} - 3 \, a b d^{2} \tan\left(e\right)^{2} + 3 \, a b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 3 \, a^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, b^{2} c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, a b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, b^{2} c^{2} \tan\left(f x\right) - 12 \, a b c d \tan\left(f x\right) - 3 \, a^{2} d^{2} \tan\left(f x\right) + 3 \, b^{2} d^{2} \tan\left(f x\right) - 3 \, b^{2} c^{2} \tan\left(e\right) - 12 \, a b c d \tan\left(e\right) - 3 \, a^{2} d^{2} \tan\left(e\right) + 3 \, b^{2} d^{2} \tan\left(e\right) - 3 \, b^{2} c d - 3 \, a b d^{2}}{3 \, {\left(f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/3*(3*a^2*c^2*f*x*tan(f*x)^3*tan(e)^3 - 3*b^2*c^2*f*x*tan(f*x)^3*tan(e)^3 - 12*a*b*c*d*f*x*tan(f*x)^3*tan(e)^3 - 3*a^2*d^2*f*x*tan(f*x)^3*tan(e)^3 + 3*b^2*d^2*f*x*tan(f*x)^3*tan(e)^3 - 3*a*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 3*a^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*a*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 9*a^2*c^2*f*x*tan(f*x)^2*tan(e)^2 + 9*b^2*c^2*f*x*tan(f*x)^2*tan(e)^2 + 36*a*b*c*d*f*x*tan(f*x)^2*tan(e)^2 + 9*a^2*d^2*f*x*tan(f*x)^2*tan(e)^2 - 9*b^2*d^2*f*x*tan(f*x)^2*tan(e)^2 + 3*b^2*c*d*tan(f*x)^3*tan(e)^3 + 3*a*b*d^2*tan(f*x)^3*tan(e)^3 + 9*a*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 9*a^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*a*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 3*b^2*c^2*tan(f*x)^3*tan(e)^2 - 12*a*b*c*d*tan(f*x)^3*tan(e)^2 - 3*a^2*d^2*tan(f*x)^3*tan(e)^2 + 3*b^2*d^2*tan(f*x)^3*tan(e)^2 - 3*b^2*c^2*tan(f*x)^2*tan(e)^3 - 12*a*b*c*d*tan(f*x)^2*tan(e)^3 - 3*a^2*d^2*tan(f*x)^2*tan(e)^3 + 3*b^2*d^2*tan(f*x)^2*tan(e)^3 + 9*a^2*c^2*f*x*tan(f*x)*tan(e) - 9*b^2*c^2*f*x*tan(f*x)*tan(e) - 36*a*b*c*d*f*x*tan(f*x)*tan(e) - 9*a^2*d^2*f*x*tan(f*x)*tan(e) + 9*b^2*d^2*f*x*tan(f*x)*tan(e) + 3*b^2*c*d*tan(f*x)^3*tan(e) + 3*a*b*d^2*tan(f*x)^3*tan(e) - 3*b^2*c*d*tan(f*x)^2*tan(e)^2 - 3*a*b*d^2*tan(f*x)^2*tan(e)^2 + 3*b^2*c*d*tan(f*x)*tan(e)^3 + 3*a*b*d^2*tan(f*x)*tan(e)^3 - b^2*d^2*tan(f*x)^3 - 9*a*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 9*a^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*a*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 6*b^2*c^2*tan(f*x)^2*tan(e) + 24*a*b*c*d*tan(f*x)^2*tan(e) + 6*a^2*d^2*tan(f*x)^2*tan(e) - 9*b^2*d^2*tan(f*x)^2*tan(e) + 6*b^2*c^2*tan(f*x)*tan(e)^2 + 24*a*b*c*d*tan(f*x)*tan(e)^2 + 6*a^2*d^2*tan(f*x)*tan(e)^2 - 9*b^2*d^2*tan(f*x)*tan(e)^2 - b^2*d^2*tan(e)^3 - 3*a^2*c^2*f*x + 3*b^2*c^2*f*x + 12*a*b*c*d*f*x + 3*a^2*d^2*f*x - 3*b^2*d^2*f*x - 3*b^2*c*d*tan(f*x)^2 - 3*a*b*d^2*tan(f*x)^2 + 3*b^2*c*d*tan(f*x)*tan(e) + 3*a*b*d^2*tan(f*x)*tan(e) - 3*b^2*c*d*tan(e)^2 - 3*a*b*d^2*tan(e)^2 + 3*a*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 3*a^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*b^2*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*a*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*b^2*c^2*tan(f*x) - 12*a*b*c*d*tan(f*x) - 3*a^2*d^2*tan(f*x) + 3*b^2*d^2*tan(f*x) - 3*b^2*c^2*tan(e) - 12*a*b*c*d*tan(e) - 3*a^2*d^2*tan(e) + 3*b^2*d^2*tan(e) - 3*b^2*c*d - 3*a*b*d^2)/(f*tan(f*x)^3*tan(e)^3 - 3*f*tan(f*x)^2*tan(e)^2 + 3*f*tan(f*x)*tan(e) - f)","B",0
1199,1,968,0,1.379269," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{2 \, a c^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, b c d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, a d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, a c^{2} f x \tan\left(f x\right) \tan\left(e\right) + 8 \, b c d f x \tan\left(f x\right) \tan\left(e\right) + 4 \, a d^{2} f x \tan\left(f x\right) \tan\left(e\right) + b d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 2 \, b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 4 \, a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 2 \, b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 4 \, b c d \tan\left(f x\right)^{2} \tan\left(e\right) - 2 \, a d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 4 \, b c d \tan\left(f x\right) \tan\left(e\right)^{2} - 2 \, a d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 2 \, a c^{2} f x - 4 \, b c d f x - 2 \, a d^{2} f x + b d^{2} \tan\left(f x\right)^{2} + b d^{2} \tan\left(e\right)^{2} - b c^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 2 \, a c d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + b d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 4 \, b c d \tan\left(f x\right) + 2 \, a d^{2} \tan\left(f x\right) + 4 \, b c d \tan\left(e\right) + 2 \, a d^{2} \tan\left(e\right) + b d^{2}}{2 \, {\left(f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/2*(2*a*c^2*f*x*tan(f*x)^2*tan(e)^2 - 4*b*c*d*f*x*tan(f*x)^2*tan(e)^2 - 2*a*d^2*f*x*tan(f*x)^2*tan(e)^2 - b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 2*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 4*a*c^2*f*x*tan(f*x)*tan(e) + 8*b*c*d*f*x*tan(f*x)*tan(e) + 4*a*d^2*f*x*tan(f*x)*tan(e) + b*d^2*tan(f*x)^2*tan(e)^2 + 2*b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 4*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 2*b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 4*b*c*d*tan(f*x)^2*tan(e) - 2*a*d^2*tan(f*x)^2*tan(e) - 4*b*c*d*tan(f*x)*tan(e)^2 - 2*a*d^2*tan(f*x)*tan(e)^2 + 2*a*c^2*f*x - 4*b*c*d*f*x - 2*a*d^2*f*x + b*d^2*tan(f*x)^2 + b*d^2*tan(e)^2 - b*c^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 2*a*c*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + b*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 4*b*c*d*tan(f*x) + 2*a*d^2*tan(f*x) + 4*b*c*d*tan(e) + 2*a*d^2*tan(e) + b*d^2)/(f*tan(f*x)^2*tan(e)^2 - 2*f*tan(f*x)*tan(e) + f)","B",0
1200,1,127,0,0.995830," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a c^{2} + 2 \, b c d - a d^{2}\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} - \frac{{\left(b c^{2} - 2 \, a c d - b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b + b^{3}}}{2 \, f}"," ",0,"1/2*(2*(a*c^2 + 2*b*c*d - a*d^2)*(f*x + e)/(a^2 + b^2) - (b*c^2 - 2*a*c*d - b*d^2)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(b*tan(f*x + e) + a))/(a^2*b + b^3))/f","A",0
1201,1,332,0,1.462420," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(a^{2} c^{2} - b^{2} c^{2} + 4 \, a b c d - a^{2} d^{2} + b^{2} d^{2}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a b c^{2} - a^{2} c d + b^{2} c d - a b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(a b^{2} c^{2} - a^{2} b c d + b^{3} c d - a b^{2} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b + 2 \, a^{2} b^{3} + b^{5}} - \frac{2 \, a b^{3} c^{2} \tan\left(f x + e\right) - 2 \, a^{2} b^{2} c d \tan\left(f x + e\right) + 2 \, b^{4} c d \tan\left(f x + e\right) - 2 \, a b^{3} d^{2} \tan\left(f x + e\right) + 3 \, a^{2} b^{2} c^{2} + b^{4} c^{2} - 4 \, a^{3} b c d + a^{4} d^{2} - a^{2} b^{2} d^{2}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{f}"," ",0,"((a^2*c^2 - b^2*c^2 + 4*a*b*c*d - a^2*d^2 + b^2*d^2)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) - (a*b*c^2 - a^2*c*d + b^2*c*d - a*b*d^2)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(a*b^2*c^2 - a^2*b*c*d + b^3*c*d - a*b^2*d^2)*log(abs(b*tan(f*x + e) + a))/(a^4*b + 2*a^2*b^3 + b^5) - (2*a*b^3*c^2*tan(f*x + e) - 2*a^2*b^2*c*d*tan(f*x + e) + 2*b^4*c*d*tan(f*x + e) - 2*a*b^3*d^2*tan(f*x + e) + 3*a^2*b^2*c^2 + b^4*c^2 - 4*a^3*b*c*d + a^4*d^2 - a^2*b^2*d^2)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(f*x + e) + a)))/f","B",0
1202,1,614,0,1.919075," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} c^{2} - 3 \, a b^{2} c^{2} + 6 \, a^{2} b c d - 2 \, b^{3} c d - a^{3} d^{2} + 3 \, a b^{2} d^{2}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b c^{2} - b^{3} c^{2} - 2 \, a^{3} c d + 6 \, a b^{2} c d - 3 \, a^{2} b d^{2} + b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(3 \, a^{2} b^{2} c^{2} - b^{4} c^{2} - 2 \, a^{3} b c d + 6 \, a b^{3} c d - 3 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{9 \, a^{2} b^{4} c^{2} \tan\left(f x + e\right)^{2} - 3 \, b^{6} c^{2} \tan\left(f x + e\right)^{2} - 6 \, a^{3} b^{3} c d \tan\left(f x + e\right)^{2} + 18 \, a b^{5} c d \tan\left(f x + e\right)^{2} - 9 \, a^{2} b^{4} d^{2} \tan\left(f x + e\right)^{2} + 3 \, b^{6} d^{2} \tan\left(f x + e\right)^{2} + 22 \, a^{3} b^{3} c^{2} \tan\left(f x + e\right) - 2 \, a b^{5} c^{2} \tan\left(f x + e\right) - 16 \, a^{4} b^{2} c d \tan\left(f x + e\right) + 36 \, a^{2} b^{4} c d \tan\left(f x + e\right) + 4 \, b^{6} c d \tan\left(f x + e\right) - 22 \, a^{3} b^{3} d^{2} \tan\left(f x + e\right) + 2 \, a b^{5} d^{2} \tan\left(f x + e\right) + 14 \, a^{4} b^{2} c^{2} + 3 \, a^{2} b^{4} c^{2} + b^{6} c^{2} - 12 \, a^{5} b c d + 14 \, a^{3} b^{3} c d + 2 \, a b^{5} c d + a^{6} d^{2} - 11 \, a^{4} b^{2} d^{2}}{{\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^3*c^2 - 3*a*b^2*c^2 + 6*a^2*b*c*d - 2*b^3*c*d - a^3*d^2 + 3*a*b^2*d^2)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b*c^2 - b^3*c^2 - 2*a^3*c*d + 6*a*b^2*c*d - 3*a^2*b*d^2 + b^3*d^2)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*a^2*b^2*c^2 - b^4*c^2 - 2*a^3*b*c*d + 6*a*b^3*c*d - 3*a^2*b^2*d^2 + b^4*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - (9*a^2*b^4*c^2*tan(f*x + e)^2 - 3*b^6*c^2*tan(f*x + e)^2 - 6*a^3*b^3*c*d*tan(f*x + e)^2 + 18*a*b^5*c*d*tan(f*x + e)^2 - 9*a^2*b^4*d^2*tan(f*x + e)^2 + 3*b^6*d^2*tan(f*x + e)^2 + 22*a^3*b^3*c^2*tan(f*x + e) - 2*a*b^5*c^2*tan(f*x + e) - 16*a^4*b^2*c*d*tan(f*x + e) + 36*a^2*b^4*c*d*tan(f*x + e) + 4*b^6*c*d*tan(f*x + e) - 22*a^3*b^3*d^2*tan(f*x + e) + 2*a*b^5*d^2*tan(f*x + e) + 14*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 - 12*a^5*b*c*d + 14*a^3*b^3*c*d + 2*a*b^5*c*d + a^6*d^2 - 11*a^4*b^2*d^2)/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*(b*tan(f*x + e) + a)^2))/f","B",0
1203,1,8276,0,110.677233," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{60 \, a^{3} c^{3} f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 180 \, a b^{2} c^{3} f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 540 \, a^{2} b c^{2} d f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 180 \, b^{3} c^{2} d f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 180 \, a^{3} c d^{2} f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 540 \, a b^{2} c d^{2} f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 180 \, a^{2} b d^{3} f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 60 \, b^{3} d^{3} f x \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 90 \, a^{2} b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 30 \, b^{3} c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 90 \, a^{3} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 270 \, a b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 270 \, a^{2} b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 90 \, b^{3} c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 30 \, a^{3} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 90 \, a b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 300 \, a^{3} c^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 900 \, a b^{2} c^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 2700 \, a^{2} b c^{2} d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 900 \, b^{3} c^{2} d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 900 \, a^{3} c d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 2700 \, a b^{2} c d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 900 \, a^{2} b d^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 300 \, b^{3} d^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 30 \, b^{3} c^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 270 \, a b^{2} c^{2} d \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 270 \, a^{2} b c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 135 \, b^{3} c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 30 \, a^{3} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 135 \, a b^{2} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{5} + 450 \, a^{2} b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 150 \, b^{3} c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 450 \, a^{3} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 1350 \, a b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 1350 \, a^{2} b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 450 \, b^{3} c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 150 \, a^{3} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 450 \, a b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 180 \, a b^{2} c^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} - 540 \, a^{2} b c^{2} d \tan\left(f x\right)^{5} \tan\left(e\right)^{4} + 180 \, b^{3} c^{2} d \tan\left(f x\right)^{5} \tan\left(e\right)^{4} - 180 \, a^{3} c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} + 540 \, a b^{2} c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} + 180 \, a^{2} b d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} - 60 \, b^{3} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{4} - 180 \, a b^{2} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} - 540 \, a^{2} b c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{5} + 180 \, b^{3} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{5} - 180 \, a^{3} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} + 540 \, a b^{2} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} + 180 \, a^{2} b d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} - 60 \, b^{3} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{5} + 600 \, a^{3} c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 1800 \, a b^{2} c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 5400 \, a^{2} b c^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 1800 \, b^{3} c^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 1800 \, a^{3} c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 5400 \, a b^{2} c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 1800 \, a^{2} b d^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 600 \, b^{3} d^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 30 \, b^{3} c^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{3} + 270 \, a b^{2} c^{2} d \tan\left(f x\right)^{5} \tan\left(e\right)^{3} + 270 \, a^{2} b c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{3} - 90 \, b^{3} c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{3} + 30 \, a^{3} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{3} - 90 \, a b^{2} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{3} - 90 \, b^{3} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 810 \, a b^{2} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 810 \, a^{2} b c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 495 \, b^{3} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 90 \, a^{3} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 495 \, a b^{2} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 30 \, b^{3} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{5} + 270 \, a b^{2} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{5} + 270 \, a^{2} b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{5} - 90 \, b^{3} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{5} + 30 \, a^{3} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{5} - 90 \, a b^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{5} - 60 \, b^{3} c^{2} d \tan\left(f x\right)^{5} \tan\left(e\right)^{2} - 180 \, a b^{2} c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right)^{2} - 60 \, a^{2} b d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{2} + 20 \, b^{3} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right)^{2} - 900 \, a^{2} b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 300 \, b^{3} c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 900 \, a^{3} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 2700 \, a b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 2700 \, a^{2} b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 900 \, b^{3} c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 300 \, a^{3} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 900 \, a b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 720 \, a b^{2} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 2160 \, a^{2} b c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 900 \, b^{3} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 720 \, a^{3} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 2700 \, a b^{2} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 900 \, a^{2} b d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 300 \, b^{3} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 720 \, a b^{2} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 2160 \, a^{2} b c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 900 \, b^{3} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 720 \, a^{3} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 2700 \, a b^{2} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 900 \, a^{2} b d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 300 \, b^{3} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 60 \, b^{3} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{5} - 180 \, a b^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{5} - 60 \, a^{2} b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{5} + 20 \, b^{3} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{5} + 45 \, b^{3} c d^{2} \tan\left(f x\right)^{5} \tan\left(e\right) + 45 \, a b^{2} d^{3} \tan\left(f x\right)^{5} \tan\left(e\right) - 600 \, a^{3} c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 1800 \, a b^{2} c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 5400 \, a^{2} b c^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 1800 \, b^{3} c^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 1800 \, a^{3} c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 5400 \, a b^{2} c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 1800 \, a^{2} b d^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 600 \, b^{3} d^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 90 \, b^{3} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 810 \, a b^{2} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 810 \, a^{2} b c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 450 \, b^{3} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 90 \, a^{3} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 450 \, a b^{2} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 120 \, b^{3} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 1080 \, a b^{2} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 1080 \, a^{2} b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 540 \, b^{3} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 120 \, a^{3} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 540 \, a b^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 90 \, b^{3} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 810 \, a b^{2} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 810 \, a^{2} b c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 450 \, b^{3} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 90 \, a^{3} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 450 \, a b^{2} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 45 \, b^{3} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{5} + 45 \, a b^{2} d^{3} \tan\left(f x\right) \tan\left(e\right)^{5} - 12 \, b^{3} d^{3} \tan\left(f x\right)^{5} + 120 \, b^{3} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right) + 360 \, a b^{2} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right) + 120 \, a^{2} b d^{3} \tan\left(f x\right)^{4} \tan\left(e\right) - 100 \, b^{3} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right) + 900 \, a^{2} b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 300 \, b^{3} c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 900 \, a^{3} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2700 \, a b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 2700 \, a^{2} b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 900 \, b^{3} c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 300 \, a^{3} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 900 \, a b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 1080 \, a b^{2} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 3240 \, a^{2} b c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 1440 \, b^{3} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 1080 \, a^{3} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 4320 \, a b^{2} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 1440 \, a^{2} b d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 600 \, b^{3} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 1080 \, a b^{2} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 3240 \, a^{2} b c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 1440 \, b^{3} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 1080 \, a^{3} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 4320 \, a b^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 1440 \, a^{2} b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 600 \, b^{3} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 120 \, b^{3} c^{2} d \tan\left(f x\right) \tan\left(e\right)^{4} + 360 \, a b^{2} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{4} + 120 \, a^{2} b d^{3} \tan\left(f x\right) \tan\left(e\right)^{4} - 100 \, b^{3} d^{3} \tan\left(f x\right) \tan\left(e\right)^{4} - 12 \, b^{3} d^{3} \tan\left(e\right)^{5} - 45 \, b^{3} c d^{2} \tan\left(f x\right)^{4} - 45 \, a b^{2} d^{3} \tan\left(f x\right)^{4} + 300 \, a^{3} c^{3} f x \tan\left(f x\right) \tan\left(e\right) - 900 \, a b^{2} c^{3} f x \tan\left(f x\right) \tan\left(e\right) - 2700 \, a^{2} b c^{2} d f x \tan\left(f x\right) \tan\left(e\right) + 900 \, b^{3} c^{2} d f x \tan\left(f x\right) \tan\left(e\right) - 900 \, a^{3} c d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 2700 \, a b^{2} c d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 900 \, a^{2} b d^{3} f x \tan\left(f x\right) \tan\left(e\right) - 300 \, b^{3} d^{3} f x \tan\left(f x\right) \tan\left(e\right) + 90 \, b^{3} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right) + 810 \, a b^{2} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) + 810 \, a^{2} b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 450 \, b^{3} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) + 90 \, a^{3} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) - 450 \, a b^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) - 120 \, b^{3} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 1080 \, a b^{2} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 1080 \, a^{2} b c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 540 \, b^{3} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 120 \, a^{3} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 540 \, a b^{2} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 90 \, b^{3} c^{3} \tan\left(f x\right) \tan\left(e\right)^{3} + 810 \, a b^{2} c^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} + 810 \, a^{2} b c d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 450 \, b^{3} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} + 90 \, a^{3} d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} - 450 \, a b^{2} d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} - 45 \, b^{3} c d^{2} \tan\left(e\right)^{4} - 45 \, a b^{2} d^{3} \tan\left(e\right)^{4} - 60 \, b^{3} c^{2} d \tan\left(f x\right)^{3} - 180 \, a b^{2} c d^{2} \tan\left(f x\right)^{3} - 60 \, a^{2} b d^{3} \tan\left(f x\right)^{3} + 20 \, b^{3} d^{3} \tan\left(f x\right)^{3} - 450 \, a^{2} b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 150 \, b^{3} c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 450 \, a^{3} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 1350 \, a b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 1350 \, a^{2} b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 450 \, b^{3} c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 150 \, a^{3} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 450 \, a b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 720 \, a b^{2} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right) + 2160 \, a^{2} b c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) - 900 \, b^{3} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) + 720 \, a^{3} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 2700 \, a b^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 900 \, a^{2} b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right) + 300 \, b^{3} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right) + 720 \, a b^{2} c^{3} \tan\left(f x\right) \tan\left(e\right)^{2} + 2160 \, a^{2} b c^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} - 900 \, b^{3} c^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} + 720 \, a^{3} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 2700 \, a b^{2} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 900 \, a^{2} b d^{3} \tan\left(f x\right) \tan\left(e\right)^{2} + 300 \, b^{3} d^{3} \tan\left(f x\right) \tan\left(e\right)^{2} - 60 \, b^{3} c^{2} d \tan\left(e\right)^{3} - 180 \, a b^{2} c d^{2} \tan\left(e\right)^{3} - 60 \, a^{2} b d^{3} \tan\left(e\right)^{3} + 20 \, b^{3} d^{3} \tan\left(e\right)^{3} - 60 \, a^{3} c^{3} f x + 180 \, a b^{2} c^{3} f x + 540 \, a^{2} b c^{2} d f x - 180 \, b^{3} c^{2} d f x + 180 \, a^{3} c d^{2} f x - 540 \, a b^{2} c d^{2} f x - 180 \, a^{2} b d^{3} f x + 60 \, b^{3} d^{3} f x - 30 \, b^{3} c^{3} \tan\left(f x\right)^{2} - 270 \, a b^{2} c^{2} d \tan\left(f x\right)^{2} - 270 \, a^{2} b c d^{2} \tan\left(f x\right)^{2} + 90 \, b^{3} c d^{2} \tan\left(f x\right)^{2} - 30 \, a^{3} d^{3} \tan\left(f x\right)^{2} + 90 \, a b^{2} d^{3} \tan\left(f x\right)^{2} + 90 \, b^{3} c^{3} \tan\left(f x\right) \tan\left(e\right) + 810 \, a b^{2} c^{2} d \tan\left(f x\right) \tan\left(e\right) + 810 \, a^{2} b c d^{2} \tan\left(f x\right) \tan\left(e\right) - 495 \, b^{3} c d^{2} \tan\left(f x\right) \tan\left(e\right) + 90 \, a^{3} d^{3} \tan\left(f x\right) \tan\left(e\right) - 495 \, a b^{2} d^{3} \tan\left(f x\right) \tan\left(e\right) - 30 \, b^{3} c^{3} \tan\left(e\right)^{2} - 270 \, a b^{2} c^{2} d \tan\left(e\right)^{2} - 270 \, a^{2} b c d^{2} \tan\left(e\right)^{2} + 90 \, b^{3} c d^{2} \tan\left(e\right)^{2} - 30 \, a^{3} d^{3} \tan\left(e\right)^{2} + 90 \, a b^{2} d^{3} \tan\left(e\right)^{2} + 90 \, a^{2} b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 30 \, b^{3} c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 90 \, a^{3} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 270 \, a b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 270 \, a^{2} b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 90 \, b^{3} c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 30 \, a^{3} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 90 \, a b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 180 \, a b^{2} c^{3} \tan\left(f x\right) - 540 \, a^{2} b c^{2} d \tan\left(f x\right) + 180 \, b^{3} c^{2} d \tan\left(f x\right) - 180 \, a^{3} c d^{2} \tan\left(f x\right) + 540 \, a b^{2} c d^{2} \tan\left(f x\right) + 180 \, a^{2} b d^{3} \tan\left(f x\right) - 60 \, b^{3} d^{3} \tan\left(f x\right) - 180 \, a b^{2} c^{3} \tan\left(e\right) - 540 \, a^{2} b c^{2} d \tan\left(e\right) + 180 \, b^{3} c^{2} d \tan\left(e\right) - 180 \, a^{3} c d^{2} \tan\left(e\right) + 540 \, a b^{2} c d^{2} \tan\left(e\right) + 180 \, a^{2} b d^{3} \tan\left(e\right) - 60 \, b^{3} d^{3} \tan\left(e\right) - 30 \, b^{3} c^{3} - 270 \, a b^{2} c^{2} d - 270 \, a^{2} b c d^{2} + 135 \, b^{3} c d^{2} - 30 \, a^{3} d^{3} + 135 \, a b^{2} d^{3}}{60 \, {\left(f \tan\left(f x\right)^{5} \tan\left(e\right)^{5} - 5 \, f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 10 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 10 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 5 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/60*(60*a^3*c^3*f*x*tan(f*x)^5*tan(e)^5 - 180*a*b^2*c^3*f*x*tan(f*x)^5*tan(e)^5 - 540*a^2*b*c^2*d*f*x*tan(f*x)^5*tan(e)^5 + 180*b^3*c^2*d*f*x*tan(f*x)^5*tan(e)^5 - 180*a^3*c*d^2*f*x*tan(f*x)^5*tan(e)^5 + 540*a*b^2*c*d^2*f*x*tan(f*x)^5*tan(e)^5 + 180*a^2*b*d^3*f*x*tan(f*x)^5*tan(e)^5 - 60*b^3*d^3*f*x*tan(f*x)^5*tan(e)^5 - 90*a^2*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 + 30*b^3*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 - 90*a^3*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 + 270*a*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 + 270*a^2*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 - 90*b^3*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 + 30*a^3*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 - 90*a*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^5*tan(e)^5 - 300*a^3*c^3*f*x*tan(f*x)^4*tan(e)^4 + 900*a*b^2*c^3*f*x*tan(f*x)^4*tan(e)^4 + 2700*a^2*b*c^2*d*f*x*tan(f*x)^4*tan(e)^4 - 900*b^3*c^2*d*f*x*tan(f*x)^4*tan(e)^4 + 900*a^3*c*d^2*f*x*tan(f*x)^4*tan(e)^4 - 2700*a*b^2*c*d^2*f*x*tan(f*x)^4*tan(e)^4 - 900*a^2*b*d^3*f*x*tan(f*x)^4*tan(e)^4 + 300*b^3*d^3*f*x*tan(f*x)^4*tan(e)^4 + 30*b^3*c^3*tan(f*x)^5*tan(e)^5 + 270*a*b^2*c^2*d*tan(f*x)^5*tan(e)^5 + 270*a^2*b*c*d^2*tan(f*x)^5*tan(e)^5 - 135*b^3*c*d^2*tan(f*x)^5*tan(e)^5 + 30*a^3*d^3*tan(f*x)^5*tan(e)^5 - 135*a*b^2*d^3*tan(f*x)^5*tan(e)^5 + 450*a^2*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 150*b^3*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 450*a^3*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 1350*a*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 1350*a^2*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 450*b^3*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 150*a^3*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 450*a*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 180*a*b^2*c^3*tan(f*x)^5*tan(e)^4 - 540*a^2*b*c^2*d*tan(f*x)^5*tan(e)^4 + 180*b^3*c^2*d*tan(f*x)^5*tan(e)^4 - 180*a^3*c*d^2*tan(f*x)^5*tan(e)^4 + 540*a*b^2*c*d^2*tan(f*x)^5*tan(e)^4 + 180*a^2*b*d^3*tan(f*x)^5*tan(e)^4 - 60*b^3*d^3*tan(f*x)^5*tan(e)^4 - 180*a*b^2*c^3*tan(f*x)^4*tan(e)^5 - 540*a^2*b*c^2*d*tan(f*x)^4*tan(e)^5 + 180*b^3*c^2*d*tan(f*x)^4*tan(e)^5 - 180*a^3*c*d^2*tan(f*x)^4*tan(e)^5 + 540*a*b^2*c*d^2*tan(f*x)^4*tan(e)^5 + 180*a^2*b*d^3*tan(f*x)^4*tan(e)^5 - 60*b^3*d^3*tan(f*x)^4*tan(e)^5 + 600*a^3*c^3*f*x*tan(f*x)^3*tan(e)^3 - 1800*a*b^2*c^3*f*x*tan(f*x)^3*tan(e)^3 - 5400*a^2*b*c^2*d*f*x*tan(f*x)^3*tan(e)^3 + 1800*b^3*c^2*d*f*x*tan(f*x)^3*tan(e)^3 - 1800*a^3*c*d^2*f*x*tan(f*x)^3*tan(e)^3 + 5400*a*b^2*c*d^2*f*x*tan(f*x)^3*tan(e)^3 + 1800*a^2*b*d^3*f*x*tan(f*x)^3*tan(e)^3 - 600*b^3*d^3*f*x*tan(f*x)^3*tan(e)^3 + 30*b^3*c^3*tan(f*x)^5*tan(e)^3 + 270*a*b^2*c^2*d*tan(f*x)^5*tan(e)^3 + 270*a^2*b*c*d^2*tan(f*x)^5*tan(e)^3 - 90*b^3*c*d^2*tan(f*x)^5*tan(e)^3 + 30*a^3*d^3*tan(f*x)^5*tan(e)^3 - 90*a*b^2*d^3*tan(f*x)^5*tan(e)^3 - 90*b^3*c^3*tan(f*x)^4*tan(e)^4 - 810*a*b^2*c^2*d*tan(f*x)^4*tan(e)^4 - 810*a^2*b*c*d^2*tan(f*x)^4*tan(e)^4 + 495*b^3*c*d^2*tan(f*x)^4*tan(e)^4 - 90*a^3*d^3*tan(f*x)^4*tan(e)^4 + 495*a*b^2*d^3*tan(f*x)^4*tan(e)^4 + 30*b^3*c^3*tan(f*x)^3*tan(e)^5 + 270*a*b^2*c^2*d*tan(f*x)^3*tan(e)^5 + 270*a^2*b*c*d^2*tan(f*x)^3*tan(e)^5 - 90*b^3*c*d^2*tan(f*x)^3*tan(e)^5 + 30*a^3*d^3*tan(f*x)^3*tan(e)^5 - 90*a*b^2*d^3*tan(f*x)^3*tan(e)^5 - 60*b^3*c^2*d*tan(f*x)^5*tan(e)^2 - 180*a*b^2*c*d^2*tan(f*x)^5*tan(e)^2 - 60*a^2*b*d^3*tan(f*x)^5*tan(e)^2 + 20*b^3*d^3*tan(f*x)^5*tan(e)^2 - 900*a^2*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 300*b^3*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 900*a^3*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 2700*a*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 2700*a^2*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 900*b^3*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 300*a^3*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 900*a*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 720*a*b^2*c^3*tan(f*x)^4*tan(e)^3 + 2160*a^2*b*c^2*d*tan(f*x)^4*tan(e)^3 - 900*b^3*c^2*d*tan(f*x)^4*tan(e)^3 + 720*a^3*c*d^2*tan(f*x)^4*tan(e)^3 - 2700*a*b^2*c*d^2*tan(f*x)^4*tan(e)^3 - 900*a^2*b*d^3*tan(f*x)^4*tan(e)^3 + 300*b^3*d^3*tan(f*x)^4*tan(e)^3 + 720*a*b^2*c^3*tan(f*x)^3*tan(e)^4 + 2160*a^2*b*c^2*d*tan(f*x)^3*tan(e)^4 - 900*b^3*c^2*d*tan(f*x)^3*tan(e)^4 + 720*a^3*c*d^2*tan(f*x)^3*tan(e)^4 - 2700*a*b^2*c*d^2*tan(f*x)^3*tan(e)^4 - 900*a^2*b*d^3*tan(f*x)^3*tan(e)^4 + 300*b^3*d^3*tan(f*x)^3*tan(e)^4 - 60*b^3*c^2*d*tan(f*x)^2*tan(e)^5 - 180*a*b^2*c*d^2*tan(f*x)^2*tan(e)^5 - 60*a^2*b*d^3*tan(f*x)^2*tan(e)^5 + 20*b^3*d^3*tan(f*x)^2*tan(e)^5 + 45*b^3*c*d^2*tan(f*x)^5*tan(e) + 45*a*b^2*d^3*tan(f*x)^5*tan(e) - 600*a^3*c^3*f*x*tan(f*x)^2*tan(e)^2 + 1800*a*b^2*c^3*f*x*tan(f*x)^2*tan(e)^2 + 5400*a^2*b*c^2*d*f*x*tan(f*x)^2*tan(e)^2 - 1800*b^3*c^2*d*f*x*tan(f*x)^2*tan(e)^2 + 1800*a^3*c*d^2*f*x*tan(f*x)^2*tan(e)^2 - 5400*a*b^2*c*d^2*f*x*tan(f*x)^2*tan(e)^2 - 1800*a^2*b*d^3*f*x*tan(f*x)^2*tan(e)^2 + 600*b^3*d^3*f*x*tan(f*x)^2*tan(e)^2 - 90*b^3*c^3*tan(f*x)^4*tan(e)^2 - 810*a*b^2*c^2*d*tan(f*x)^4*tan(e)^2 - 810*a^2*b*c*d^2*tan(f*x)^4*tan(e)^2 + 450*b^3*c*d^2*tan(f*x)^4*tan(e)^2 - 90*a^3*d^3*tan(f*x)^4*tan(e)^2 + 450*a*b^2*d^3*tan(f*x)^4*tan(e)^2 + 120*b^3*c^3*tan(f*x)^3*tan(e)^3 + 1080*a*b^2*c^2*d*tan(f*x)^3*tan(e)^3 + 1080*a^2*b*c*d^2*tan(f*x)^3*tan(e)^3 - 540*b^3*c*d^2*tan(f*x)^3*tan(e)^3 + 120*a^3*d^3*tan(f*x)^3*tan(e)^3 - 540*a*b^2*d^3*tan(f*x)^3*tan(e)^3 - 