1,1,81,0,0.772404," ","integrate(tan(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-12 i \, a \tan\left(d x + c\right)^{5} - 15 \, a \tan\left(d x + c\right)^{4} + 20 i \, a \tan\left(d x + c\right)^{3} + 30 \, a \tan\left(d x + c\right)^{2} + 60 i \, {\left(d x + c\right)} a - 30 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 i \, a \tan\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(-12*I*a*tan(d*x + c)^5 - 15*a*tan(d*x + c)^4 + 20*I*a*tan(d*x + c)^3 + 30*a*tan(d*x + c)^2 + 60*I*(d*x + c)*a - 30*a*log(tan(d*x + c)^2 + 1) - 60*I*a*tan(d*x + c))/d","A",0
2,1,70,0,0.897161," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-3 i \, a \tan\left(d x + c\right)^{4} - 4 \, a \tan\left(d x + c\right)^{3} + 6 i \, a \tan\left(d x + c\right)^{2} - 12 \, {\left(d x + c\right)} a - 6 i \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(-3*I*a*tan(d*x + c)^4 - 4*a*tan(d*x + c)^3 + 6*I*a*tan(d*x + c)^2 - 12*(d*x + c)*a - 6*I*a*log(tan(d*x + c)^2 + 1) + 12*a*tan(d*x + c))/d","A",0
3,1,59,0,0.820787," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-2 i \, a \tan\left(d x + c\right)^{3} - 3 \, a \tan\left(d x + c\right)^{2} - 6 i \, {\left(d x + c\right)} a + 3 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 i \, a \tan\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(-2*I*a*tan(d*x + c)^3 - 3*a*tan(d*x + c)^2 - 6*I*(d*x + c)*a + 3*a*log(tan(d*x + c)^2 + 1) + 6*I*a*tan(d*x + c))/d","A",0
4,1,48,0,0.922041," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-i \, a \tan\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)} a + i \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(-I*a*tan(d*x + c)^2 + 2*(d*x + c)*a + I*a*log(tan(d*x + c)^2 + 1) - 2*a*tan(d*x + c))/d","A",0
5,1,37,0,0.813313," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 i \, {\left(d x + c\right)} a - a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 i \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*I*(d*x + c)*a - a*log(tan(d*x + c)^2 + 1) - 2*I*a*tan(d*x + c))/d","A",0
6,1,17,0,0.388497," ","integrate(a+I*a*tan(d*x+c),x, algorithm=""maxima"")","a x + \frac{i \, a \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a*x + I*a*log(sec(d*x + c))/d","A",0
7,1,37,0,0.580946," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-2 i \, {\left(d x + c\right)} a + a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, a \log\left(\tan\left(d x + c\right)\right)}{2 \, d}"," ",0,"-1/2*(-2*I*(d*x + c)*a + a*log(tan(d*x + c)^2 + 1) - 2*a*log(tan(d*x + c)))/d","B",0
8,1,49,0,0.542170," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} a + i \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 i \, a \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*a + I*a*log(tan(d*x + c)^2 + 1) - 2*I*a*log(tan(d*x + c)) + 2*a/tan(d*x + c))/d","A",0
9,1,58,0,0.739743," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 i \, {\left(d x + c\right)} a - a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, a \log\left(\tan\left(d x + c\right)\right) + \frac{2 i \, a \tan\left(d x + c\right) + a}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*I*(d*x + c)*a - a*log(tan(d*x + c)^2 + 1) + 2*a*log(tan(d*x + c)) + (2*I*a*tan(d*x + c) + a)/tan(d*x + c)^2)/d","A",0
10,1,71,0,0.417933," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a + 3 i \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 i \, a \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, a \tan\left(d x + c\right)^{2} - 3 i \, a \tan\left(d x + c\right) - 2 \, a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*a + 3*I*a*log(tan(d*x + c)^2 + 1) - 6*I*a*log(tan(d*x + c)) + (6*a*tan(d*x + c)^2 - 3*I*a*tan(d*x + c) - 2*a)/tan(d*x + c)^3)/d","A",0
11,1,83,0,0.609955," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-12 i \, {\left(d x + c\right)} a + 6 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 12 \, a \log\left(\tan\left(d x + c\right)\right) - \frac{12 i \, a \tan\left(d x + c\right)^{3} + 6 \, a \tan\left(d x + c\right)^{2} - 4 i \, a \tan\left(d x + c\right) - 3 \, a}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(-12*I*(d*x + c)*a + 6*a*log(tan(d*x + c)^2 + 1) - 12*a*log(tan(d*x + c)) - (12*I*a*tan(d*x + c)^3 + 6*a*tan(d*x + c)^2 - 4*I*a*tan(d*x + c) - 3*a)/tan(d*x + c)^4)/d","A",0
12,1,93,0,0.784531," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, {\left(d x + c\right)} a + 30 i \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 i \, a \log\left(\tan\left(d x + c\right)\right) + \frac{60 \, a \tan\left(d x + c\right)^{4} - 30 i \, a \tan\left(d x + c\right)^{3} - 20 \, a \tan\left(d x + c\right)^{2} + 15 i \, a \tan\left(d x + c\right) + 12 \, a}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)*a + 30*I*a*log(tan(d*x + c)^2 + 1) - 60*I*a*log(tan(d*x + c)) + (60*a*tan(d*x + c)^4 - 30*I*a*tan(d*x + c)^3 - 20*a*tan(d*x + c)^2 + 15*I*a*tan(d*x + c) + 12*a)/tan(d*x + c)^5)/d","A",0
13,1,95,0,0.810879," ","integrate(tan(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, a^{2} \tan\left(d x + c\right)^{5} - 15 i \, a^{2} \tan\left(d x + c\right)^{4} - 20 \, a^{2} \tan\left(d x + c\right)^{3} + 30 i \, a^{2} \tan\left(d x + c\right)^{2} - 60 \, {\left(d x + c\right)} a^{2} - 30 i \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, a^{2} \tan\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(6*a^2*tan(d*x + c)^5 - 15*I*a^2*tan(d*x + c)^4 - 20*a^2*tan(d*x + c)^3 + 30*I*a^2*tan(d*x + c)^2 - 60*(d*x + c)*a^2 - 30*I*a^2*log(tan(d*x + c)^2 + 1) + 60*a^2*tan(d*x + c))/d","A",0
14,1,82,0,0.580442," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} \tan\left(d x + c\right)^{4} - 8 i \, a^{2} \tan\left(d x + c\right)^{3} - 12 \, a^{2} \tan\left(d x + c\right)^{2} - 24 i \, {\left(d x + c\right)} a^{2} + 12 \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 24 i \, a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a^2*tan(d*x + c)^4 - 8*I*a^2*tan(d*x + c)^3 - 12*a^2*tan(d*x + c)^2 - 24*I*(d*x + c)*a^2 + 12*a^2*log(tan(d*x + c)^2 + 1) + 24*I*a^2*tan(d*x + c))/d","A",0
15,1,68,0,0.735438," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \tan\left(d x + c\right)^{3} - 3 i \, a^{2} \tan\left(d x + c\right)^{2} + 6 \, {\left(d x + c\right)} a^{2} + 3 i \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, a^{2} \tan\left(d x + c\right)}{3 \, d}"," ",0,"-1/3*(a^2*tan(d*x + c)^3 - 3*I*a^2*tan(d*x + c)^2 + 6*(d*x + c)*a^2 + 3*I*a^2*log(tan(d*x + c)^2 + 1) - 6*a^2*tan(d*x + c))/d","A",0
16,1,55,0,0.789152," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \tan\left(d x + c\right)^{2} + 4 i \, {\left(d x + c\right)} a^{2} - 2 \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 4 i \, a^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a^2*tan(d*x + c)^2 + 4*I*(d*x + c)*a^2 - 2*a^2*log(tan(d*x + c)^2 + 1) - 4*I*a^2*tan(d*x + c))/d","A",0
17,1,41,0,0.937511," ","integrate((a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x + \frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a^{2}}{d} + \frac{2 i \, a^{2} \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^2*x + (d*x + c - tan(d*x + c))*a^2/d + 2*I*a^2*log(sec(d*x + c))/d","A",0
18,1,42,0,0.530303," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 i \, {\left(d x + c\right)} a^{2} - a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + a^{2} \log\left(\tan\left(d x + c\right)\right)}{d}"," ",0,"(2*I*(d*x + c)*a^2 - a^2*log(tan(d*x + c)^2 + 1) + a^2*log(tan(d*x + c)))/d","A",0
19,1,56,0,0.457233," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} a^{2} + i \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 i \, a^{2} \log\left(\tan\left(d x + c\right)\right) + \frac{a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(2*(d*x + c)*a^2 + I*a^2*log(tan(d*x + c)^2 + 1) - 2*I*a^2*log(tan(d*x + c)) + a^2/tan(d*x + c))/d","A",0
20,1,68,0,0.813484," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 i \, {\left(d x + c\right)} a^{2} - 2 \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 4 \, a^{2} \log\left(\tan\left(d x + c\right)\right) + \frac{4 i \, a^{2} \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(4*I*(d*x + c)*a^2 - 2*a^2*log(tan(d*x + c)^2 + 1) + 4*a^2*log(tan(d*x + c)) + (4*I*a^2*tan(d*x + c) + a^2)/tan(d*x + c)^2)/d","A",0
21,1,83,0,0.885766," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a^{2} + 3 i \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 i \, a^{2} \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, a^{2} \tan\left(d x + c\right)^{2} - 3 i \, a^{2} \tan\left(d x + c\right) - a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(6*(d*x + c)*a^2 + 3*I*a^2*log(tan(d*x + c)^2 + 1) - 6*I*a^2*log(tan(d*x + c)) + (6*a^2*tan(d*x + c)^2 - 3*I*a^2*tan(d*x + c) - a^2)/tan(d*x + c)^3)/d","A",0
22,1,97,0,0.598646," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{-24 i \, {\left(d x + c\right)} a^{2} + 12 \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 24 \, a^{2} \log\left(\tan\left(d x + c\right)\right) - \frac{24 i \, a^{2} \tan\left(d x + c\right)^{3} + 12 \, a^{2} \tan\left(d x + c\right)^{2} - 8 i \, a^{2} \tan\left(d x + c\right) - 3 \, a^{2}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(-24*I*(d*x + c)*a^2 + 12*a^2*log(tan(d*x + c)^2 + 1) - 24*a^2*log(tan(d*x + c)) - (24*I*a^2*tan(d*x + c)^3 + 12*a^2*tan(d*x + c)^2 - 8*I*a^2*tan(d*x + c) - 3*a^2)/tan(d*x + c)^4)/d","A",0
23,1,109,0,0.753275," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{60 \, {\left(d x + c\right)} a^{2} + 30 i \, a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 i \, a^{2} \log\left(\tan\left(d x + c\right)\right) + \frac{60 \, a^{2} \tan\left(d x + c\right)^{4} - 30 i \, a^{2} \tan\left(d x + c\right)^{3} - 20 \, a^{2} \tan\left(d x + c\right)^{2} + 15 i \, a^{2} \tan\left(d x + c\right) + 6 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"-1/30*(60*(d*x + c)*a^2 + 30*I*a^2*log(tan(d*x + c)^2 + 1) - 60*I*a^2*log(tan(d*x + c)) + (60*a^2*tan(d*x + c)^4 - 30*I*a^2*tan(d*x + c)^3 - 20*a^2*tan(d*x + c)^2 + 15*I*a^2*tan(d*x + c) + 6*a^2)/tan(d*x + c)^5)/d","A",0
24,1,95,0,0.582250," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{12 i \, a^{3} \tan\left(d x + c\right)^{5} + 45 \, a^{3} \tan\left(d x + c\right)^{4} - 80 i \, a^{3} \tan\left(d x + c\right)^{3} - 120 \, a^{3} \tan\left(d x + c\right)^{2} - 240 i \, {\left(d x + c\right)} a^{3} + 120 \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 240 i \, a^{3} \tan\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*I*a^3*tan(d*x + c)^5 + 45*a^3*tan(d*x + c)^4 - 80*I*a^3*tan(d*x + c)^3 - 120*a^3*tan(d*x + c)^2 - 240*I*(d*x + c)*a^3 + 120*a^3*log(tan(d*x + c)^2 + 1) + 240*I*a^3*tan(d*x + c))/d","A",0
25,1,82,0,0.782126," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{i \, a^{3} \tan\left(d x + c\right)^{4} + 4 \, a^{3} \tan\left(d x + c\right)^{3} - 8 i \, a^{3} \tan\left(d x + c\right)^{2} + 16 \, {\left(d x + c\right)} a^{3} + 8 i \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 16 \, a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*(I*a^3*tan(d*x + c)^4 + 4*a^3*tan(d*x + c)^3 - 8*I*a^3*tan(d*x + c)^2 + 16*(d*x + c)*a^3 + 8*I*a^3*log(tan(d*x + c)^2 + 1) - 16*a^3*tan(d*x + c))/d","A",0
26,1,69,0,0.582490," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 i \, a^{3} \tan\left(d x + c\right)^{3} + 9 \, a^{3} \tan\left(d x + c\right)^{2} + 24 i \, {\left(d x + c\right)} a^{3} - 12 \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 24 i \, a^{3} \tan\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*I*a^3*tan(d*x + c)^3 + 9*a^3*tan(d*x + c)^2 + 24*I*(d*x + c)*a^3 - 12*a^3*log(tan(d*x + c)^2 + 1) - 24*I*a^3*tan(d*x + c))/d","A",0
27,1,76,0,0.705512," ","integrate((a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x + \frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3}}{d} + \frac{i \, a^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{2 \, d} + \frac{3 i \, a^{3} \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^3*x + 3*(d*x + c - tan(d*x + c))*a^3/d + 1/2*I*a^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 3*I*a^3*log(sec(d*x + c))/d","A",0
28,1,53,0,0.642264," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 i \, {\left(d x + c\right)} a^{3} - 2 \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + a^{3} \log\left(\tan\left(d x + c\right)\right) - i \, a^{3} \tan\left(d x + c\right)}{d}"," ",0,"(4*I*(d*x + c)*a^3 - 2*a^3*log(tan(d*x + c)^2 + 1) + a^3*log(tan(d*x + c)) - I*a^3*tan(d*x + c))/d","A",0
29,1,56,0,0.672096," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c\right)} a^{3} + 2 i \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 3 i \, a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{a^{3}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(4*(d*x + c)*a^3 + 2*I*a^3*log(tan(d*x + c)^2 + 1) - 3*I*a^3*log(tan(d*x + c)) + a^3/tan(d*x + c))/d","A",0
30,1,68,0,0.560199," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{8 i \, {\left(d x + c\right)} a^{3} - 4 \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 8 \, a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{6 i \, a^{3} \tan\left(d x + c\right) + a^{3}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(8*I*(d*x + c)*a^3 - 4*a^3*log(tan(d*x + c)^2 + 1) + 8*a^3*log(tan(d*x + c)) + (6*I*a^3*tan(d*x + c) + a^3)/tan(d*x + c)^2)/d","A",0
31,1,83,0,0.512952," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{24 \, {\left(d x + c\right)} a^{3} + 12 i \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 24 i \, a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{24 \, a^{3} \tan\left(d x + c\right)^{2} - 9 i \, a^{3} \tan\left(d x + c\right) - 2 \, a^{3}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(24*(d*x + c)*a^3 + 12*I*a^3*log(tan(d*x + c)^2 + 1) - 24*I*a^3*log(tan(d*x + c)) + (24*a^3*tan(d*x + c)^2 - 9*I*a^3*tan(d*x + c) - 2*a^3)/tan(d*x + c)^3)/d","A",0
32,1,94,0,0.552021," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{-16 i \, {\left(d x + c\right)} a^{3} + 8 \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 16 \, a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{-16 i \, a^{3} \tan\left(d x + c\right)^{3} - 8 \, a^{3} \tan\left(d x + c\right)^{2} + 4 i \, a^{3} \tan\left(d x + c\right) + a^{3}}{\tan\left(d x + c\right)^{4}}}{4 \, d}"," ",0,"-1/4*(-16*I*(d*x + c)*a^3 + 8*a^3*log(tan(d*x + c)^2 + 1) - 16*a^3*log(tan(d*x + c)) + (-16*I*a^3*tan(d*x + c)^3 - 8*a^3*tan(d*x + c)^2 + 4*I*a^3*tan(d*x + c) + a^3)/tan(d*x + c)^4)/d","A",0
33,1,109,0,0.526115," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{240 \, {\left(d x + c\right)} a^{3} + 120 i \, a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 240 i \, a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{240 \, a^{3} \tan\left(d x + c\right)^{4} - 120 i \, a^{3} \tan\left(d x + c\right)^{3} - 80 \, a^{3} \tan\left(d x + c\right)^{2} + 45 i \, a^{3} \tan\left(d x + c\right) + 12 \, a^{3}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(240*(d*x + c)*a^3 + 120*I*a^3*log(tan(d*x + c)^2 + 1) - 240*I*a^3*log(tan(d*x + c)) + (240*a^3*tan(d*x + c)^4 - 120*I*a^3*tan(d*x + c)^3 - 80*a^3*tan(d*x + c)^2 + 45*I*a^3*tan(d*x + c) + 12*a^3)/tan(d*x + c)^5)/d","A",0
34,1,108,0,0.649528," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{10 \, a^{4} \tan\left(d x + c\right)^{6} - 48 i \, a^{4} \tan\left(d x + c\right)^{5} - 105 \, a^{4} \tan\left(d x + c\right)^{4} + 160 i \, a^{4} \tan\left(d x + c\right)^{3} + 240 \, a^{4} \tan\left(d x + c\right)^{2} + 480 i \, {\left(d x + c\right)} a^{4} - 240 \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 480 i \, a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*a^4*tan(d*x + c)^6 - 48*I*a^4*tan(d*x + c)^5 - 105*a^4*tan(d*x + c)^4 + 160*I*a^4*tan(d*x + c)^3 + 240*a^4*tan(d*x + c)^2 + 480*I*(d*x + c)*a^4 - 240*a^4*log(tan(d*x + c)^2 + 1) - 480*I*a^4*tan(d*x + c))/d","A",0
35,1,95,0,0.750082," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} \tan\left(d x + c\right)^{5} - 15 i \, a^{4} \tan\left(d x + c\right)^{4} - 35 \, a^{4} \tan\left(d x + c\right)^{3} + 60 i \, a^{4} \tan\left(d x + c\right)^{2} - 120 \, {\left(d x + c\right)} a^{4} - 60 i \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 120 \, a^{4} \tan\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*a^4*tan(d*x + c)^5 - 15*I*a^4*tan(d*x + c)^4 - 35*a^4*tan(d*x + c)^3 + 60*I*a^4*tan(d*x + c)^2 - 120*(d*x + c)*a^4 - 60*I*a^4*log(tan(d*x + c)^2 + 1) + 120*a^4*tan(d*x + c))/d","A",0
36,1,82,0,0.687625," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} \tan\left(d x + c\right)^{4} - 16 i \, a^{4} \tan\left(d x + c\right)^{3} - 42 \, a^{4} \tan\left(d x + c\right)^{2} - 96 i \, {\left(d x + c\right)} a^{4} + 48 \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 96 i \, a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a^4*tan(d*x + c)^4 - 16*I*a^4*tan(d*x + c)^3 - 42*a^4*tan(d*x + c)^2 - 96*I*(d*x + c)*a^4 + 48*a^4*log(tan(d*x + c)^2 + 1) + 96*I*a^4*tan(d*x + c))/d","A",0
37,1,108,0,0.747644," ","integrate((a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{4}}{3 \, d} + \frac{6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{4}}{d} + \frac{2 i \, a^{4} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{d} + \frac{4 i \, a^{4} \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^4*x + 1/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^4/d + 6*(d*x + c - tan(d*x + c))*a^4/d + 2*I*a^4*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 4*I*a^4*log(sec(d*x + c))/d","A",0
38,1,67,0,0.516644," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{a^{4} \tan\left(d x + c\right)^{2} + 16 i \, {\left(d x + c\right)} a^{4} - 8 \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, a^{4} \log\left(\tan\left(d x + c\right)\right) - 8 i \, a^{4} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a^4*tan(d*x + c)^2 + 16*I*(d*x + c)*a^4 - 8*a^4*log(tan(d*x + c)^2 + 1) + 2*a^4*log(tan(d*x + c)) - 8*I*a^4*tan(d*x + c))/d","A",0
39,1,67,0,0.723964," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{8 \, {\left(d x + c\right)} a^{4} + 4 i \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 4 i \, a^{4} \log\left(\tan\left(d x + c\right)\right) - a^{4} \tan\left(d x + c\right) + \frac{a^{4}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(8*(d*x + c)*a^4 + 4*I*a^4*log(tan(d*x + c)^2 + 1) - 4*I*a^4*log(tan(d*x + c)) - a^4*tan(d*x + c) + a^4/tan(d*x + c))/d","A",0
40,1,68,0,0.512972," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{16 i \, {\left(d x + c\right)} a^{4} - 8 \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 14 \, a^{4} \log\left(\tan\left(d x + c\right)\right) + \frac{8 i \, a^{4} \tan\left(d x + c\right) + a^{4}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(16*I*(d*x + c)*a^4 - 8*a^4*log(tan(d*x + c)^2 + 1) + 14*a^4*log(tan(d*x + c)) + (8*I*a^4*tan(d*x + c) + a^4)/tan(d*x + c)^2)/d","A",0
41,1,83,0,0.503861," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{24 \, {\left(d x + c\right)} a^{4} + 12 i \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 24 i \, a^{4} \log\left(\tan\left(d x + c\right)\right) + \frac{21 \, a^{4} \tan\left(d x + c\right)^{2} - 6 i \, a^{4} \tan\left(d x + c\right) - a^{4}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(24*(d*x + c)*a^4 + 12*I*a^4*log(tan(d*x + c)^2 + 1) - 24*I*a^4*log(tan(d*x + c)) + (21*a^4*tan(d*x + c)^2 - 6*I*a^4*tan(d*x + c) - a^4)/tan(d*x + c)^3)/d","A",0
42,1,96,0,0.654980," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{-96 i \, {\left(d x + c\right)} a^{4} + 48 \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 96 \, a^{4} \log\left(\tan\left(d x + c\right)\right) + \frac{-96 i \, a^{4} \tan\left(d x + c\right)^{3} - 42 \, a^{4} \tan\left(d x + c\right)^{2} + 16 i \, a^{4} \tan\left(d x + c\right) + 3 \, a^{4}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(-96*I*(d*x + c)*a^4 + 48*a^4*log(tan(d*x + c)^2 + 1) - 96*a^4*log(tan(d*x + c)) + (-96*I*a^4*tan(d*x + c)^3 - 42*a^4*tan(d*x + c)^2 + 16*I*a^4*tan(d*x + c) + 3*a^4)/tan(d*x + c)^4)/d","A",0
43,1,109,0,0.805359," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{120 \, {\left(d x + c\right)} a^{4} + 60 i \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 120 i \, a^{4} \log\left(\tan\left(d x + c\right)\right) + \frac{120 \, a^{4} \tan\left(d x + c\right)^{4} - 60 i \, a^{4} \tan\left(d x + c\right)^{3} - 35 \, a^{4} \tan\left(d x + c\right)^{2} + 15 i \, a^{4} \tan\left(d x + c\right) + 3 \, a^{4}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(120*(d*x + c)*a^4 + 60*I*a^4*log(tan(d*x + c)^2 + 1) - 120*I*a^4*log(tan(d*x + c)) + (120*a^4*tan(d*x + c)^4 - 60*I*a^4*tan(d*x + c)^3 - 35*a^4*tan(d*x + c)^2 + 15*I*a^4*tan(d*x + c) + 3*a^4)/tan(d*x + c)^5)/d","A",0
44,1,123,0,0.859331," ","integrate(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{480 i \, {\left(d x + c\right)} a^{4} - 240 \, a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 480 \, a^{4} \log\left(\tan\left(d x + c\right)\right) - \frac{-480 i \, a^{4} \tan\left(d x + c\right)^{5} - 240 \, a^{4} \tan\left(d x + c\right)^{4} + 160 i \, a^{4} \tan\left(d x + c\right)^{3} + 105 \, a^{4} \tan\left(d x + c\right)^{2} - 48 i \, a^{4} \tan\left(d x + c\right) - 10 \, a^{4}}{\tan\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(480*I*(d*x + c)*a^4 - 240*a^4*log(tan(d*x + c)^2 + 1) + 480*a^4*log(tan(d*x + c)) - (-480*I*a^4*tan(d*x + c)^5 - 240*a^4*tan(d*x + c)^4 + 160*I*a^4*tan(d*x + c)^3 + 105*a^4*tan(d*x + c)^2 - 48*I*a^4*tan(d*x + c) - 10*a^4)/tan(d*x + c)^6)/d","A",0
45,-2,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
46,-2,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
47,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
48,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
49,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
50,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
51,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
52,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
53,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
54,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
55,-2,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
56,-2,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
57,-2,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
58,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
59,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
60,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
61,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
62,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
63,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
64,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
65,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
66,-2,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
67,-2,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
68,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
69,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
70,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
71,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
72,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
73,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
74,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
75,-2,0,0,0.000000," ","integrate(tan(d*x+c)^6/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
76,-2,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
77,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
78,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
79,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
80,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
81,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
82,-2,0,0,0.000000," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
83,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
84,1,120,0,0.526415," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""maxima"")","\frac{i \, {\left(105 \, \sqrt{2} a^{\frac{11}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 60 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 168 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3} + 280 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4}\right)}}{210 \, a^{5} d}"," ",0,"1/210*I*(105*sqrt(2)*a^(11/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 60*(I*a*tan(d*x + c) + a)^(7/2)*a^2 - 168*(I*a*tan(d*x + c) + a)^(5/2)*a^3 + 280*(I*a*tan(d*x + c) + a)^(3/2)*a^4)/(a^5*d)","A",0
85,1,120,0,0.910311," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 20 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 60 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}}{30 \, a^{4} d}"," ",0,"-1/30*(15*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 12*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 20*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 60*sqrt(I*a*tan(d*x + c) + a)*a^4)/(a^4*d)","A",0