90*b^3*c^3*tan(f*x)^2*tan(e)^4 - 810*a*b^2*c^2*d*tan(f*x)^2*tan(e)^4 - 810*a^2*b*c*d^2*tan(f*x)^2*tan(e)^4 + 450*b^3*c*d^2*tan(f*x)^2*tan(e)^4 - 90*a^3*d^3*tan(f*x)^2*tan(e)^4 + 450*a*b^2*d^3*tan(f*x)^2*tan(e)^4 + 45*b^3*c*d^2*tan(f*x)*tan(e)^5 + 45*a*b^2*d^3*tan(f*x)*tan(e)^5 - 12*b^3*d^3*tan(f*x)^5 + 120*b^3*c^2*d*tan(f*x)^4*tan(e) + 360*a*b^2*c*d^2*tan(f*x)^4*tan(e) + 120*a^2*b*d^3*tan(f*x)^4*tan(e) - 100*b^3*d^3*tan(f*x)^4*tan(e) + 900*a^2*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 300*b^3*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 900*a^3*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 2700*a*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 2700*a^2*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 900*b^3*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 300*a^3*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 900*a*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 1080*a*b^2*c^3*tan(f*x)^3*tan(e)^2 - 3240*a^2*b*c^2*d*tan(f*x)^3*tan(e)^2 + 1440*b^3*c^2*d*tan(f*x)^3*tan(e)^2 - 1080*a^3*c*d^2*tan(f*x)^3*tan(e)^2 + 4320*a*b^2*c*d^2*tan(f*x)^3*tan(e)^2 + 1440*a^2*b*d^3*tan(f*x)^3*tan(e)^2 - 600*b^3*d^3*tan(f*x)^3*tan(e)^2 - 1080*a*b^2*c^3*tan(f*x)^2*tan(e)^3 - 3240*a^2*b*c^2*d*tan(f*x)^2*tan(e)^3 + 1440*b^3*c^2*d*tan(f*x)^2*tan(e)^3 - 1080*a^3*c*d^2*tan(f*x)^2*tan(e)^3 + 4320*a*b^2*c*d^2*tan(f*x)^2*tan(e)^3 + 1440*a^2*b*d^3*tan(f*x)^2*tan(e)^3 - 600*b^3*d^3*tan(f*x)^2*tan(e)^3 + 120*b^3*c^2*d*tan(f*x)*tan(e)^4 + 360*a*b^2*c*d^2*tan(f*x)*tan(e)^4 + 120*a^2*b*d^3*tan(f*x)*tan(e)^4 - 100*b^3*d^3*tan(f*x)*tan(e)^4 - 12*b^3*d^3*tan(e)^5 - 45*b^3*c*d^2*tan(f*x)^4 - 45*a*b^2*d^3*tan(f*x)^4 + 300*a^3*c^3*f*x*tan(f*x)*tan(e) - 900*a*b^2*c^3*f*x*tan(f*x)*tan(e) - 2700*a^2*b*c^2*d*f*x*tan(f*x)*tan(e) + 900*b^3*c^2*d*f*x*tan(f*x)*tan(e) - 900*a^3*c*d^2*f*x*tan(f*x)*tan(e) + 2700*a*b^2*c*d^2*f*x*tan(f*x)*tan(e) + 900*a^2*b*d^3*f*x*tan(f*x)*tan(e) - 300*b^3*d^3*f*x*tan(f*x)*tan(e) + 90*b^3*c^3*tan(f*x)^3*tan(e) + 810*a*b^2*c^2*d*tan(f*x)^3*tan(e) + 810*a^2*b*c*d^2*tan(f*x)^3*tan(e) - 450*b^3*c*d^2*tan(f*x)^3*tan(e) + 90*a^3*d^3*tan(f*x)^3*tan(e) - 450*a*b^2*d^3*tan(f*x)^3*tan(e) - 120*b^3*c^3*tan(f*x)^2*tan(e)^2 - 1080*a*b^2*c^2*d*tan(f*x)^2*tan(e)^2 - 1080*a^2*b*c*d^2*tan(f*x)^2*tan(e)^2 + 540*b^3*c*d^2*tan(f*x)^2*tan(e)^2 - 120*a^3*d^3*tan(f*x)^2*tan(e)^2 + 540*a*b^2*d^3*tan(f*x)^2*tan(e)^2 + 90*b^3*c^3*tan(f*x)*tan(e)^3 + 810*a*b^2*c^2*d*tan(f*x)*tan(e)^3 + 810*a^2*b*c*d^2*tan(f*x)*tan(e)^3 - 450*b^3*c*d^2*tan(f*x)*tan(e)^3 + 90*a^3*d^3*tan(f*x)*tan(e)^3 - 450*a*b^2*d^3*tan(f*x)*tan(e)^3 - 45*b^3*c*d^2*tan(e)^4 - 45*a*b^2*d^3*tan(e)^4 - 60*b^3*c^2*d*tan(f*x)^3 - 180*a*b^2*c*d^2*tan(f*x)^3 - 60*a^2*b*d^3*tan(f*x)^3 + 20*b^3*d^3*tan(f*x)^3 - 450*a^2*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 150*b^3*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 450*a^3*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 1350*a*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 1350*a^2*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 450*b^3*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 150*a^3*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 450*a*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 720*a*b^2*c^3*tan(f*x)^2*tan(e) + 2160*a^2*b*c^2*d*tan(f*x)^2*tan(e) - 900*b^3*c^2*d*tan(f*x)^2*tan(e) + 720*a^3*c*d^2*tan(f*x)^2*tan(e) - 2700*a*b^2*c*d^2*tan(f*x)^2*tan(e) - 900*a^2*b*d^3*tan(f*x)^2*tan(e) + 300*b^3*d^3*tan(f*x)^2*tan(e) + 720*a*b^2*c^3*tan(f*x)*tan(e)^2 + 2160*a^2*b*c^2*d*tan(f*x)*tan(e)^2 - 900*b^3*c^2*d*tan(f*x)*tan(e)^2 + 720*a^3*c*d^2*tan(f*x)*tan(e)^2 - 2700*a*b^2*c*d^2*tan(f*x)*tan(e)^2 - 900*a^2*b*d^3*tan(f*x)*tan(e)^2 + 300*b^3*d^3*tan(f*x)*tan(e)^2 - 60*b^3*c^2*d*tan(e)^3 - 180*a*b^2*c*d^2*tan(e)^3 - 60*a^2*b*d^3*tan(e)^3 + 20*b^3*d^3*tan(e)^3 - 60*a^3*c^3*f*x + 180*a*b^2*c^3*f*x + 540*a^2*b*c^2*d*f*x - 180*b^3*c^2*d*f*x + 180*a^3*c*d^2*f*x - 540*a*b^2*c*d^2*f*x - 180*a^2*b*d^3*f*x + 60*b^3*d^3*f*x - 30*b^3*c^3*tan(f*x)^2 - 270*a*b^2*c^2*d*tan(f*x)^2 - 270*a^2*b*c*d^2*tan(f*x)^2 + 90*b^3*c*d^2*tan(f*x)^2 - 30*a^3*d^3*tan(f*x)^2 + 90*a*b^2*d^3*tan(f*x)^2 + 90*b^3*c^3*tan(f*x)*tan(e) + 810*a*b^2*c^2*d*tan(f*x)*tan(e) + 810*a^2*b*c*d^2*tan(f*x)*tan(e) - 495*b^3*c*d^2*tan(f*x)*tan(e) + 90*a^3*d^3*tan(f*x)*tan(e) - 495*a*b^2*d^3*tan(f*x)*tan(e) - 30*b^3*c^3*tan(e)^2 - 270*a*b^2*c^2*d*tan(e)^2 - 270*a^2*b*c*d^2*tan(e)^2 + 90*b^3*c*d^2*tan(e)^2 - 30*a^3*d^3*tan(e)^2 + 90*a*b^2*d^3*tan(e)^2 + 90*a^2*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 30*b^3*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 90*a^3*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 270*a*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 270*a^2*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 90*b^3*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 30*a^3*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 90*a*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 180*a*b^2*c^3*tan(f*x) - 540*a^2*b*c^2*d*tan(f*x) + 180*b^3*c^2*d*tan(f*x) - 180*a^3*c*d^2*tan(f*x) + 540*a*b^2*c*d^2*tan(f*x) + 180*a^2*b*d^3*tan(f*x) - 60*b^3*d^3*tan(f*x) - 180*a*b^2*c^3*tan(e) - 540*a^2*b*c^2*d*tan(e) + 180*b^3*c^2*d*tan(e) - 180*a^3*c*d^2*tan(e) + 540*a*b^2*c*d^2*tan(e) + 180*a^2*b*d^3*tan(e) - 60*b^3*d^3*tan(e) - 30*b^3*c^3 - 270*a*b^2*c^2*d - 270*a^2*b*c*d^2 + 135*b^3*c*d^2 - 30*a^3*d^3 + 135*a*b^2*d^3)/(f*tan(f*x)^5*tan(e)^5 - 5*f*tan(f*x)^4*tan(e)^4 + 10*f*tan(f*x)^3*tan(e)^3 - 10*f*tan(f*x)^2*tan(e)^2 + 5*f*tan(f*x)*tan(e) - f)","B",0
1204,1,4557,0,13.087092," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{12 \, a^{2} c^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, b^{2} c^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 72 \, a b c^{2} d f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 36 \, a^{2} c d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, b^{2} c d^{2} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 24 \, a b d^{3} f x \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 12 \, a b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 18 \, a^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 18 \, b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, a b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, a^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 6 \, b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 48 \, a^{2} c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 48 \, b^{2} c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 288 \, a b c^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 144 \, a^{2} c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 144 \, b^{2} c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 96 \, a b d^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 18 \, b^{2} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 36 \, a b c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 6 \, a^{2} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 9 \, b^{2} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{4} + 48 \, a b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 72 \, a^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 72 \, b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 144 \, a b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 24 \, a^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, b^{2} c^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 72 \, a b c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 36 \, a^{2} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 36 \, b^{2} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} + 24 \, a b d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{3} - 12 \, b^{2} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 72 \, a b c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{4} - 36 \, a^{2} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 36 \, b^{2} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 24 \, a b d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{4} + 72 \, a^{2} c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 72 \, b^{2} c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 432 \, a b c^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 216 \, a^{2} c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 216 \, b^{2} c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 144 \, a b d^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 18 \, b^{2} c^{2} d \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 36 \, a b c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} + 6 \, a^{2} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 6 \, b^{2} d^{3} \tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 36 \, b^{2} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 72 \, a b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 12 \, a^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 24 \, b^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 18 \, b^{2} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 36 \, a b c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} + 6 \, a^{2} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 6 \, b^{2} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{4} - 12 \, b^{2} c d^{2} \tan\left(f x\right)^{4} \tan\left(e\right) - 8 \, a b d^{3} \tan\left(f x\right)^{4} \tan\left(e\right) - 72 \, a b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 108 \, a^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 108 \, b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 216 \, a b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, a^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 36 \, b^{2} c^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 216 \, a b c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 108 \, a^{2} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 144 \, b^{2} c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 96 \, a b d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 36 \, b^{2} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 216 \, a b c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 108 \, a^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 144 \, b^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 96 \, a b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 12 \, b^{2} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{4} - 8 \, a b d^{3} \tan\left(f x\right) \tan\left(e\right)^{4} + 3 \, b^{2} d^{3} \tan\left(f x\right)^{4} - 48 \, a^{2} c^{3} f x \tan\left(f x\right) \tan\left(e\right) + 48 \, b^{2} c^{3} f x \tan\left(f x\right) \tan\left(e\right) + 288 \, a b c^{2} d f x \tan\left(f x\right) \tan\left(e\right) + 144 \, a^{2} c d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 144 \, b^{2} c d^{2} f x \tan\left(f x\right) \tan\left(e\right) - 96 \, a b d^{3} f x \tan\left(f x\right) \tan\left(e\right) - 36 \, b^{2} c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right) - 72 \, a b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) - 12 \, a^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) + 24 \, b^{2} d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) + 36 \, b^{2} c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 72 \, a b c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 12 \, a^{2} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 12 \, b^{2} d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 36 \, b^{2} c^{2} d \tan\left(f x\right) \tan\left(e\right)^{3} - 72 \, a b c d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} - 12 \, a^{2} d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} + 24 \, b^{2} d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, b^{2} d^{3} \tan\left(e\right)^{4} + 12 \, b^{2} c d^{2} \tan\left(f x\right)^{3} + 8 \, a b d^{3} \tan\left(f x\right)^{3} + 48 \, a b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 72 \, a^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 72 \, b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 144 \, a b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 24 \, a^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 24 \, b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 36 \, b^{2} c^{3} \tan\left(f x\right)^{2} \tan\left(e\right) - 216 \, a b c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) - 108 \, a^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 144 \, b^{2} c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) + 96 \, a b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right) - 36 \, b^{2} c^{3} \tan\left(f x\right) \tan\left(e\right)^{2} - 216 \, a b c^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} - 108 \, a^{2} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 144 \, b^{2} c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} + 96 \, a b d^{3} \tan\left(f x\right) \tan\left(e\right)^{2} + 12 \, b^{2} c d^{2} \tan\left(e\right)^{3} + 8 \, a b d^{3} \tan\left(e\right)^{3} + 12 \, a^{2} c^{3} f x - 12 \, b^{2} c^{3} f x - 72 \, a b c^{2} d f x - 36 \, a^{2} c d^{2} f x + 36 \, b^{2} c d^{2} f x + 24 \, a b d^{3} f x + 18 \, b^{2} c^{2} d \tan\left(f x\right)^{2} + 36 \, a b c d^{2} \tan\left(f x\right)^{2} + 6 \, a^{2} d^{3} \tan\left(f x\right)^{2} - 6 \, b^{2} d^{3} \tan\left(f x\right)^{2} - 36 \, b^{2} c^{2} d \tan\left(f x\right) \tan\left(e\right) - 72 \, a b c d^{2} \tan\left(f x\right) \tan\left(e\right) - 12 \, a^{2} d^{3} \tan\left(f x\right) \tan\left(e\right) + 24 \, b^{2} d^{3} \tan\left(f x\right) \tan\left(e\right) + 18 \, b^{2} c^{2} d \tan\left(e\right)^{2} + 36 \, a b c d^{2} \tan\left(e\right)^{2} + 6 \, a^{2} d^{3} \tan\left(e\right)^{2} - 6 \, b^{2} d^{3} \tan\left(e\right)^{2} - 12 \, a b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 18 \, a^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 18 \, b^{2} c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 36 \, a b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 6 \, a^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 6 \, b^{2} d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 12 \, b^{2} c^{3} \tan\left(f x\right) + 72 \, a b c^{2} d \tan\left(f x\right) + 36 \, a^{2} c d^{2} \tan\left(f x\right) - 36 \, b^{2} c d^{2} \tan\left(f x\right) - 24 \, a b d^{3} \tan\left(f x\right) + 12 \, b^{2} c^{3} \tan\left(e\right) + 72 \, a b c^{2} d \tan\left(e\right) + 36 \, a^{2} c d^{2} \tan\left(e\right) - 36 \, b^{2} c d^{2} \tan\left(e\right) - 24 \, a b d^{3} \tan\left(e\right) + 18 \, b^{2} c^{2} d + 36 \, a b c d^{2} + 6 \, a^{2} d^{3} - 9 \, b^{2} d^{3}}{12 \, {\left(f \tan\left(f x\right)^{4} \tan\left(e\right)^{4} - 4 \, f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 4 \, f \tan\left(f x\right) \tan\left(e\right) + f\right)}}"," ",0,"1/12*(12*a^2*c^3*f*x*tan(f*x)^4*tan(e)^4 - 12*b^2*c^3*f*x*tan(f*x)^4*tan(e)^4 - 72*a*b*c^2*d*f*x*tan(f*x)^4*tan(e)^4 - 36*a^2*c*d^2*f*x*tan(f*x)^4*tan(e)^4 + 36*b^2*c*d^2*f*x*tan(f*x)^4*tan(e)^4 + 24*a*b*d^3*f*x*tan(f*x)^4*tan(e)^4 - 12*a*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 18*a^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 18*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 36*a*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 + 6*a^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 6*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^4*tan(e)^4 - 48*a^2*c^3*f*x*tan(f*x)^3*tan(e)^3 + 48*b^2*c^3*f*x*tan(f*x)^3*tan(e)^3 + 288*a*b*c^2*d*f*x*tan(f*x)^3*tan(e)^3 + 144*a^2*c*d^2*f*x*tan(f*x)^3*tan(e)^3 - 144*b^2*c*d^2*f*x*tan(f*x)^3*tan(e)^3 - 96*a*b*d^3*f*x*tan(f*x)^3*tan(e)^3 + 18*b^2*c^2*d*tan(f*x)^4*tan(e)^4 + 36*a*b*c*d^2*tan(f*x)^4*tan(e)^4 + 6*a^2*d^3*tan(f*x)^4*tan(e)^4 - 9*b^2*d^3*tan(f*x)^4*tan(e)^4 + 48*a*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 72*a^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 72*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 144*a*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 24*a^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 24*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 12*b^2*c^3*tan(f*x)^4*tan(e)^3 - 72*a*b*c^2*d*tan(f*x)^4*tan(e)^3 - 36*a^2*c*d^2*tan(f*x)^4*tan(e)^3 + 36*b^2*c*d^2*tan(f*x)^4*tan(e)^3 + 24*a*b*d^3*tan(f*x)^4*tan(e)^3 - 12*b^2*c^3*tan(f*x)^3*tan(e)^4 - 72*a*b*c^2*d*tan(f*x)^3*tan(e)^4 - 36*a^2*c*d^2*tan(f*x)^3*tan(e)^4 + 36*b^2*c*d^2*tan(f*x)^3*tan(e)^4 + 24*a*b*d^3*tan(f*x)^3*tan(e)^4 + 72*a^2*c^3*f*x*tan(f*x)^2*tan(e)^2 - 72*b^2*c^3*f*x*tan(f*x)^2*tan(e)^2 - 432*a*b*c^2*d*f*x*tan(f*x)^2*tan(e)^2 - 216*a^2*c*d^2*f*x*tan(f*x)^2*tan(e)^2 + 216*b^2*c*d^2*f*x*tan(f*x)^2*tan(e)^2 + 144*a*b*d^3*f*x*tan(f*x)^2*tan(e)^2 + 18*b^2*c^2*d*tan(f*x)^4*tan(e)^2 + 36*a*b*c*d^2*tan(f*x)^4*tan(e)^2 + 6*a^2*d^3*tan(f*x)^4*tan(e)^2 - 6*b^2*d^3*tan(f*x)^4*tan(e)^2 - 36*b^2*c^2*d*tan(f*x)^3*tan(e)^3 - 72*a*b*c*d^2*tan(f*x)^3*tan(e)^3 - 12*a^2*d^3*tan(f*x)^3*tan(e)^3 + 24*b^2*d^3*tan(f*x)^3*tan(e)^3 + 18*b^2*c^2*d*tan(f*x)^2*tan(e)^4 + 36*a*b*c*d^2*tan(f*x)^2*tan(e)^4 + 6*a^2*d^3*tan(f*x)^2*tan(e)^4 - 6*b^2*d^3*tan(f*x)^2*tan(e)^4 - 12*b^2*c*d^2*tan(f*x)^4*tan(e) - 8*a*b*d^3*tan(f*x)^4*tan(e) - 72*a*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 108*a^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 108*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 216*a*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*a^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 36*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 36*b^2*c^3*tan(f*x)^3*tan(e)^2 + 216*a*b*c^2*d*tan(f*x)^3*tan(e)^2 + 108*a^2*c*d^2*tan(f*x)^3*tan(e)^2 - 144*b^2*c*d^2*tan(f*x)^3*tan(e)^2 - 96*a*b*d^3*tan(f*x)^3*tan(e)^2 + 36*b^2*c^3*tan(f*x)^2*tan(e)^3 + 216*a*b*c^2*d*tan(f*x)^2*tan(e)^3 + 108*a^2*c*d^2*tan(f*x)^2*tan(e)^3 - 144*b^2*c*d^2*tan(f*x)^2*tan(e)^3 - 96*a*b*d^3*tan(f*x)^2*tan(e)^3 - 12*b^2*c*d^2*tan(f*x)*tan(e)^4 - 8*a*b*d^3*tan(f*x)*tan(e)^4 + 3*b^2*d^3*tan(f*x)^4 - 48*a^2*c^3*f*x*tan(f*x)*tan(e) + 48*b^2*c^3*f*x*tan(f*x)*tan(e) + 288*a*b*c^2*d*f*x*tan(f*x)*tan(e) + 144*a^2*c*d^2*f*x*tan(f*x)*tan(e) - 144*b^2*c*d^2*f*x*tan(f*x)*tan(e) - 96*a*b*d^3*f*x*tan(f*x)*tan(e) - 36*b^2*c^2*d*tan(f*x)^3*tan(e) - 72*a*b*c*d^2*tan(f*x)^3*tan(e) - 12*a^2*d^3*tan(f*x)^3*tan(e) + 24*b^2*d^3*tan(f*x)^3*tan(e) + 36*b^2*c^2*d*tan(f*x)^2*tan(e)^2 + 72*a*b*c*d^2*tan(f*x)^2*tan(e)^2 + 12*a^2*d^3*tan(f*x)^2*tan(e)^2 - 12*b^2*d^3*tan(f*x)^2*tan(e)^2 - 36*b^2*c^2*d*tan(f*x)*tan(e)^3 - 72*a*b*c*d^2*tan(f*x)*tan(e)^3 - 12*a^2*d^3*tan(f*x)*tan(e)^3 + 24*b^2*d^3*tan(f*x)*tan(e)^3 + 3*b^2*d^3*tan(e)^4 + 12*b^2*c*d^2*tan(f*x)^3 + 8*a*b*d^3*tan(f*x)^3 + 48*a*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 72*a^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 72*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 144*a*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 24*a^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 24*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 36*b^2*c^3*tan(f*x)^2*tan(e) - 216*a*b*c^2*d*tan(f*x)^2*tan(e) - 108*a^2*c*d^2*tan(f*x)^2*tan(e) + 144*b^2*c*d^2*tan(f*x)^2*tan(e) + 96*a*b*d^3*tan(f*x)^2*tan(e) - 36*b^2*c^3*tan(f*x)*tan(e)^2 - 216*a*b*c^2*d*tan(f*x)*tan(e)^2 - 108*a^2*c*d^2*tan(f*x)*tan(e)^2 + 144*b^2*c*d^2*tan(f*x)*tan(e)^2 + 96*a*b*d^3*tan(f*x)*tan(e)^2 + 12*b^2*c*d^2*tan(e)^3 + 8*a*b*d^3*tan(e)^3 + 12*a^2*c^3*f*x - 12*b^2*c^3*f*x - 72*a*b*c^2*d*f*x - 36*a^2*c*d^2*f*x + 36*b^2*c*d^2*f*x + 24*a*b*d^3*f*x + 18*b^2*c^2*d*tan(f*x)^2 + 36*a*b*c*d^2*tan(f*x)^2 + 6*a^2*d^3*tan(f*x)^2 - 6*b^2*d^3*tan(f*x)^2 - 36*b^2*c^2*d*tan(f*x)*tan(e) - 72*a*b*c*d^2*tan(f*x)*tan(e) - 12*a^2*d^3*tan(f*x)*tan(e) + 24*b^2*d^3*tan(f*x)*tan(e) + 18*b^2*c^2*d*tan(e)^2 + 36*a*b*c*d^2*tan(e)^2 + 6*a^2*d^3*tan(e)^2 - 6*b^2*d^3*tan(e)^2 - 12*a*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 18*a^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 18*b^2*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 36*a*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 6*a^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 6*b^2*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 12*b^2*c^3*tan(f*x) + 72*a*b*c^2*d*tan(f*x) + 36*a^2*c*d^2*tan(f*x) - 36*b^2*c*d^2*tan(f*x) - 24*a*b*d^3*tan(f*x) + 12*b^2*c^3*tan(e) + 72*a*b*c^2*d*tan(e) + 36*a^2*c*d^2*tan(e) - 36*b^2*c*d^2*tan(e) - 24*a*b*d^3*tan(e) + 18*b^2*c^2*d + 36*a*b*c*d^2 + 6*a^2*d^3 - 9*b^2*d^3)/(f*tan(f*x)^4*tan(e)^4 - 4*f*tan(f*x)^3*tan(e)^3 + 6*f*tan(f*x)^2*tan(e)^2 - 4*f*tan(f*x)*tan(e) + f)","B",0
1205,1,2046,0,4.809088," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{6 \, a c^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, b c^{2} d f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, a c d^{2} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 6 \, b d^{3} f x \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 9 \, a c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, a d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 18 \, a c^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 54 \, b c^{2} d f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 54 \, a c d^{2} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, b d^{3} f x \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 3 \, a d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{3} + 9 \, b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 27 \, a c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 27 \, b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 9 \, a d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 18 \, b c^{2} d \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 18 \, a c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} + 6 \, b d^{3} \tan\left(f x\right)^{3} \tan\left(e\right)^{2} - 18 \, b c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right)^{3} - 18 \, a c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 6 \, b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{3} + 18 \, a c^{3} f x \tan\left(f x\right) \tan\left(e\right) - 54 \, b c^{2} d f x \tan\left(f x\right) \tan\left(e\right) - 54 \, a c d^{2} f x \tan\left(f x\right) \tan\left(e\right) + 18 \, b d^{3} f x \tan\left(f x\right) \tan\left(e\right) + 9 \, b c d^{2} \tan\left(f x\right)^{3} \tan\left(e\right) + 3 \, a d^{3} \tan\left(f x\right)^{3} \tan\left(e\right) - 9 \, b c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} - 3 \, a d^{3} \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 9 \, b c d^{2} \tan\left(f x\right) \tan\left(e\right)^{3} + 3 \, a d^{3} \tan\left(f x\right) \tan\left(e\right)^{3} - 2 \, b d^{3} \tan\left(f x\right)^{3} - 9 \, b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) - 27 \, a c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 27 \, b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 9 \, a d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) \tan\left(f x\right) \tan\left(e\right) + 36 \, b c^{2} d \tan\left(f x\right)^{2} \tan\left(e\right) + 36 \, a c d^{2} \tan\left(f x\right)^{2} \tan\left(e\right) - 18 \, b d^{3} \tan\left(f x\right)^{2} \tan\left(e\right) + 36 \, b c^{2} d \tan\left(f x\right) \tan\left(e\right)^{2} + 36 \, a c d^{2} \tan\left(f x\right) \tan\left(e\right)^{2} - 18 \, b d^{3} \tan\left(f x\right) \tan\left(e\right)^{2} - 2 \, b d^{3} \tan\left(e\right)^{3} - 6 \, a c^{3} f x + 18 \, b c^{2} d f x + 18 \, a c d^{2} f x - 6 \, b d^{3} f x - 9 \, b c d^{2} \tan\left(f x\right)^{2} - 3 \, a d^{3} \tan\left(f x\right)^{2} + 9 \, b c d^{2} \tan\left(f x\right) \tan\left(e\right) + 3 \, a d^{3} \tan\left(f x\right) \tan\left(e\right) - 9 \, b c d^{2} \tan\left(e\right)^{2} - 3 \, a d^{3} \tan\left(e\right)^{2} + 3 \, b c^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) + 9 \, a c^{2} d \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 9 \, b c d^{2} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 3 \, a d^{3} \log\left(\frac{4 \, {\left(\tan\left(f x\right)^{4} \tan\left(e\right)^{2} - 2 \, \tan\left(f x\right)^{3} \tan\left(e\right) + \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + \tan\left(f x\right)^{2} - 2 \, \tan\left(f x\right) \tan\left(e\right) + 1\right)}}{\tan\left(e\right)^{2} + 1}\right) - 18 \, b c^{2} d \tan\left(f x\right) - 18 \, a c d^{2} \tan\left(f x\right) + 6 \, b d^{3} \tan\left(f x\right) - 18 \, b c^{2} d \tan\left(e\right) - 18 \, a c d^{2} \tan\left(e\right) + 6 \, b d^{3} \tan\left(e\right) - 9 \, b c d^{2} - 3 \, a d^{3}}{6 \, {\left(f \tan\left(f x\right)^{3} \tan\left(e\right)^{3} - 3 \, f \tan\left(f x\right)^{2} \tan\left(e\right)^{2} + 3 \, f \tan\left(f x\right) \tan\left(e\right) - f\right)}}"," ",0,"1/6*(6*a*c^3*f*x*tan(f*x)^3*tan(e)^3 - 18*b*c^2*d*f*x*tan(f*x)^3*tan(e)^3 - 18*a*c*d^2*f*x*tan(f*x)^3*tan(e)^3 + 6*b*d^3*f*x*tan(f*x)^3*tan(e)^3 - 3*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 9*a*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 9*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 + 3*a*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^3*tan(e)^3 - 18*a*c^3*f*x*tan(f*x)^2*tan(e)^2 + 54*b*c^2*d*f*x*tan(f*x)^2*tan(e)^2 + 54*a*c*d^2*f*x*tan(f*x)^2*tan(e)^2 - 18*b*d^3*f*x*tan(f*x)^2*tan(e)^2 + 9*b*c*d^2*tan(f*x)^3*tan(e)^3 + 3*a*d^3*tan(f*x)^3*tan(e)^3 + 9*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 + 27*a*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 27*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 9*a*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)^2*tan(e)^2 - 18*b*c^2*d*tan(f*x)^3*tan(e)^2 - 18*a*c*d^2*tan(f*x)^3*tan(e)^2 + 6*b*d^3*tan(f*x)^3*tan(e)^2 - 18*b*c^2*d*tan(f*x)^2*tan(e)^3 - 18*a*c*d^2*tan(f*x)^2*tan(e)^3 + 6*b*d^3*tan(f*x)^2*tan(e)^3 + 18*a*c^3*f*x*tan(f*x)*tan(e) - 54*b*c^2*d*f*x*tan(f*x)*tan(e) - 54*a*c*d^2*f*x*tan(f*x)*tan(e) + 18*b*d^3*f*x*tan(f*x)*tan(e) + 9*b*c*d^2*tan(f*x)^3*tan(e) + 3*a*d^3*tan(f*x)^3*tan(e) - 9*b*c*d^2*tan(f*x)^2*tan(e)^2 - 3*a*d^3*tan(f*x)^2*tan(e)^2 + 9*b*c*d^2*tan(f*x)*tan(e)^3 + 3*a*d^3*tan(f*x)*tan(e)^3 - 2*b*d^3*tan(f*x)^3 - 9*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) - 27*a*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 27*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 9*a*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1))*tan(f*x)*tan(e) + 36*b*c^2*d*tan(f*x)^2*tan(e) + 36*a*c*d^2*tan(f*x)^2*tan(e) - 18*b*d^3*tan(f*x)^2*tan(e) + 36*b*c^2*d*tan(f*x)*tan(e)^2 + 36*a*c*d^2*tan(f*x)*tan(e)^2 - 18*b*d^3*tan(f*x)*tan(e)^2 - 2*b*d^3*tan(e)^3 - 6*a*c^3*f*x + 18*b*c^2*d*f*x + 18*a*c*d^2*f*x - 6*b*d^3*f*x - 9*b*c*d^2*tan(f*x)^2 - 3*a*d^3*tan(f*x)^2 + 9*b*c*d^2*tan(f*x)*tan(e) + 3*a*d^3*tan(f*x)*tan(e) - 9*b*c*d^2*tan(e)^2 - 3*a*d^3*tan(e)^2 + 3*b*c^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) + 9*a*c^2*d*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 9*b*c*d^2*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 3*a*d^3*log(4*(tan(f*x)^4*tan(e)^2 - 2*tan(f*x)^3*tan(e) + tan(f*x)^2*tan(e)^2 + tan(f*x)^2 - 2*tan(f*x)*tan(e) + 1)/(tan(e)^2 + 1)) - 18*b*c^2*d*tan(f*x) - 18*a*c*d^2*tan(f*x) + 6*b*d^3*tan(f*x) - 18*b*c^2*d*tan(e) - 18*a*c*d^2*tan(e) + 6*b*d^3*tan(e) - 9*b*c*d^2 - 3*a*d^3)/(f*tan(f*x)^3*tan(e)^3 - 3*f*tan(f*x)^2*tan(e)^2 + 3*f*tan(f*x)*tan(e) - f)","B",0
1206,1,176,0,2.106503," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, d^{3} \tan\left(f x + e\right)}{b} + \frac{2 \, {\left(a c^{3} + 3 \, b c^{2} d - 3 \, a c d^{2} - b d^{3}\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} - \frac{{\left(b c^{3} - 3 \, a c^{2} d - 3 \, b c d^{2} + a d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{2} + b^{4}}}{2 \, f}"," ",0,"1/2*(2*d^3*tan(f*x + e)/b + 2*(a*c^3 + 3*b*c^2*d - 3*a*c*d^2 - b*d^3)*(f*x + e)/(a^2 + b^2) - (b*c^3 - 3*a*c^2*d - 3*b*c*d^2 + a*d^3)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2) + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(b*tan(f*x + e) + a))/(a^2*b^2 + b^4))/f","A",0
1207,1,448,0,2.247430," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{2} c^{3} - b^{2} c^{3} + 6 \, a b c^{2} d - 3 \, a^{2} c d^{2} + 3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a b c^{3} - 3 \, a^{2} c^{2} d + 3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + a^{2} d^{3} - b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, b^{4} c^{2} d - 6 \, a b^{3} c d^{2} + a^{4} d^{3} + 3 \, a^{2} b^{2} d^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} - \frac{2 \, {\left(2 \, a b^{3} c^{3} \tan\left(f x + e\right) - 3 \, a^{2} b^{2} c^{2} d \tan\left(f x + e\right) + 3 \, b^{4} c^{2} d \tan\left(f x + e\right) - 6 \, a b^{3} c d^{2} \tan\left(f x + e\right) + a^{4} d^{3} \tan\left(f x + e\right) + 3 \, a^{2} b^{2} d^{3} \tan\left(f x + e\right) + 3 \, a^{2} b^{2} c^{3} + b^{4} c^{3} - 6 \, a^{3} b c^{2} d + 3 \, a^{4} c d^{2} - 3 \, a^{2} b^{2} c d^{2} + 2 \, a^{3} b d^{3}\right)}}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{2 \, f}"," ",0,"1/2*(2*(a^2*c^3 - b^2*c^3 + 6*a*b*c^2*d - 3*a^2*c*d^2 + 3*b^2*c*d^2 - 2*a*b*d^3)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) - (2*a*b*c^3 - 3*a^2*c^2*d + 3*b^2*c^2*d - 6*a*b*c*d^2 + a^2*d^3 - b^2*d^3)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*b^4*c^2*d - 6*a*b^3*c*d^2 + a^4*d^3 + 3*a^2*b^2*d^3)*log(abs(b*tan(f*x + e) + a))/(a^4*b^2 + 2*a^2*b^4 + b^6) - 2*(2*a*b^3*c^3*tan(f*x + e) - 3*a^2*b^2*c^2*d*tan(f*x + e) + 3*b^4*c^2*d*tan(f*x + e) - 6*a*b^3*c*d^2*tan(f*x + e) + a^4*d^3*tan(f*x + e) + 3*a^2*b^2*d^3*tan(f*x + e) + 3*a^2*b^2*c^3 + b^4*c^3 - 6*a^3*b*c^2*d + 3*a^4*c*d^2 - 3*a^2*b^2*c*d^2 + 2*a^3*b*d^3)/((a^4*b + 2*a^2*b^3 + b^5)*(b*tan(f*x + e) + a)))/f","A",0
1208,1,830,0,2.975558," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} c^{3} - 3 \, a b^{2} c^{3} + 9 \, a^{2} b c^{2} d - 3 \, b^{3} c^{2} d - 3 \, a^{3} c d^{2} + 9 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + b^{3} d^{3}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(3 \, a^{2} b c^{3} - b^{3} c^{3} - 3 \, a^{3} c^{2} d + 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 3 \, b^{3} c d^{2} + a^{3} d^{3} - 3 \, a b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left(3 \, a^{2} b^{2} c^{3} - b^{4} c^{3} - 3 \, a^{3} b c^{2} d + 9 \, a b^{3} c^{2} d - 9 \, a^{2} b^{2} c d^{2} + 3 \, b^{4} c d^{2} + a^{3} b d^{3} - 3 \, a b^{3} d^{3}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}} - \frac{9 \, a^{2} b^{5} c^{3} \tan\left(f x + e\right)^{2} - 3 \, b^{7} c^{3} \tan\left(f x + e\right)^{2} - 9 \, a^{3} b^{4} c^{2} d \tan\left(f x + e\right)^{2} + 27 \, a b^{6} c^{2} d \tan\left(f x + e\right)^{2} - 27 \, a^{2} b^{5} c d^{2} \tan\left(f x + e\right)^{2} + 9 \, b^{7} c d^{2} \tan\left(f x + e\right)^{2} + 3 \, a^{3} b^{4} d^{3} \tan\left(f x + e\right)^{2} - 9 \, a b^{6} d^{3} \tan\left(f x + e\right)^{2} + 22 \, a^{3} b^{4} c^{3} \tan\left(f x + e\right) - 2 \, a b^{6} c^{3} \tan\left(f x + e\right) - 24 \, a^{4} b^{3} c^{2} d \tan\left(f x + e\right) + 54 \, a^{2} b^{5} c^{2} d \tan\left(f x + e\right) + 6 \, b^{7} c^{2} d \tan\left(f x + e\right) - 66 \, a^{3} b^{4} c d^{2} \tan\left(f x + e\right) + 6 \, a b^{6} c d^{2} \tan\left(f x + e\right) + 2 \, a^{6} b d^{3} \tan\left(f x + e\right) + 14 \, a^{4} b^{3} d^{3} \tan\left(f x + e\right) - 12 \, a^{2} b^{5} d^{3} \tan\left(f x + e\right) + 14 \, a^{4} b^{3} c^{3} + 3 \, a^{2} b^{5} c^{3} + b^{7} c^{3} - 18 \, a^{5} b^{2} c^{2} d + 21 \, a^{3} b^{4} c^{2} d + 3 \, a b^{6} c^{2} d + 3 \, a^{6} b c d^{2} - 33 \, a^{4} b^{3} c d^{2} + a^{7} d^{3} + 9 \, a^{5} b^{2} d^{3} - 4 \, a^{3} b^{4} d^{3}}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^3*c^3 - 3*a*b^2*c^3 + 9*a^2*b*c^2*d - 3*b^3*c^2*d - 3*a^3*c*d^2 + 9*a*b^2*c*d^2 - 3*a^2*b*d^3 + b^3*d^3)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (3*a^2*b*c^3 - b^3*c^3 - 3*a^3*c^2*d + 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 3*b^3*c*d^2 + a^3*d^3 - 3*a*b^2*d^3)*log(tan(f*x + e)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*a^2*b^2*c^3 - b^4*c^3 - 3*a^3*b*c^2*d + 9*a*b^3*c^2*d - 9*a^2*b^2*c*d^2 + 3*b^4*c*d^2 + a^3*b*d^3 - 3*a*b^3*d^3)*log(abs(b*tan(f*x + e) + a))/(a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7) - (9*a^2*b^5*c^3*tan(f*x + e)^2 - 3*b^7*c^3*tan(f*x + e)^2 - 9*a^3*b^4*c^2*d*tan(f*x + e)^2 + 27*a*b^6*c^2*d*tan(f*x + e)^2 - 27*a^2*b^5*c*d^2*tan(f*x + e)^2 + 9*b^7*c*d^2*tan(f*x + e)^2 + 3*a^3*b^4*d^3*tan(f*x + e)^2 - 9*a*b^6*d^3*tan(f*x + e)^2 + 22*a^3*b^4*c^3*tan(f*x + e) - 2*a*b^6*c^3*tan(f*x + e) - 24*a^4*b^3*c^2*d*tan(f*x + e) + 54*a^2*b^5*c^2*d*tan(f*x + e) + 6*b^7*c^2*d*tan(f*x + e) - 66*a^3*b^4*c*d^2*tan(f*x + e) + 6*a*b^6*c*d^2*tan(f*x + e) + 2*a^6*b*d^3*tan(f*x + e) + 14*a^4*b^3*d^3*tan(f*x + e) - 12*a^2*b^5*d^3*tan(f*x + e) + 14*a^4*b^3*c^3 + 3*a^2*b^5*c^3 + b^7*c^3 - 18*a^5*b^2*c^2*d + 21*a^3*b^4*c^2*d + 3*a*b^6*c^2*d + 3*a^6*b*c*d^2 - 33*a^4*b^3*c*d^2 + a^7*d^3 + 9*a^5*b^2*d^3 - 4*a^3*b^4*d^3)/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*(b*tan(f*x + e) + a)^2))/f","B",0
1209,1,238,0,3.389153," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{4} c - 6 \, a^{2} b^{2} c + b^{4} c + 4 \, a^{3} b d - 4 \, a b^{3} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(4 \, a^{3} b c - 4 \, a b^{3} c - a^{4} d + 6 \, a^{2} b^{2} d - b^{4} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{2 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d^{3} + d^{5}} + \frac{b^{4} d \tan\left(f x + e\right)^{2} - 2 \, b^{4} c \tan\left(f x + e\right) + 8 \, a b^{3} d \tan\left(f x + e\right)}{d^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^4*c - 6*a^2*b^2*c + b^4*c + 4*a^3*b*d - 4*a*b^3*d)*(f*x + e)/(c^2 + d^2) + (4*a^3*b*c - 4*a*b^3*c - a^4*d + 6*a^2*b^2*d - b^4*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) + 2*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(abs(d*tan(f*x + e) + c))/(c^2*d^3 + d^5) + (b^4*d*tan(f*x + e)^2 - 2*b^4*c*tan(f*x + e) + 8*a*b^3*d*tan(f*x + e))/d^2)/f","A",0
1210,1,177,0,1.830419," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{3} \tan\left(f x + e\right)}{d} + \frac{2 \, {\left(a^{3} c - 3 \, a b^{2} c + 3 \, a^{2} b d - b^{3} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(3 \, a^{2} b c - b^{3} c - a^{3} d + 3 \, a b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} - \frac{2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d^{2} + d^{4}}}{2 \, f}"," ",0,"1/2*(2*b^3*tan(f*x + e)/d + 2*(a^3*c - 3*a*b^2*c + 3*a^2*b*d - b^3*d)*(f*x + e)/(c^2 + d^2) + (3*a^2*b*c - b^3*c - a^3*d + 3*a*b^2*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(abs(d*tan(f*x + e) + c))/(c^2*d^2 + d^4))/f","A",0
1211,1,126,0,1.026311," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{2} c - b^{2} c + 2 \, a b d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(2 \, a b c - a^{2} d + b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d + d^{3}}}{2 \, f}"," ",0,"1/2*(2*(a^2*c - b^2*c + 2*a*b*d)*(f*x + e)/(c^2 + d^2) + (2*a*b*c - a^2*d + b^2*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(abs(d*tan(f*x + e) + c))/(c^2*d + d^3))/f","A",0
1212,1,97,0,0.772175," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a c + b d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(b c - a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} - \frac{2 \, {\left(b c d - a d^{2}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{2} d + d^{3}}}{2 \, f}"," ",0,"1/2*(2*(a*c + b*d)*(f*x + e)/(c^2 + d^2) + (b*c - a*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) - 2*(b*c*d - a*d^2)*log(abs(d*tan(f*x + e) + c))/(c^2*d + d^3))/f","A",0
1213,1,201,0,0.618854," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, b^{3} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{2} c + b^{4} c - a^{3} b d - a b^{3} d} - \frac{2 \, d^{3} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b c^{3} d - a c^{2} d^{2} + b c d^{3} - a d^{4}} + \frac{2 \, {\left(a c - b d\right)} {\left(f x + e\right)}}{a^{2} c^{2} + b^{2} c^{2} + a^{2} d^{2} + b^{2} d^{2}} - \frac{{\left(b c + a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} c^{2} + b^{2} c^{2} + a^{2} d^{2} + b^{2} d^{2}}}{2 \, f}"," ",0,"1/2*(2*b^3*log(abs(b*tan(f*x + e) + a))/(a^2*b^2*c + b^4*c - a^3*b*d - a*b^3*d) - 2*d^3*log(abs(d*tan(f*x + e) + c))/(b*c^3*d - a*c^2*d^2 + b*c*d^3 - a*d^4) + 2*(a*c - b*d)*(f*x + e)/(a^2*c^2 + b^2*c^2 + a^2*d^2 + b^2*d^2) - (b*c + a*d)*log(tan(f*x + e)^2 + 1)/(a^2*c^2 + b^2*c^2 + a^2*d^2 + b^2*d^2))/f","A",0
1214,1,542,0,1.157974," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\frac{\frac{2 \, d^{4} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{2} c^{4} d - 2 \, a b c^{3} d^{2} + a^{2} c^{2} d^{3} + b^{2} c^{2} d^{3} - 2 \, a b c d^{4} + a^{2} d^{5}} + \frac{2 \, {\left(a^{2} c - b^{2} c - 2 \, a b d\right)} {\left(f x + e\right)}}{a^{4} c^{2} + 2 \, a^{2} b^{2} c^{2} + b^{4} c^{2} + a^{4} d^{2} + 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a b c + a^{2} d - b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} c^{2} + 2 \, a^{2} b^{2} c^{2} + b^{4} c^{2} + a^{4} d^{2} + 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} + \frac{2 \, {\left(2 \, a b^{4} c - 3 \, a^{2} b^{3} d - b^{5} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{3} c^{2} + 2 \, a^{2} b^{5} c^{2} + b^{7} c^{2} - 2 \, a^{5} b^{2} c d - 4 \, a^{3} b^{4} c d - 2 \, a b^{6} c d + a^{6} b d^{2} + 2 \, a^{4} b^{3} d^{2} + a^{2} b^{5} d^{2}} - \frac{2 \, {\left(2 \, a b^{4} c \tan\left(f x + e\right) - 3 \, a^{2} b^{3} d \tan\left(f x + e\right) - b^{5} d \tan\left(f x + e\right) + 3 \, a^{2} b^{3} c + b^{5} c - 4 \, a^{3} b^{2} d - 2 \, a b^{4} d\right)}}{{\left(a^{4} b^{2} c^{2} + 2 \, a^{2} b^{4} c^{2} + b^{6} c^{2} - 2 \, a^{5} b c d - 4 \, a^{3} b^{3} c d - 2 \, a b^{5} c d + a^{6} d^{2} + 2 \, a^{4} b^{2} d^{2} + a^{2} b^{4} d^{2}\right)} {\left(b \tan\left(f x + e\right) + a\right)}}}{2 \, f}"," ",0,"1/2*(2*d^4*log(abs(d*tan(f*x + e) + c))/(b^2*c^4*d - 2*a*b*c^3*d^2 + a^2*c^2*d^3 + b^2*c^2*d^3 - 2*a*b*c*d^4 + a^2*d^5) + 2*(a^2*c - b^2*c - 2*a*b*d)*(f*x + e)/(a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^4*d^2 + 2*a^2*b^2*d^2 + b^4*d^2) - (2*a*b*c + a^2*d - b^2*d)*log(tan(f*x + e)^2 + 1)/(a^4*c^2 + 2*a^2*b^2*c^2 + b^4*c^2 + a^4*d^2 + 2*a^2*b^2*d^2 + b^4*d^2) + 2*(2*a*b^4*c - 3*a^2*b^3*d - b^5*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^3*c^2 + 2*a^2*b^5*c^2 + b^7*c^2 - 2*a^5*b^2*c*d - 4*a^3*b^4*c*d - 2*a*b^6*c*d + a^6*b*d^2 + 2*a^4*b^3*d^2 + a^2*b^5*d^2) - 2*(2*a*b^4*c*tan(f*x + e) - 3*a^2*b^3*d*tan(f*x + e) - b^5*d*tan(f*x + e) + 3*a^2*b^3*c + b^5*c - 4*a^3*b^2*d - 2*a*b^4*d)/((a^4*b^2*c^2 + 2*a^2*b^4*c^2 + b^6*c^2 - 2*a^5*b*c*d - 4*a^3*b^3*c*d - 2*a*b^5*c*d + a^6*d^2 + 2*a^4*b^2*d^2 + a^2*b^4*d^2)*(b*tan(f*x + e) + a)))/f","B",0
1215,1,1111,0,1.664687," ","integrate(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""giac"")","-\frac{\frac{2 \, d^{5} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{3} c^{5} d - 3 \, a b^{2} c^{4} d^{2} + 3 \, a^{2} b c^{3} d^{3} + b^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 3 \, a b^{2} c^{2} d^{4} + 3 \, a^{2} b c d^{5} - a^{3} d^{6}} - \frac{2 \, {\left(a^{3} c - 3 \, a b^{2} c - 3 \, a^{2} b d + b^{3} d\right)} {\left(f x + e\right)}}{a^{6} c^{2} + 3 \, a^{4} b^{2} c^{2} + 3 \, a^{2} b^{4} c^{2} + b^{6} c^{2} + a^{6} d^{2} + 3 \, a^{4} b^{2} d^{2} + 3 \, a^{2} b^{4} d^{2} + b^{6} d^{2}} + \frac{{\left(3 \, a^{2} b c - b^{3} c + a^{3} d - 3 \, a b^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} c^{2} + 3 \, a^{4} b^{2} c^{2} + 3 \, a^{2} b^{4} c^{2} + b^{6} c^{2} + a^{6} d^{2} + 3 \, a^{4} b^{2} d^{2} + 3 \, a^{2} b^{4} d^{2} + b^{6} d^{2}} - \frac{2 \, {\left(3 \, a^{2} b^{5} c^{2} - b^{7} c^{2} - 8 \, a^{3} b^{4} c d + 6 \, a^{4} b^{3} d^{2} + 3 \, a^{2} b^{5} d^{2} + b^{7} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b^{4} c^{3} + 3 \, a^{4} b^{6} c^{3} + 3 \, a^{2} b^{8} c^{3} + b^{10} c^{3} - 3 \, a^{7} b^{3} c^{2} d - 9 \, a^{5} b^{5} c^{2} d - 9 \, a^{3} b^{7} c^{2} d - 3 \, a b^{9} c^{2} d + 3 \, a^{8} b^{2} c d^{2} + 9 \, a^{6} b^{4} c d^{2} + 9 \, a^{4} b^{6} c d^{2} + 3 \, a^{2} b^{8} c d^{2} - a^{9} b d^{3} - 3 \, a^{7} b^{3} d^{3} - 3 \, a^{5} b^{5} d^{3} - a^{3} b^{7} d^{3}} + \frac{9 \, a^{2} b^{6} c^{2} \tan\left(f x + e\right)^{2} - 3 \, b^{8} c^{2} \tan\left(f x + e\right)^{2} - 24 \, a^{3} b^{5} c d \tan\left(f x + e\right)^{2} + 18 \, a^{4} b^{4} d^{2} \tan\left(f x + e\right)^{2} + 9 \, a^{2} b^{6} d^{2} \tan\left(f x + e\right)^{2} + 3 \, b^{8} d^{2} \tan\left(f x + e\right)^{2} + 22 \, a^{3} b^{5} c^{2} \tan\left(f x + e\right) - 2 \, a b^{7} c^{2} \tan\left(f x + e\right) - 58 \, a^{4} b^{4} c d \tan\left(f x + e\right) - 12 \, a^{2} b^{6} c d \tan\left(f x + e\right) - 2 \, b^{8} c d \tan\left(f x + e\right) + 42 \, a^{5} b^{3} d^{2} \tan\left(f x + e\right) + 26 \, a^{3} b^{5} d^{2} \tan\left(f x + e\right) + 8 \, a b^{7} d^{2} \tan\left(f x + e\right) + 14 \, a^{4} b^{4} c^{2} + 3 \, a^{2} b^{6} c^{2} + b^{8} c^{2} - 36 \, a^{5} b^{3} c d - 16 \, a^{3} b^{5} c d - 4 \, a b^{7} c d + 25 \, a^{6} b^{2} d^{2} + 19 \, a^{4} b^{4} d^{2} + 6 \, a^{2} b^{6} d^{2}}{{\left(a^{6} b^{3} c^{3} + 3 \, a^{4} b^{5} c^{3} + 3 \, a^{2} b^{7} c^{3} + b^{9} c^{3} - 3 \, a^{7} b^{2} c^{2} d - 9 \, a^{5} b^{4} c^{2} d - 9 \, a^{3} b^{6} c^{2} d - 3 \, a b^{8} c^{2} d + 3 \, a^{8} b c d^{2} + 9 \, a^{6} b^{3} c d^{2} + 9 \, a^{4} b^{5} c d^{2} + 3 \, a^{2} b^{7} c d^{2} - a^{9} d^{3} - 3 \, a^{7} b^{2} d^{3} - 3 \, a^{5} b^{4} d^{3} - a^{3} b^{6} d^{3}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"-1/2*(2*d^5*log(abs(d*tan(f*x + e) + c))/(b^3*c^5*d - 3*a*b^2*c^4*d^2 + 3*a^2*b*c^3*d^3 + b^3*c^3*d^3 - a^3*c^2*d^4 - 3*a*b^2*c^2*d^4 + 3*a^2*b*c*d^5 - a^3*d^6) - 2*(a^3*c - 3*a*b^2*c - 3*a^2*b*d + b^3*d)*(f*x + e)/(a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 + a^6*d^2 + 3*a^4*b^2*d^2 + 3*a^2*b^4*d^2 + b^6*d^2) + (3*a^2*b*c - b^3*c + a^3*d - 3*a*b^2*d)*log(tan(f*x + e)^2 + 1)/(a^6*c^2 + 3*a^4*b^2*c^2 + 3*a^2*b^4*c^2 + b^6*c^2 + a^6*d^2 + 3*a^4*b^2*d^2 + 3*a^2*b^4*d^2 + b^6*d^2) - 2*(3*a^2*b^5*c^2 - b^7*c^2 - 8*a^3*b^4*c*d + 6*a^4*b^3*d^2 + 3*a^2*b^5*d^2 + b^7*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b^4*c^3 + 3*a^4*b^6*c^3 + 3*a^2*b^8*c^3 + b^10*c^3 - 3*a^7*b^3*c^2*d - 9*a^5*b^5*c^2*d - 9*a^3*b^7*c^2*d - 3*a*b^9*c^2*d + 3*a^8*b^2*c*d^2 + 9*a^6*b^4*c*d^2 + 9*a^4*b^6*c*d^2 + 3*a^2*b^8*c*d^2 - a^9*b*d^3 - 3*a^7*b^3*d^3 - 3*a^5*b^5*d^3 - a^3*b^7*d^3) + (9*a^2*b^6*c^2*tan(f*x + e)^2 - 3*b^8*c^2*tan(f*x + e)^2 - 24*a^3*b^5*c*d*tan(f*x + e)^2 + 18*a^4*b^4*d^2*tan(f*x + e)^2 + 9*a^2*b^6*d^2*tan(f*x + e)^2 + 3*b^8*d^2*tan(f*x + e)^2 + 22*a^3*b^5*c^2*tan(f*x + e) - 2*a*b^7*c^2*tan(f*x + e) - 58*a^4*b^4*c*d*tan(f*x + e) - 12*a^2*b^6*c*d*tan(f*x + e) - 2*b^8*c*d*tan(f*x + e) + 42*a^5*b^3*d^2*tan(f*x + e) + 26*a^3*b^5*d^2*tan(f*x + e) + 8*a*b^7*d^2*tan(f*x + e) + 14*a^4*b^4*c^2 + 3*a^2*b^6*c^2 + b^8*c^2 - 36*a^5*b^3*c*d - 16*a^3*b^5*c*d - 4*a*b^7*c*d + 25*a^6*b^2*d^2 + 19*a^4*b^4*d^2 + 6*a^2*b^6*d^2)/((a^6*b^3*c^3 + 3*a^4*b^5*c^3 + 3*a^2*b^7*c^3 + b^9*c^3 - 3*a^7*b^2*c^2*d - 9*a^5*b^4*c^2*d - 9*a^3*b^6*c^2*d - 3*a*b^8*c^2*d + 3*a^8*b*c*d^2 + 9*a^6*b^3*c*d^2 + 9*a^4*b^5*c*d^2 + 3*a^2*b^7*c*d^2 - a^9*d^3 - 3*a^7*b^2*d^3 - 3*a^5*b^4*d^3 - a^3*b^6*d^3)*(b*tan(f*x + e) + a)^2))/f","B",0
1216,1,589,0,3.656342," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{b^{4} \tan\left(f x + e\right)}{d^{2}} + \frac{{\left(a^{4} c^{2} - 6 \, a^{2} b^{2} c^{2} + b^{4} c^{2} + 8 \, a^{3} b c d - 8 \, a b^{3} c d - a^{4} d^{2} + 6 \, a^{2} b^{2} d^{2} - b^{4} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(2 \, a^{3} b c^{2} - 2 \, a b^{3} c^{2} - a^{4} c d + 6 \, a^{2} b^{2} c d - b^{4} c d - 2 \, a^{3} b d^{2} + 2 \, a b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(b^{4} c^{5} - 2 \, a b^{3} c^{4} d + 2 \, b^{4} c^{3} d^{2} + 2 \, a^{3} b c^{2} d^{3} - 6 \, a b^{3} c^{2} d^{3} - a^{4} c d^{4} + 6 \, a^{2} b^{2} c d^{4} - 2 \, a^{3} b d^{5}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}} + \frac{2 \, b^{4} c^{5} d \tan\left(f x + e\right) - 4 \, a b^{3} c^{4} d^{2} \tan\left(f x + e\right) + 4 \, b^{4} c^{3} d^{3} \tan\left(f x + e\right) + 4 \, a^{3} b c^{2} d^{4} \tan\left(f x + e\right) - 12 \, a b^{3} c^{2} d^{4} \tan\left(f x + e\right) - 2 \, a^{4} c d^{5} \tan\left(f x + e\right) + 12 \, a^{2} b^{2} c d^{5} \tan\left(f x + e\right) - 4 \, a^{3} b d^{6} \tan\left(f x + e\right) + b^{4} c^{6} - 6 \, a^{2} b^{2} c^{4} d^{2} + 3 \, b^{4} c^{4} d^{2} + 8 \, a^{3} b c^{3} d^{3} - 8 \, a b^{3} c^{3} d^{3} - 3 \, a^{4} c^{2} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{4} - a^{4} d^{6}}{{\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{f}"," ",0,"(b^4*tan(f*x + e)/d^2 + (a^4*c^2 - 6*a^2*b^2*c^2 + b^4*c^2 + 8*a^3*b*c*d - 8*a*b^3*c*d - a^4*d^2 + 6*a^2*b^2*d^2 - b^4*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (2*a^3*b*c^2 - 2*a*b^3*c^2 - a^4*c*d + 6*a^2*b^2*c*d - b^4*c*d - 2*a^3*b*d^2 + 2*a*b^3*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 2*(b^4*c^5 - 2*a*b^3*c^4*d + 2*b^4*c^3*d^2 + 2*a^3*b*c^2*d^3 - 6*a*b^3*c^2*d^3 - a^4*c*d^4 + 6*a^2*b^2*c*d^4 - 2*a^3*b*d^5)*log(abs(d*tan(f*x + e) + c))/(c^4*d^3 + 2*c^2*d^5 + d^7) + (2*b^4*c^5*d*tan(f*x + e) - 4*a*b^3*c^4*d^2*tan(f*x + e) + 4*b^4*c^3*d^3*tan(f*x + e) + 4*a^3*b*c^2*d^4*tan(f*x + e) - 12*a*b^3*c^2*d^4*tan(f*x + e) - 2*a^4*c*d^5*tan(f*x + e) + 12*a^2*b^2*c*d^5*tan(f*x + e) - 4*a^3*b*d^6*tan(f*x + e) + b^4*c^6 - 6*a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 8*a^3*b*c^3*d^3 - 8*a*b^3*c^3*d^3 - 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 - a^4*d^6)/((c^4*d^3 + 2*c^2*d^5 + d^7)*(d*tan(f*x + e) + c)))/f","B",0
1217,1,447,0,2.635217," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} c^{2} - 3 \, a b^{2} c^{2} + 6 \, a^{2} b c d - 2 \, b^{3} c d - a^{3} d^{2} + 3 \, a b^{2} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(3 \, a^{2} b c^{2} - b^{3} c^{2} - 2 \, a^{3} c d + 6 \, a b^{2} c d - 3 \, a^{2} b d^{2} + b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(b^{3} c^{4} - 3 \, a^{2} b c^{2} d^{2} + 3 \, b^{3} c^{2} d^{2} + 2 \, a^{3} c d^{3} - 6 \, a b^{2} c d^{3} + 3 \, a^{2} b d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(b^{3} c^{4} \tan\left(f x + e\right) - 3 \, a^{2} b c^{2} d^{2} \tan\left(f x + e\right) + 3 \, b^{3} c^{2} d^{2} \tan\left(f x + e\right) + 2 \, a^{3} c d^{3} \tan\left(f x + e\right) - 6 \, a b^{2} c d^{3} \tan\left(f x + e\right) + 3 \, a^{2} b d^{4} \tan\left(f x + e\right) + 3 \, a b^{2} c^{4} - 6 \, a^{2} b c^{3} d + 2 \, b^{3} c^{3} d + 3 \, a^{3} c^{2} d^{2} - 3 \, a b^{2} c^{2} d^{2} + a^{3} d^{4}\right)}}{{\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*(a^3*c^2 - 3*a*b^2*c^2 + 6*a^2*b*c*d - 2*b^3*c*d - a^3*d^2 + 3*a*b^2*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (3*a^2*b*c^2 - b^3*c^2 - 2*a^3*c*d + 6*a*b^2*c*d - 3*a^2*b*d^2 + b^3*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(b^3*c^4 - 3*a^2*b*c^2*d^2 + 3*b^3*c^2*d^2 + 2*a^3*c*d^3 - 6*a*b^2*c*d^3 + 3*a^2*b*d^4)*log(abs(d*tan(f*x + e) + c))/(c^4*d^2 + 2*c^2*d^4 + d^6) - 2*(b^3*c^4*tan(f*x + e) - 3*a^2*b*c^2*d^2*tan(f*x + e) + 3*b^3*c^2*d^2*tan(f*x + e) + 2*a^3*c*d^3*tan(f*x + e) - 6*a*b^2*c*d^3*tan(f*x + e) + 3*a^2*b*d^4*tan(f*x + e) + 3*a*b^2*c^4 - 6*a^2*b*c^3*d + 2*b^3*c^3*d + 3*a^3*c^2*d^2 - 3*a*b^2*c^2*d^2 + a^3*d^4)/((c^4*d + 2*c^2*d^3 + d^5)*(d*tan(f*x + e) + c)))/f","B",0
1218,1,331,0,1.593681," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(a^{2} c^{2} - b^{2} c^{2} + 4 \, a b c d - a^{2} d^{2} + b^{2} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(a b c^{2} - a^{2} c d + b^{2} c d - a b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(a b c^{2} d - a^{2} c d^{2} + b^{2} c d^{2} - a b d^{3}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d + 2 \, c^{2} d^{3} + d^{5}} + \frac{2 \, a b c^{2} d^{2} \tan\left(f x + e\right) - 2 \, a^{2} c d^{3} \tan\left(f x + e\right) + 2 \, b^{2} c d^{3} \tan\left(f x + e\right) - 2 \, a b d^{4} \tan\left(f x + e\right) - b^{2} c^{4} + 4 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + b^{2} c^{2} d^{2} - a^{2} d^{4}}{{\left(c^{4} d + 2 \, c^{2} d^{3} + d^{5}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{f}"," ",0,"((a^2*c^2 - b^2*c^2 + 4*a*b*c*d - a^2*d^2 + b^2*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (a*b*c^2 - a^2*c*d + b^2*c*d - a*b*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 2*(a*b*c^2*d - a^2*c*d^2 + b^2*c*d^2 - a*b*d^3)*log(abs(d*tan(f*x + e) + c))/(c^4*d + 2*c^2*d^3 + d^5) + (2*a*b*c^2*d^2*tan(f*x + e) - 2*a^2*c*d^3*tan(f*x + e) + 2*b^2*c*d^3*tan(f*x + e) - 2*a*b*d^4*tan(f*x + e) - b^2*c^4 + 4*a*b*c^3*d - 3*a^2*c^2*d^2 + b^2*c^2*d^2 - a^2*d^4)/((c^4*d + 2*c^2*d^3 + d^5)*(d*tan(f*x + e) + c)))/f","B",0
1219,1,241,0,0.758973," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a c^{2} + 2 \, b c d - a d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(b c^{2} - 2 \, a c d - b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(b c^{2} d - 2 \, a c d^{2} - b d^{3}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{4} d + 2 \, c^{2} d^{3} + d^{5}} + \frac{2 \, {\left(b c^{2} d \tan\left(f x + e\right) - 2 \, a c d^{2} \tan\left(f x + e\right) - b d^{3} \tan\left(f x + e\right) + 2 \, b c^{3} - 3 \, a c^{2} d - a d^{3}\right)}}{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*(a*c^2 + 2*b*c*d - a*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (b*c^2 - 2*a*c*d - b*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - 2*(b*c^2*d - 2*a*c*d^2 - b*d^3)*log(abs(d*tan(f*x + e) + c))/(c^4*d + 2*c^2*d^3 + d^5) + 2*(b*c^2*d*tan(f*x + e) - 2*a*c*d^2*tan(f*x + e) - b*d^3*tan(f*x + e) + 2*b*c^3 - 3*a*c^2*d - a*d^3)/((c^4 + 2*c^2*d^2 + d^4)*(d*tan(f*x + e) + c)))/f","B",0