86,1,84,0,0.617776," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""maxima"")","-\frac{i \, {\left(3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2}\right)}}{6 \, a^{3} d}"," ",0,"-1/6*I*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(I*a*tan(d*x + c) + a)^(3/2)*a^2)/(a^3*d)","A",0
87,1,83,0,0.853483," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""maxima"")","\frac{\sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 4 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}}{2 \, a^{2} d}"," ",0,"1/2*(sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*sqrt(I*a*tan(d*x + c) + a)*a^2)/(a^2*d)","A",0
88,1,60,0,0.451598," ","integrate((a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{2 \, d}"," ",0,"1/2*I*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/d","A",0
89,1,107,0,0.587594," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - 2 \, \sqrt{a} \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{2 \, d}"," ",0,"-1/2*(sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 2*sqrt(a)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))))/d","A",0
90,1,134,0,0.603791," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{\sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} - \frac{\log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{2 i \, \sqrt{i \, a \tan\left(d x + c\right) + a}}{a \tan\left(d x + c\right)}\right)}}{2 \, d}"," ",0,"-1/2*I*a*(sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) - log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/sqrt(a) - 2*I*sqrt(I*a*tan(d*x + c) + a)/(a*tan(d*x + c)))/d","A",0
91,1,179,0,0.568429," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, {\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} + \sqrt{i \, a \tan\left(d x + c\right) + a} a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} + a^{3}} + \frac{4 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}} - \frac{7 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)}}{8 \, d}"," ",0,"1/8*a^2*(2*((I*a*tan(d*x + c) + a)^(3/2) + sqrt(I*a*tan(d*x + c) + a)*a)/((I*a*tan(d*x + c) + a)^2*a - 2*(I*a*tan(d*x + c) + a)*a^2 + a^3) + 4*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(3/2) - 7*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(3/2))/d","A",0
92,1,138,0,0.903742," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{105 \, \sqrt{2} a^{\frac{11}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 30 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 42 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3} + 70 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4} + 210 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{5}}{105 \, a^{4} d}"," ",0,"-1/105*(105*sqrt(2)*a^(11/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 30*(I*a*tan(d*x + c) + a)^(7/2)*a^2 - 42*(I*a*tan(d*x + c) + a)^(5/2)*a^3 + 70*(I*a*tan(d*x + c) + a)^(3/2)*a^4 + 210*sqrt(I*a*tan(d*x + c) + a)*a^5)/(a^4*d)","A",0
93,1,102,0,0.923042," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(5 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} + 10 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}\right)}}{5 \, a^{3} d}"," ",0,"-1/5*I*(5*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 2*(I*a*tan(d*x + c) + a)^(5/2)*a^2 + 10*sqrt(I*a*tan(d*x + c) + a)*a^4)/(a^3*d)","A",0
94,1,102,0,0.972320," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} + 6 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3}}{3 \, a^{2} d}"," ",0,"1/3*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 2*(I*a*tan(d*x + c) + a)^(3/2)*a^2 + 6*sqrt(I*a*tan(d*x + c) + a)*a^3)/(a^2*d)","A",0
95,1,83,0,0.774220," ","integrate((a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 2 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}\right)}}{a d}"," ",0,"I*(sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 2*sqrt(I*a*tan(d*x + c) + a)*a^2)/(a*d)","A",0
96,1,107,0,0.709978," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - a^{\frac{3}{2}} \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{d}"," ",0,"-(sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - a^(3/2)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))))/d","A",0
97,1,132,0,0.594132," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - 3 \, \sqrt{a} \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right) - \frac{2 i \, \sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)}\right)} a}{2 \, d}"," ",0,"-1/2*I*(2*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 3*sqrt(a)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))) - 2*I*sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c))*a/d","A",0
98,1,178,0,0.558542," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{8 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} - \frac{11 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{\sqrt{a}} + \frac{2 \, {\left(5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} - 3 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + a^{2}}\right)}}{8 \, d}"," ",0,"1/8*a^2*(8*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) - 11*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/sqrt(a) + 2*(5*(I*a*tan(d*x + c) + a)^(3/2) - 3*sqrt(I*a*tan(d*x + c) + a)*a)/((I*a*tan(d*x + c) + a)^2 - 2*(I*a*tan(d*x + c) + a)*a + a^2))/d","A",0
99,1,156,0,0.515280," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(315 \, \sqrt{2} a^{\frac{13}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 35 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{2} - 45 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} + 63 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4} + 105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{5} + 630 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{6}\right)}}{315 \, a^{4} d}"," ",0,"-2/315*(315*sqrt(2)*a^(13/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 35*(I*a*tan(d*x + c) + a)^(9/2)*a^2 - 45*(I*a*tan(d*x + c) + a)^(7/2)*a^3 + 63*(I*a*tan(d*x + c) + a)^(5/2)*a^4 + 105*(I*a*tan(d*x + c) + a)^(3/2)*a^5 + 630*sqrt(I*a*tan(d*x + c) + a)*a^6)/(a^4*d)","A",0
100,1,120,0,0.579314," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(21 \, \sqrt{2} a^{\frac{11}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} + 7 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4} + 42 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{5}\right)}}{21 \, a^{3} d}"," ",0,"-2/21*I*(21*sqrt(2)*a^(11/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 3*(I*a*tan(d*x + c) + a)^(7/2)*a^2 + 7*(I*a*tan(d*x + c) + a)^(3/2)*a^4 + 42*sqrt(I*a*tan(d*x + c) + a)*a^5)/(a^3*d)","A",0
101,1,120,0,0.585981," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 \, {\left(15 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} + 5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 30 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}\right)}}{15 \, a^{2} d}"," ",0,"2/15*(15*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 3*(I*a*tan(d*x + c) + a)^(5/2)*a^2 + 5*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 30*sqrt(I*a*tan(d*x + c) + a)*a^4)/(a^2*d)","A",0
102,1,101,0,0.716991," ","integrate((a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} + 6 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3}\right)}}{3 \, a d}"," ",0,"2/3*I*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + (I*a*tan(d*x + c) + a)^(3/2)*a^2 + 6*sqrt(I*a*tan(d*x + c) + a)*a^3)/(a*d)","A",0
103,1,126,0,0.649469," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - a^{\frac{5}{2}} \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right) + 2 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}}{d}"," ",0,"-(2*sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - a^(5/2)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))) + 2*sqrt(I*a*tan(d*x + c) + a)*a^2)/d","A",0
104,1,133,0,0.496928," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(4 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - 5 \, a^{\frac{3}{2}} \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right) - \frac{2 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} a}{\tan\left(d x + c\right)}\right)} a}{2 \, d}"," ",0,"-1/2*I*(4*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 5*a^(3/2)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))) - 2*I*sqrt(I*a*tan(d*x + c) + a)*a/tan(d*x + c))*a/d","A",0
105,1,181,0,0.464374," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{{\left(16 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - 23 \, \sqrt{a} \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right) + \frac{2 \, {\left(9 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a - 7 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + a^{2}}\right)} a^{2}}{8 \, d}"," ",0,"1/8*(16*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 23*sqrt(a)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))) + 2*(9*(I*a*tan(d*x + c) + a)^(3/2)*a - 7*sqrt(I*a*tan(d*x + c) + a)*a^2)/((I*a*tan(d*x + c) + a)^2 - 2*(I*a*tan(d*x + c) + a)*a + a^2))*a^2/d","A",0
106,1,216,0,0.654873," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, a^{3} {\left(\frac{96 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} - \frac{135 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{\sqrt{a}} + \frac{2 \, {\left(57 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} - 88 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a + 39 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} - 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - a^{3}}\right)}}{48 \, d}"," ",0,"1/48*I*a^3*(96*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) - 135*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/sqrt(a) + 2*(57*(I*a*tan(d*x + c) + a)^(5/2) - 88*(I*a*tan(d*x + c) + a)^(3/2)*a + 39*sqrt(I*a*tan(d*x + c) + a)*a^2)/((I*a*tan(d*x + c) + a)^3 - 3*(I*a*tan(d*x + c) + a)^2*a + 3*(I*a*tan(d*x + c) + a)*a^2 - a^3))/d","A",0
107,1,120,0,0.569622," ","integrate((a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(30 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 60 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}\right)}}{15 \, a d}"," ",0,"2/15*I*(30*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 3*(I*a*tan(d*x + c) + a)^(5/2)*a^2 + 10*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 60*sqrt(I*a*tan(d*x + c) + a)*a^4)/(a*d)","A",0
108,1,156,0,0.654147," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{105 \, \sqrt{2} a^{\frac{11}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 120 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2} - 504 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{3} + 1120 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{4} - 1680 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{5} - \frac{420 \, a^{6}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{420 \, a^{6} d}"," ",0,"1/420*(105*sqrt(2)*a^(11/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 120*(I*a*tan(d*x + c) + a)^(7/2)*a^2 - 504*(I*a*tan(d*x + c) + a)^(5/2)*a^3 + 1120*(I*a*tan(d*x + c) + a)^(3/2)*a^4 - 1680*sqrt(I*a*tan(d*x + c) + a)*a^5 - 420*a^6/sqrt(I*a*tan(d*x + c) + a))/(a^6*d)","A",0
109,1,138,0,0.737297," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(15 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 24 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 80 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 240 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4} + \frac{60 \, a^{5}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}}{60 \, a^{5} d}"," ",0,"1/60*I*(15*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 24*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 80*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 240*sqrt(I*a*tan(d*x + c) + a)*a^4 + 60*a^5/sqrt(I*a*tan(d*x + c) + a))/(a^5*d)","A",0
110,1,120,0,0.516406," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} - 24 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3} - \frac{12 \, a^{4}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{12 \, a^{4} d}"," ",0,"-1/12*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 8*(I*a*tan(d*x + c) + a)^(3/2)*a^2 - 24*sqrt(I*a*tan(d*x + c) + a)*a^3 - 12*a^4/sqrt(I*a*tan(d*x + c) + a))/(a^4*d)","A",0
111,1,101,0,0.766067," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 8 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2} + \frac{4 \, a^{3}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}}{4 \, a^{3} d}"," ",0,"-1/4*I*(sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 8*sqrt(I*a*tan(d*x + c) + a)*a^2 + 4*a^3/sqrt(I*a*tan(d*x + c) + a))/(a^3*d)","A",0
112,1,83,0,0.429520," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - \frac{4 \, a^{2}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{4 \, a^{2} d}"," ",0,"1/4*(sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 4*a^2/sqrt(I*a*tan(d*x + c) + a))/(a^2*d)","A",0
113,1,81,0,0.683103," ","integrate(1/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(\sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, a}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}}{4 \, a d}"," ",0,"1/4*I*(sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*a/sqrt(I*a*tan(d*x + c) + a))/(a*d)","A",0
114,1,122,0,0.700801," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} - \frac{4 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{\sqrt{a}} - \frac{4}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{4 \, d}"," ",0,"-1/4*(sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) - 4*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/sqrt(a) - 4/sqrt(I*a*tan(d*x + c) + a))/d","A",0
115,1,160,0,0.914882," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, a {\left(\frac{4 \, {\left(-2 i \, a \tan\left(d x + c\right) - a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a - \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2}} - \frac{\sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}} - \frac{2 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}}\right)}}{4 \, d}"," ",0,"1/4*I*a*(4*(-2*I*a*tan(d*x + c) - a)/((I*a*tan(d*x + c) + a)^(3/2)*a - sqrt(I*a*tan(d*x + c) + a)*a^2) - sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(3/2) - 2*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(3/2))/d","A",0
116,1,203,0,0.579937," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(7 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 13 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + 4 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4}} - \frac{2 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{5}{2}}} + \frac{11 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{5}{2}}}\right)}}{8 \, d}"," ",0,"-1/8*a^2*(2*(7*(I*a*tan(d*x + c) + a)^2 - 13*(I*a*tan(d*x + c) + a)*a + 4*a^2)/((I*a*tan(d*x + c) + a)^(5/2)*a^2 - 2*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + sqrt(I*a*tan(d*x + c) + a)*a^4) - 2*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(5/2) + 11*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(5/2))/d","A",0
117,1,157,0,0.704842," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{15 \, \sqrt{2} a^{\frac{9}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 48 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - 240 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3} + 960 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{4} + \frac{20 \, {\left(27 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{5} - 2 \, a^{6}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}}{120 \, a^{6} d}"," ",0,"1/120*(15*sqrt(2)*a^(9/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 48*(I*a*tan(d*x + c) + a)^(5/2)*a^2 - 240*(I*a*tan(d*x + c) + a)^(3/2)*a^3 + 960*sqrt(I*a*tan(d*x + c) + a)*a^4 + 20*(27*(I*a*tan(d*x + c) + a)*a^5 - 2*a^6)/(I*a*tan(d*x + c) + a)^(3/2))/(a^6*d)","A",0
118,1,139,0,0.543727," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(3 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 16 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} - 96 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3} - \frac{4 \, {\left(21 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} - 2 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\right)}}{24 \, a^{5} d}"," ",0,"1/24*I*(3*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 16*(I*a*tan(d*x + c) + a)^(3/2)*a^2 - 96*sqrt(I*a*tan(d*x + c) + a)*a^3 - 4*(21*(I*a*tan(d*x + c) + a)*a^4 - 2*a^5)/(I*a*tan(d*x + c) + a)^(3/2))/(a^5*d)","A",0
119,1,121,0,0.980172," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 48 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2} + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{3} - 2 \, a^{4}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}}{24 \, a^{4} d}"," ",0,"-1/24*(3*sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 48*sqrt(I*a*tan(d*x + c) + a)*a^2 + 4*(15*(I*a*tan(d*x + c) + a)*a^3 - 2*a^4)/(I*a*tan(d*x + c) + a)^(3/2))/(a^4*d)","A",0
120,1,103,0,0.644493," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(3 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - \frac{4 \, {\left(9 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - 2 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\right)}}{24 \, a^{3} d}"," ",0,"-1/24*I*(3*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 4*(9*(I*a*tan(d*x + c) + a)*a^2 - 2*a^3)/(I*a*tan(d*x + c) + a)^(3/2))/(a^3*d)","A",0
121,1,101,0,0.490708," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a - 2 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}}{24 \, a^{2} d}"," ",0,"1/24*(3*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(3*(I*a*tan(d*x + c) + a)*a - 2*a^2)/(I*a*tan(d*x + c) + a)^(3/2))/(a^2*d)","A",0
122,1,94,0,0.926577," ","integrate(1/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{3 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(3 i \, a \tan\left(d x + c\right) + 5 \, a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\right)}}{24 \, a d}"," ",0,"1/24*I*(3*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) + 4*(3*I*a*tan(d*x + c) + 5*a)/(I*a*tan(d*x + c) + a)^(3/2))/(a*d)","A",0
123,1,139,0,0.694040," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}} - \frac{24 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{3}{2}}} - \frac{4 \, {\left(9 i \, a \tan\left(d x + c\right) + 11 \, a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a}}{24 \, d}"," ",0,"-1/24*(3*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(3/2) - 24*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(3/2) - 4*(9*I*a*tan(d*x + c) + 11*a)/((I*a*tan(d*x + c) + a)^(3/2)*a))/d","A",0
124,1,184,0,0.542912," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{4 \, {\left(21 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 13 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a - 2 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2} - {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{3}} + \frac{3 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{5}{2}}} + \frac{36 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{5}{2}}}\right)}}{24 \, d}"," ",0,"-1/24*I*a*(4*(21*(I*a*tan(d*x + c) + a)^2 - 13*(I*a*tan(d*x + c) + a)*a - 2*a^2)/((I*a*tan(d*x + c) + a)^(5/2)*a^2 - (I*a*tan(d*x + c) + a)^(3/2)*a^3) + 3*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(5/2) + 36*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(5/2))/d","A",0
125,1,221,0,0.563506," ","integrate(cot(d*x+c)^3/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(63 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} - 107 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a + 34 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} + 4 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{5}} - \frac{3 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{7}{2}}} + \frac{69 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{7}{2}}}\right)}}{24 \, d}"," ",0,"-1/24*a^2*(2*(63*(I*a*tan(d*x + c) + a)^3 - 107*(I*a*tan(d*x + c) + a)^2*a + 34*(I*a*tan(d*x + c) + a)*a^2 + 4*a^3)/((I*a*tan(d*x + c) + a)^(7/2)*a^3 - 2*(I*a*tan(d*x + c) + a)^(5/2)*a^4 + (I*a*tan(d*x + c) + a)^(3/2)*a^5) - 3*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(7/2) + 69*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(7/2))/d","A",0
126,1,157,0,0.669621," ","integrate(tan(d*x+c)^5/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{15 \, \sqrt{2} a^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 160 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} a^{2} - 1440 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{3} - \frac{12 \, {\left(155 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{4} - 30 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{5} + 4 \, a^{6}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}}{240 \, a^{6} d}"," ",0,"1/240*(15*sqrt(2)*a^(7/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 160*(I*a*tan(d*x + c) + a)^(3/2)*a^2 - 1440*sqrt(I*a*tan(d*x + c) + a)*a^3 - 12*(155*(I*a*tan(d*x + c) + a)^2*a^4 - 30*(I*a*tan(d*x + c) + a)*a^5 + 4*a^6)/(I*a*tan(d*x + c) + a)^(5/2))/(a^6*d)","A",0
127,1,139,0,0.602734," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(15 \, \sqrt{2} a^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + 480 \, \sqrt{i \, a \tan\left(d x + c\right) + a} a^{2} + \frac{4 \, {\left(255 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} - 70 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} + 12 \, a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\right)}}{240 \, a^{5} d}"," ",0,"1/240*I*(15*sqrt(2)*a^(5/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 480*sqrt(I*a*tan(d*x + c) + a)*a^2 + 4*(255*(I*a*tan(d*x + c) + a)^2*a^3 - 70*(I*a*tan(d*x + c) + a)*a^4 + 12*a^5)/(I*a*tan(d*x + c) + a)^(5/2))/(a^5*d)","A",0
128,1,121,0,0.789736," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} a^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) - \frac{4 \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{2} - 50 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{3} + 12 \, a^{4}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}}{240 \, a^{4} d}"," ",0,"-1/240*(15*sqrt(2)*a^(3/2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) - 4*(105*(I*a*tan(d*x + c) + a)^2*a^2 - 50*(I*a*tan(d*x + c) + a)*a^3 + 12*a^4)/(I*a*tan(d*x + c) + a)^(5/2))/(a^4*d)","A",0
129,1,119,0,0.691994," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(5 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right) + \frac{4 \, {\left(5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} + 4 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\right)}}{80 \, a^{3} d}"," ",0,"-1/80*I*(5*sqrt(2)*sqrt(a)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a))) + 4*(5*(I*a*tan(d*x + c) + a)^2*a - 10*(I*a*tan(d*x + c) + a)*a^2 + 4*a^3)/(I*a*tan(d*x + c) + a)^(5/2))/(a^3*d)","A",0
130,1,116,0,0.575006," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{15 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a - 12 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}}{240 \, a^{2} d}"," ",0,"1/240*(15*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/sqrt(a) + 4*(15*(I*a*tan(d*x + c) + a)^2 + 10*(I*a*tan(d*x + c) + a)*a - 12*a^2)/(I*a*tan(d*x + c) + a)^(5/2))/(a^2*d)","A",0
131,1,119,0,0.596934," ","integrate(1/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{15 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{3}{2}}} + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + 12 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a}\right)}}{240 \, a d}"," ",0,"1/240*I*(15*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(3/2) + 4*(15*(I*a*tan(d*x + c) + a)^2 + 10*(I*a*tan(d*x + c) + a)*a + 12*a^2)/((I*a*tan(d*x + c) + a)^(5/2)*a))/(a*d)","A",0
132,1,161,0,0.457546," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{5 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{5}{2}}} - \frac{80 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{5}{2}}} - \frac{4 \, {\left(35 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + 4 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2}}}{80 \, d}"," ",0,"-1/80*(5*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(5/2) - 80*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(5/2) - 4*(35*(I*a*tan(d*x + c) + a)^2 + 10*(I*a*tan(d*x + c) + a)*a + 4*a^2)/((I*a*tan(d*x + c) + a)^(5/2)*a^2))/d","A",0
133,1,202,0,0.575990," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{4 \, {\left(315 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} - 205 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a - 38 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - 12 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{3} - {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{4}} + \frac{15 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{7}{2}}} + \frac{600 \, \log\left(\frac{\sqrt{i \, a \tan\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{i \, a \tan\left(d x + c\right) + a} + \sqrt{a}}\right)}{a^{\frac{7}{2}}}\right)}}{240 \, d}"," ",0,"-1/240*I*a*(4*(315*(I*a*tan(d*x + c) + a)^3 - 205*(I*a*tan(d*x + c) + a)^2*a - 38*(I*a*tan(d*x + c) + a)*a^2 - 12*a^3)/((I*a*tan(d*x + c) + a)^(7/2)*a^3 - (I*a*tan(d*x + c) + a)^(5/2)*a^4) + 15*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(7/2) + 600*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(7/2))/d","A",0
134,1,137,0,0.499418," ","integrate(1/(a+I*a*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{105 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}{a^{\frac{5}{2}}} + \frac{4 \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} + 70 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a + 84 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} + 120 \, a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{2}}\right)}}{3360 \, a d}"," ",0,"1/3360*I*(105*sqrt(2)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(d*x + c) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(d*x + c) + a)))/a^(5/2) + 4*(105*(I*a*tan(d*x + c) + a)^3 + 70*(I*a*tan(d*x + c) + a)^2*a + 84*(I*a*tan(d*x + c) + a)*a^2 + 120*a^3)/((I*a*tan(d*x + c) + a)^(7/2)*a^2))/(a*d)","A",0
135,1,209,0,0.530430," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{15 \, a d^{4} {\left(\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 24 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a d + 40 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d^{2} - 120 i \, \sqrt{d \tan\left(f x + e\right)} a d^{3}}{60 \, d f}"," ",0,"1/60*(15*a*d^4*((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 24*I*(d*tan(f*x + e))^(5/2)*a*d + 40*(d*tan(f*x + e))^(3/2)*a*d^2 - 120*I*sqrt(d*tan(f*x + e))*a*d^3)/(d*f)","B",0
136,1,193,0,0.721543," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, a d^{3} {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 8 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d + 24 \, \sqrt{d \tan\left(f x + e\right)} a d^{2}}{12 \, d f}"," ",0,"1/12*(3*a*d^3*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 8*I*(d*tan(f*x + e))^(3/2)*a*d + 24*sqrt(d*tan(f*x + e))*a*d^2)/(d*f)","B",0
137,1,176,0,0.500794," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{a d^{2} {\left(\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - 8 i \, \sqrt{d \tan\left(f x + e\right)} a d}{4 \, d f}"," ",0,"-1/4*(a*d^2*((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 8*I*sqrt(d*tan(f*x + e))*a*d)/(d*f)","B",0
138,1,154,0,0.661158," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{a {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{4 \, f}"," ",0,"-1/4*a*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/f","C",0
139,1,172,0,0.453173," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{a {\left(\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{8 \, a}{\sqrt{d \tan\left(f x + e\right)}}}{4 \, d f}"," ",0,"1/4*(a*((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 8*a/sqrt(d*tan(f*x + e)))/(d*f)","C",0
140,1,192,0,0.850660," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, a {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d} - \frac{8 \, {\left(3 i \, a d \tan\left(f x + e\right) + a d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{12 \, d f}"," ",0,"1/12*(3*a*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d - 8*(3*I*a*d*tan(f*x + e) + a*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","B",0
141,1,211,0,0.567616," ","integrate((a+I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, a {\left(\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{2}} - \frac{8 \, {\left(15 \, a d^{2} \tan\left(f x + e\right)^{2} - 5 i \, a d^{2} \tan\left(f x + e\right) - 3 \, a d^{2}\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} d^{2}}}{60 \, d f}"," ",0,"-1/60*(15*a*((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^2 - 8*(15*a*d^2*tan(f*x + e)^2 - 5*I*a*d^2*tan(f*x + e) - 3*a*d^2)/((d*tan(f*x + e))^(5/2)*d^2))/(d*f)","B",0
142,1,209,0,0.592984," ","integrate((d*tan(f*x+e))^(5/2)*(a-I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{15 \, a d^{4} {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - 24 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a d + 40 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d^{2} + 120 i \, \sqrt{d \tan\left(f x + e\right)} a d^{3}}{60 \, d f}"," ",0,"1/60*(15*a*d^4*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 24*I*(d*tan(f*x + e))^(5/2)*a*d + 40*(d*tan(f*x + e))^(3/2)*a*d^2 + 120*I*sqrt(d*tan(f*x + e))*a*d^3)/(d*f)","B",0
143,1,193,0,0.667927," ","integrate((d*tan(f*x+e))^(3/2)*(a-I*a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{3 \, a d^{3} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 8 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d - 24 \, \sqrt{d \tan\left(f x + e\right)} a d^{2}}{12 \, d f}"," ",0,"-1/12*(3*a*d^3*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 8*I*(d*tan(f*x + e))^(3/2)*a*d - 24*sqrt(d*tan(f*x + e))*a*d^2)/(d*f)","B",0
144,1,176,0,0.686377," ","integrate((d*tan(f*x+e))^(1/2)*(a-I*a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{a d^{2} {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 8 i \, \sqrt{d \tan\left(f x + e\right)} a d}{4 \, d f}"," ",0,"-1/4*(a*d^2*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 8*I*sqrt(d*tan(f*x + e))*a*d)/(d*f)","B",0
145,1,154,0,0.595926," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{a {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{4 \, f}"," ",0,"1/4*a*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/f","C",0
146,1,172,0,0.717580," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{a {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{8 \, a}{\sqrt{d \tan\left(f x + e\right)}}}{4 \, d f}"," ",0,"1/4*(a*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 8*a/sqrt(d*tan(f*x + e)))/(d*f)","C",0
147,1,193,0,0.622920," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, a {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d} - \frac{8 \, {\left(3 i \, a d \tan\left(f x + e\right) - a d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{12 \, d f}"," ",0,"-1/12*(3*a*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d - 8*(3*I*a*d*tan(f*x + e) - a*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","B",0
148,1,211,0,0.634450," ","integrate((a-I*a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, a {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{2}} - \frac{8 \, {\left(15 \, a d^{2} \tan\left(f x + e\right)^{2} + 5 i \, a d^{2} \tan\left(f x + e\right) - 3 \, a d^{2}\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} d^{2}}}{60 \, d f}"," ",0,"-1/60*(15*a*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^2 - 8*(15*a*d^2*tan(f*x + e)^2 + 5*I*a*d^2*tan(f*x + e) - 3*a*d^2)/((d*tan(f*x + e))^(5/2)*d^2))/(d*f)","B",0
149,1,232,0,0.593611," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{105 \, a^{2} d^{4} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 60 \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{2} - 168 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{2} d - 280 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} d^{2} + 840 i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3}}{210 \, d f}"," ",0,"-1/210*(105*a^2*d^4*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 60*(d*tan(f*x + e))^(7/2)*a^2 - 168*I*(d*tan(f*x + e))^(5/2)*a^2*d - 280*(d*tan(f*x + e))^(3/2)*a^2*d^2 + 840*I*sqrt(d*tan(f*x + e))*a^2*d^3)/(d*f)","B",0
150,1,214,0,0.451185," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{15 \, a^{2} d^{3} {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - 12 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{2} + 40 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} d + 120 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{2}}{30 \, d f}"," ",0,"1/30*(15*a^2*d^3*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 12*(d*tan(f*x + e))^(5/2)*a^2 + 40*I*(d*tan(f*x + e))^(3/2)*a^2*d + 120*sqrt(d*tan(f*x + e))*a^2*d^2)/(d*f)","B",0
151,1,196,0,0.684584," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} d^{2} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - 4 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} + 24 i \, \sqrt{d \tan\left(f x + e\right)} a^{2} d}{6 \, d f}"," ",0,"1/6*(3*a^2*d^2*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 4*(d*tan(f*x + e))^(3/2)*a^2 + 24*I*sqrt(d*tan(f*x + e))*a^2*d)/(d*f)","B",0
152,1,177,0,0.528653," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{a^{2} d {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 4 \, \sqrt{d \tan\left(f x + e\right)} a^{2}}{2 \, d f}"," ",0,"-1/2*(a^2*d*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 4*sqrt(d*tan(f*x + e))*a^2)/(d*f)","C",0
153,1,176,0,1.163213," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{a^{2} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + \frac{4 \, a^{2}}{\sqrt{d \tan\left(f x + e\right)}}}{2 \, d f}"," ",0,"-1/2*(a^2*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 4*a^2/sqrt(d*tan(f*x + e)))/(d*f)","C",0
154,1,198,0,0.826171," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{2} {\left(-\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d} - \frac{4 \, {\left(6 i \, a^{2} d \tan\left(f x + e\right) + a^{2} d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{6 \, d f}"," ",0,"1/6*(3*a^2*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d - 4*(6*I*a^2*d*tan(f*x + e) + a^2*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","B",0
155,1,219,0,0.485397," ","integrate((a+I*a*tan(f*x+e))^2/(d*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{\frac{15 \, a^{2} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{2}} + \frac{4 \, {\left(30 \, a^{2} d^{2} \tan\left(f x + e\right)^{2} - 10 i \, a^{2} d^{2} \tan\left(f x + e\right) - 3 \, a^{2} d^{2}\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} d^{2}}}{30 \, d f}"," ",0,"1/30*(15*a^2*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^2 + 4*(30*a^2*d^2*tan(f*x + e)^2 - 10*I*a^2*d^2*tan(f*x + e) - 3*a^2*d^2)/((d*tan(f*x + e))^(5/2)*d^2))/(d*f)","B",0
156,1,256,0,0.640537," ","integrate((d*tan(f*x+e))^(5/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{315 \, a^{3} d^{4} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{2 \, {\left(-35 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{9}{2}} a^{3} - 135 \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{3} d + 252 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} d^{2} + 420 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d^{3} - 1260 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{4}\right)}}{d}}{315 \, d f}"," ",0,"-1/315*(315*a^3*d^4*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 2*(-35*I*(d*tan(f*x + e))^(9/2)*a^3 - 135*(d*tan(f*x + e))^(7/2)*a^3*d + 252*I*(d*tan(f*x + e))^(5/2)*a^3*d^2 + 420*(d*tan(f*x + e))^(3/2)*a^3*d^3 - 1260*I*sqrt(d*tan(f*x + e))*a^3*d^4)/d)/(d*f)","A",0
157,1,238,0,0.473899," ","integrate((d*tan(f*x+e))^(3/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{105 \, a^{3} d^{3} {\left(\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{2 \, {\left(-15 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{3} - 63 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} d + 140 i \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d^{2} + 420 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{3}\right)}}{d}}{105 \, d f}"," ",0,"-1/105*(105*a^3*d^3*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 2*(-15*I*(d*tan(f*x + e))^(7/2)*a^3 - 63*(d*tan(f*x + e))^(5/2)*a^3*d + 140*I*(d*tan(f*x + e))^(3/2)*a^3*d^2 + 420*sqrt(d*tan(f*x + e))*a^3*d^3)/d)/(d*f)","A",0
158,1,220,0,0.586451," ","integrate((d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{5 \, a^{3} d^{2} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + \frac{2 \, {\left(-i \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} - 5 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d + 20 i \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{2}\right)}}{d}}{5 \, d f}"," ",0,"1/5*(5*a^3*d^2*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 2*(-I*(d*tan(f*x + e))^(5/2)*a^3 - 5*(d*tan(f*x + e))^(3/2)*a^3*d + 20*I*sqrt(d*tan(f*x + e))*a^3*d^2)/d)/(d*f)","B",0
159,1,200,0,0.502630," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{3 \, a^{3} d {\left(\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + \frac{2 \, {\left(-i \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} - 9 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d\right)}}{d}}{3 \, d f}"," ",0,"1/3*(3*a^3*d*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 2*(-I*(d*tan(f*x + e))^(3/2)*a^3 - 9*sqrt(d*tan(f*x + e))*a^3*d)/d)/(d*f)","B",0
160,1,194,0,0.548515," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{a^{3} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + \frac{2 \, a^{3}}{\sqrt{d \tan\left(f x + e\right)}} + \frac{2 i \, \sqrt{d \tan\left(f x + e\right)} a^{3}}{d}}{d f}"," ",0,"-(a^3*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 2*a^3/sqrt(d*tan(f*x + e)) + 2*I*sqrt(d*tan(f*x + e))*a^3/d)/(d*f)","B",0
161,1,198,0,0.870612," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, a^{3} {\left(\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d} + \frac{2 \, {\left(9 i \, a^{3} d \tan\left(f x + e\right) + a^{3} d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{3 \, d f}"," ",0,"-1/3*(3*a^3*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d + 2*(9*I*a^3*d*tan(f*x + e) + a^3*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","B",0
162,1,219,0,0.462417," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{\frac{5 \, a^{3} {\left(-\frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i + 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{2}} + \frac{2 \, {\left(20 \, a^{3} d^{2} \tan\left(f x + e\right)^{2} - 5 i \, a^{3} d^{2} \tan\left(f x + e\right) - a^{3} d^{2}\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} d^{2}}}{5 \, d f}"," ",0,"1/5*(5*a^3*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I + 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I + 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^2 + 2*(20*a^3*d^2*tan(f*x + e)^2 - 5*I*a^3*d^2*tan(f*x + e) - a^3*d^2)/((d*tan(f*x + e))^(5/2)*d^2))/(d*f)","A",0
163,1,235,0,0.589183," ","integrate((a+I*a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","\frac{\frac{105 \, a^{3} {\left(\frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\left(i - 1\right) \, \sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{3}} - \frac{2 \, {\left(-420 i \, a^{3} d^{3} \tan\left(f x + e\right)^{3} - 140 \, a^{3} d^{3} \tan\left(f x + e\right)^{2} + 63 i \, a^{3} d^{3} \tan\left(f x + e\right) + 15 \, a^{3} d^{3}\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} d^{3}}}{105 \, d f}"," ",0,"1/105*(105*a^3*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - (I - 1)*sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + (I - 1)*sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^3 - 2*(-420*I*a^3*d^3*tan(f*x + e)^3 - 140*a^3*d^3*tan(f*x + e)^2 + 63*I*a^3*d^3*tan(f*x + e) + 15*a^3*d^3)/((d*tan(f*x + e))^(7/2)*d^3))/(d*f)","A",0
164,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
165,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
166,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
167,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
168,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
169,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
170,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
171,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
172,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
173,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
174,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
175,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
176,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
177,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
178,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
179,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
180,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
181,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
182,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
183,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
184,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
185,-2,0,0,0.000000," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
186,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \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
187,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \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
188,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\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
189,1,379,0,0.592581," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(\left(2 i + 2\right) \, \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + \left(i - 1\right) \, \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)}}{2 \, d}"," ",0,"1/2*sqrt(a)*((2*I + 2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (I - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))/d","B",0
190,1,548,0,0.609061," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} {\left(-\left(2 i - 2\right) \, \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + \left(i + 1\right) \, \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} + {\left({\left(-\left(4 i - 4\right) \, \cos\left(d x + c\right) + \left(4 i + 4\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\left(4 i + 4\right) \, \cos\left(d x + c\right) + \left(4 i - 4\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"-1/2*((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a)*(-(2*I - 2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (I + 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))))) + ((-(4*I - 4)*cos(d*x + c) + (4*I + 4)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((4*I + 4)*cos(d*x + c) + (4*I - 4)*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
191,1,968,0,0.670341," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(36 i + 36\right) \, \cos\left(3 \, d x + 3 \, c\right) - \left(12 i + 12\right) \, \cos\left(d x + c\right) - \left(36 i - 36\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(36 i - 36\right) \, \cos\left(3 \, d x + 3 \, c\right) - \left(12 i - 12\right) \, \cos\left(d x + c\right) + \left(36 i + 36\right) \, \sin\left(3 \, d x + 3 \, c\right) + \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(36 i + 36\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(36 i + 36\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(72 i + 72\right) \, \cos\left(2 \, d x + 2 \, c\right) + 36 i + 36\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(\left(18 i - 18\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(18 i - 18\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(36 i - 36\right) \, \cos\left(2 \, d x + 2 \, c\right) + 18 i - 18\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i + 24\right) \, \cos\left(d x + c\right) - \left(24 i - 24\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i - 24\right) \, \cos\left(d x + c\right) + \left(24 i + 24\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{36 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/36*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(36*I + 36)*cos(3*d*x + 3*c) - (12*I + 12)*cos(d*x + c) - (36*I - 36)*sin(3*d*x + 3*c) - (12*I - 12)*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(36*I - 36)*cos(3*d*x + 3*c) - (12*I - 12)*cos(d*x + c) + (36*I + 36)*sin(3*d*x + 3*c) + (12*I + 12)*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((36*I + 36)*cos(2*d*x + 2*c)^2 + (36*I + 36)*sin(2*d*x + 2*c)^2 - (72*I + 72)*cos(2*d*x + 2*c) + 36*I + 36)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + ((18*I - 18)*cos(2*d*x + 2*c)^2 + (18*I - 18)*sin(2*d*x + 2*c)^2 - (36*I - 36)*cos(2*d*x + 2*c) + 18*I - 18)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((12*I + 12)*cos(d*x + c) + (12*I - 12)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I + 12)*cos(d*x + c) + (12*I - 12)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I + 24)*cos(d*x + c) - (24*I - 24)*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I + 12)*cos(d*x + c) + (12*I - 12)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((12*I - 12)*cos(d*x + c) - (12*I + 12)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I - 12)*cos(d*x + c) - (12*I + 12)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I - 24)*cos(d*x + c) + (24*I + 24)*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I - 12)*cos(d*x + c) - (12*I + 12)*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
192,1,1144,0,0.749247," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(900 i - 900\right) \, \cos\left(3 \, d x + 3 \, c\right) + \left(1170 i - 1170\right) \, \cos\left(d x + c\right) + \left(900 i + 900\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(1170 i + 1170\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\left(900 i + 900\right) \, \cos\left(3 \, d x + 3 \, c\right) - \left(1170 i + 1170\right) \, \cos\left(d x + c\right) + \left(900 i - 900\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(1170 i - 1170\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(900 i - 900\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i - 900\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(1800 i - 1800\right) \, \cos\left(2 \, d x + 2 \, c\right) + 900 i - 900\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(-\left(450 i + 450\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(450 i + 450\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i + 900\right) \, \cos\left(2 \, d x + 2 \, c\right) - 450 i - 450\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(900 i - 900\right) \, \cos\left(5 \, d x + 5 \, c\right) + \left(150 i - 150\right) \, \cos\left(3 \, d x + 3 \, c\right) + \left(390 i - 390\right) \, \cos\left(d x + c\right) - \left(900 i + 900\right) \, \sin\left(5 \, d x + 5 \, c\right) - \left(150 i + 150\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(390 i + 390\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(240 i - 240\right) \, \cos\left(d x + c\right) - \left(240 i + 240\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(240 i - 240\right) \, \cos\left(d x + c\right) - \left(240 i + 240\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(480 i - 480\right) \, \cos\left(d x + c\right) + \left(480 i + 480\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(240 i - 240\right) \, \cos\left(d x + c\right) - \left(240 i + 240\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(900 i + 900\right) \, \cos\left(5 \, d x + 5 \, c\right) - \left(150 i + 150\right) \, \cos\left(3 \, d x + 3 \, c\right) - \left(390 i + 390\right) \, \cos\left(d x + c\right) - \left(900 i - 900\right) \, \sin\left(5 \, d x + 5 \, c\right) - \left(150 i - 150\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(390 i - 390\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(240 i + 240\right) \, \cos\left(d x + c\right) - \left(240 i - 240\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(240 i + 240\right) \, \cos\left(d x + c\right) - \left(240 i - 240\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(480 i + 480\right) \, \cos\left(d x + c\right) + \left(480 i - 480\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(240 i + 240\right) \, \cos\left(d x + c\right) - \left(240 i - 240\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{900 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/900*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(900*I - 900)*cos(3*d*x + 3*c) + (1170*I - 1170)*cos(d*x + c) + (900*I + 900)*sin(3*d*x + 3*c) - (1170*I + 1170)*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((900*I + 900)*cos(3*d*x + 3*c) - (1170*I + 1170)*cos(d*x + c) + (900*I - 900)*sin(3*d*x + 3*c) - (1170*I - 1170)*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((900*I - 900)*cos(2*d*x + 2*c)^2 + (900*I - 900)*sin(2*d*x + 2*c)^2 - (1800*I - 1800)*cos(2*d*x + 2*c) + 900*I - 900)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (-(450*I + 450)*cos(2*d*x + 2*c)^2 - (450*I + 450)*sin(2*d*x + 2*c)^2 + (900*I + 900)*cos(2*d*x + 2*c) - 450*I - 450)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((900*I - 900)*cos(5*d*x + 5*c) + (150*I - 150)*cos(3*d*x + 3*c) + (390*I - 390)*cos(d*x + c) - (900*I + 900)*sin(5*d*x + 5*c) - (150*I + 150)*sin(3*d*x + 3*c) - (390*I + 390)*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((240*I - 240)*cos(d*x + c) - (240*I + 240)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((240*I - 240)*cos(d*x + c) - (240*I + 240)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(480*I - 480)*cos(d*x + c) + (480*I + 480)*sin(d*x + c))*cos(2*d*x + 2*c) + (240*I - 240)*cos(d*x + c) - (240*I + 240)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(900*I + 900)*cos(5*d*x + 5*c) - (150*I + 150)*cos(3*d*x + 3*c) - (390*I + 390)*cos(d*x + c) - (900*I - 900)*sin(5*d*x + 5*c) - (150*I - 150)*sin(3*d*x + 3*c) - (390*I - 390)*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(240*I + 240)*cos(d*x + c) - (240*I - 240)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(240*I + 240)*cos(d*x + c) - (240*I - 240)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((480*I + 480)*cos(d*x + c) + (480*I - 480)*sin(d*x + c))*cos(2*d*x + 2*c) - (240*I + 240)*cos(d*x + c) - (240*I - 240)*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