1220,1,541,0,1.241584," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, b^{4} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{3} c^{2} + b^{5} c^{2} - 2 \, a^{3} b^{2} c d - 2 \, a b^{4} c d + a^{4} b d^{2} + a^{2} b^{3} d^{2}} + \frac{2 \, {\left(a c^{2} - 2 \, b c d - a d^{2}\right)} {\left(f x + e\right)}}{a^{2} c^{4} + b^{2} c^{4} + 2 \, a^{2} c^{2} d^{2} + 2 \, b^{2} c^{2} d^{2} + a^{2} d^{4} + b^{2} d^{4}} - \frac{{\left(b c^{2} + 2 \, a c d - b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} c^{4} + b^{2} c^{4} + 2 \, a^{2} c^{2} d^{2} + 2 \, b^{2} c^{2} d^{2} + a^{2} d^{4} + b^{2} d^{4}} - \frac{2 \, {\left(3 \, b c^{2} d^{3} - 2 \, a c d^{4} + b d^{5}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{2} c^{6} d - 2 \, a b c^{5} d^{2} + a^{2} c^{4} d^{3} + 2 \, b^{2} c^{4} d^{3} - 4 \, a b c^{3} d^{4} + 2 \, a^{2} c^{2} d^{5} + b^{2} c^{2} d^{5} - 2 \, a b c d^{6} + a^{2} d^{7}} + \frac{2 \, {\left(3 \, b c^{2} d^{3} \tan\left(f x + e\right) - 2 \, a c d^{4} \tan\left(f x + e\right) + b d^{5} \tan\left(f x + e\right) + 4 \, b c^{3} d^{2} - 3 \, a c^{2} d^{3} + 2 \, b c d^{4} - a d^{5}\right)}}{{\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2} + 2 \, b^{2} c^{4} d^{2} - 4 \, a b c^{3} d^{3} + 2 \, a^{2} c^{2} d^{4} + b^{2} c^{2} d^{4} - 2 \, a b c d^{5} + a^{2} d^{6}\right)} {\left(d \tan\left(f x + e\right) + c\right)}}}{2 \, f}"," ",0,"1/2*(2*b^4*log(abs(b*tan(f*x + e) + a))/(a^2*b^3*c^2 + b^5*c^2 - 2*a^3*b^2*c*d - 2*a*b^4*c*d + a^4*b*d^2 + a^2*b^3*d^2) + 2*(a*c^2 - 2*b*c*d - a*d^2)*(f*x + e)/(a^2*c^4 + b^2*c^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2 + a^2*d^4 + b^2*d^4) - (b*c^2 + 2*a*c*d - b*d^2)*log(tan(f*x + e)^2 + 1)/(a^2*c^4 + b^2*c^4 + 2*a^2*c^2*d^2 + 2*b^2*c^2*d^2 + a^2*d^4 + b^2*d^4) - 2*(3*b*c^2*d^3 - 2*a*c*d^4 + b*d^5)*log(abs(d*tan(f*x + e) + c))/(b^2*c^6*d - 2*a*b*c^5*d^2 + a^2*c^4*d^3 + 2*b^2*c^4*d^3 - 4*a*b*c^3*d^4 + 2*a^2*c^2*d^5 + b^2*c^2*d^5 - 2*a*b*c*d^6 + a^2*d^7) + 2*(3*b*c^2*d^3*tan(f*x + e) - 2*a*c*d^4*tan(f*x + e) + b*d^5*tan(f*x + e) + 4*b*c^3*d^2 - 3*a*c^2*d^3 + 2*b*c*d^4 - a*d^5)/((b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2 + 2*b^2*c^4*d^2 - 4*a*b*c^3*d^3 + 2*a^2*c^2*d^4 + b^2*c^2*d^4 - 2*a*b*c*d^5 + a^2*d^6)*(d*tan(f*x + e) + c)))/f","B",0
1221,1,1395,0,1.848306," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{{\left(a^{2} c^{2} - b^{2} c^{2} - 4 \, a b c d - a^{2} d^{2} + b^{2} d^{2}\right)} {\left(f x + e\right)}}{a^{4} c^{4} + 2 \, a^{2} b^{2} c^{4} + b^{4} c^{4} + 2 \, a^{4} c^{2} d^{2} + 4 \, a^{2} b^{2} c^{2} d^{2} + 2 \, b^{4} c^{2} d^{2} + a^{4} d^{4} + 2 \, a^{2} b^{2} d^{4} + b^{4} d^{4}} - \frac{{\left(a b c^{2} + a^{2} c d - b^{2} c d - a b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} c^{4} + 2 \, a^{2} b^{2} c^{4} + b^{4} c^{4} + 2 \, a^{4} c^{2} d^{2} + 4 \, a^{2} b^{2} c^{2} d^{2} + 2 \, b^{4} c^{2} d^{2} + a^{4} d^{4} + 2 \, a^{2} b^{2} d^{4} + b^{4} d^{4}} + \frac{2 \, {\left(a b^{5} c - 2 \, a^{2} b^{4} d - b^{6} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{4} c^{3} + 2 \, a^{2} b^{6} c^{3} + b^{8} c^{3} - 3 \, a^{5} b^{3} c^{2} d - 6 \, a^{3} b^{5} c^{2} d - 3 \, a b^{7} c^{2} d + 3 \, a^{6} b^{2} c d^{2} + 6 \, a^{4} b^{4} c d^{2} + 3 \, a^{2} b^{6} c d^{2} - a^{7} b d^{3} - 2 \, a^{5} b^{3} d^{3} - a^{3} b^{5} d^{3}} + \frac{2 \, {\left(2 \, b c^{2} d^{4} - a c d^{5} + b d^{6}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{3} c^{7} d - 3 \, a b^{2} c^{6} d^{2} + 3 \, a^{2} b c^{5} d^{3} + 2 \, b^{3} c^{5} d^{3} - a^{3} c^{4} d^{4} - 6 \, a b^{2} c^{4} d^{4} + 6 \, a^{2} b c^{3} d^{5} + b^{3} c^{3} d^{5} - 2 \, a^{3} c^{2} d^{6} - 3 \, a b^{2} c^{2} d^{6} + 3 \, a^{2} b c d^{7} - a^{3} d^{8}} - \frac{a b^{4} c^{4} d \tan\left(f x + e\right)^{2} - a^{2} b^{3} c^{3} d^{2} \tan\left(f x + e\right)^{2} - b^{5} c^{3} d^{2} \tan\left(f x + e\right)^{2} - a^{3} b^{2} c^{2} d^{3} \tan\left(f x + e\right)^{2} + a b^{4} c^{2} d^{3} \tan\left(f x + e\right)^{2} + a^{4} b c d^{4} \tan\left(f x + e\right)^{2} + a^{2} b^{3} c d^{4} \tan\left(f x + e\right)^{2} - a^{3} b^{2} d^{5} \tan\left(f x + e\right)^{2} + a b^{4} c^{5} \tan\left(f x + e\right) + a^{2} b^{3} c^{4} d \tan\left(f x + e\right) - 2 \, a^{3} b^{2} c^{3} d^{2} \tan\left(f x + e\right) + a^{4} b c^{2} d^{3} \tan\left(f x + e\right) + 6 \, a^{2} b^{3} c^{2} d^{3} \tan\left(f x + e\right) + 3 \, b^{5} c^{2} d^{3} \tan\left(f x + e\right) + a^{5} c d^{4} \tan\left(f x + e\right) + 3 \, a^{2} b^{3} d^{5} \tan\left(f x + e\right) + 2 \, b^{5} d^{5} \tan\left(f x + e\right) + 2 \, a^{2} b^{3} c^{5} + b^{5} c^{5} - a^{3} b^{2} c^{4} d - a b^{4} c^{4} d - a^{4} b c^{3} d^{2} + 3 \, a^{2} b^{3} c^{3} d^{2} + 2 \, b^{5} c^{3} d^{2} + 2 \, a^{5} c^{2} d^{3} + 3 \, a^{3} b^{2} c^{2} d^{3} + a b^{4} c^{2} d^{3} - a^{4} b c d^{4} + a^{2} b^{3} c d^{4} + b^{5} c d^{4} + a^{5} d^{5} + 2 \, a^{3} b^{2} d^{5} + a b^{4} d^{5}}{{\left(a^{4} b^{2} c^{6} + 2 \, a^{2} b^{4} c^{6} + b^{6} c^{6} - 2 \, a^{5} b c^{5} d - 4 \, a^{3} b^{3} c^{5} d - 2 \, a b^{5} c^{5} d + a^{6} c^{4} d^{2} + 4 \, a^{4} b^{2} c^{4} d^{2} + 5 \, a^{2} b^{4} c^{4} d^{2} + 2 \, b^{6} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} - 8 \, a^{3} b^{3} c^{3} d^{3} - 4 \, a b^{5} c^{3} d^{3} + 2 \, a^{6} c^{2} d^{4} + 5 \, a^{4} b^{2} c^{2} d^{4} + 4 \, a^{2} b^{4} c^{2} d^{4} + b^{6} c^{2} d^{4} - 2 \, a^{5} b c d^{5} - 4 \, a^{3} b^{3} c d^{5} - 2 \, a b^{5} c d^{5} + a^{6} d^{6} + 2 \, a^{4} b^{2} d^{6} + a^{2} b^{4} d^{6}\right)} {\left(b d \tan\left(f x + e\right)^{2} + b c \tan\left(f x + e\right) + a d \tan\left(f x + e\right) + a c\right)}}}{f}"," ",0,"((a^2*c^2 - b^2*c^2 - 4*a*b*c*d - a^2*d^2 + b^2*d^2)*(f*x + e)/(a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 + 2*a^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2 + 2*b^4*c^2*d^2 + a^4*d^4 + 2*a^2*b^2*d^4 + b^4*d^4) - (a*b*c^2 + a^2*c*d - b^2*c*d - a*b*d^2)*log(tan(f*x + e)^2 + 1)/(a^4*c^4 + 2*a^2*b^2*c^4 + b^4*c^4 + 2*a^4*c^2*d^2 + 4*a^2*b^2*c^2*d^2 + 2*b^4*c^2*d^2 + a^4*d^4 + 2*a^2*b^2*d^4 + b^4*d^4) + 2*(a*b^5*c - 2*a^2*b^4*d - b^6*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^4*c^3 + 2*a^2*b^6*c^3 + b^8*c^3 - 3*a^5*b^3*c^2*d - 6*a^3*b^5*c^2*d - 3*a*b^7*c^2*d + 3*a^6*b^2*c*d^2 + 6*a^4*b^4*c*d^2 + 3*a^2*b^6*c*d^2 - a^7*b*d^3 - 2*a^5*b^3*d^3 - a^3*b^5*d^3) + 2*(2*b*c^2*d^4 - a*c*d^5 + b*d^6)*log(abs(d*tan(f*x + e) + c))/(b^3*c^7*d - 3*a*b^2*c^6*d^2 + 3*a^2*b*c^5*d^3 + 2*b^3*c^5*d^3 - a^3*c^4*d^4 - 6*a*b^2*c^4*d^4 + 6*a^2*b*c^3*d^5 + b^3*c^3*d^5 - 2*a^3*c^2*d^6 - 3*a*b^2*c^2*d^6 + 3*a^2*b*c*d^7 - a^3*d^8) - (a*b^4*c^4*d*tan(f*x + e)^2 - a^2*b^3*c^3*d^2*tan(f*x + e)^2 - b^5*c^3*d^2*tan(f*x + e)^2 - a^3*b^2*c^2*d^3*tan(f*x + e)^2 + a*b^4*c^2*d^3*tan(f*x + e)^2 + a^4*b*c*d^4*tan(f*x + e)^2 + a^2*b^3*c*d^4*tan(f*x + e)^2 - a^3*b^2*d^5*tan(f*x + e)^2 + a*b^4*c^5*tan(f*x + e) + a^2*b^3*c^4*d*tan(f*x + e) - 2*a^3*b^2*c^3*d^2*tan(f*x + e) + a^4*b*c^2*d^3*tan(f*x + e) + 6*a^2*b^3*c^2*d^3*tan(f*x + e) + 3*b^5*c^2*d^3*tan(f*x + e) + a^5*c*d^4*tan(f*x + e) + 3*a^2*b^3*d^5*tan(f*x + e) + 2*b^5*d^5*tan(f*x + e) + 2*a^2*b^3*c^5 + b^5*c^5 - a^3*b^2*c^4*d - a*b^4*c^4*d - a^4*b*c^3*d^2 + 3*a^2*b^3*c^3*d^2 + 2*b^5*c^3*d^2 + 2*a^5*c^2*d^3 + 3*a^3*b^2*c^2*d^3 + a*b^4*c^2*d^3 - a^4*b*c*d^4 + a^2*b^3*c*d^4 + b^5*c*d^4 + a^5*d^5 + 2*a^3*b^2*d^5 + a*b^4*d^5)/((a^4*b^2*c^6 + 2*a^2*b^4*c^6 + b^6*c^6 - 2*a^5*b*c^5*d - 4*a^3*b^3*c^5*d - 2*a*b^5*c^5*d + a^6*c^4*d^2 + 4*a^4*b^2*c^4*d^2 + 5*a^2*b^4*c^4*d^2 + 2*b^6*c^4*d^2 - 4*a^5*b*c^3*d^3 - 8*a^3*b^3*c^3*d^3 - 4*a*b^5*c^3*d^3 + 2*a^6*c^2*d^4 + 5*a^4*b^2*c^2*d^4 + 4*a^2*b^4*c^2*d^4 + b^6*c^2*d^4 - 2*a^5*b*c*d^5 - 4*a^3*b^3*c*d^5 - 2*a*b^5*c*d^5 + a^6*d^6 + 2*a^4*b^2*d^6 + a^2*b^4*d^6)*(b*d*tan(f*x + e)^2 + b*c*tan(f*x + e) + a*d*tan(f*x + e) + a*c)))/f","B",0
1222,1,1759,0,11.459416," ","integrate(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} c^{2} - 3 \, a b^{2} c^{2} - 6 \, a^{2} b c d + 2 \, b^{3} c d - a^{3} d^{2} + 3 \, a b^{2} d^{2}\right)} {\left(f x + e\right)}}{a^{6} c^{4} + 3 \, a^{4} b^{2} c^{4} + 3 \, a^{2} b^{4} c^{4} + b^{6} c^{4} + 2 \, a^{6} c^{2} d^{2} + 6 \, a^{4} b^{2} c^{2} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{2} + 2 \, b^{6} c^{2} d^{2} + a^{6} d^{4} + 3 \, a^{4} b^{2} d^{4} + 3 \, a^{2} b^{4} d^{4} + b^{6} d^{4}} - \frac{{\left(3 \, a^{2} b c^{2} - b^{3} c^{2} + 2 \, a^{3} c d - 6 \, a b^{2} c d - 3 \, a^{2} b d^{2} + b^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{6} c^{4} + 3 \, a^{4} b^{2} c^{4} + 3 \, a^{2} b^{4} c^{4} + b^{6} c^{4} + 2 \, a^{6} c^{2} d^{2} + 6 \, a^{4} b^{2} c^{2} d^{2} + 6 \, a^{2} b^{4} c^{2} d^{2} + 2 \, b^{6} c^{2} d^{2} + a^{6} d^{4} + 3 \, a^{4} b^{2} d^{4} + 3 \, a^{2} b^{4} d^{4} + b^{6} d^{4}} + \frac{2 \, {\left(3 \, a^{2} b^{6} c^{2} - b^{8} c^{2} - 10 \, a^{3} b^{5} c d - 2 \, a b^{7} c d + 10 \, a^{4} b^{4} d^{2} + 9 \, a^{2} b^{6} d^{2} + 3 \, b^{8} d^{2}\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{6} b^{5} c^{4} + 3 \, a^{4} b^{7} c^{4} + 3 \, a^{2} b^{9} c^{4} + b^{11} c^{4} - 4 \, a^{7} b^{4} c^{3} d - 12 \, a^{5} b^{6} c^{3} d - 12 \, a^{3} b^{8} c^{3} d - 4 \, a b^{10} c^{3} d + 6 \, a^{8} b^{3} c^{2} d^{2} + 18 \, a^{6} b^{5} c^{2} d^{2} + 18 \, a^{4} b^{7} c^{2} d^{2} + 6 \, a^{2} b^{9} c^{2} d^{2} - 4 \, a^{9} b^{2} c d^{3} - 12 \, a^{7} b^{4} c d^{3} - 12 \, a^{5} b^{6} c d^{3} - 4 \, a^{3} b^{8} c d^{3} + a^{10} b d^{4} + 3 \, a^{8} b^{3} d^{4} + 3 \, a^{6} b^{5} d^{4} + a^{4} b^{7} d^{4}} - \frac{2 \, {\left(5 \, b c^{2} d^{5} - 2 \, a c d^{6} + 3 \, b d^{7}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{4} c^{8} d - 4 \, a b^{3} c^{7} d^{2} + 6 \, a^{2} b^{2} c^{6} d^{3} + 2 \, b^{4} c^{6} d^{3} - 4 \, a^{3} b c^{5} d^{4} - 8 \, a b^{3} c^{5} d^{4} + a^{4} c^{4} d^{5} + 12 \, a^{2} b^{2} c^{4} d^{5} + b^{4} c^{4} d^{5} - 8 \, a^{3} b c^{3} d^{6} - 4 \, a b^{3} c^{3} d^{6} + 2 \, a^{4} c^{2} d^{7} + 6 \, a^{2} b^{2} c^{2} d^{7} - 4 \, a^{3} b c d^{8} + a^{4} d^{9}} + \frac{2 \, {\left(5 \, b c^{2} d^{5} \tan\left(f x + e\right) - 2 \, a c d^{6} \tan\left(f x + e\right) + 3 \, b d^{7} \tan\left(f x + e\right) + 6 \, b c^{3} d^{4} - 3 \, a c^{2} d^{5} + 4 \, b c d^{6} - a d^{7}\right)}}{{\left(b^{4} c^{8} - 4 \, a b^{3} c^{7} d + 6 \, a^{2} b^{2} c^{6} d^{2} + 2 \, b^{4} c^{6} d^{2} - 4 \, a^{3} b c^{5} d^{3} - 8 \, a b^{3} c^{5} d^{3} + a^{4} c^{4} d^{4} + 12 \, a^{2} b^{2} c^{4} d^{4} + b^{4} c^{4} d^{4} - 8 \, a^{3} b c^{3} d^{5} - 4 \, a b^{3} c^{3} d^{5} + 2 \, a^{4} c^{2} d^{6} + 6 \, a^{2} b^{2} c^{2} d^{6} - 4 \, a^{3} b c d^{7} + a^{4} d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}} - \frac{9 \, a^{2} b^{7} c^{2} \tan\left(f x + e\right)^{2} - 3 \, b^{9} c^{2} \tan\left(f x + e\right)^{2} - 30 \, a^{3} b^{6} c d \tan\left(f x + e\right)^{2} - 6 \, a b^{8} c d \tan\left(f x + e\right)^{2} + 30 \, a^{4} b^{5} d^{2} \tan\left(f x + e\right)^{2} + 27 \, a^{2} b^{7} d^{2} \tan\left(f x + e\right)^{2} + 9 \, b^{9} d^{2} \tan\left(f x + e\right)^{2} + 22 \, a^{3} b^{6} c^{2} \tan\left(f x + e\right) - 2 \, a b^{8} c^{2} \tan\left(f x + e\right) - 72 \, a^{4} b^{5} c d \tan\left(f x + e\right) - 28 \, a^{2} b^{7} c d \tan\left(f x + e\right) - 4 \, b^{9} c d \tan\left(f x + e\right) + 68 \, a^{5} b^{4} d^{2} \tan\left(f x + e\right) + 66 \, a^{3} b^{6} d^{2} \tan\left(f x + e\right) + 22 \, a b^{8} d^{2} \tan\left(f x + e\right) + 14 \, a^{4} b^{5} c^{2} + 3 \, a^{2} b^{7} c^{2} + b^{9} c^{2} - 44 \, a^{5} b^{4} c d - 26 \, a^{3} b^{6} c d - 6 \, a b^{8} c d + 39 \, a^{6} b^{3} d^{2} + 41 \, a^{4} b^{5} d^{2} + 14 \, a^{2} b^{7} d^{2}}{{\left(a^{6} b^{4} c^{4} + 3 \, a^{4} b^{6} c^{4} + 3 \, a^{2} b^{8} c^{4} + b^{10} c^{4} - 4 \, a^{7} b^{3} c^{3} d - 12 \, a^{5} b^{5} c^{3} d - 12 \, a^{3} b^{7} c^{3} d - 4 \, a b^{9} c^{3} d + 6 \, a^{8} b^{2} c^{2} d^{2} + 18 \, a^{6} b^{4} c^{2} d^{2} + 18 \, a^{4} b^{6} c^{2} d^{2} + 6 \, a^{2} b^{8} c^{2} d^{2} - 4 \, a^{9} b c d^{3} - 12 \, a^{7} b^{3} c d^{3} - 12 \, a^{5} b^{5} c d^{3} - 4 \, a^{3} b^{7} c d^{3} + a^{10} d^{4} + 3 \, a^{8} b^{2} d^{4} + 3 \, a^{6} b^{4} d^{4} + a^{4} b^{6} d^{4}\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^3*c^2 - 3*a*b^2*c^2 - 6*a^2*b*c*d + 2*b^3*c*d - a^3*d^2 + 3*a*b^2*d^2)*(f*x + e)/(a^6*c^4 + 3*a^4*b^2*c^4 + 3*a^2*b^4*c^4 + b^6*c^4 + 2*a^6*c^2*d^2 + 6*a^4*b^2*c^2*d^2 + 6*a^2*b^4*c^2*d^2 + 2*b^6*c^2*d^2 + a^6*d^4 + 3*a^4*b^2*d^4 + 3*a^2*b^4*d^4 + b^6*d^4) - (3*a^2*b*c^2 - b^3*c^2 + 2*a^3*c*d - 6*a*b^2*c*d - 3*a^2*b*d^2 + b^3*d^2)*log(tan(f*x + e)^2 + 1)/(a^6*c^4 + 3*a^4*b^2*c^4 + 3*a^2*b^4*c^4 + b^6*c^4 + 2*a^6*c^2*d^2 + 6*a^4*b^2*c^2*d^2 + 6*a^2*b^4*c^2*d^2 + 2*b^6*c^2*d^2 + a^6*d^4 + 3*a^4*b^2*d^4 + 3*a^2*b^4*d^4 + b^6*d^4) + 2*(3*a^2*b^6*c^2 - b^8*c^2 - 10*a^3*b^5*c*d - 2*a*b^7*c*d + 10*a^4*b^4*d^2 + 9*a^2*b^6*d^2 + 3*b^8*d^2)*log(abs(b*tan(f*x + e) + a))/(a^6*b^5*c^4 + 3*a^4*b^7*c^4 + 3*a^2*b^9*c^4 + b^11*c^4 - 4*a^7*b^4*c^3*d - 12*a^5*b^6*c^3*d - 12*a^3*b^8*c^3*d - 4*a*b^10*c^3*d + 6*a^8*b^3*c^2*d^2 + 18*a^6*b^5*c^2*d^2 + 18*a^4*b^7*c^2*d^2 + 6*a^2*b^9*c^2*d^2 - 4*a^9*b^2*c*d^3 - 12*a^7*b^4*c*d^3 - 12*a^5*b^6*c*d^3 - 4*a^3*b^8*c*d^3 + a^10*b*d^4 + 3*a^8*b^3*d^4 + 3*a^6*b^5*d^4 + a^4*b^7*d^4) - 2*(5*b*c^2*d^5 - 2*a*c*d^6 + 3*b*d^7)*log(abs(d*tan(f*x + e) + c))/(b^4*c^8*d - 4*a*b^3*c^7*d^2 + 6*a^2*b^2*c^6*d^3 + 2*b^4*c^6*d^3 - 4*a^3*b*c^5*d^4 - 8*a*b^3*c^5*d^4 + a^4*c^4*d^5 + 12*a^2*b^2*c^4*d^5 + b^4*c^4*d^5 - 8*a^3*b*c^3*d^6 - 4*a*b^3*c^3*d^6 + 2*a^4*c^2*d^7 + 6*a^2*b^2*c^2*d^7 - 4*a^3*b*c*d^8 + a^4*d^9) + 2*(5*b*c^2*d^5*tan(f*x + e) - 2*a*c*d^6*tan(f*x + e) + 3*b*d^7*tan(f*x + e) + 6*b*c^3*d^4 - 3*a*c^2*d^5 + 4*b*c*d^6 - a*d^7)/((b^4*c^8 - 4*a*b^3*c^7*d + 6*a^2*b^2*c^6*d^2 + 2*b^4*c^6*d^2 - 4*a^3*b*c^5*d^3 - 8*a*b^3*c^5*d^3 + a^4*c^4*d^4 + 12*a^2*b^2*c^4*d^4 + b^4*c^4*d^4 - 8*a^3*b*c^3*d^5 - 4*a*b^3*c^3*d^5 + 2*a^4*c^2*d^6 + 6*a^2*b^2*c^2*d^6 - 4*a^3*b*c*d^7 + a^4*d^8)*(d*tan(f*x + e) + c)) - (9*a^2*b^7*c^2*tan(f*x + e)^2 - 3*b^9*c^2*tan(f*x + e)^2 - 30*a^3*b^6*c*d*tan(f*x + e)^2 - 6*a*b^8*c*d*tan(f*x + e)^2 + 30*a^4*b^5*d^2*tan(f*x + e)^2 + 27*a^2*b^7*d^2*tan(f*x + e)^2 + 9*b^9*d^2*tan(f*x + e)^2 + 22*a^3*b^6*c^2*tan(f*x + e) - 2*a*b^8*c^2*tan(f*x + e) - 72*a^4*b^5*c*d*tan(f*x + e) - 28*a^2*b^7*c*d*tan(f*x + e) - 4*b^9*c*d*tan(f*x + e) + 68*a^5*b^4*d^2*tan(f*x + e) + 66*a^3*b^6*d^2*tan(f*x + e) + 22*a*b^8*d^2*tan(f*x + e) + 14*a^4*b^5*c^2 + 3*a^2*b^7*c^2 + b^9*c^2 - 44*a^5*b^4*c*d - 26*a^3*b^6*c*d - 6*a*b^8*c*d + 39*a^6*b^3*d^2 + 41*a^4*b^5*d^2 + 14*a^2*b^7*d^2)/((a^6*b^4*c^4 + 3*a^4*b^6*c^4 + 3*a^2*b^8*c^4 + b^10*c^4 - 4*a^7*b^3*c^3*d - 12*a^5*b^5*c^3*d - 12*a^3*b^7*c^3*d - 4*a*b^9*c^3*d + 6*a^8*b^2*c^2*d^2 + 18*a^6*b^4*c^2*d^2 + 18*a^4*b^6*c^2*d^2 + 6*a^2*b^8*c^2*d^2 - 4*a^9*b*c*d^3 - 12*a^7*b^3*c*d^3 - 12*a^5*b^5*c*d^3 - 4*a^3*b^7*c*d^3 + a^10*d^4 + 3*a^8*b^2*d^4 + 3*a^6*b^4*d^4 + a^4*b^6*d^4)*(b*tan(f*x + e) + a)^2))/f","B",0
1223,1,1066,0,4.681440," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{4} c^{3} - 6 \, a^{2} b^{2} c^{3} + b^{4} c^{3} + 12 \, a^{3} b c^{2} d - 12 \, a b^{3} c^{2} d - 3 \, a^{4} c d^{2} + 18 \, a^{2} b^{2} c d^{2} - 3 \, b^{4} c d^{2} - 4 \, a^{3} b d^{3} + 4 \, a b^{3} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(4 \, a^{3} b c^{3} - 4 \, a b^{3} c^{3} - 3 \, a^{4} c^{2} d + 18 \, a^{2} b^{2} c^{2} d - 3 \, b^{4} c^{2} d - 12 \, a^{3} b c d^{2} + 12 \, a b^{3} c d^{2} + a^{4} d^{3} - 6 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{2 \, {\left(b^{4} c^{6} + 3 \, b^{4} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + 4 \, a b^{3} c^{3} d^{3} + 3 \, a^{4} c^{2} d^{4} - 18 \, a^{2} b^{2} c^{2} d^{4} + 6 \, b^{4} c^{2} d^{4} + 12 \, a^{3} b c d^{5} - 12 \, a b^{3} c d^{5} - a^{4} d^{6} + 6 \, a^{2} b^{2} d^{6}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d^{3} + 3 \, c^{4} d^{5} + 3 \, c^{2} d^{7} + d^{9}} - \frac{3 \, b^{4} c^{6} d \tan\left(f x + e\right)^{2} + 9 \, b^{4} c^{4} d^{3} \tan\left(f x + e\right)^{2} - 12 \, a^{3} b c^{3} d^{4} \tan\left(f x + e\right)^{2} + 12 \, a b^{3} c^{3} d^{4} \tan\left(f x + e\right)^{2} + 9 \, a^{4} c^{2} d^{5} \tan\left(f x + e\right)^{2} - 54 \, a^{2} b^{2} c^{2} d^{5} \tan\left(f x + e\right)^{2} + 18 \, b^{4} c^{2} d^{5} \tan\left(f x + e\right)^{2} + 36 \, a^{3} b c d^{6} \tan\left(f x + e\right)^{2} - 36 \, a b^{3} c d^{6} \tan\left(f x + e\right)^{2} - 3 \, a^{4} d^{7} \tan\left(f x + e\right)^{2} + 18 \, a^{2} b^{2} d^{7} \tan\left(f x + e\right)^{2} + 2 \, b^{4} c^{7} \tan\left(f x + e\right) + 8 \, a b^{3} c^{6} d \tan\left(f x + e\right) + 6 \, b^{4} c^{5} d^{2} \tan\left(f x + e\right) - 32 \, a^{3} b c^{4} d^{3} \tan\left(f x + e\right) + 56 \, a b^{3} c^{4} d^{3} \tan\left(f x + e\right) + 22 \, a^{4} c^{3} d^{4} \tan\left(f x + e\right) - 132 \, a^{2} b^{2} c^{3} d^{4} \tan\left(f x + e\right) + 28 \, b^{4} c^{3} d^{4} \tan\left(f x + e\right) + 72 \, a^{3} b c^{2} d^{5} \tan\left(f x + e\right) - 48 \, a b^{3} c^{2} d^{5} \tan\left(f x + e\right) - 2 \, a^{4} c d^{6} \tan\left(f x + e\right) + 12 \, a^{2} b^{2} c d^{6} \tan\left(f x + e\right) + 8 \, a^{3} b d^{7} \tan\left(f x + e\right) + 4 \, a b^{3} c^{7} + 6 \, a^{2} b^{2} c^{6} d - b^{4} c^{6} d - 24 \, a^{3} b c^{5} d^{2} + 36 \, a b^{3} c^{5} d^{2} + 14 \, a^{4} c^{4} d^{3} - 66 \, a^{2} b^{2} c^{4} d^{3} + 11 \, b^{4} c^{4} d^{3} + 28 \, a^{3} b c^{3} d^{4} - 16 \, a b^{3} c^{3} d^{4} + 3 \, a^{4} c^{2} d^{5} + 4 \, a^{3} b c d^{6} + a^{4} d^{7}}{{\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^4*c^3 - 6*a^2*b^2*c^3 + b^4*c^3 + 12*a^3*b*c^2*d - 12*a*b^3*c^2*d - 3*a^4*c*d^2 + 18*a^2*b^2*c*d^2 - 3*b^4*c*d^2 - 4*a^3*b*d^3 + 4*a*b^3*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (4*a^3*b*c^3 - 4*a*b^3*c^3 - 3*a^4*c^2*d + 18*a^2*b^2*c^2*d - 3*b^4*c^2*d - 12*a^3*b*c*d^2 + 12*a*b^3*c*d^2 + a^4*d^3 - 6*a^2*b^2*d^3 + b^4*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + 2*(b^4*c^6 + 3*b^4*c^4*d^2 - 4*a^3*b*c^3*d^3 + 4*a*b^3*c^3*d^3 + 3*a^4*c^2*d^4 - 18*a^2*b^2*c^2*d^4 + 6*b^4*c^2*d^4 + 12*a^3*b*c*d^5 - 12*a*b^3*c*d^5 - a^4*d^6 + 6*a^2*b^2*d^6)*log(abs(d*tan(f*x + e) + c))/(c^6*d^3 + 3*c^4*d^5 + 3*c^2*d^7 + d^9) - (3*b^4*c^6*d*tan(f*x + e)^2 + 9*b^4*c^4*d^3*tan(f*x + e)^2 - 12*a^3*b*c^3*d^4*tan(f*x + e)^2 + 12*a*b^3*c^3*d^4*tan(f*x + e)^2 + 9*a^4*c^2*d^5*tan(f*x + e)^2 - 54*a^2*b^2*c^2*d^5*tan(f*x + e)^2 + 18*b^4*c^2*d^5*tan(f*x + e)^2 + 36*a^3*b*c*d^6*tan(f*x + e)^2 - 36*a*b^3*c*d^6*tan(f*x + e)^2 - 3*a^4*d^7*tan(f*x + e)^2 + 18*a^2*b^2*d^7*tan(f*x + e)^2 + 2*b^4*c^7*tan(f*x + e) + 8*a*b^3*c^6*d*tan(f*x + e) + 6*b^4*c^5*d^2*tan(f*x + e) - 32*a^3*b*c^4*d^3*tan(f*x + e) + 56*a*b^3*c^4*d^3*tan(f*x + e) + 22*a^4*c^3*d^4*tan(f*x + e) - 132*a^2*b^2*c^3*d^4*tan(f*x + e) + 28*b^4*c^3*d^4*tan(f*x + e) + 72*a^3*b*c^2*d^5*tan(f*x + e) - 48*a*b^3*c^2*d^5*tan(f*x + e) - 2*a^4*c*d^6*tan(f*x + e) + 12*a^2*b^2*c*d^6*tan(f*x + e) + 8*a^3*b*d^7*tan(f*x + e) + 4*a*b^3*c^7 + 6*a^2*b^2*c^6*d - b^4*c^6*d - 24*a^3*b*c^5*d^2 + 36*a*b^3*c^5*d^2 + 14*a^4*c^4*d^3 - 66*a^2*b^2*c^4*d^3 + 11*b^4*c^4*d^3 + 28*a^3*b*c^3*d^4 - 16*a*b^3*c^3*d^4 + 3*a^4*c^2*d^5 + 4*a^3*b*c*d^6 + a^4*d^7)/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*(d*tan(f*x + e) + c)^2))/f","B",0