193,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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
194,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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
195,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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((I*a*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c)), x)","F",0
196,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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((I*a*tan(d*x + c) + a)^(3/2)/sqrt(tan(d*x + c)), x)","F",0
197,1,554,0,0.596727," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{{\left(-\left(2 i - 2\right) \, a \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + \left(i + 1\right) \, a \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(-\left(2 i - 2\right) \, a \cos\left(d x + c\right) + \left(2 i + 2\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\left(2 i + 2\right) \, a \cos\left(d x + c\right) + \left(2 i - 2\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"-((-(2*I - 2)*a*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (I + 1)*a*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((-(2*I - 2)*a*cos(d*x + c) + (2*I + 2)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((2*I + 2)*a*cos(d*x + c) + (2*I - 2)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
198,1,1002,0,0.677988," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(18 i + 18\right) \, a \cos\left(3 \, d x + 3 \, c\right) + \left(6 i + 6\right) \, a \cos\left(d x + c\right) - \left(18 i - 18\right) \, a \sin\left(3 \, d x + 3 \, c\right) + \left(6 i - 6\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(18 i - 18\right) \, a \cos\left(3 \, d x + 3 \, c\right) + \left(6 i - 6\right) \, a \cos\left(d x + c\right) + \left(18 i + 18\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(6 i + 6\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(18 i + 18\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(18 i + 18\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(36 i + 36\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(18 i + 18\right) \, a\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(\left(9 i - 9\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(9 i - 9\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(18 i - 18\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(9 i - 9\right) \, a\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(12 i + 12\right) \, a \cos\left(d x + c\right) + \left(12 i - 12\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i + 12\right) \, a \cos\left(d x + c\right) + \left(12 i - 12\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i + 24\right) \, a \cos\left(d x + c\right) - \left(24 i - 24\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i + 12\right) \, a \cos\left(d x + c\right) + \left(12 i - 12\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(12 i - 12\right) \, a \cos\left(d x + c\right) - \left(12 i + 12\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i - 12\right) \, a \cos\left(d x + c\right) - \left(12 i + 12\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i - 24\right) \, a \cos\left(d x + c\right) + \left(24 i + 24\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i - 12\right) \, a \cos\left(d x + c\right) - \left(12 i + 12\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{9 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/9*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(18*I + 18)*a*cos(3*d*x + 3*c) + (6*I + 6)*a*cos(d*x + c) - (18*I - 18)*a*sin(3*d*x + 3*c) + (6*I - 6)*a*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(18*I - 18)*a*cos(3*d*x + 3*c) + (6*I - 6)*a*cos(d*x + c) + (18*I + 18)*a*sin(3*d*x + 3*c) - (6*I + 6)*a*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((18*I + 18)*a*cos(2*d*x + 2*c)^2 + (18*I + 18)*a*sin(2*d*x + 2*c)^2 - (36*I + 36)*a*cos(2*d*x + 2*c) + (18*I + 18)*a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + ((9*I - 9)*a*cos(2*d*x + 2*c)^2 + (9*I - 9)*a*sin(2*d*x + 2*c)^2 - (18*I - 18)*a*cos(2*d*x + 2*c) + (9*I - 9)*a)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((12*I + 12)*a*cos(d*x + c) + (12*I - 12)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I + 12)*a*cos(d*x + c) + (12*I - 12)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I + 24)*a*cos(d*x + c) - (24*I - 24)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I + 12)*a*cos(d*x + c) + (12*I - 12)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((12*I - 12)*a*cos(d*x + c) - (12*I + 12)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I - 12)*a*cos(d*x + c) - (12*I + 12)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I - 24)*a*cos(d*x + c) + (24*I + 24)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I - 12)*a*cos(d*x + c) - (12*I + 12)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
199,1,1190,0,0.718973," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(450 i - 450\right) \, a \cos\left(3 \, d x + 3 \, c\right) + \left(480 i - 480\right) \, a \cos\left(d x + c\right) + \left(450 i + 450\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(480 i + 480\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\left(450 i + 450\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(480 i + 480\right) \, a \cos\left(d x + c\right) + \left(450 i - 450\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(480 i - 480\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(450 i - 450\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(450 i - 450\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(900 i - 900\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(450 i - 450\right) \, a\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(-\left(225 i + 225\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(225 i + 225\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(450 i + 450\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(225 i + 225\right) \, a\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(450 i - 450\right) \, a \cos\left(5 \, d x + 5 \, c\right) - \left(150 i - 150\right) \, a \cos\left(3 \, d x + 3 \, c\right) + \left(60 i - 60\right) \, a \cos\left(d x + c\right) - \left(450 i + 450\right) \, a \sin\left(5 \, d x + 5 \, c\right) + \left(150 i + 150\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(60 i + 60\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(90 i - 90\right) \, a \cos\left(d x + c\right) + \left(90 i + 90\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(90 i - 90\right) \, a \cos\left(d x + c\right) + \left(90 i + 90\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(180 i - 180\right) \, a \cos\left(d x + c\right) - \left(180 i + 180\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(90 i - 90\right) \, a \cos\left(d x + c\right) + \left(90 i + 90\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(450 i + 450\right) \, a \cos\left(5 \, d x + 5 \, c\right) + \left(150 i + 150\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(60 i + 60\right) \, a \cos\left(d x + c\right) - \left(450 i - 450\right) \, a \sin\left(5 \, d x + 5 \, c\right) + \left(150 i - 150\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(60 i - 60\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(90 i + 90\right) \, a \cos\left(d x + c\right) + \left(90 i - 90\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(90 i + 90\right) \, a \cos\left(d x + c\right) + \left(90 i - 90\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(180 i + 180\right) \, a \cos\left(d x + c\right) - \left(180 i - 180\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(90 i + 90\right) \, a \cos\left(d x + c\right) + \left(90 i - 90\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{225 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/225*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(450*I - 450)*a*cos(3*d*x + 3*c) + (480*I - 480)*a*cos(d*x + c) + (450*I + 450)*a*sin(3*d*x + 3*c) - (480*I + 480)*a*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((450*I + 450)*a*cos(3*d*x + 3*c) - (480*I + 480)*a*cos(d*x + c) + (450*I - 450)*a*sin(3*d*x + 3*c) - (480*I - 480)*a*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((450*I - 450)*a*cos(2*d*x + 2*c)^2 + (450*I - 450)*a*sin(2*d*x + 2*c)^2 - (900*I - 900)*a*cos(2*d*x + 2*c) + (450*I - 450)*a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (-(225*I + 225)*a*cos(2*d*x + 2*c)^2 - (225*I + 225)*a*sin(2*d*x + 2*c)^2 + (450*I + 450)*a*cos(2*d*x + 2*c) - (225*I + 225)*a)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((450*I - 450)*a*cos(5*d*x + 5*c) - (150*I - 150)*a*cos(3*d*x + 3*c) + (60*I - 60)*a*cos(d*x + c) - (450*I + 450)*a*sin(5*d*x + 5*c) + (150*I + 150)*a*sin(3*d*x + 3*c) - (60*I + 60)*a*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(90*I - 90)*a*cos(d*x + c) + (90*I + 90)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(90*I - 90)*a*cos(d*x + c) + (90*I + 90)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((180*I - 180)*a*cos(d*x + c) - (180*I + 180)*a*sin(d*x + c))*cos(2*d*x + 2*c) - (90*I - 90)*a*cos(d*x + c) + (90*I + 90)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(450*I + 450)*a*cos(5*d*x + 5*c) + (150*I + 150)*a*cos(3*d*x + 3*c) - (60*I + 60)*a*cos(d*x + c) - (450*I - 450)*a*sin(5*d*x + 5*c) + (150*I - 150)*a*sin(3*d*x + 3*c) - (60*I - 60)*a*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((90*I + 90)*a*cos(d*x + c) + (90*I - 90)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((90*I + 90)*a*cos(d*x + c) + (90*I - 90)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(180*I + 180)*a*cos(d*x + c) - (180*I - 180)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (90*I + 90)*a*cos(d*x + c) + (90*I - 90)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
200,1,2840,0,1.019754," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(352800 i + 352800\right) \, a \cos\left(7 \, d x + 7 \, c\right) + \left(176400 i + 176400\right) \, a \cos\left(5 \, d x + 5 \, c\right) - \left(167580 i + 167580\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(59220 i + 59220\right) \, a \cos\left(d x + c\right) - \left(352800 i - 352800\right) \, a \sin\left(7 \, d x + 7 \, c\right) + \left(176400 i - 176400\right) \, a \sin\left(5 \, d x + 5 \, c\right) - \left(167580 i - 167580\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(59220 i - 59220\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(236880 i + 236880\right) \, a \cos\left(d x + c\right) + \left(236880 i - 236880\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(236880 i + 236880\right) \, a \cos\left(d x + c\right) + \left(236880 i - 236880\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(352800 i + 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(352800 i + 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(705600 i + 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(352800 i + 352800\right) \, a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(473760 i + 473760\right) \, a \cos\left(d x + c\right) - \left(473760 i - 473760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(236880 i + 236880\right) \, a \cos\left(d x + c\right) + {\left(-\left(352800 i - 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(352800 i - 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(352800 i - 352800\right) \, a\right)} \sin\left(3 \, d x + 3 \, c\right) + \left(236880 i - 236880\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(352800 i - 352800\right) \, a \cos\left(7 \, d x + 7 \, c\right) + \left(176400 i - 176400\right) \, a \cos\left(5 \, d x + 5 \, c\right) - \left(167580 i - 167580\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(59220 i - 59220\right) \, a \cos\left(d x + c\right) + \left(352800 i + 352800\right) \, a \sin\left(7 \, d x + 7 \, c\right) - \left(176400 i + 176400\right) \, a \sin\left(5 \, d x + 5 \, c\right) + \left(167580 i + 167580\right) \, a \sin\left(3 \, d x + 3 \, c\right) + \left(59220 i + 59220\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(236880 i - 236880\right) \, a \cos\left(d x + c\right) - \left(236880 i + 236880\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(236880 i - 236880\right) \, a \cos\left(d x + c\right) - \left(236880 i + 236880\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(352800 i - 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(352800 i - 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(352800 i - 352800\right) \, a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(473760 i - 473760\right) \, a \cos\left(d x + c\right) + \left(473760 i + 473760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(236880 i - 236880\right) \, a \cos\left(d x + c\right) + {\left(\left(352800 i + 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(352800 i + 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(705600 i + 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(352800 i + 352800\right) \, a\right)} \sin\left(3 \, d x + 3 \, c\right) - \left(236880 i + 236880\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(352800 i + 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{4} + \left(352800 i + 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{4} - \left(1411200 i + 1411200\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{3} + \left(2116800 i + 2116800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(705600 i + 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(1411200 i + 1411200\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(705600 i + 705600\right) \, a\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(1411200 i + 1411200\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(352800 i + 352800\right) \, a\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(\left(176400 i - 176400\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{4} + \left(176400 i - 176400\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{4} - \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{3} + \left(1058400 i - 1058400\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i - 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(352800 i - 352800\right) \, a\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(176400 i - 176400\right) \, a\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(524580 i + 524580\right) \, a \cos\left(d x + c\right) + \left(524580 i - 524580\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(524580 i + 524580\right) \, a \cos\left(d x + c\right) + \left(524580 i - 524580\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i + 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(352800 i + 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(705600 i + 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(352800 i + 352800\right) \, a\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(823200 i + 823200\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(823200 i + 823200\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(1646400 i + 1646400\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(823200 i + 823200\right) \, a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(1049160 i + 1049160\right) \, a \cos\left(d x + c\right) - \left(1049160 i - 1049160\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(524580 i + 524580\right) \, a \cos\left(d x + c\right) + {\left(\left(352800 i - 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(352800 i - 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(352800 i - 352800\right) \, a\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(823200 i - 823200\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(823200 i - 823200\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(1646400 i - 1646400\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(823200 i - 823200\right) \, a\right)} \sin\left(3 \, d x + 3 \, c\right) + \left(524580 i - 524580\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(349440 i + 349440\right) \, a \cos\left(d x + c\right) - \left(349440 i - 349440\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(349440 i + 349440\right) \, a \cos\left(d x + c\right) - \left(349440 i - 349440\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(1397760 i + 1397760\right) \, a \cos\left(d x + c\right) + \left(1397760 i - 1397760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(2096640 i + 2096640\right) \, a \cos\left(d x + c\right) - \left(2096640 i - 2096640\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(698880 i + 698880\right) \, a \cos\left(d x + c\right) - \left(698880 i - 698880\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1397760 i + 1397760\right) \, a \cos\left(d x + c\right) + \left(1397760 i - 1397760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(698880 i + 698880\right) \, a \cos\left(d x + c\right) - \left(698880 i - 698880\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1397760 i + 1397760\right) \, a \cos\left(d x + c\right) + \left(1397760 i - 1397760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(349440 i + 349440\right) \, a \cos\left(d x + c\right) - \left(349440 i - 349440\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(524580 i - 524580\right) \, a \cos\left(d x + c\right) - \left(524580 i + 524580\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(524580 i - 524580\right) \, a \cos\left(d x + c\right) - \left(524580 i + 524580\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i - 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(352800 i - 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(705600 i - 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(352800 i - 352800\right) \, a\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(823200 i - 823200\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(823200 i - 823200\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(1646400 i - 1646400\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(823200 i - 823200\right) \, a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(1049160 i - 1049160\right) \, a \cos\left(d x + c\right) + \left(1049160 i + 1049160\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(524580 i - 524580\right) \, a \cos\left(d x + c\right) + {\left(-\left(352800 i + 352800\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(352800 i + 352800\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(705600 i + 705600\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(352800 i + 352800\right) \, a\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(823200 i + 823200\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(823200 i + 823200\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(1646400 i + 1646400\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(823200 i + 823200\right) \, a\right)} \sin\left(3 \, d x + 3 \, c\right) - \left(524580 i + 524580\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(349440 i - 349440\right) \, a \cos\left(d x + c\right) + \left(349440 i + 349440\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(349440 i - 349440\right) \, a \cos\left(d x + c\right) + \left(349440 i + 349440\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(1397760 i - 1397760\right) \, a \cos\left(d x + c\right) - \left(1397760 i + 1397760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(2096640 i - 2096640\right) \, a \cos\left(d x + c\right) + \left(2096640 i + 2096640\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(698880 i - 698880\right) \, a \cos\left(d x + c\right) + \left(698880 i + 698880\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1397760 i - 1397760\right) \, a \cos\left(d x + c\right) - \left(1397760 i + 1397760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(698880 i - 698880\right) \, a \cos\left(d x + c\right) + \left(698880 i + 698880\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1397760 i - 1397760\right) \, a \cos\left(d x + c\right) - \left(1397760 i + 1397760\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(349440 i - 349440\right) \, a \cos\left(d x + c\right) + \left(349440 i + 349440\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{176400 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{4} + \sin\left(2 \, d x + 2 \, c\right)^{4} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/176400*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(352800*I + 352800)*a*cos(7*d*x + 7*c) + (176400*I + 176400)*a*cos(5*d*x + 5*c) - (167580*I + 167580)*a*cos(3*d*x + 3*c) - (59220*I + 59220)*a*cos(d*x + c) - (352800*I - 352800)*a*sin(7*d*x + 7*c) + (176400*I - 176400)*a*sin(5*d*x + 5*c) - (167580*I - 167580)*a*sin(3*d*x + 3*c) - (59220*I - 59220)*a*sin(d*x + c))*cos(7/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((236880*I + 236880)*a*cos(d*x + c) + (236880*I - 236880)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((236880*I + 236880)*a*cos(d*x + c) + (236880*I - 236880)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(352800*I + 352800)*a*cos(2*d*x + 2*c)^2 - (352800*I + 352800)*a*sin(2*d*x + 2*c)^2 + (705600*I + 705600)*a*cos(2*d*x + 2*c) - (352800*I + 352800)*a)*cos(3*d*x + 3*c) + (-(473760*I + 473760)*a*cos(d*x + c) - (473760*I - 473760)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (236880*I + 236880)*a*cos(d*x + c) + (-(352800*I - 352800)*a*cos(2*d*x + 2*c)^2 - (352800*I - 352800)*a*sin(2*d*x + 2*c)^2 + (705600*I - 705600)*a*cos(2*d*x + 2*c) - (352800*I - 352800)*a)*sin(3*d*x + 3*c) + (236880*I - 236880)*a*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(352800*I - 352800)*a*cos(7*d*x + 7*c) + (176400*I - 176400)*a*cos(5*d*x + 5*c) - (167580*I - 167580)*a*cos(3*d*x + 3*c) - (59220*I - 59220)*a*cos(d*x + c) + (352800*I + 352800)*a*sin(7*d*x + 7*c) - (176400*I + 176400)*a*sin(5*d*x + 5*c) + (167580*I + 167580)*a*sin(3*d*x + 3*c) + (59220*I + 59220)*a*sin(d*x + c))*sin(7/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((236880*I - 236880)*a*cos(d*x + c) - (236880*I + 236880)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((236880*I - 236880)*a*cos(d*x + c) - (236880*I + 236880)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(352800*I - 352800)*a*cos(2*d*x + 2*c)^2 - (352800*I - 352800)*a*sin(2*d*x + 2*c)^2 + (705600*I - 705600)*a*cos(2*d*x + 2*c) - (352800*I - 352800)*a)*cos(3*d*x + 3*c) + (-(473760*I - 473760)*a*cos(d*x + c) + (473760*I + 473760)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (236880*I - 236880)*a*cos(d*x + c) + ((352800*I + 352800)*a*cos(2*d*x + 2*c)^2 + (352800*I + 352800)*a*sin(2*d*x + 2*c)^2 - (705600*I + 705600)*a*cos(2*d*x + 2*c) + (352800*I + 352800)*a)*sin(3*d*x + 3*c) - (236880*I + 236880)*a*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((352800*I + 352800)*a*cos(2*d*x + 2*c)^4 + (352800*I + 352800)*a*sin(2*d*x + 2*c)^4 - (1411200*I + 1411200)*a*cos(2*d*x + 2*c)^3 + (2116800*I + 2116800)*a*cos(2*d*x + 2*c)^2 + ((705600*I + 705600)*a*cos(2*d*x + 2*c)^2 - (1411200*I + 1411200)*a*cos(2*d*x + 2*c) + (705600*I + 705600)*a)*sin(2*d*x + 2*c)^2 - (1411200*I + 1411200)*a*cos(2*d*x + 2*c) + (352800*I + 352800)*a)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + ((176400*I - 176400)*a*cos(2*d*x + 2*c)^4 + (176400*I - 176400)*a*sin(2*d*x + 2*c)^4 - (705600*I - 705600)*a*cos(2*d*x + 2*c)^3 + (1058400*I - 1058400)*a*cos(2*d*x + 2*c)^2 + ((352800*I - 352800)*a*cos(2*d*x + 2*c)^2 - (705600*I - 705600)*a*cos(2*d*x + 2*c) + (352800*I - 352800)*a)*sin(2*d*x + 2*c)^2 - (705600*I - 705600)*a*cos(2*d*x + 2*c) + (176400*I - 176400)*a)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((524580*I + 524580)*a*cos(d*x + c) + (524580*I - 524580)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((524580*I + 524580)*a*cos(d*x + c) + (524580*I - 524580)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((352800*I + 352800)*a*cos(2*d*x + 2*c)^2 + (352800*I + 352800)*a*sin(2*d*x + 2*c)^2 - (705600*I + 705600)*a*cos(2*d*x + 2*c) + (352800*I + 352800)*a)*cos(5*d*x + 5*c) + (-(823200*I + 823200)*a*cos(2*d*x + 2*c)^2 - (823200*I + 823200)*a*sin(2*d*x + 2*c)^2 + (1646400*I + 1646400)*a*cos(2*d*x + 2*c) - (823200*I + 823200)*a)*cos(3*d*x + 3*c) + (-(1049160*I + 1049160)*a*cos(d*x + c) - (1049160*I - 1049160)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (524580*I + 524580)*a*cos(d*x + c) + ((352800*I - 352800)*a*cos(2*d*x + 2*c)^2 + (352800*I - 352800)*a*sin(2*d*x + 2*c)^2 - (705600*I - 705600)*a*cos(2*d*x + 2*c) + (352800*I - 352800)*a)*sin(5*d*x + 5*c) + (-(823200*I - 823200)*a*cos(2*d*x + 2*c)^2 - (823200*I - 823200)*a*sin(2*d*x + 2*c)^2 + (1646400*I - 1646400)*a*cos(2*d*x + 2*c) - (823200*I - 823200)*a)*sin(3*d*x + 3*c) + (524580*I - 524580)*a*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(349440*I + 349440)*a*cos(d*x + c) - (349440*I - 349440)*a*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(349440*I + 349440)*a*cos(d*x + c) - (349440*I - 349440)*a*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((1397760*I + 1397760)*a*cos(d*x + c) + (1397760*I - 1397760)*a*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(2096640*I + 2096640)*a*cos(d*x + c) - (2096640*I - 2096640)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(698880*I + 698880)*a*cos(d*x + c) - (698880*I - 698880)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((1397760*I + 1397760)*a*cos(d*x + c) + (1397760*I - 1397760)*a*sin(d*x + c))*cos(2*d*x + 2*c) - (698880*I + 698880)*a*cos(d*x + c) - (698880*I - 698880)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((1397760*I + 1397760)*a*cos(d*x + c) + (1397760*I - 1397760)*a*sin(d*x + c))*cos(2*d*x + 2*c) - (349440*I + 349440)*a*cos(d*x + c) - (349440*I - 349440)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((524580*I - 524580)*a*cos(d*x + c) - (524580*I + 524580)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((524580*I - 524580)*a*cos(d*x + c) - (524580*I + 524580)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((352800*I - 352800)*a*cos(2*d*x + 2*c)^2 + (352800*I - 352800)*a*sin(2*d*x + 2*c)^2 - (705600*I - 705600)*a*cos(2*d*x + 2*c) + (352800*I - 352800)*a)*cos(5*d*x + 5*c) + (-(823200*I - 823200)*a*cos(2*d*x + 2*c)^2 - (823200*I - 823200)*a*sin(2*d*x + 2*c)^2 + (1646400*I - 1646400)*a*cos(2*d*x + 2*c) - (823200*I - 823200)*a)*cos(3*d*x + 3*c) + (-(1049160*I - 1049160)*a*cos(d*x + c) + (1049160*I + 1049160)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (524580*I - 524580)*a*cos(d*x + c) + (-(352800*I + 352800)*a*cos(2*d*x + 2*c)^2 - (352800*I + 352800)*a*sin(2*d*x + 2*c)^2 + (705600*I + 705600)*a*cos(2*d*x + 2*c) - (352800*I + 352800)*a)*sin(5*d*x + 5*c) + ((823200*I + 823200)*a*cos(2*d*x + 2*c)^2 + (823200*I + 823200)*a*sin(2*d*x + 2*c)^2 - (1646400*I + 1646400)*a*cos(2*d*x + 2*c) + (823200*I + 823200)*a)*sin(3*d*x + 3*c) - (524580*I + 524580)*a*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(349440*I - 349440)*a*cos(d*x + c) + (349440*I + 349440)*a*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(349440*I - 349440)*a*cos(d*x + c) + (349440*I + 349440)*a*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((1397760*I - 1397760)*a*cos(d*x + c) - (1397760*I + 1397760)*a*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(2096640*I - 2096640)*a*cos(d*x + c) + (2096640*I + 2096640)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(698880*I - 698880)*a*cos(d*x + c) + (698880*I + 698880)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((1397760*I - 1397760)*a*cos(d*x + c) - (1397760*I + 1397760)*a*sin(d*x + c))*cos(2*d*x + 2*c) - (698880*I - 698880)*a*cos(d*x + c) + (698880*I + 698880)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((1397760*I - 1397760)*a*cos(d*x + c) - (1397760*I + 1397760)*a*sin(d*x + c))*cos(2*d*x + 2*c) - (349440*I - 349440)*a*cos(d*x + c) + (349440*I + 349440)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^4 + sin(2*d*x + 2*c)^4 - 4*cos(2*d*x + 2*c)^3 + 2*(cos(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c)^2 - 4*cos(2*d*x + 2*c) + 1)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
201,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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
202,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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((I*a*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(3/2), x)","F",0
203,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\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((I*a*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c)), x)","F",0
204,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\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((I*a*tan(d*x + c) + a)^(5/2)/sqrt(tan(d*x + c)), x)","F",0
205,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\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((I*a*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(3/2), x)","F",0
206,1,1066,0,1.086872," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(36 i + 36\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(24 i + 24\right) \, a^{2} \cos\left(d x + c\right) - \left(36 i - 36\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(24 i - 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(36 i - 36\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(24 i - 24\right) \, a^{2} \cos\left(d x + c\right) + \left(36 i + 36\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(24 i + 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(36 i + 36\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(36 i + 36\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(72 i + 72\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(36 i + 36\right) \, a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(\left(18 i - 18\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(18 i - 18\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(36 i - 36\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(18 i - 18\right) \, a^{2}\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(12 i + 12\right) \, a^{2} \cos\left(d x + c\right) + \left(12 i - 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i + 12\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(12 i + 12\right) \, a^{2} \cos\left(d x + c\right) + \left(12 i - 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i - 12\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(24 i + 24\right) \, a^{2} \cos\left(d x + c\right) - \left(24 i - 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(12 i - 12\right) \, a^{2} \cos\left(d x + c\right) - \left(12 i + 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i - 12\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(12 i - 12\right) \, a^{2} \cos\left(d x + c\right) - \left(12 i + 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12 i + 12\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(24 i - 24\right) \, a^{2} \cos\left(d x + c\right) + \left(24 i + 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{9 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/9*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(36*I + 36)*a^2*cos(3*d*x + 3*c) + (24*I + 24)*a^2*cos(d*x + c) - (36*I - 36)*a^2*sin(3*d*x + 3*c) + (24*I - 24)*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(36*I - 36)*a^2*cos(3*d*x + 3*c) + (24*I - 24)*a^2*cos(d*x + c) + (36*I + 36)*a^2*sin(3*d*x + 3*c) - (24*I + 24)*a^2*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((36*I + 36)*a^2*cos(2*d*x + 2*c)^2 + (36*I + 36)*a^2*sin(2*d*x + 2*c)^2 - (72*I + 72)*a^2*cos(2*d*x + 2*c) + (36*I + 36)*a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + ((18*I - 18)*a^2*cos(2*d*x + 2*c)^2 + (18*I - 18)*a^2*sin(2*d*x + 2*c)^2 - (36*I - 36)*a^2*cos(2*d*x + 2*c) + (18*I - 18)*a^2)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((12*I + 12)*a^2*cos(d*x + c) + (12*I - 12)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12*I + 12)*a^2*cos(d*x + c) + ((12*I + 12)*a^2*cos(d*x + c) + (12*I - 12)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (12*I - 12)*a^2*sin(d*x + c) + (-(24*I + 24)*a^2*cos(d*x + c) - (24*I - 24)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((12*I - 12)*a^2*cos(d*x + c) - (12*I + 12)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12*I - 12)*a^2*cos(d*x + c) + ((12*I - 12)*a^2*cos(d*x + c) - (12*I + 12)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (12*I + 12)*a^2*sin(d*x + c) + (-(24*I - 24)*a^2*cos(d*x + c) + (24*I + 24)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
207,1,1278,0,0.877998," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(900 i - 900\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(930 i - 930\right) \, a^{2} \cos\left(d x + c\right) + \left(900 i + 900\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(930 i + 930\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\left(900 i + 900\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(930 i + 930\right) \, a^{2} \cos\left(d x + c\right) + \left(900 i - 900\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(930 i - 930\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(900 i - 900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i - 900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(1800 i - 1800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(900 i - 900\right) \, a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(-\left(450 i + 450\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(450 i + 450\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i + 900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(450 i + 450\right) \, a^{2}\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(900 i - 900\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - \left(750 i - 750\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(210 i - 210\right) \, a^{2} \cos\left(d x + c\right) - \left(900 i + 900\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(750 i + 750\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(210 i + 210\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(240 i - 240\right) \, a^{2} \cos\left(d x + c\right) + \left(240 i + 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(240 i - 240\right) \, a^{2} \cos\left(d x + c\right) + {\left(-\left(240 i - 240\right) \, a^{2} \cos\left(d x + c\right) + \left(240 i + 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(240 i + 240\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(480 i - 480\right) \, a^{2} \cos\left(d x + c\right) - \left(480 i + 480\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(900 i + 900\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + \left(750 i + 750\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(210 i + 210\right) \, a^{2} \cos\left(d x + c\right) - \left(900 i - 900\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(750 i - 750\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(210 i - 210\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(240 i + 240\right) \, a^{2} \cos\left(d x + c\right) + \left(240 i - 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(240 i + 240\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(240 i + 240\right) \, a^{2} \cos\left(d x + c\right) + \left(240 i - 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(240 i - 240\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(480 i + 480\right) \, a^{2} \cos\left(d x + c\right) - \left(480 i - 480\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{225 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/225*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(900*I - 900)*a^2*cos(3*d*x + 3*c) + (930*I - 930)*a^2*cos(d*x + c) + (900*I + 900)*a^2*sin(3*d*x + 3*c) - (930*I + 930)*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((900*I + 900)*a^2*cos(3*d*x + 3*c) - (930*I + 930)*a^2*cos(d*x + c) + (900*I - 900)*a^2*sin(3*d*x + 3*c) - (930*I - 930)*a^2*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((900*I - 900)*a^2*cos(2*d*x + 2*c)^2 + (900*I - 900)*a^2*sin(2*d*x + 2*c)^2 - (1800*I - 1800)*a^2*cos(2*d*x + 2*c) + (900*I - 900)*a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (-(450*I + 450)*a^2*cos(2*d*x + 2*c)^2 - (450*I + 450)*a^2*sin(2*d*x + 2*c)^2 + (900*I + 900)*a^2*cos(2*d*x + 2*c) - (450*I + 450)*a^2)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((900*I - 900)*a^2*cos(5*d*x + 5*c) - (750*I - 750)*a^2*cos(3*d*x + 3*c) + (210*I - 210)*a^2*cos(d*x + c) - (900*I + 900)*a^2*sin(5*d*x + 5*c) + (750*I + 750)*a^2*sin(3*d*x + 3*c) - (210*I + 210)*a^2*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(240*I - 240)*a^2*cos(d*x + c) + (240*I + 240)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (240*I - 240)*a^2*cos(d*x + c) + (-(240*I - 240)*a^2*cos(d*x + c) + (240*I + 240)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (240*I + 240)*a^2*sin(d*x + c) + ((480*I - 480)*a^2*cos(d*x + c) - (480*I + 480)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(900*I + 900)*a^2*cos(5*d*x + 5*c) + (750*I + 750)*a^2*cos(3*d*x + 3*c) - (210*I + 210)*a^2*cos(d*x + c) - (900*I - 900)*a^2*sin(5*d*x + 5*c) + (750*I - 750)*a^2*sin(3*d*x + 3*c) - (210*I - 210)*a^2*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((240*I + 240)*a^2*cos(d*x + c) + (240*I - 240)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (240*I + 240)*a^2*cos(d*x + c) + ((240*I + 240)*a^2*cos(d*x + c) + (240*I - 240)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (240*I - 240)*a^2*sin(d*x + c) + (-(480*I + 480)*a^2*cos(d*x + c) - (480*I - 480)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
208,1,3140,0,1.690159," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(44100 i + 44100\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) + \left(44100 i + 44100\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - \left(26460 i + 26460\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(1260 i + 1260\right) \, a^{2} \cos\left(d x + c\right) - \left(44100 i - 44100\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) + \left(44100 i - 44100\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) - \left(26460 i - 26460\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(1260 i - 1260\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(27300 i + 27300\right) \, a^{2} \cos\left(d x + c\right) + \left(27300 i - 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(27300 i + 27300\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(27300 i + 27300\right) \, a^{2} \cos\left(d x + c\right) + \left(27300 i - 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(27300 i - 27300\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i + 44100\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(54600 i + 54600\right) \, a^{2} \cos\left(d x + c\right) - \left(54600 i - 54600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i - 44100\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(44100 i - 44100\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) + \left(44100 i - 44100\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - \left(26460 i - 26460\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(1260 i - 1260\right) \, a^{2} \cos\left(d x + c\right) + \left(44100 i + 44100\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) - \left(44100 i + 44100\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(26460 i + 26460\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(1260 i + 1260\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(27300 i - 27300\right) \, a^{2} \cos\left(d x + c\right) - \left(27300 i + 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(27300 i - 27300\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(27300 i - 27300\right) \, a^{2} \cos\left(d x + c\right) - \left(27300 i + 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(27300 i + 27300\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i - 44100\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(54600 i - 54600\right) \, a^{2} \cos\left(d x + c\right) + \left(54600 i + 54600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i + 44100\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} - \left(176400 i + 176400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + \left(264600 i + 264600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(176400 i + 176400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(176400 i + 176400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(88200 i + 88200\right) \, a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i + 44100\right) \, a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(\left(22050 i - 22050\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + \left(22050 i - 22050\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + \left(132300 i - 132300\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(22050 i - 22050\right) \, a^{2}\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(63840 i + 63840\right) \, a^{2} \cos\left(d x + c\right) + \left(63840 i - 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(63840 i + 63840\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i + 63840\right) \, a^{2} \cos\left(d x + c\right) + \left(63840 i - 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(63840 i - 63840\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i + 44100\right) \, a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(102900 i + 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(102900 i + 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(205800 i + 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(102900 i + 102900\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(127680 i + 127680\right) \, a^{2} \cos\left(d x + c\right) - \left(127680 i - 127680\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(102900 i - 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(102900 i - 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(205800 i - 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(102900 i - 102900\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(48300 i + 48300\right) \, a^{2} \cos\left(d x + c\right) - \left(48300 i - 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(48300 i + 48300\right) \, a^{2} \cos\left(d x + c\right) - \left(48300 i - 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(193200 i + 193200\right) \, a^{2} \cos\left(d x + c\right) + \left(193200 i - 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(289800 i + 289800\right) \, a^{2} \cos\left(d x + c\right) - \left(289800 i - 289800\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(48300 i + 48300\right) \, a^{2} \cos\left(d x + c\right) + {\left({\left(-\left(96600 i + 96600\right) \, a^{2} \cos\left(d x + c\right) - \left(96600 i - 96600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(96600 i + 96600\right) \, a^{2} \cos\left(d x + c\right) - \left(96600 i - 96600\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i + 193200\right) \, a^{2} \cos\left(d x + c\right) + \left(193200 i - 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(48300 i - 48300\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i + 193200\right) \, a^{2} \cos\left(d x + c\right) + \left(193200 i - 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(63840 i - 63840\right) \, a^{2} \cos\left(d x + c\right) - \left(63840 i + 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(63840 i - 63840\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i - 63840\right) \, a^{2} \cos\left(d x + c\right) - \left(63840 i + 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(63840 i + 63840\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(102900 i - 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(102900 i - 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(205800 i - 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(102900 i - 102900\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(127680 i - 127680\right) \, a^{2} \cos\left(d x + c\right) + \left(127680 i + 127680\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i + 44100\right) \, a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(102900 i + 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(102900 i + 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(205800 i + 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(102900 i + 102900\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(48300 i - 48300\right) \, a^{2} \cos\left(d x + c\right) + \left(48300 i + 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(48300 i - 48300\right) \, a^{2} \cos\left(d x + c\right) + \left(48300 i + 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(193200 i - 193200\right) \, a^{2} \cos\left(d x + c\right) - \left(193200 i + 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(289800 i - 289800\right) \, a^{2} \cos\left(d x + c\right) + \left(289800 i + 289800\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(48300 i - 48300\right) \, a^{2} \cos\left(d x + c\right) + {\left({\left(-\left(96600 i - 96600\right) \, a^{2} \cos\left(d x + c\right) + \left(96600 i + 96600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(96600 i - 96600\right) \, a^{2} \cos\left(d x + c\right) + \left(96600 i + 96600\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, a^{2} \cos\left(d x + c\right) - \left(193200 i + 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(48300 i + 48300\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, a^{2} \cos\left(d x + c\right) - \left(193200 i + 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{11025 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{4} + \sin\left(2 \, d x + 2 \, c\right)^{4} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/11025*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(44100*I + 44100)*a^2*cos(7*d*x + 7*c) + (44100*I + 44100)*a^2*cos(5*d*x + 5*c) - (26460*I + 26460)*a^2*cos(3*d*x + 3*c) + (1260*I + 1260)*a^2*cos(d*x + c) - (44100*I - 44100)*a^2*sin(7*d*x + 7*c) + (44100*I - 44100)*a^2*sin(5*d*x + 5*c) - (26460*I - 26460)*a^2*sin(3*d*x + 3*c) + (1260*I - 1260)*a^2*sin(d*x + c))*cos(7/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((27300*I + 27300)*a^2*cos(d*x + c) + (27300*I - 27300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (27300*I + 27300)*a^2*cos(d*x + c) + ((27300*I + 27300)*a^2*cos(d*x + c) + (27300*I - 27300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (27300*I - 27300)*a^2*sin(d*x + c) + (-(44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 - (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 + (88200*I + 88200)*a^2*cos(2*d*x + 2*c) - (44100*I + 44100)*a^2)*cos(3*d*x + 3*c) + (-(54600*I + 54600)*a^2*cos(d*x + c) - (54600*I - 54600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (-(44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 - (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 + (88200*I - 88200)*a^2*cos(2*d*x + 2*c) - (44100*I - 44100)*a^2)*sin(3*d*x + 3*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(44100*I - 44100)*a^2*cos(7*d*x + 7*c) + (44100*I - 44100)*a^2*cos(5*d*x + 5*c) - (26460*I - 26460)*a^2*cos(3*d*x + 3*c) + (1260*I - 1260)*a^2*cos(d*x + c) + (44100*I + 44100)*a^2*sin(7*d*x + 7*c) - (44100*I + 44100)*a^2*sin(5*d*x + 5*c) + (26460*I + 26460)*a^2*sin(3*d*x + 3*c) - (1260*I + 1260)*a^2*sin(d*x + c))*sin(7/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((27300*I - 27300)*a^2*cos(d*x + c) - (27300*I + 27300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (27300*I - 27300)*a^2*cos(d*x + c) + ((27300*I - 27300)*a^2*cos(d*x + c) - (27300*I + 27300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (27300*I + 27300)*a^2*sin(d*x + c) + (-(44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 - (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 + (88200*I - 88200)*a^2*cos(2*d*x + 2*c) - (44100*I - 44100)*a^2)*cos(3*d*x + 3*c) + (-(54600*I - 54600)*a^2*cos(d*x + c) + (54600*I + 54600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I + 88200)*a^2*cos(2*d*x + 2*c) + (44100*I + 44100)*a^2)*sin(3*d*x + 3*c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((44100*I + 44100)*a^2*cos(2*d*x + 2*c)^4 + (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^4 - (176400*I + 176400)*a^2*cos(2*d*x + 2*c)^3 + (264600*I + 264600)*a^2*cos(2*d*x + 2*c)^2 - (176400*I + 176400)*a^2*cos(2*d*x + 2*c) + ((88200*I + 88200)*a^2*cos(2*d*x + 2*c)^2 - (176400*I + 176400)*a^2*cos(2*d*x + 2*c) + (88200*I + 88200)*a^2)*sin(2*d*x + 2*c)^2 + (44100*I + 44100)*a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + ((22050*I - 22050)*a^2*cos(2*d*x + 2*c)^4 + (22050*I - 22050)*a^2*sin(2*d*x + 2*c)^4 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c)^3 + (132300*I - 132300)*a^2*cos(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*sin(2*d*x + 2*c)^2 + (22050*I - 22050)*a^2)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((63840*I + 63840)*a^2*cos(d*x + c) + (63840*I - 63840)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (63840*I + 63840)*a^2*cos(d*x + c) + ((63840*I + 63840)*a^2*cos(d*x + c) + (63840*I - 63840)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (63840*I - 63840)*a^2*sin(d*x + c) + ((44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I + 88200)*a^2*cos(2*d*x + 2*c) + (44100*I + 44100)*a^2)*cos(5*d*x + 5*c) + (-(102900*I + 102900)*a^2*cos(2*d*x + 2*c)^2 - (102900*I + 102900)*a^2*sin(2*d*x + 2*c)^2 + (205800*I + 205800)*a^2*cos(2*d*x + 2*c) - (102900*I + 102900)*a^2)*cos(3*d*x + 3*c) + (-(127680*I + 127680)*a^2*cos(d*x + c) - (127680*I - 127680)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*sin(5*d*x + 5*c) + (-(102900*I - 102900)*a^2*cos(2*d*x + 2*c)^2 - (102900*I - 102900)*a^2*sin(2*d*x + 2*c)^2 + (205800*I - 205800)*a^2*cos(2*d*x + 2*c) - (102900*I - 102900)*a^2)*sin(3*d*x + 3*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(48300*I + 48300)*a^2*cos(d*x + c) - (48300*I - 48300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(48300*I + 48300)*a^2*cos(d*x + c) - (48300*I - 48300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((193200*I + 193200)*a^2*cos(d*x + c) + (193200*I - 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(289800*I + 289800)*a^2*cos(d*x + c) - (289800*I - 289800)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (48300*I + 48300)*a^2*cos(d*x + c) + ((-(96600*I + 96600)*a^2*cos(d*x + c) - (96600*I - 96600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (96600*I + 96600)*a^2*cos(d*x + c) - (96600*I - 96600)*a^2*sin(d*x + c) + ((193200*I + 193200)*a^2*cos(d*x + c) + (193200*I - 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 - (48300*I - 48300)*a^2*sin(d*x + c) + ((193200*I + 193200)*a^2*cos(d*x + c) + (193200*I - 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((63840*I - 63840)*a^2*cos(d*x + c) - (63840*I + 63840)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (63840*I - 63840)*a^2*cos(d*x + c) + ((63840*I - 63840)*a^2*cos(d*x + c) - (63840*I + 63840)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (63840*I + 63840)*a^2*sin(d*x + c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*cos(5*d*x + 5*c) + (-(102900*I - 102900)*a^2*cos(2*d*x + 2*c)^2 - (102900*I - 102900)*a^2*sin(2*d*x + 2*c)^2 + (205800*I - 205800)*a^2*cos(2*d*x + 2*c) - (102900*I - 102900)*a^2)*cos(3*d*x + 3*c) + (-(127680*I - 127680)*a^2*cos(d*x + c) + (127680*I + 127680)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (-(44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 - (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 + (88200*I + 88200)*a^2*cos(2*d*x + 2*c) - (44100*I + 44100)*a^2)*sin(5*d*x + 5*c) + ((102900*I + 102900)*a^2*cos(2*d*x + 2*c)^2 + (102900*I + 102900)*a^2*sin(2*d*x + 2*c)^2 - (205800*I + 205800)*a^2*cos(2*d*x + 2*c) + (102900*I + 102900)*a^2)*sin(3*d*x + 3*c))*sin(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(48300*I - 48300)*a^2*cos(d*x + c) + (48300*I + 48300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(48300*I - 48300)*a^2*cos(d*x + c) + (48300*I + 48300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((193200*I - 193200)*a^2*cos(d*x + c) - (193200*I + 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(289800*I - 289800)*a^2*cos(d*x + c) + (289800*I + 289800)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (48300*I - 48300)*a^2*cos(d*x + c) + ((-(96600*I - 96600)*a^2*cos(d*x + c) + (96600*I + 96600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (96600*I - 96600)*a^2*cos(d*x + c) + (96600*I + 96600)*a^2*sin(d*x + c) + ((193200*I - 193200)*a^2*cos(d*x + c) - (193200*I + 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (48300*I + 48300)*a^2*sin(d*x + c) + ((193200*I - 193200)*a^2*cos(d*x + c) - (193200*I + 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^4 + sin(2*d*x + 2*c)^4 - 4*cos(2*d*x + 2*c)^3 + 2*(cos(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c)^2 - 4*cos(2*d*x + 2*c) + 1)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
209,1,3464,0,1.979829," ","integrate((a+I*a*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(-\left(6350400 i - 6350400\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) + \left(21168000 i - 21168000\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - \left(25824960 i - 25824960\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(11429460 i - 11429460\right) \, a^{2} \cos\left(d x + c\right) + \left(6350400 i + 6350400\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) - \left(21168000 i + 21168000\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(25824960 i + 25824960\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(11429460 i + 11429460\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(1219680 i - 1219680\right) \, a^{2} \cos\left(d x + c\right) - \left(1219680 i + 1219680\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(1219680 i - 1219680\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i - 1219680\right) \, a^{2} \cos\left(d x + c\right) - \left(1219680 i + 1219680\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(1219680 i + 1219680\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(6350400 i - 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(6350400 i - 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12700800 i - 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(6350400 i - 6350400\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(2439360 i - 2439360\right) \, a^{2} \cos\left(d x + c\right) + \left(2439360 i + 2439360\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(6350400 i + 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(6350400 i + 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(6350400 i + 6350400\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(\left(6350400 i + 6350400\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) - \left(21168000 i + 21168000\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + \left(25824960 i + 25824960\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(11429460 i + 11429460\right) \, a^{2} \cos\left(d x + c\right) + \left(6350400 i - 6350400\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) - \left(21168000 i - 21168000\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(25824960 i - 25824960\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(11429460 i - 11429460\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(1219680 i + 1219680\right) \, a^{2} \cos\left(d x + c\right) - \left(1219680 i - 1219680\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(1219680 i + 1219680\right) \, a^{2} \cos\left(d x + c\right) + {\left(-\left(1219680 i + 1219680\right) \, a^{2} \cos\left(d x + c\right) - \left(1219680 i - 1219680\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(1219680 i - 1219680\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(6350400 i + 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(6350400 i + 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(6350400 i + 6350400\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(2439360 i + 2439360\right) \, a^{2} \cos\left(d x + c\right) + \left(2439360 i - 2439360\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(6350400 i - 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(6350400 i - 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12700800 i - 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(6350400 i - 6350400\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(6350400 i - 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + \left(6350400 i - 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} - \left(25401600 i - 25401600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + \left(38102400 i - 38102400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(25401600 i - 25401600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(12700800 i - 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(25401600 i - 25401600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(12700800 i - 12700800\right) \, a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(6350400 i - 6350400\right) \, a^{2}\right)} \arctan\left({\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \cos\left(d x + c\right), {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) - \sin\left(d x + c\right)\right) + {\left(-\left(3175200 i + 3175200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} - \left(3175200 i + 3175200\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} - \left(19051200 i + 19051200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i + 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(6350400 i + 6350400\right) \, a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(3175200 i + 3175200\right) \, a^{2}\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)^{2}\right)} - 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) \sin\left(d x + c\right) + \cos\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(6350400 i - 6350400\right) \, a^{2} \cos\left(9 \, d x + 9 \, c\right) - \left(7408800 i - 7408800\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) + \left(8414280 i - 8414280\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - \left(631260 i - 631260\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(1079820 i - 1079820\right) \, a^{2} \cos\left(d x + c\right) - \left(6350400 i + 6350400\right) \, a^{2} \sin\left(9 \, d x + 9 \, c\right) + \left(7408800 i + 7408800\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) - \left(8414280 i + 8414280\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(631260 i + 631260\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(1079820 i + 1079820\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(7159320 i - 7159320\right) \, a^{2} \cos\left(d x + c\right) - \left(7159320 i + 7159320\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(7159320 i - 7159320\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(7159320 i - 7159320\right) \, a^{2} \cos\left(d x + c\right) - \left(7159320 i + 7159320\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(7159320 i + 7159320\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(6350400 i - 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(6350400 i - 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12700800 i - 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(6350400 i - 6350400\right) \, a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(14817600 i - 14817600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(14817600 i - 14817600\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(29635200 i - 29635200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(14817600 i - 14817600\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(14318640 i - 14318640\right) \, a^{2} \cos\left(d x + c\right) + \left(14318640 i + 14318640\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i + 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(6350400 i + 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(6350400 i + 6350400\right) \, a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(14817600 i + 14817600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(14817600 i + 14817600\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(29635200 i + 29635200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(14817600 i + 14817600\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(12378240 i - 12378240\right) \, a^{2} \cos\left(d x + c\right) + \left(12378240 i + 12378240\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(12378240 i - 12378240\right) \, a^{2} \cos\left(d x + c\right) + \left(12378240 i + 12378240\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(49512960 i - 49512960\right) \, a^{2} \cos\left(d x + c\right) - \left(49512960 i + 49512960\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(74269440 i - 74269440\right) \, a^{2} \cos\left(d x + c\right) + \left(74269440 i + 74269440\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(12378240 i - 12378240\right) \, a^{2} \cos\left(d x + c\right) + {\left({\left(-\left(24756480 i - 24756480\right) \, a^{2} \cos\left(d x + c\right) + \left(24756480 i + 24756480\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(24756480 i - 24756480\right) \, a^{2} \cos\left(d x + c\right) + \left(24756480 i + 24756480\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(49512960 i - 49512960\right) \, a^{2} \cos\left(d x + c\right) - \left(49512960 i + 49512960\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12378240 i + 12378240\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(49512960 i - 49512960\right) \, a^{2} \cos\left(d x + c\right) - \left(49512960 i + 49512960\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left(-\left(6350400 i + 6350400\right) \, a^{2} \cos\left(9 \, d x + 9 \, c\right) + \left(7408800 i + 7408800\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) - \left(8414280 i + 8414280\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + \left(631260 i + 631260\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(1079820 i + 1079820\right) \, a^{2} \cos\left(d x + c\right) - \left(6350400 i - 6350400\right) \, a^{2} \sin\left(9 \, d x + 9 \, c\right) + \left(7408800 i - 7408800\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) - \left(8414280 i - 8414280\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(631260 i - 631260\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(1079820 i - 1079820\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(-\left(7159320 i + 7159320\right) \, a^{2} \cos\left(d x + c\right) - \left(7159320 i - 7159320\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(7159320 i + 7159320\right) \, a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i + 7159320\right) \, a^{2} \cos\left(d x + c\right) - \left(7159320 i - 7159320\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(7159320 i - 7159320\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(6350400 i + 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(6350400 i + 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12700800 i + 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(6350400 i + 6350400\right) \, a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(14817600 i + 14817600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(14817600 i + 14817600\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(29635200 i + 29635200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(14817600 i + 14817600\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(14318640 i + 14318640\right) \, a^{2} \cos\left(d x + c\right) + \left(14318640 i - 14318640\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i - 6350400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(6350400 i - 6350400\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12700800 i - 12700800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(6350400 i - 6350400\right) \, a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(14817600 i - 14817600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(14817600 i - 14817600\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(29635200 i - 29635200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(14817600 i - 14817600\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right) + {\left({\left(\left(12378240 i + 12378240\right) \, a^{2} \cos\left(d x + c\right) + \left(12378240 i - 12378240\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(12378240 i + 12378240\right) \, a^{2} \cos\left(d x + c\right) + \left(12378240 i - 12378240\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(49512960 i + 49512960\right) \, a^{2} \cos\left(d x + c\right) - \left(49512960 i - 49512960\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(\left(74269440 i + 74269440\right) \, a^{2} \cos\left(d x + c\right) + \left(74269440 i - 74269440\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12378240 i + 12378240\right) \, a^{2} \cos\left(d x + c\right) + {\left({\left(\left(24756480 i + 24756480\right) \, a^{2} \cos\left(d x + c\right) + \left(24756480 i - 24756480\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(24756480 i + 24756480\right) \, a^{2} \cos\left(d x + c\right) + \left(24756480 i - 24756480\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(49512960 i + 49512960\right) \, a^{2} \cos\left(d x + c\right) - \left(49512960 i - 49512960\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12378240 i - 12378240\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(49512960 i + 49512960\right) \, a^{2} \cos\left(d x + c\right) - \left(49512960 i - 49512960\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), -\cos\left(2 \, d x + 2 \, c\right) + 1\right)\right)\right)} \sqrt{a}}{1587600 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{4} + \sin\left(2 \, d x + 2 \, c\right)^{4} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/1587600*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*((-(6350400*I - 6350400)*a^2*cos(7*d*x + 7*c) + (21168000*I - 21168000)*a^2*cos(5*d*x + 5*c) - (25824960*I - 25824960)*a^2*cos(3*d*x + 3*c) + (11429460*I - 11429460)*a^2*cos(d*x + c) + (6350400*I + 6350400)*a^2*sin(7*d*x + 7*c) - (21168000*I + 21168000)*a^2*sin(5*d*x + 5*c) + (25824960*I + 25824960)*a^2*sin(3*d*x + 3*c) - (11429460*I + 11429460)*a^2*sin(d*x + c))*cos(7/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((1219680*I - 1219680)*a^2*cos(d*x + c) - (1219680*I + 1219680)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (1219680*I - 1219680)*a^2*cos(d*x + c) + ((1219680*I - 1219680)*a^2*cos(d*x + c) - (1219680*I + 1219680)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (1219680*I + 1219680)*a^2*sin(d*x + c) + (-(6350400*I - 6350400)*a^2*cos(2*d*x + 2*c)^2 - (6350400*I - 6350400)*a^2*sin(2*d*x + 2*c)^2 + (12700800*I - 12700800)*a^2*cos(2*d*x + 2*c) - (6350400*I - 6350400)*a^2)*cos(3*d*x + 3*c) + (-(2439360*I - 2439360)*a^2*cos(d*x + c) + (2439360*I + 2439360)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((6350400*I + 6350400)*a^2*cos(2*d*x + 2*c)^2 + (6350400*I + 6350400)*a^2*sin(2*d*x + 2*c)^2 - (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c) + (6350400*I + 6350400)*a^2)*sin(3*d*x + 3*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((6350400*I + 6350400)*a^2*cos(7*d*x + 7*c) - (21168000*I + 21168000)*a^2*cos(5*d*x + 5*c) + (25824960*I + 25824960)*a^2*cos(3*d*x + 3*c) - (11429460*I + 11429460)*a^2*cos(d*x + c) + (6350400*I - 6350400)*a^2*sin(7*d*x + 7*c) - (21168000*I - 21168000)*a^2*sin(5*d*x + 5*c) + (25824960*I - 25824960)*a^2*sin(3*d*x + 3*c) - (11429460*I - 11429460)*a^2*sin(d*x + c))*sin(7/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(1219680*I + 1219680)*a^2*cos(d*x + c) - (1219680*I - 1219680)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (1219680*I + 1219680)*a^2*cos(d*x + c) + (-(1219680*I + 1219680)*a^2*cos(d*x + c) - (1219680*I - 1219680)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (1219680*I - 1219680)*a^2*sin(d*x + c) + ((6350400*I + 6350400)*a^2*cos(2*d*x + 2*c)^2 + (6350400*I + 6350400)*a^2*sin(2*d*x + 2*c)^2 - (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c) + (6350400*I + 6350400)*a^2)*cos(3*d*x + 3*c) + ((2439360*I + 2439360)*a^2*cos(d*x + c) + (2439360*I - 2439360)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((6350400*I - 6350400)*a^2*cos(2*d*x + 2*c)^2 + (6350400*I - 6350400)*a^2*sin(2*d*x + 2*c)^2 - (12700800*I - 12700800)*a^2*cos(2*d*x + 2*c) + (6350400*I - 6350400)*a^2)*sin(3*d*x + 3*c))*sin(3/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a) + (((6350400*I - 6350400)*a^2*cos(2*d*x + 2*c)^4 + (6350400*I - 6350400)*a^2*sin(2*d*x + 2*c)^4 - (25401600*I - 25401600)*a^2*cos(2*d*x + 2*c)^3 + (38102400*I - 38102400)*a^2*cos(2*d*x + 2*c)^2 - (25401600*I - 25401600)*a^2*cos(2*d*x + 2*c) + ((12700800*I - 12700800)*a^2*cos(2*d*x + 2*c)^2 - (25401600*I - 25401600)*a^2*cos(2*d*x + 2*c) + (12700800*I - 12700800)*a^2)*sin(2*d*x + 2*c)^2 + (6350400*I - 6350400)*a^2)*arctan2((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - cos(d*x + c), (cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) - sin(d*x + c)) + (-(3175200*I + 3175200)*a^2*cos(2*d*x + 2*c)^4 - (3175200*I + 3175200)*a^2*sin(2*d*x + 2*c)^4 + (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c)^3 - (19051200*I + 19051200)*a^2*cos(2*d*x + 2*c)^2 + (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c) + (-(6350400*I + 6350400)*a^2*cos(2*d*x + 2*c)^2 + (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c) - (6350400*I + 6350400)*a^2)*sin(2*d*x + 2*c)^2 - (3175200*I + 3175200)*a^2)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))^2) - 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1))*sin(d*x + c) + cos(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((6350400*I - 6350400)*a^2*cos(9*d*x + 9*c) - (7408800*I - 7408800)*a^2*cos(7*d*x + 7*c) + (8414280*I - 8414280)*a^2*cos(5*d*x + 5*c) - (631260*I - 631260)*a^2*cos(3*d*x + 3*c) - (1079820*I - 1079820)*a^2*cos(d*x + c) - (6350400*I + 6350400)*a^2*sin(9*d*x + 9*c) + (7408800*I + 7408800)*a^2*sin(7*d*x + 7*c) - (8414280*I + 8414280)*a^2*sin(5*d*x + 5*c) + (631260*I + 631260)*a^2*sin(3*d*x + 3*c) + (1079820*I + 1079820)*a^2*sin(d*x + c))*cos(9/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((7159320*I - 7159320)*a^2*cos(d*x + c) - (7159320*I + 7159320)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (7159320*I - 7159320)*a^2*cos(d*x + c) + ((7159320*I - 7159320)*a^2*cos(d*x + c) - (7159320*I + 7159320)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (7159320*I + 7159320)*a^2*sin(d*x + c) + ((6350400*I - 6350400)*a^2*cos(2*d*x + 2*c)^2 + (6350400*I - 6350400)*a^2*sin(2*d*x + 2*c)^2 - (12700800*I - 12700800)*a^2*cos(2*d*x + 2*c) + (6350400*I - 6350400)*a^2)*cos(5*d*x + 5*c) + (-(14817600*I - 14817600)*a^2*cos(2*d*x + 2*c)^2 - (14817600*I - 14817600)*a^2*sin(2*d*x + 2*c)^2 + (29635200*I - 29635200)*a^2*cos(2*d*x + 2*c) - (14817600*I - 14817600)*a^2)*cos(3*d*x + 3*c) + (-(14318640*I - 14318640)*a^2*cos(d*x + c) + (14318640*I + 14318640)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (-(6350400*I + 6350400)*a^2*cos(2*d*x + 2*c)^2 - (6350400*I + 6350400)*a^2*sin(2*d*x + 2*c)^2 + (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c) - (6350400*I + 6350400)*a^2)*sin(5*d*x + 5*c) + ((14817600*I + 14817600)*a^2*cos(2*d*x + 2*c)^2 + (14817600*I + 14817600)*a^2*sin(2*d*x + 2*c)^2 - (29635200*I + 29635200)*a^2*cos(2*d*x + 2*c) + (14817600*I + 14817600)*a^2)*sin(3*d*x + 3*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(12378240*I - 12378240)*a^2*cos(d*x + c) + (12378240*I + 12378240)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(12378240*I - 12378240)*a^2*cos(d*x + c) + (12378240*I + 12378240)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((49512960*I - 49512960)*a^2*cos(d*x + c) - (49512960*I + 49512960)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(74269440*I - 74269440)*a^2*cos(d*x + c) + (74269440*I + 74269440)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (12378240*I - 12378240)*a^2*cos(d*x + c) + ((-(24756480*I - 24756480)*a^2*cos(d*x + c) + (24756480*I + 24756480)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (24756480*I - 24756480)*a^2*cos(d*x + c) + (24756480*I + 24756480)*a^2*sin(d*x + c) + ((49512960*I - 49512960)*a^2*cos(d*x + c) - (49512960*I + 49512960)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (12378240*I + 12378240)*a^2*sin(d*x + c) + ((49512960*I - 49512960)*a^2*cos(d*x + c) - (49512960*I + 49512960)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (-(6350400*I + 6350400)*a^2*cos(9*d*x + 9*c) + (7408800*I + 7408800)*a^2*cos(7*d*x + 7*c) - (8414280*I + 8414280)*a^2*cos(5*d*x + 5*c) + (631260*I + 631260)*a^2*cos(3*d*x + 3*c) + (1079820*I + 1079820)*a^2*cos(d*x + c) - (6350400*I - 6350400)*a^2*sin(9*d*x + 9*c) + (7408800*I - 7408800)*a^2*sin(7*d*x + 7*c) - (8414280*I - 8414280)*a^2*sin(5*d*x + 5*c) + (631260*I - 631260)*a^2*sin(3*d*x + 3*c) + (1079820*I - 1079820)*a^2*sin(d*x + c))*sin(9/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + ((-(7159320*I + 7159320)*a^2*cos(d*x + c) - (7159320*I - 7159320)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (7159320*I + 7159320)*a^2*cos(d*x + c) + (-(7159320*I + 7159320)*a^2*cos(d*x + c) - (7159320*I - 7159320)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (7159320*I - 7159320)*a^2*sin(d*x + c) + (-(6350400*I + 6350400)*a^2*cos(2*d*x + 2*c)^2 - (6350400*I + 6350400)*a^2*sin(2*d*x + 2*c)^2 + (12700800*I + 12700800)*a^2*cos(2*d*x + 2*c) - (6350400*I + 6350400)*a^2)*cos(5*d*x + 5*c) + ((14817600*I + 14817600)*a^2*cos(2*d*x + 2*c)^2 + (14817600*I + 14817600)*a^2*sin(2*d*x + 2*c)^2 - (29635200*I + 29635200)*a^2*cos(2*d*x + 2*c) + (14817600*I + 14817600)*a^2)*cos(3*d*x + 3*c) + ((14318640*I + 14318640)*a^2*cos(d*x + c) + (14318640*I - 14318640)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (-(6350400*I - 6350400)*a^2*cos(2*d*x + 2*c)^2 - (6350400*I - 6350400)*a^2*sin(2*d*x + 2*c)^2 + (12700800*I - 12700800)*a^2*cos(2*d*x + 2*c) - (6350400*I - 6350400)*a^2)*sin(5*d*x + 5*c) + ((14817600*I - 14817600)*a^2*cos(2*d*x + 2*c)^2 + (14817600*I - 14817600)*a^2*sin(2*d*x + 2*c)^2 - (29635200*I - 29635200)*a^2*cos(2*d*x + 2*c) + (14817600*I - 14817600)*a^2)*sin(3*d*x + 3*c))*sin(5/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)) + (((12378240*I + 12378240)*a^2*cos(d*x + c) + (12378240*I - 12378240)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + ((12378240*I + 12378240)*a^2*cos(d*x + c) + (12378240*I - 12378240)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + (-(49512960*I + 49512960)*a^2*cos(d*x + c) - (49512960*I - 49512960)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + ((74269440*I + 74269440)*a^2*cos(d*x + c) + (74269440*I - 74269440)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12378240*I + 12378240)*a^2*cos(d*x + c) + (((24756480*I + 24756480)*a^2*cos(d*x + c) + (24756480*I - 24756480)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (24756480*I + 24756480)*a^2*cos(d*x + c) + (24756480*I - 24756480)*a^2*sin(d*x + c) + (-(49512960*I + 49512960)*a^2*cos(d*x + c) - (49512960*I - 49512960)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (12378240*I - 12378240)*a^2*sin(d*x + c) + (-(49512960*I + 49512960)*a^2*cos(d*x + c) - (49512960*I - 49512960)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), -cos(2*d*x + 2*c) + 1)))*sqrt(a))/((cos(2*d*x + 2*c)^4 + sin(2*d*x + 2*c)^4 - 4*cos(2*d*x + 2*c)^3 + 2*(cos(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c)^2 - 4*cos(2*d*x + 2*c) + 1)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