1224,1,830,0,2.747009," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{3} c^{3} - 3 \, a b^{2} c^{3} + 9 \, a^{2} b c^{2} d - 3 \, b^{3} c^{2} d - 3 \, a^{3} c d^{2} + 9 \, a b^{2} c d^{2} - 3 \, a^{2} b d^{3} + b^{3} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(3 \, a^{2} b c^{3} - b^{3} c^{3} - 3 \, a^{3} c^{2} d + 9 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 3 \, b^{3} c d^{2} + a^{3} d^{3} - 3 \, a b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(3 \, a^{2} b c^{3} d - b^{3} c^{3} d - 3 \, a^{3} c^{2} d^{2} + 9 \, a b^{2} c^{2} d^{2} - 9 \, a^{2} b c d^{3} + 3 \, b^{3} c d^{3} + a^{3} d^{4} - 3 \, a b^{2} d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}} + \frac{9 \, a^{2} b c^{3} d^{4} \tan\left(f x + e\right)^{2} - 3 \, b^{3} c^{3} d^{4} \tan\left(f x + e\right)^{2} - 9 \, a^{3} c^{2} d^{5} \tan\left(f x + e\right)^{2} + 27 \, a b^{2} c^{2} d^{5} \tan\left(f x + e\right)^{2} - 27 \, a^{2} b c d^{6} \tan\left(f x + e\right)^{2} + 9 \, b^{3} c d^{6} \tan\left(f x + e\right)^{2} + 3 \, a^{3} d^{7} \tan\left(f x + e\right)^{2} - 9 \, a b^{2} d^{7} \tan\left(f x + e\right)^{2} - 2 \, b^{3} c^{6} d \tan\left(f x + e\right) + 24 \, a^{2} b c^{4} d^{3} \tan\left(f x + e\right) - 14 \, b^{3} c^{4} d^{3} \tan\left(f x + e\right) - 22 \, a^{3} c^{3} d^{4} \tan\left(f x + e\right) + 66 \, a b^{2} c^{3} d^{4} \tan\left(f x + e\right) - 54 \, a^{2} b c^{2} d^{5} \tan\left(f x + e\right) + 12 \, b^{3} c^{2} d^{5} \tan\left(f x + e\right) + 2 \, a^{3} c d^{6} \tan\left(f x + e\right) - 6 \, a b^{2} c d^{6} \tan\left(f x + e\right) - 6 \, a^{2} b d^{7} \tan\left(f x + e\right) - b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 18 \, a^{2} b c^{5} d^{2} - 9 \, b^{3} c^{5} d^{2} - 14 \, a^{3} c^{4} d^{3} + 33 \, a b^{2} c^{4} d^{3} - 21 \, a^{2} b c^{3} d^{4} + 4 \, b^{3} c^{3} d^{4} - 3 \, a^{3} c^{2} d^{5} - 3 \, a^{2} b c d^{6} - a^{3} d^{7}}{{\left(c^{6} d^{2} + 3 \, c^{4} d^{4} + 3 \, c^{2} d^{6} + d^{8}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^3*c^3 - 3*a*b^2*c^3 + 9*a^2*b*c^2*d - 3*b^3*c^2*d - 3*a^3*c*d^2 + 9*a*b^2*c*d^2 - 3*a^2*b*d^3 + b^3*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (3*a^2*b*c^3 - b^3*c^3 - 3*a^3*c^2*d + 9*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 3*b^3*c*d^2 + a^3*d^3 - 3*a*b^2*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(3*a^2*b*c^3*d - b^3*c^3*d - 3*a^3*c^2*d^2 + 9*a*b^2*c^2*d^2 - 9*a^2*b*c*d^3 + 3*b^3*c*d^3 + a^3*d^4 - 3*a*b^2*d^4)*log(abs(d*tan(f*x + e) + c))/(c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7) + (9*a^2*b*c^3*d^4*tan(f*x + e)^2 - 3*b^3*c^3*d^4*tan(f*x + e)^2 - 9*a^3*c^2*d^5*tan(f*x + e)^2 + 27*a*b^2*c^2*d^5*tan(f*x + e)^2 - 27*a^2*b*c*d^6*tan(f*x + e)^2 + 9*b^3*c*d^6*tan(f*x + e)^2 + 3*a^3*d^7*tan(f*x + e)^2 - 9*a*b^2*d^7*tan(f*x + e)^2 - 2*b^3*c^6*d*tan(f*x + e) + 24*a^2*b*c^4*d^3*tan(f*x + e) - 14*b^3*c^4*d^3*tan(f*x + e) - 22*a^3*c^3*d^4*tan(f*x + e) + 66*a*b^2*c^3*d^4*tan(f*x + e) - 54*a^2*b*c^2*d^5*tan(f*x + e) + 12*b^3*c^2*d^5*tan(f*x + e) + 2*a^3*c*d^6*tan(f*x + e) - 6*a*b^2*c*d^6*tan(f*x + e) - 6*a^2*b*d^7*tan(f*x + e) - b^3*c^7 - 3*a*b^2*c^6*d + 18*a^2*b*c^5*d^2 - 9*b^3*c^5*d^2 - 14*a^3*c^4*d^3 + 33*a*b^2*c^4*d^3 - 21*a^2*b*c^3*d^4 + 4*b^3*c^3*d^4 - 3*a^3*c^2*d^5 - 3*a^2*b*c*d^6 - a^3*d^7)/((c^6*d^2 + 3*c^4*d^4 + 3*c^2*d^6 + d^8)*(d*tan(f*x + e) + c)^2))/f","B",0
1225,1,614,0,2.151618," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{2} c^{3} - b^{2} c^{3} + 6 \, a b c^{2} d - 3 \, a^{2} c d^{2} + 3 \, b^{2} c d^{2} - 2 \, a b d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(2 \, a b c^{3} - 3 \, a^{2} c^{2} d + 3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + a^{2} d^{3} - b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(2 \, a b c^{3} d - 3 \, a^{2} c^{2} d^{2} + 3 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + a^{2} d^{4} - b^{2} d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}} + \frac{6 \, a b c^{3} d^{3} \tan\left(f x + e\right)^{2} - 9 \, a^{2} c^{2} d^{4} \tan\left(f x + e\right)^{2} + 9 \, b^{2} c^{2} d^{4} \tan\left(f x + e\right)^{2} - 18 \, a b c d^{5} \tan\left(f x + e\right)^{2} + 3 \, a^{2} d^{6} \tan\left(f x + e\right)^{2} - 3 \, b^{2} d^{6} \tan\left(f x + e\right)^{2} + 16 \, a b c^{4} d^{2} \tan\left(f x + e\right) - 22 \, a^{2} c^{3} d^{3} \tan\left(f x + e\right) + 22 \, b^{2} c^{3} d^{3} \tan\left(f x + e\right) - 36 \, a b c^{2} d^{4} \tan\left(f x + e\right) + 2 \, a^{2} c d^{5} \tan\left(f x + e\right) - 2 \, b^{2} c d^{5} \tan\left(f x + e\right) - 4 \, a b d^{6} \tan\left(f x + e\right) - b^{2} c^{6} + 12 \, a b c^{5} d - 14 \, a^{2} c^{4} d^{2} + 11 \, b^{2} c^{4} d^{2} - 14 \, a b c^{3} d^{3} - 3 \, a^{2} c^{2} d^{4} - 2 \, a b c d^{5} - a^{2} d^{6}}{{\left(c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^2*c^3 - b^2*c^3 + 6*a*b*c^2*d - 3*a^2*c*d^2 + 3*b^2*c*d^2 - 2*a*b*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (2*a*b*c^3 - 3*a^2*c^2*d + 3*b^2*c^2*d - 6*a*b*c*d^2 + a^2*d^3 - b^2*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(2*a*b*c^3*d - 3*a^2*c^2*d^2 + 3*b^2*c^2*d^2 - 6*a*b*c*d^3 + a^2*d^4 - b^2*d^4)*log(abs(d*tan(f*x + e) + c))/(c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7) + (6*a*b*c^3*d^3*tan(f*x + e)^2 - 9*a^2*c^2*d^4*tan(f*x + e)^2 + 9*b^2*c^2*d^4*tan(f*x + e)^2 - 18*a*b*c*d^5*tan(f*x + e)^2 + 3*a^2*d^6*tan(f*x + e)^2 - 3*b^2*d^6*tan(f*x + e)^2 + 16*a*b*c^4*d^2*tan(f*x + e) - 22*a^2*c^3*d^3*tan(f*x + e) + 22*b^2*c^3*d^3*tan(f*x + e) - 36*a*b*c^2*d^4*tan(f*x + e) + 2*a^2*c*d^5*tan(f*x + e) - 2*b^2*c*d^5*tan(f*x + e) - 4*a*b*d^6*tan(f*x + e) - b^2*c^6 + 12*a*b*c^5*d - 14*a^2*c^4*d^2 + 11*b^2*c^4*d^2 - 14*a*b*c^3*d^3 - 3*a^2*c^2*d^4 - 2*a*b*c*d^5 - a^2*d^6)/((c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7)*(d*tan(f*x + e) + c)^2))/f","B",0
1226,1,422,0,1.108051," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a c^{3} + 3 \, b c^{2} d - 3 \, a c d^{2} - b d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(b c^{3} - 3 \, a c^{2} d - 3 \, b c d^{2} + a d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(b c^{3} d - 3 \, a c^{2} d^{2} - 3 \, b c d^{3} + a d^{4}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{c^{6} d + 3 \, c^{4} d^{3} + 3 \, c^{2} d^{5} + d^{7}} + \frac{3 \, b c^{3} d^{2} \tan\left(f x + e\right)^{2} - 9 \, a c^{2} d^{3} \tan\left(f x + e\right)^{2} - 9 \, b c d^{4} \tan\left(f x + e\right)^{2} + 3 \, a d^{5} \tan\left(f x + e\right)^{2} + 8 \, b c^{4} d \tan\left(f x + e\right) - 22 \, a c^{3} d^{2} \tan\left(f x + e\right) - 18 \, b c^{2} d^{3} \tan\left(f x + e\right) + 2 \, a c d^{4} \tan\left(f x + e\right) - 2 \, b d^{5} \tan\left(f x + e\right) + 6 \, b c^{5} - 14 \, a c^{4} d - 7 \, b c^{3} d^{2} - 3 \, a c^{2} d^{3} - b c d^{4} - a d^{5}}{{\left(c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a*c^3 + 3*b*c^2*d - 3*a*c*d^2 - b*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (b*c^3 - 3*a*c^2*d - 3*b*c*d^2 + a*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(b*c^3*d - 3*a*c^2*d^2 - 3*b*c*d^3 + a*d^4)*log(abs(d*tan(f*x + e) + c))/(c^6*d + 3*c^4*d^3 + 3*c^2*d^5 + d^7) + (3*b*c^3*d^2*tan(f*x + e)^2 - 9*a*c^2*d^3*tan(f*x + e)^2 - 9*b*c*d^4*tan(f*x + e)^2 + 3*a*d^5*tan(f*x + e)^2 + 8*b*c^4*d*tan(f*x + e) - 22*a*c^3*d^2*tan(f*x + e) - 18*b*c^2*d^3*tan(f*x + e) + 2*a*c*d^4*tan(f*x + e) - 2*b*d^5*tan(f*x + e) + 6*b*c^5 - 14*a*c^4*d - 7*b*c^3*d^2 - 3*a*c^2*d^3 - b*c*d^4 - a*d^5)/((c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6)*(d*tan(f*x + e) + c)^2))/f","B",0
1227,1,1112,0,2.476410," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, b^{5} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{2} b^{4} c^{3} + b^{6} c^{3} - 3 \, a^{3} b^{3} c^{2} d - 3 \, a b^{5} c^{2} d + 3 \, a^{4} b^{2} c d^{2} + 3 \, a^{2} b^{4} c d^{2} - a^{5} b d^{3} - a^{3} b^{3} d^{3}} + \frac{2 \, {\left(a c^{3} - 3 \, b c^{2} d - 3 \, a c d^{2} + b d^{3}\right)} {\left(f x + e\right)}}{a^{2} c^{6} + b^{2} c^{6} + 3 \, a^{2} c^{4} d^{2} + 3 \, b^{2} c^{4} d^{2} + 3 \, a^{2} c^{2} d^{4} + 3 \, b^{2} c^{2} d^{4} + a^{2} d^{6} + b^{2} d^{6}} - \frac{{\left(b c^{3} + 3 \, a c^{2} d - 3 \, b c d^{2} - a d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{2} c^{6} + b^{2} c^{6} + 3 \, a^{2} c^{4} d^{2} + 3 \, b^{2} c^{4} d^{2} + 3 \, a^{2} c^{2} d^{4} + 3 \, b^{2} c^{2} d^{4} + a^{2} d^{6} + b^{2} d^{6}} - \frac{2 \, {\left(6 \, b^{2} c^{4} d^{3} - 8 \, a b c^{3} d^{4} + 3 \, a^{2} c^{2} d^{5} + 3 \, b^{2} c^{2} d^{5} - a^{2} d^{7} + b^{2} d^{7}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{3} c^{9} d - 3 \, a b^{2} c^{8} d^{2} + 3 \, a^{2} b c^{7} d^{3} + 3 \, b^{3} c^{7} d^{3} - a^{3} c^{6} d^{4} - 9 \, a b^{2} c^{6} d^{4} + 9 \, a^{2} b c^{5} d^{5} + 3 \, b^{3} c^{5} d^{5} - 3 \, a^{3} c^{4} d^{6} - 9 \, a b^{2} c^{4} d^{6} + 9 \, a^{2} b c^{3} d^{7} + b^{3} c^{3} d^{7} - 3 \, a^{3} c^{2} d^{8} - 3 \, a b^{2} c^{2} d^{8} + 3 \, a^{2} b c d^{9} - a^{3} d^{10}} + \frac{18 \, b^{2} c^{4} d^{4} \tan\left(f x + e\right)^{2} - 24 \, a b c^{3} d^{5} \tan\left(f x + e\right)^{2} + 9 \, a^{2} c^{2} d^{6} \tan\left(f x + e\right)^{2} + 9 \, b^{2} c^{2} d^{6} \tan\left(f x + e\right)^{2} - 3 \, a^{2} d^{8} \tan\left(f x + e\right)^{2} + 3 \, b^{2} d^{8} \tan\left(f x + e\right)^{2} + 42 \, b^{2} c^{5} d^{3} \tan\left(f x + e\right) - 58 \, a b c^{4} d^{4} \tan\left(f x + e\right) + 22 \, a^{2} c^{3} d^{5} \tan\left(f x + e\right) + 26 \, b^{2} c^{3} d^{5} \tan\left(f x + e\right) - 12 \, a b c^{2} d^{6} \tan\left(f x + e\right) - 2 \, a^{2} c d^{7} \tan\left(f x + e\right) + 8 \, b^{2} c d^{7} \tan\left(f x + e\right) - 2 \, a b d^{8} \tan\left(f x + e\right) + 25 \, b^{2} c^{6} d^{2} - 36 \, a b c^{5} d^{3} + 14 \, a^{2} c^{4} d^{4} + 19 \, b^{2} c^{4} d^{4} - 16 \, a b c^{3} d^{5} + 3 \, a^{2} c^{2} d^{6} + 6 \, b^{2} c^{2} d^{6} - 4 \, a b c d^{7} + a^{2} d^{8}}{{\left(b^{3} c^{9} - 3 \, a b^{2} c^{8} d + 3 \, a^{2} b c^{7} d^{2} + 3 \, b^{3} c^{7} d^{2} - a^{3} c^{6} d^{3} - 9 \, a b^{2} c^{6} d^{3} + 9 \, a^{2} b c^{5} d^{4} + 3 \, b^{3} c^{5} d^{4} - 3 \, a^{3} c^{4} d^{5} - 9 \, a b^{2} c^{4} d^{5} + 9 \, a^{2} b c^{3} d^{6} + b^{3} c^{3} d^{6} - 3 \, a^{3} c^{2} d^{7} - 3 \, a b^{2} c^{2} d^{7} + 3 \, a^{2} b c d^{8} - a^{3} d^{9}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*b^5*log(abs(b*tan(f*x + e) + a))/(a^2*b^4*c^3 + b^6*c^3 - 3*a^3*b^3*c^2*d - 3*a*b^5*c^2*d + 3*a^4*b^2*c*d^2 + 3*a^2*b^4*c*d^2 - a^5*b*d^3 - a^3*b^3*d^3) + 2*(a*c^3 - 3*b*c^2*d - 3*a*c*d^2 + b*d^3)*(f*x + e)/(a^2*c^6 + b^2*c^6 + 3*a^2*c^4*d^2 + 3*b^2*c^4*d^2 + 3*a^2*c^2*d^4 + 3*b^2*c^2*d^4 + a^2*d^6 + b^2*d^6) - (b*c^3 + 3*a*c^2*d - 3*b*c*d^2 - a*d^3)*log(tan(f*x + e)^2 + 1)/(a^2*c^6 + b^2*c^6 + 3*a^2*c^4*d^2 + 3*b^2*c^4*d^2 + 3*a^2*c^2*d^4 + 3*b^2*c^2*d^4 + a^2*d^6 + b^2*d^6) - 2*(6*b^2*c^4*d^3 - 8*a*b*c^3*d^4 + 3*a^2*c^2*d^5 + 3*b^2*c^2*d^5 - a^2*d^7 + b^2*d^7)*log(abs(d*tan(f*x + e) + c))/(b^3*c^9*d - 3*a*b^2*c^8*d^2 + 3*a^2*b*c^7*d^3 + 3*b^3*c^7*d^3 - a^3*c^6*d^4 - 9*a*b^2*c^6*d^4 + 9*a^2*b*c^5*d^5 + 3*b^3*c^5*d^5 - 3*a^3*c^4*d^6 - 9*a*b^2*c^4*d^6 + 9*a^2*b*c^3*d^7 + b^3*c^3*d^7 - 3*a^3*c^2*d^8 - 3*a*b^2*c^2*d^8 + 3*a^2*b*c*d^9 - a^3*d^10) + (18*b^2*c^4*d^4*tan(f*x + e)^2 - 24*a*b*c^3*d^5*tan(f*x + e)^2 + 9*a^2*c^2*d^6*tan(f*x + e)^2 + 9*b^2*c^2*d^6*tan(f*x + e)^2 - 3*a^2*d^8*tan(f*x + e)^2 + 3*b^2*d^8*tan(f*x + e)^2 + 42*b^2*c^5*d^3*tan(f*x + e) - 58*a*b*c^4*d^4*tan(f*x + e) + 22*a^2*c^3*d^5*tan(f*x + e) + 26*b^2*c^3*d^5*tan(f*x + e) - 12*a*b*c^2*d^6*tan(f*x + e) - 2*a^2*c*d^7*tan(f*x + e) + 8*b^2*c*d^7*tan(f*x + e) - 2*a*b*d^8*tan(f*x + e) + 25*b^2*c^6*d^2 - 36*a*b*c^5*d^3 + 14*a^2*c^4*d^4 + 19*b^2*c^4*d^4 - 16*a*b*c^3*d^5 + 3*a^2*c^2*d^6 + 6*b^2*c^2*d^6 - 4*a*b*c*d^7 + a^2*d^8)/((b^3*c^9 - 3*a*b^2*c^8*d + 3*a^2*b*c^7*d^2 + 3*b^3*c^7*d^2 - a^3*c^6*d^3 - 9*a*b^2*c^6*d^3 + 9*a^2*b*c^5*d^4 + 3*b^3*c^5*d^4 - 3*a^3*c^4*d^5 - 9*a*b^2*c^4*d^5 + 9*a^2*b*c^3*d^6 + b^3*c^3*d^6 - 3*a^3*c^2*d^7 - 3*a*b^2*c^2*d^7 + 3*a^2*b*c*d^8 - a^3*d^9)*(d*tan(f*x + e) + c)^2))/f","B",0
1228,1,1758,0,13.275719," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\frac{\frac{2 \, {\left(a^{2} c^{3} - b^{2} c^{3} - 6 \, a b c^{2} d - 3 \, a^{2} c d^{2} + 3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} {\left(f x + e\right)}}{a^{4} c^{6} + 2 \, a^{2} b^{2} c^{6} + b^{4} c^{6} + 3 \, a^{4} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{4} d^{2} + 3 \, b^{4} c^{4} d^{2} + 3 \, a^{4} c^{2} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{4} + 3 \, b^{4} c^{2} d^{4} + a^{4} d^{6} + 2 \, a^{2} b^{2} d^{6} + b^{4} d^{6}} - \frac{{\left(2 \, a b c^{3} + 3 \, a^{2} c^{2} d - 3 \, b^{2} c^{2} d - 6 \, a b c d^{2} - a^{2} d^{3} + b^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} c^{6} + 2 \, a^{2} b^{2} c^{6} + b^{4} c^{6} + 3 \, a^{4} c^{4} d^{2} + 6 \, a^{2} b^{2} c^{4} d^{2} + 3 \, b^{4} c^{4} d^{2} + 3 \, a^{4} c^{2} d^{4} + 6 \, a^{2} b^{2} c^{2} d^{4} + 3 \, b^{4} c^{2} d^{4} + a^{4} d^{6} + 2 \, a^{2} b^{2} d^{6} + b^{4} d^{6}} + \frac{2 \, {\left(2 \, a b^{6} c - 5 \, a^{2} b^{5} d - 3 \, b^{7} d\right)} \log\left({\left| b \tan\left(f x + e\right) + a \right|}\right)}{a^{4} b^{5} c^{4} + 2 \, a^{2} b^{7} c^{4} + b^{9} c^{4} - 4 \, a^{5} b^{4} c^{3} d - 8 \, a^{3} b^{6} c^{3} d - 4 \, a b^{8} c^{3} d + 6 \, a^{6} b^{3} c^{2} d^{2} + 12 \, a^{4} b^{5} c^{2} d^{2} + 6 \, a^{2} b^{7} c^{2} d^{2} - 4 \, a^{7} b^{2} c d^{3} - 8 \, a^{5} b^{4} c d^{3} - 4 \, a^{3} b^{6} c d^{3} + a^{8} b d^{4} + 2 \, a^{6} b^{3} d^{4} + a^{4} b^{5} d^{4}} + \frac{2 \, {\left(10 \, b^{2} c^{4} d^{4} - 10 \, a b c^{3} d^{5} + 3 \, a^{2} c^{2} d^{6} + 9 \, b^{2} c^{2} d^{6} - 2 \, a b c d^{7} - a^{2} d^{8} + 3 \, b^{2} d^{8}\right)} \log\left({\left| d \tan\left(f x + e\right) + c \right|}\right)}{b^{4} c^{10} d - 4 \, a b^{3} c^{9} d^{2} + 6 \, a^{2} b^{2} c^{8} d^{3} + 3 \, b^{4} c^{8} d^{3} - 4 \, a^{3} b c^{7} d^{4} - 12 \, a b^{3} c^{7} d^{4} + a^{4} c^{6} d^{5} + 18 \, a^{2} b^{2} c^{6} d^{5} + 3 \, b^{4} c^{6} d^{5} - 12 \, a^{3} b c^{5} d^{6} - 12 \, a b^{3} c^{5} d^{6} + 3 \, a^{4} c^{4} d^{7} + 18 \, a^{2} b^{2} c^{4} d^{7} + b^{4} c^{4} d^{7} - 12 \, a^{3} b c^{3} d^{8} - 4 \, a b^{3} c^{3} d^{8} + 3 \, a^{4} c^{2} d^{9} + 6 \, a^{2} b^{2} c^{2} d^{9} - 4 \, a^{3} b c d^{10} + a^{4} d^{11}} - \frac{2 \, {\left(2 \, a b^{6} c \tan\left(f x + e\right) - 5 \, a^{2} b^{5} d \tan\left(f x + e\right) - 3 \, b^{7} d \tan\left(f x + e\right) + 3 \, a^{2} b^{5} c + b^{7} c - 6 \, a^{3} b^{4} d - 4 \, a b^{6} d\right)}}{{\left(a^{4} b^{4} c^{4} + 2 \, a^{2} b^{6} c^{4} + b^{8} c^{4} - 4 \, a^{5} b^{3} c^{3} d - 8 \, a^{3} b^{5} c^{3} d - 4 \, a b^{7} c^{3} d + 6 \, a^{6} b^{2} c^{2} d^{2} + 12 \, a^{4} b^{4} c^{2} d^{2} + 6 \, a^{2} b^{6} c^{2} d^{2} - 4 \, a^{7} b c d^{3} - 8 \, a^{5} b^{3} c d^{3} - 4 \, a^{3} b^{5} c d^{3} + a^{8} d^{4} + 2 \, a^{6} b^{2} d^{4} + a^{4} b^{4} d^{4}\right)} {\left(b \tan\left(f x + e\right) + a\right)}} - \frac{30 \, b^{2} c^{4} d^{5} \tan\left(f x + e\right)^{2} - 30 \, a b c^{3} d^{6} \tan\left(f x + e\right)^{2} + 9 \, a^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} + 27 \, b^{2} c^{2} d^{7} \tan\left(f x + e\right)^{2} - 6 \, a b c d^{8} \tan\left(f x + e\right)^{2} - 3 \, a^{2} d^{9} \tan\left(f x + e\right)^{2} + 9 \, b^{2} d^{9} \tan\left(f x + e\right)^{2} + 68 \, b^{2} c^{5} d^{4} \tan\left(f x + e\right) - 72 \, a b c^{4} d^{5} \tan\left(f x + e\right) + 22 \, a^{2} c^{3} d^{6} \tan\left(f x + e\right) + 66 \, b^{2} c^{3} d^{6} \tan\left(f x + e\right) - 28 \, a b c^{2} d^{7} \tan\left(f x + e\right) - 2 \, a^{2} c d^{8} \tan\left(f