219,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
220,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
221,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
222,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
223,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
224,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
225,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
226,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
227,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
228,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
229,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
230,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
231,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
232,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
233,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
234,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
235,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
236,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
237,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
238,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
239,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
240,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(14/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
241,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(10/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
242,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(8/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
243,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
244,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
245,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
246,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
247,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/3)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
248,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{4}{3}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(4/3), x)","F",0
249,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{2}{3}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(2/3), x)","F",0
250,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{1}{3}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(1/3), x)","F",0
251,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c)^(1/3), x)","F",0
252,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c)^(2/3), x)","F",0
253,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{\sqrt{i \, a \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(d*x + c) + a)/tan(d*x + c)^(4/3), x)","F",0
254,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(4/3), x)","F",0
255,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(2/3), x)","F",0
256,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\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((I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(1/3), x)","F",0
257,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{{\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((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(1/3), x)","F",0
258,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{{\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((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(2/3), x)","F",0
259,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)/tan(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{{\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((I*a*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(4/3), x)","F",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
267,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
268,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
269,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
270,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(2/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
271,-2,0,0,0.000000," ","integrate(1/tan(d*x+c)^(4/3)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
272,1,190,0,0.808339," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{14 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{13}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 7 \cdot 2^{\frac{1}{3}} a^{\frac{13}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 14 \cdot 2^{\frac{1}{3}} a^{\frac{13}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{3}} a^{2} + 21 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a^{3} - 84 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{4}}{28 \, a^{4} d}"," ",0,"1/28*(14*sqrt(3)*2^(1/3)*a^(13/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 7*2^(1/3)*a^(13/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 14*2^(1/3)*a^(13/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 12*(I*a*tan(d*x + c) + a)^(7/3)*a^2 + 21*(I*a*tan(d*x + c) + a)^(4/3)*a^3 - 84*(I*a*tan(d*x + c) + a)^(1/3)*a^4)/(a^4*d)","A",0
273,1,153,0,0.704249," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{10}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{10}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{10}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a^{2}\right)}}{4 \, a^{3} d}"," ",0,"1/4*I*(2*sqrt(3)*2^(1/3)*a^(10/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 2^(1/3)*a^(10/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(10/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 3*(I*a*tan(d*x + c) + a)^(4/3)*a^2)/(a^3*d)","A",0
274,1,153,0,0.544398," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{7}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{7}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{7}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{2}}{4 \, a^{2} d}"," ",0,"-1/4*(2*sqrt(3)*2^(1/3)*a^(7/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 2^(1/3)*a^(7/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(7/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 12*(I*a*tan(d*x + c) + a)^(1/3)*a^2)/(a^2*d)","A",0
275,1,135,0,0.627883," ","integrate((a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{4}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{4}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{4}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)\right)}}{4 \, a d}"," ",0,"-1/4*I*(2*sqrt(3)*2^(1/3)*a^(4/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 2^(1/3)*a^(4/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(4/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)))/(a*d)","A",0
276,1,233,0,0.951782," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 4 \, \sqrt{3} a^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 2 \, a^{\frac{1}{3}} \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 4 \, a^{\frac{1}{3}} \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{4 \, d}"," ",0,"1/4*(2*sqrt(3)*2^(1/3)*a^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 4*sqrt(3)*a^(1/3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3)) + 2^(1/3)*a^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 2*a^(1/3)*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3)) + 4*a^(1/3)*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3)))/d","A",0
277,1,261,0,0.878814," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{6 \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{2}{3}}} - \frac{4 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{2}{3}}} + \frac{3 \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}} - \frac{6 \cdot 2^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{2}{3}}} - \frac{2 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}} + \frac{4 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{2}{3}}} + \frac{12 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}{a \tan\left(d x + c\right)}\right)} a}{12 \, d}"," ",0,"1/12*I*(6*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(2/3) - 4*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(2/3) + 3*2^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(2/3) - 6*2^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(2/3) - 2*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(2/3) + 4*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(2/3) + 12*I*(I*a*tan(d*x + c) + a)^(1/3)/(a*tan(d*x + c)))*a/d","A",0
278,1,306,0,0.574290," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{18 \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{5}{3}}} - \frac{6 \, {\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} + a^{3}} - \frac{32 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{5}{3}}} + \frac{9 \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{5}{3}}} - \frac{18 \cdot 2^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{5}{3}}} - \frac{16 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{5}{3}}} + \frac{32 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{5}{3}}}\right)}}{36 \, d}"," ",0,"-1/36*a^2*(18*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(5/3) - 6*((I*a*tan(d*x + c) + a)^(4/3) + 2*(I*a*tan(d*x + c) + a)^(1/3)*a)/((I*a*tan(d*x + c) + a)^2*a - 2*(I*a*tan(d*x + c) + a)*a^2 + a^3) - 32*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(5/3) + 9*2^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(5/3) - 18*2^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(5/3) - 16*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(5/3) + 32*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(5/3))/d","A",0
279,1,136,0,0.482629," ","integrate((a+I*a*tan(d*x+c))^(2/3),x, algorithm=""maxima"")","\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{5}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{5}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{5}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)\right)}}{4 \, a d}"," ",0,"1/4*I*(2*sqrt(3)*2^(2/3)*a^(5/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(5/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(5/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)))/(a*d)","A",0
280,1,208,0,0.691584," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{140 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{16}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 70 \cdot 2^{\frac{1}{3}} a^{\frac{16}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 140 \cdot 2^{\frac{1}{3}} a^{\frac{16}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 42 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{10}{3}} a^{2} + 60 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{3}} a^{3} - 105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a^{4} - 420 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{5}}{140 \, a^{4} d}"," ",0,"1/140*(140*sqrt(3)*2^(1/3)*a^(16/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 70*2^(1/3)*a^(16/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 140*2^(1/3)*a^(16/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 42*(I*a*tan(d*x + c) + a)^(10/3)*a^2 + 60*(I*a*tan(d*x + c) + a)^(7/3)*a^3 - 105*(I*a*tan(d*x + c) + a)^(4/3)*a^4 - 420*(I*a*tan(d*x + c) + a)^(1/3)*a^5)/(a^4*d)","A",0
281,1,172,0,0.852549," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{i \, {\left(14 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{13}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 7 \cdot 2^{\frac{1}{3}} a^{\frac{13}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 14 \cdot 2^{\frac{1}{3}} a^{\frac{13}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{3}} a^{2} - 42 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{4}\right)}}{14 \, a^{3} d}"," ",0,"1/14*I*(14*sqrt(3)*2^(1/3)*a^(13/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 7*2^(1/3)*a^(13/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 14*2^(1/3)*a^(13/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 6*(I*a*tan(d*x + c) + a)^(7/3)*a^2 - 42*(I*a*tan(d*x + c) + a)^(1/3)*a^4)/(a^3*d)","A",0
282,1,172,0,0.751066," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{4 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{10}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 2 \cdot 2^{\frac{1}{3}} a^{\frac{10}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 4 \cdot 2^{\frac{1}{3}} a^{\frac{10}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a^{2} - 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{3}}{4 \, a^{2} d}"," ",0,"-1/4*(4*sqrt(3)*2^(1/3)*a^(10/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 2*2^(1/3)*a^(10/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 4*2^(1/3)*a^(10/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 3*(I*a*tan(d*x + c) + a)^(4/3)*a^2 - 12*(I*a*tan(d*x + c) + a)^(1/3)*a^3)/(a^2*d)","A",0
283,1,153,0,0.708944," ","integrate((a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{7}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{7}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{7}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{2}\right)}}{2 \, a d}"," ",0,"-1/2*I*(2*sqrt(3)*2^(1/3)*a^(7/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 2^(1/3)*a^(7/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(7/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 6*(I*a*tan(d*x + c) + a)^(1/3)*a^2)/(a*d)","A",0
284,1,233,0,0.560424," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{4}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2 \, \sqrt{3} a^{\frac{4}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{4}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{4}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - a^{\frac{4}{3}} \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 2 \, a^{\frac{4}{3}} \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{2 \, d}"," ",0,"1/2*(2*sqrt(3)*2^(1/3)*a^(4/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2*sqrt(3)*a^(4/3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3)) + 2^(1/3)*a^(4/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(4/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - a^(4/3)*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3)) + 2*a^(4/3)*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3)))/d","A",0
285,1,258,0,0.507711," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{i \, {\left(6 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 8 \, \sqrt{3} a^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right) + 3 \cdot 2^{\frac{1}{3}} a^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 6 \cdot 2^{\frac{1}{3}} a^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - 4 \, a^{\frac{1}{3}} \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right) + 8 \, a^{\frac{1}{3}} \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right) + \frac{6 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}{\tan\left(d x + c\right)}\right)} a}{6 \, d}"," ",0,"1/6*I*(6*sqrt(3)*2^(1/3)*a^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 8*sqrt(3)*a^(1/3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3)) + 3*2^(1/3)*a^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 6*2^(1/3)*a^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 4*a^(1/3)*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3)) + 8*a^(1/3)*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3)) + 6*I*(I*a*tan(d*x + c) + a)^(1/3)/tan(d*x + c))*a/d","A",0
286,1,304,0,0.520953," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{{\left(\frac{18 \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{2}{3}}} - \frac{22 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{2}{3}}} + \frac{9 \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}} - \frac{18 \cdot 2^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{2}{3}}} - \frac{11 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}} + \frac{22 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{2}{3}}} - \frac{3 \, {\left(7 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a + a^{2}}\right)} a^{2}}{18 \, d}"," ",0,"-1/18*(18*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(2/3) - 22*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(2/3) + 9*2^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(2/3) - 18*2^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(2/3) - 11*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(2/3) + 22*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(2/3) - 3*(7*(I*a*tan(d*x + c) + a)^(4/3) - 4*(I*a*tan(d*x + c) + a)^(1/3)*a)/((I*a*tan(d*x + c) + a)^2 - 2*(I*a*tan(d*x + c) + a)*a + a^2))*a^2/d","A",0
287,1,154,0,0.629048," ","integrate((a+I*a*tan(d*x+c))^(5/3),x, algorithm=""maxima"")","\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{8}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{8}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{8}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} a^{2}\right)}}{2 \, a d}"," ",0,"1/2*I*(2*sqrt(3)*2^(2/3)*a^(8/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(8/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(8/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 3*(I*a*tan(d*x + c) + a)^(2/3)*a^2)/(a*d)","A",0
288,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\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=""maxima"")","\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
290,1,208,0,0.527589," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{i \, {\left(10 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{14}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 5 \cdot 2^{\frac{2}{3}} a^{\frac{14}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 10 \cdot 2^{\frac{2}{3}} a^{\frac{14}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + 15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{8}{3}} a^{2} - 48 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}} a^{3} + 120 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} a^{4} + \frac{60 \, a^{5}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\right)}}{40 \, a^{5} d}"," ",0,"1/40*I*(10*sqrt(3)*2^(2/3)*a^(14/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 5*2^(2/3)*a^(14/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 10*2^(2/3)*a^(14/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 15*(I*a*tan(d*x + c) + a)^(8/3)*a^2 - 48*(I*a*tan(d*x + c) + a)^(5/3)*a^3 + 120*(I*a*tan(d*x + c) + a)^(2/3)*a^4 + 60*a^5/(I*a*tan(d*x + c) + a)^(1/3))/(a^5*d)","A",0
291,1,190,0,0.850339," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{10 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{11}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 5 \cdot 2^{\frac{2}{3}} a^{\frac{11}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 10 \cdot 2^{\frac{2}{3}} a^{\frac{11}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + 24 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}} a^{2} - 60 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} a^{3} - \frac{60 \, a^{4}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}}{40 \, a^{4} d}"," ",0,"-1/40*(10*sqrt(3)*2^(2/3)*a^(11/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 5*2^(2/3)*a^(11/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 10*2^(2/3)*a^(11/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 24*(I*a*tan(d*x + c) + a)^(5/3)*a^2 - 60*(I*a*tan(d*x + c) + a)^(2/3)*a^3 - 60*a^4/(I*a*tan(d*x + c) + a)^(1/3))/(a^4*d)","A",0
292,1,172,0,0.496557," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{8}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{8}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{8}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + 12 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} a^{2} + \frac{12 \, a^{3}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\right)}}{8 \, a^{3} d}"," ",0,"-1/8*I*(2*sqrt(3)*2^(2/3)*a^(8/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(8/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(8/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 12*(I*a*tan(d*x + c) + a)^(2/3)*a^2 + 12*a^3/(I*a*tan(d*x + c) + a)^(1/3))/(a^3*d)","A",0
293,1,154,0,0.795007," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{5}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{5}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{5}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - \frac{12 \, a^{2}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}}{8 \, a^{2} d}"," ",0,"1/8*(2*sqrt(3)*2^(2/3)*a^(5/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(5/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(5/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 12*a^2/(I*a*tan(d*x + c) + a)^(1/3))/(a^2*d)","A",0
294,1,152,0,0.649000," ","integrate(1/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + \frac{12 \, a}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\right)}}{8 \, a d}"," ",0,"1/8*I*(2*sqrt(3)*2^(2/3)*a^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 12*a/(I*a*tan(d*x + c) + a)^(1/3))/(a*d)","A",0
295,1,249,0,0.685915," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{1}{3}}} - \frac{2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{1}{3}}} + \frac{2 \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{1}{3}}} - \frac{8 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{1}{3}}} + \frac{4 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{1}{3}}} - \frac{8 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{1}{3}}} - \frac{12}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}}{8 \, d}"," ",0,"-1/8*(2*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(1/3) - 2^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(1/3) + 2*2^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(1/3) - 8*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(1/3) + 4*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(1/3) - 8*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(1/3) - 12/(I*a*tan(d*x + c) + a)^(1/3))/d","A",0
296,1,286,0,0.954029," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{6 \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{4}{3}}} - \frac{3 \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{4}{3}}} + \frac{6 \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{4}{3}}} + \frac{8 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{4}{3}}} - \frac{12 \, {\left(-5 i \, a \tan\left(d x + c\right) - 2 \, a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a - {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{2}} - \frac{4 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{4}{3}}} + \frac{8 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{4}{3}}}\right)}}{24 \, d}"," ",0,"-1/24*I*a*(6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(4/3) - 3*2^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(4/3) + 6*2^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(4/3) + 8*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(4/3) - 12*(-5*I*a*tan(d*x + c) - 2*a)/((I*a*tan(d*x + c) + a)^(4/3)*a - (I*a*tan(d*x + c) + a)^(1/3)*a^2) - 4*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(4/3) + 8*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(4/3))/d","A",0