x + e\right) + 22 \, b^{2} c d^{8} \tan\left(f x + e\right) - 4 \, a b d^{9} \tan\left(f x + e\right) + 39 \, b^{2} c^{6} d^{3} - 44 \, a b c^{5} d^{4} + 14 \, a^{2} c^{4} d^{5} + 41 \, b^{2} c^{4} d^{5} - 26 \, a b c^{3} d^{6} + 3 \, a^{2} c^{2} d^{7} + 14 \, b^{2} c^{2} d^{7} - 6 \, a b c d^{8} + a^{2} d^{9}}{{\left(b^{4} c^{10} - 4 \, a b^{3} c^{9} d + 6 \, a^{2} b^{2} c^{8} d^{2} + 3 \, b^{4} c^{8} d^{2} - 4 \, a^{3} b c^{7} d^{3} - 12 \, a b^{3} c^{7} d^{3} + a^{4} c^{6} d^{4} + 18 \, a^{2} b^{2} c^{6} d^{4} + 3 \, b^{4} c^{6} d^{4} - 12 \, a^{3} b c^{5} d^{5} - 12 \, a b^{3} c^{5} d^{5} + 3 \, a^{4} c^{4} d^{6} + 18 \, a^{2} b^{2} c^{4} d^{6} + b^{4} c^{4} d^{6} - 12 \, a^{3} b c^{3} d^{7} - 4 \, a b^{3} c^{3} d^{7} + 3 \, a^{4} c^{2} d^{8} + 6 \, a^{2} b^{2} c^{2} d^{8} - 4 \, a^{3} b c d^{9} + a^{4} d^{10}\right)} {\left(d \tan\left(f x + e\right) + c\right)}^{2}}}{2 \, f}"," ",0,"1/2*(2*(a^2*c^3 - b^2*c^3 - 6*a*b*c^2*d - 3*a^2*c*d^2 + 3*b^2*c*d^2 + 2*a*b*d^3)*(f*x + e)/(a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 + 3*a^4*c^4*d^2 + 6*a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 + 3*b^4*c^2*d^4 + a^4*d^6 + 2*a^2*b^2*d^6 + b^4*d^6) - (2*a*b*c^3 + 3*a^2*c^2*d - 3*b^2*c^2*d - 6*a*b*c*d^2 - a^2*d^3 + b^2*d^3)*log(tan(f*x + e)^2 + 1)/(a^4*c^6 + 2*a^2*b^2*c^6 + b^4*c^6 + 3*a^4*c^4*d^2 + 6*a^2*b^2*c^4*d^2 + 3*b^4*c^4*d^2 + 3*a^4*c^2*d^4 + 6*a^2*b^2*c^2*d^4 + 3*b^4*c^2*d^4 + a^4*d^6 + 2*a^2*b^2*d^6 + b^4*d^6) + 2*(2*a*b^6*c - 5*a^2*b^5*d - 3*b^7*d)*log(abs(b*tan(f*x + e) + a))/(a^4*b^5*c^4 + 2*a^2*b^7*c^4 + b^9*c^4 - 4*a^5*b^4*c^3*d - 8*a^3*b^6*c^3*d - 4*a*b^8*c^3*d + 6*a^6*b^3*c^2*d^2 + 12*a^4*b^5*c^2*d^2 + 6*a^2*b^7*c^2*d^2 - 4*a^7*b^2*c*d^3 - 8*a^5*b^4*c*d^3 - 4*a^3*b^6*c*d^3 + a^8*b*d^4 + 2*a^6*b^3*d^4 + a^4*b^5*d^4) + 2*(10*b^2*c^4*d^4 - 10*a*b*c^3*d^5 + 3*a^2*c^2*d^6 + 9*b^2*c^2*d^6 - 2*a*b*c*d^7 - a^2*d^8 + 3*b^2*d^8)*log(abs(d*tan(f*x + e) + c))/(b^4*c^10*d - 4*a*b^3*c^9*d^2 + 6*a^2*b^2*c^8*d^3 + 3*b^4*c^8*d^3 - 4*a^3*b*c^7*d^4 - 12*a*b^3*c^7*d^4 + a^4*c^6*d^5 + 18*a^2*b^2*c^6*d^5 + 3*b^4*c^6*d^5 - 12*a^3*b*c^5*d^6 - 12*a*b^3*c^5*d^6 + 3*a^4*c^4*d^7 + 18*a^2*b^2*c^4*d^7 + b^4*c^4*d^7 - 12*a^3*b*c^3*d^8 - 4*a*b^3*c^3*d^8 + 3*a^4*c^2*d^9 + 6*a^2*b^2*c^2*d^9 - 4*a^3*b*c*d^10 + a^4*d^11) - 2*(2*a*b^6*c*tan(f*x + e) - 5*a^2*b^5*d*tan(f*x + e) - 3*b^7*d*tan(f*x + e) + 3*a^2*b^5*c + b^7*c - 6*a^3*b^4*d - 4*a*b^6*d)/((a^4*b^4*c^4 + 2*a^2*b^6*c^4 + b^8*c^4 - 4*a^5*b^3*c^3*d - 8*a^3*b^5*c^3*d - 4*a*b^7*c^3*d + 6*a^6*b^2*c^2*d^2 + 12*a^4*b^4*c^2*d^2 + 6*a^2*b^6*c^2*d^2 - 4*a^7*b*c*d^3 - 8*a^5*b^3*c*d^3 - 4*a^3*b^5*c*d^3 + a^8*d^4 + 2*a^6*b^2*d^4 + a^4*b^4*d^4)*(b*tan(f*x + e) + a)) - (30*b^2*c^4*d^5*tan(f*x + e)^2 - 30*a*b*c^3*d^6*tan(f*x + e)^2 + 9*a^2*c^2*d^7*tan(f*x + e)^2 + 27*b^2*c^2*d^7*tan(f*x + e)^2 - 6*a*b*c*d^8*tan(f*x + e)^2 - 3*a^2*d^9*tan(f*x + e)^2 + 9*b^2*d^9*tan(f*x + e)^2 + 68*b^2*c^5*d^4*tan(f*x + e) - 72*a*b*c^4*d^5*tan(f*x + e) + 22*a^2*c^3*d^6*tan(f*x + e) + 66*b^2*c^3*d^6*tan(f*x + e) - 28*a*b*c^2*d^7*tan(f*x + e) - 2*a^2*c*d^8*tan(f*x + e) + 22*b^2*c*d^8*tan(f*x + e) - 4*a*b*d^9*tan(f*x + e) + 39*b^2*c^6*d^3 - 44*a*b*c^5*d^4 + 14*a^2*c^4*d^5 + 41*b^2*c^4*d^5 - 26*a*b*c^3*d^6 + 3*a^2*c^2*d^7 + 14*b^2*c^2*d^7 - 6*a*b*c*d^8 + a^2*d^9)/((b^4*c^10 - 4*a*b^3*c^9*d + 6*a^2*b^2*c^8*d^2 + 3*b^4*c^8*d^2 - 4*a^3*b*c^7*d^3 - 12*a*b^3*c^7*d^3 + a^4*c^6*d^4 + 18*a^2*b^2*c^6*d^4 + 3*b^4*c^6*d^4 - 12*a^3*b*c^5*d^5 - 12*a*b^3*c^5*d^5 + 3*a^4*c^4*d^6 + 18*a^2*b^2*c^4*d^6 + b^4*c^4*d^6 - 12*a^3*b*c^3*d^7 - 4*a*b^3*c^3*d^7 + 3*a^4*c^2*d^8 + 6*a^2*b^2*c^2*d^8 - 4*a^3*b*c*d^9 + a^4*d^10)*(d*tan(f*x + e) + c)^2))/f","B",0
1229,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1232,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1234,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1235,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1237,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1238,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1240,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1241,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1242,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1243,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1244,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1245,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1246,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1248,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1250,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1251,-1,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1252,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^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/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)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)Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[32,-66]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[39,65]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[-23,-48]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[63,-67]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [70,22,42,56,-9]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [-13,46,24,49,-6]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [-70,8,63,-64,2]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [62,-37,-80,-23,65]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [-85,28,-44,-22,93]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [91,31,-21,88,76]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [-66,66,5,-23,79]Warning, choosing root of [1,0,0,0,%%%{-1,[0,0,2,0,0]%%%}+%%%{-1,[0,0,0,2,0]%%%}] at parameters values [-88,9,6,-69,-8]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[48,-92,30,41,55]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[63,82,97,51,90]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-64,-40,-89,-64,-67]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-78,63,-93,-25,61]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-92,-18,-23,24,16]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-12,0,62,-54,3]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 170.46Done","F(-2)",0
1253,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1254,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1256,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1257,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1258,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1259,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1260,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1261,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1262,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1263,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),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/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)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)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)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)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)Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[85,33]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[91,90]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[68,64]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[-35,-54]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[95,-97,71,-64,68]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[58,57,-75,97,-89]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[61,54,50,93,-89]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-39,-6,-32,-10,-30]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-71,31,-76,-11,-84]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-58,-64,-88,18,79]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 175.29Done","F(-2)",0
1264,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),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/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)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)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)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)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)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)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)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)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)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)Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[-37,23]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[54,-62]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[-25,95]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,f]=[-8,-16]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-68,14,4,-60,-34]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[10,-24,-7,-73,92]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[27,-6,82,83,53]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-6,44,-75,-96,91]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-25,-21,13,-13,56]Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [tan(f*x+exp(1))]=[-76,54,33,-8,2]sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueEvaluation time: 179.34Done","F(-2)",0
1265,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1266,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1267,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1268,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1269,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1270,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1271,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1273,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1274,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1275,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1276,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1277,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1278,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1279,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1280,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1281,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1282,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1283,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(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:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c,d]=[-49,-76,20,-39]Warning, choosing root of [1,0,%%%{-2,[2,0,2,0]%%%}+%%%{-2,[2,0,0,2]%%%}+%%%{4,[1,7,1,3]%%%}+%%%{-4,[0,8,0,4]%%%}+%%%{-2,[0,2,2,0]%%%}+%%%{-2,[0,2,0,2]%%%},%%%{-8,[2,7,2,3]%%%}+%%%{-8,[2,7,0,5]%%%}+%%%{-8,[0,9,2,3]%%%}+%%%{-8,[0,9,0,5]%%%},%%%{1,[4,0,4,0]%%%}+%%%{2,[4,0,2,2]%%%}+%%%{1,[4,0,0,4]%%%}+%%%{4,[3,7,3,3]%%%}+%%%{4,[3,7,1,5]%%%}+%%%{-4,[2,14,0,8]%%%}+%%%{-4,[2,8,2,4]%%%}+%%%{-4,[2,8,0,6]%%%}+%%%{2,[2,2,4,0]%%%}+%%%{4,[2,2,2,2]%%%}+%%%{2,[2,2,0,4]%%%}+%%%{-8,[1,15,1,7]%%%}+%%%{4,[1,9,3,3]%%%}+%%%{4,[1,9,1,5]%%%}+%%%{-4,[0,16,2,6]%%%}+%%%{-4,[0,10,2,4]%%%}+%%%{-4,[0,10,0,6]%%%}+%%%{1,[0,4,4,0]%%%}+%%%{2,[0,4,2,2]%%%}+%%%{1,[0,4,0,4]%%%}] at parameters values [-49,-86,-64,-30]Evaluation time: 93.4index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
1284,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(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:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c,d]=[-48,85,18,67]Warning, choosing root of [1,0,%%%{-2,[2,0,2,0]%%%}+%%%{-2,[2,0,0,2]%%%}+%%%{4,[1,7,1,3]%%%}+%%%{-4,[0,8,0,4]%%%}+%%%{-2,[0,2,2,0]%%%}+%%%{-2,[0,2,0,2]%%%},%%%{-8,[2,7,2,3]%%%}+%%%{-8,[2,7,0,5]%%%}+%%%{-8,[0,9,2,3]%%%}+%%%{-8,[0,9,0,5]%%%},%%%{1,[4,0,4,0]%%%}+%%%{2,[4,0,2,2]%%%}+%%%{1,[4,0,0,4]%%%}+%%%{4,[3,7,3,3]%%%}+%%%{4,[3,7,1,5]%%%}+%%%{-4,[2,14,0,8]%%%}+%%%{-4,[2,8,2,4]%%%}+%%%{-4,[2,8,0,6]%%%}+%%%{2,[2,2,4,0]%%%}+%%%{4,[2,2,2,2]%%%}+%%%{2,[2,2,0,4]%%%}+%%%{-8,[1,15,1,7]%%%}+%%%{4,[1,9,3,3]%%%}+%%%{4,[1,9,1,5]%%%}+%%%{-4,[0,16,2,6]%%%}+%%%{-4,[0,10,2,4]%%%}+%%%{-4,[0,10,0,6]%%%}+%%%{1,[0,4,4,0]%%%}+%%%{2,[0,4,2,2]%%%}+%%%{1,[0,4,0,4]%%%}] at parameters values [-49,-86,-64,-30]Evaluation time: 90.2index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
1285,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(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:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c,d]=[80,76,-76,-78]Evaluation time: 93.69index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
1286,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(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:Warning, need to choose a branch for the root of a polynomial with parameters. This might be wrong.The choice was done assuming [a,b,c,d]=[80,76,-76,-78]Evaluation time: 90.64index.cc index_m operator + Error: Bad Argument Value","F(-2)",0
1287,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1288,-1,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1289,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1290,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1291,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1292,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1293,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1294,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1295,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1296,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(9/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
1297,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1300,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1301,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1302,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1303,-1,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1304,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{m} {\left(d \tan\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m*(d*tan(f*x + e) + c)^n, x)","F",0
1305,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{3} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^3*(b*tan(f*x + e) + a)^m, x)","F",0
1306,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{2} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^2*(b*tan(f*x + e) + a)^m, x)","F",0
1307,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(d \tan\left(f x + e\right) + c\right)} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m, x)","F",0
1308,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m, x)","F",0
1309,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c), x)","F",0
1310,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^2, x)","F",0
1311,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x, algorithm=""giac"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^3, x)","F",0
1312,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^m,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1315,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1316,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""giac"")","\int \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*tan(f*x + e))^p*c)^n*(I*a*tan(f*x + e) + a)^m, x)","F",0
1318,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*((d*tan(f*x + e))^p*c)^n, x)","F",0
1319,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*((d*tan(f*x + e))^p*c)^n, x)","F",0
1320,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)*((d*tan(f*x + e))^p*c)^n, x)","F",0
1321,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}}{i \, a \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*tan(f*x + e))^p*c)^n/(I*a*tan(f*x + e) + a), x)","F",0
1322,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(((d*tan(f*x + e))^p*c)^n/(I*a*tan(f*x + e) + a)^2, x)","F",0
1323,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^m,x, algorithm=""giac"")","\int \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(((d*tan(f*x + e))^p*c)^n*(b*tan(f*x + e) + a)^m, x)","F",0
1324,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^3,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*((d*tan(f*x + e))^p*c)^n, x)","F",0
1325,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*((d*tan(f*x + e))^p*c)^n, x)","F",0
1326,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int {\left(b \tan\left(f x + e\right) + a\right)} \left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)*((d*tan(f*x + e))^p*c)^n, x)","F",0
1327,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e)),x, algorithm=""giac"")","\int \frac{\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}}{b \tan\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(((d*tan(f*x + e))^p*c)^n/(b*tan(f*x + e) + a), x)","F",0
1328,0,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+b*tan(f*x+e))^2,x, algorithm=""giac"")","\int \frac{\left(\left(d \tan\left(f x + e\right)\right)^{p} c\right)^{n}}{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(((d*tan(f*x + e))^p*c)^n/(b*tan(f*x + e) + a)^2, x)","F",0