297,1,151,0,0.452353," ","integrate(1/(a+I*a*tan(d*x+c))^(2/3),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{1}{3}} a^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) + 2^{\frac{1}{3}} a^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) - 2 \cdot 2^{\frac{1}{3}} a^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - \frac{6 \, a}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\right)}}{8 \, a d}"," ",0,"-1/8*I*(2*sqrt(3)*2^(1/3)*a^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) + 2^(1/3)*a^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) - 2*2^(1/3)*a^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 6*a/(I*a*tan(d*x + c) + a)^(2/3))/(a*d)","A",0
298,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
299,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
300,1,209,0,0.492799," ","integrate(tan(d*x+c)^4/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{i \, {\left(10 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{11}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 5 \cdot 2^{\frac{2}{3}} a^{\frac{11}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 10 \cdot 2^{\frac{2}{3}} a^{\frac{11}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + 48 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}} a^{2} - 240 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} a^{3} - \frac{30 \, {\left(14 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} - a^{5}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\right)}}{80 \, a^{5} d}"," ",0,"1/80*I*(10*sqrt(3)*2^(2/3)*a^(11/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 5*2^(2/3)*a^(11/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 10*2^(2/3)*a^(11/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 48*(I*a*tan(d*x + c) + a)^(5/3)*a^2 - 240*(I*a*tan(d*x + c) + a)^(2/3)*a^3 - 30*(14*(I*a*tan(d*x + c) + a)*a^4 - a^5)/(I*a*tan(d*x + c) + a)^(4/3))/(a^5*d)","A",0
301,1,191,0,0.721242," ","integrate(tan(d*x+c)^3/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{8}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{8}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{8}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + 24 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} a^{2} + \frac{6 \, {\left(10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{3} - a^{4}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}}{16 \, a^{4} d}"," ",0,"-1/16*(2*sqrt(3)*2^(2/3)*a^(8/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(8/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(8/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 24*(I*a*tan(d*x + c) + a)^(2/3)*a^2 + 6*(10*(I*a*tan(d*x + c) + a)*a^3 - a^4)/(I*a*tan(d*x + c) + a)^(4/3))/(a^4*d)","A",0
302,1,173,0,0.435992," ","integrate(tan(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{5}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{5}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{5}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) - \frac{6 \, {\left(6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{2} - a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\right)}}{16 \, a^{3} d}"," ",0,"-1/16*I*(2*sqrt(3)*2^(2/3)*a^(5/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(5/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(5/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 6*(6*(I*a*tan(d*x + c) + a)*a^2 - a^3)/(I*a*tan(d*x + c) + a)^(4/3))/(a^3*d)","A",0
303,1,171,0,0.952950," ","integrate(tan(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} a^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right) - 2^{\frac{2}{3}} a^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right) + 2 \cdot 2^{\frac{2}{3}} a^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right) + \frac{6 \, {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a - a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}}{16 \, a^{2} d}"," ",0,"1/16*(2*sqrt(3)*2^(2/3)*a^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3)) - 2^(2/3)*a^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3)) + 2*2^(2/3)*a^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 6*(2*(I*a*tan(d*x + c) + a)*a - a^2)/(I*a*tan(d*x + c) + a)^(4/3))/(a^2*d)","A",0
304,1,164,0,0.615216," ","integrate(1/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{1}{3}}} - \frac{2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{1}{3}}} + \frac{2 \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{1}{3}}} + \frac{6 \, {\left(2 i \, a \tan\left(d x + c\right) + 3 \, a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}}}\right)}}{16 \, a d}"," ",0,"1/16*I*(2*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(1/3) - 2^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(1/3) + 2*2^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(1/3) + 6*(2*I*a*tan(d*x + c) + 3*a)/(I*a*tan(d*x + c) + a)^(4/3))/(a*d)","A",0
305,1,265,0,0.593719," ","integrate(cot(d*x+c)/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{4}{3}}} - \frac{2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{4}{3}}} + \frac{2 \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{4}{3}}} - \frac{16 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{4}{3}}} + \frac{8 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{4}{3}}} - \frac{16 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{4}{3}}} - \frac{6 \, {\left(6 i \, a \tan\left(d x + c\right) + 7 \, a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a}}{16 \, d}"," ",0,"-1/16*(2*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(4/3) - 2^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(4/3) + 2*2^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(4/3) - 16*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(4/3) + 8*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(4/3) - 16*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(4/3) - 6*(6*I*a*tan(d*x + c) + 7*a)/((I*a*tan(d*x + c) + a)^(4/3)*a))/d","A",0
306,1,310,0,0.619953," ","integrate(cot(d*x+c)^2/(a+I*a*tan(d*x+c))^(4/3),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{6 \, {\left(38 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} - 27 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a - 3 \, a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{3}} a^{2} - {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{4}{3}} a^{3}} + \frac{6 \, \sqrt{3} 2^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{7}{3}}} - \frac{3 \cdot 2^{\frac{2}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{7}{3}}} + \frac{6 \cdot 2^{\frac{2}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{7}{3}}} + \frac{64 \, \sqrt{3} \arctan\left(\frac{\sqrt{3} {\left(2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} + a^{\frac{1}{3}}\right)}}{3 \, a^{\frac{1}{3}}}\right)}{a^{\frac{7}{3}}} - \frac{32 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + a^{\frac{2}{3}}\right)}{a^{\frac{7}{3}}} + \frac{64 \, \log\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} - a^{\frac{1}{3}}\right)}{a^{\frac{7}{3}}}\right)}}{48 \, d}"," ",0,"-1/48*I*a*(6*(38*(I*a*tan(d*x + c) + a)^2 - 27*(I*a*tan(d*x + c) + a)*a - 3*a^2)/((I*a*tan(d*x + c) + a)^(7/3)*a^2 - (I*a*tan(d*x + c) + a)^(4/3)*a^3) + 6*sqrt(3)*2^(2/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(7/3) - 3*2^(2/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(7/3) + 6*2^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(7/3) + 64*sqrt(3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(7/3) - 32*log((I*a*tan(d*x + c) + a)^(2/3) + (I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + a^(2/3))/a^(7/3) + 64*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(7/3))/d","A",0
307,1,164,0,0.565614," ","integrate(1/(a+I*a*tan(d*x+c))^(5/3),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{10 \, \sqrt{3} 2^{\frac{1}{3}} \arctan\left(\frac{\sqrt{3} 2^{\frac{2}{3}} {\left(2^{\frac{1}{3}} a^{\frac{1}{3}} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}}{6 \, a^{\frac{1}{3}}}\right)}{a^{\frac{2}{3}}} + \frac{5 \cdot 2^{\frac{1}{3}} \log\left(2^{\frac{2}{3}} a^{\frac{2}{3}} + 2^{\frac{1}{3}} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\right)}{a^{\frac{2}{3}}} - \frac{10 \cdot 2^{\frac{1}{3}} \log\left(-2^{\frac{1}{3}} a^{\frac{1}{3}} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\right)}{a^{\frac{2}{3}}} - \frac{6 \, {\left(5 i \, a \tan\left(d x + c\right) + 9 \, a\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}}}\right)}}{80 \, a d}"," ",0,"-1/80*I*(10*sqrt(3)*2^(1/3)*arctan(1/6*sqrt(3)*2^(2/3)*(2^(1/3)*a^(1/3) + 2*(I*a*tan(d*x + c) + a)^(1/3))/a^(1/3))/a^(2/3) + 5*2^(1/3)*log(2^(2/3)*a^(2/3) + 2^(1/3)*(I*a*tan(d*x + c) + a)^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(2/3))/a^(2/3) - 10*2^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(2/3) - 6*(5*I*a*tan(d*x + c) + 9*a)/(I*a*tan(d*x + c) + a)^(5/3))/(a*d)","A",0
308,0,0,0,0.000000," ","integrate((e*tan(d*x+c))^m*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
315,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
316,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
317,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
318,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a-I*a*tan(f*x+e)),x, algorithm=""maxima"")","\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,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a-I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate((d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
324,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
336,1,134,0,0.544158," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{15 \, a d^{4} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 12 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a d + 20 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d^{2} - 60 \, \sqrt{d \tan\left(f x + e\right)} a d^{3}}{30 \, d f}"," ",0,"1/30*(15*a*d^4*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 12*(d*tan(f*x + e))^(5/2)*a*d + 20*(d*tan(f*x + e))^(3/2)*a*d^2 - 60*sqrt(d*tan(f*x + e))*a*d^3)/(d*f)","A",0
337,1,118,0,0.495933," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{3 \, a d^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)} - 2 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d - 6 \, \sqrt{d \tan\left(f x + e\right)} a d^{2}}{3 \, d f}"," ",0,"-1/3*(3*a*d^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d)) - 2*(d*tan(f*x + e))^(3/2)*a*d - 6*sqrt(d*tan(f*x + e))*a*d^2)/(d*f)","A",0
338,1,101,0,0.818733," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{a d^{2} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - 4 \, \sqrt{d \tan\left(f x + e\right)} a d}{2 \, d f}"," ",0,"-1/2*(a*d^2*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 4*sqrt(d*tan(f*x + e))*a*d)/(d*f)","A",0
339,1,78,0,0.597368," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{a {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{f}"," ",0,"a*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/f","A",0
340,1,97,0,0.594916," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{a {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{4 \, a}{\sqrt{d \tan\left(f x + e\right)}}}{2 \, d f}"," ",0,"1/2*(a*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 4*a/sqrt(d*tan(f*x + e)))/(d*f)","A",0
341,1,117,0,0.644753," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, a {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{d} + \frac{2 \, {\left(3 \, a d \tan\left(f x + e\right) + a d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{3 \, d f}"," ",0,"-1/3*(3*a*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/d + 2*(3*a*d*tan(f*x + e) + a*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","A",0
342,1,136,0,0.575634," ","integrate((a+a*tan(f*x+e))/(d*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, a {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{2}} - \frac{4 \, {\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)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} d^{2}}}{30 \, d f}"," ",0,"-1/30*(15*a*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^2 - 4*(15*a*d^2*tan(f*x + e)^2 - 5*a*d^2*tan(f*x + e) - 3*a*d^2)/((d*tan(f*x + e))^(5/2)*d^2))/(d*f)","A",0
343,1,210,0,0.487644," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{20 \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{2} + 56 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{2} d - 280 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d^{3} + 35 \, {\left(2 \, \sqrt{2} d^{\frac{7}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + 2 \, \sqrt{2} d^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + \sqrt{2} d^{\frac{7}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right) - \sqrt{2} d^{\frac{7}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)\right)} a^{2}}{70 \, d f}"," ",0,"1/70*(20*(d*tan(f*x + e))^(7/2)*a^2 + 56*(d*tan(f*x + e))^(5/2)*a^2*d - 280*sqrt(d*tan(f*x + e))*a^2*d^3 + 35*(2*sqrt(2)*d^(7/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + 2*sqrt(2)*d^(7/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + sqrt(2)*d^(7/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d) - sqrt(2)*d^(7/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d))*a^2)/(d*f)","A",0
344,1,195,0,0.656713," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{15 \, a^{2} d^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - 12 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{2} - 40 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} d}{30 \, d f}"," ",0,"-1/30*(15*a^2*d^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 12*(d*tan(f*x + e))^(5/2)*a^2 - 40*(d*tan(f*x + e))^(3/2)*a^2*d)/(d*f)","A",0
345,1,192,0,0.677875," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} + 24 \, \sqrt{d \tan\left(f x + e\right)} a^{2} d - 3 \, {\left(2 \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + 2 \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + \sqrt{2} d^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right) - \sqrt{2} d^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)\right)} a^{2}}{6 \, d f}"," ",0,"1/6*(4*(d*tan(f*x + e))^(3/2)*a^2 + 24*sqrt(d*tan(f*x + e))*a^2*d - 3*(2*sqrt(2)*d^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + 2*sqrt(2)*d^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + sqrt(2)*d^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d) - sqrt(2)*d^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d))*a^2)/(d*f)","A",0
346,1,176,0,0.702433," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{a^{2} d {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + 4 \, \sqrt{d \tan\left(f x + e\right)} a^{2}}{2 \, d f}"," ",0,"1/2*(a^2*d*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 4*sqrt(d*tan(f*x + e))*a^2)/(d*f)","A",0
347,1,175,0,0.602209," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{4 \, a^{2}}{\sqrt{d \tan\left(f x + e\right)}}}{2 \, d f}"," ",0,"1/2*(a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 4*a^2/sqrt(d*tan(f*x + e)))/(d*f)","A",0
348,1,197,0,0.608125," ","integrate((a+a*tan(f*x+e))^2/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, a^{2} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d} + \frac{4 \, {\left(6 \, a^{2} d \tan\left(f x + e\right) + a^{2} d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{6 \, d f}"," ",0,"-1/6*(3*a^2*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d + 4*(6*a^2*d*tan(f*x + e) + a^2*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","A",0
349,1,199,0,0.833563," ","integrate((d*tan(f*x+e))^(7/2)*(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{1155 \, a^{3} d^{5} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{2 \, {\left(105 \, \left(d \tan\left(f x + e\right)\right)^{\frac{11}{2}} a^{3} + 385 \, \left(d \tan\left(f x + e\right)\right)^{\frac{9}{2}} a^{3} d + 330 \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{3} d^{2} - 462 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} d^{3} - 770 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d^{4} + 2310 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{5}\right)}}{d}}{1155 \, d f}"," ",0,"-1/1155*(1155*a^3*d^5*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 2*(105*(d*tan(f*x + e))^(11/2)*a^3 + 385*(d*tan(f*x + e))^(9/2)*a^3*d + 330*(d*tan(f*x + e))^(7/2)*a^3*d^2 - 462*(d*tan(f*x + e))^(5/2)*a^3*d^3 - 770*(d*tan(f*x + e))^(3/2)*a^3*d^4 + 2310*sqrt(d*tan(f*x + e))*a^3*d^5)/d)/(d*f)","A",0
350,1,180,0,0.706098," ","integrate((d*tan(f*x+e))^(5/2)*(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(315 \, a^{3} d^{4} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)} + \frac{35 \, \left(d \tan\left(f x + e\right)\right)^{\frac{9}{2}} a^{3} + 135 \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{3} d + 126 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} d^{2} - 210 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d^{3} - 630 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{4}}{d}\right)}}{315 \, d f}"," ",0,"2/315*(315*a^3*d^4*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d)) + (35*(d*tan(f*x + e))^(9/2)*a^3 + 135*(d*tan(f*x + e))^(7/2)*a^3*d + 126*(d*tan(f*x + e))^(5/2)*a^3*d^2 - 210*(d*tan(f*x + e))^(3/2)*a^3*d^3 - 630*sqrt(d*tan(f*x + e))*a^3*d^4)/d)/(d*f)","A",0
351,1,163,0,0.564529," ","integrate((d*tan(f*x+e))^(3/2)*(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{105 \, a^{3} d^{3} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} + \frac{2 \, {\left(15 \, \left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{3} + 63 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} d + 70 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d^{2} - 210 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{3}\right)}}{d}}{105 \, d f}"," ",0,"1/105*(105*a^3*d^3*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) + 2*(15*(d*tan(f*x + e))^(7/2)*a^3 + 63*(d*tan(f*x + e))^(5/2)*a^3*d + 70*(d*tan(f*x + e))^(3/2)*a^3*d^2 - 210*sqrt(d*tan(f*x + e))*a^3*d^3)/d)/(d*f)","A",0
352,1,144,0,0.609409," ","integrate((d*tan(f*x+e))^(1/2)*(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(5 \, a^{3} d^{2} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)} - \frac{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} + 5 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d + 10 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d^{2}}{d}\right)}}{5 \, d f}"," ",0,"-2/5*(5*a^3*d^2*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d)) - ((d*tan(f*x + e))^(5/2)*a^3 + 5*(d*tan(f*x + e))^(3/2)*a^3*d + 10*sqrt(d*tan(f*x + e))*a^3*d^2)/d)/(d*f)","A",0
353,1,124,0,0.539445," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{3 \, a^{3} d {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)} - \frac{2 \, {\left(\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} + 9 \, \sqrt{d \tan\left(f x + e\right)} a^{3} d\right)}}{d}}{3 \, d f}"," ",0,"-1/3*(3*a^3*d*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d)) - 2*((d*tan(f*x + e))^(3/2)*a^3 + 9*sqrt(d*tan(f*x + e))*a^3*d)/d)/(d*f)","A",0
354,1,118,0,0.684637," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 \, {\left(a^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)} - \frac{a^{3}}{\sqrt{d \tan\left(f x + e\right)}} + \frac{\sqrt{d \tan\left(f x + e\right)} a^{3}}{d}\right)}}{d f}"," ",0,"2*(a^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d)) - a^3/sqrt(d*tan(f*x + e)) + sqrt(d*tan(f*x + e))*a^3/d)/(d*f)","A",0
355,1,123,0,0.894450," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{\frac{3 \, a^{3} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d} - \frac{2 \, {\left(9 \, a^{3} d \tan\left(f x + e\right) + a^{3} d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d}}{3 \, d f}"," ",0,"1/3*(3*a^3*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d - 2*(9*a^3*d*tan(f*x + e) + a^3*d)/((d*tan(f*x + e))^(3/2)*d))/(d*f)","A",0
356,1,142,0,0.578468," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{5 \, a^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{d^{2}} + \frac{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}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} d^{2}}\right)}}{5 \, d f}"," ",0,"-2/5*(5*a^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/d^2 + (10*a^3*d^2*tan(f*x + e)^2 + 5*a^3*d^2*tan(f*x + e) + a^3*d^2)/((d*tan(f*x + e))^(5/2)*d^2))/(d*f)","A",0
357,1,160,0,0.665536," ","integrate((a+a*tan(f*x+e))^3/(d*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{\frac{105 \, a^{3} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{d^{3}} - \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)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} d^{3}}}{105 \, d f}"," ",0,"-1/105*(105*a^3*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/d^3 - 2*(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)/((d*tan(f*x + e))^(7/2)*d^3))/(d*f)","A",0
358,1,130,0,0.541268," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{d^{4} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{a} + \frac{2 \, d^{\frac{7}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a} - \frac{4 \, \sqrt{d \tan\left(f x + e\right)} d^{3}}{a}}{2 \, d f}"," ",0,"-1/2*(d^4*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/a + 2*d^(7/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a - 4*sqrt(d*tan(f*x + e))*d^3/a)/(d*f)","A",0
359,1,112,0,0.700095," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{d^{3} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a} - \frac{4 \, d^{\frac{5}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a}}{4 \, d f}"," ",0,"-1/4*(d^3*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a - 4*d^(5/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a)/(d*f)","A",0
360,1,112,0,0.495411," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{d^{2} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{a} - \frac{2 \, d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a}}{2 \, d f}"," ",0,"1/2*(d^2*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/a - 2*d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a)/(d*f)","A",0
361,1,110,0,0.736221," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{d {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a} + \frac{4 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a}}{4 \, d f}"," ",0,"1/4*(d*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a + 4*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a)/(d*f)","A",0
362,1,124,0,0.521191," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}}{a} + \frac{2 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a \sqrt{d}} + \frac{4}{\sqrt{d \tan\left(f x + e\right)} a}}{2 \, d f}"," ",0,"-1/2*((sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/a + 2*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*sqrt(d)) + 4/(sqrt(d*tan(f*x + e))*a))/(d*f)","A",0
363,1,144,0,0.610951," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a d} - \frac{12 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a d^{\frac{3}{2}}} - \frac{8 \, {\left(3 \, d \tan\left(f x + e\right) - d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a d}}{12 \, d f}"," ",0,"-1/12*(3*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/(a*d) - 12*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a*d^(3/2)) - 8*(3*d*tan(f*x + e) - d)/((d*tan(f*x + e))^(3/2)*a*d))/(d*f)","A",0
364,1,217,0,0.595961," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, \sqrt{d \tan\left(f x + e\right)} d^{4}}{a^{2} d \tan\left(f x + e\right) + a^{2} d} - \frac{12 \, d^{\frac{7}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2}} + \frac{2 \, \sqrt{2} d^{\frac{7}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + 2 \, \sqrt{2} d^{\frac{7}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + \sqrt{2} d^{\frac{7}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right) - \sqrt{2} d^{\frac{7}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{a^{2}}}{8 \, d f}"," ",0,"-1/8*(4*sqrt(d*tan(f*x + e))*d^4/(a^2*d*tan(f*x + e) + a^2*d) - 12*d^(7/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^2 + (2*sqrt(2)*d^(7/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + 2*sqrt(2)*d^(7/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + sqrt(2)*d^(7/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d) - sqrt(2)*d^(7/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d))/a^2)/(d*f)","A",0
365,1,220,0,0.633550," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, \sqrt{d \tan\left(f x + e\right)} d^{3}}{a^{2} d \tan\left(f x + e\right) + a^{2} d} + \frac{d^{3} {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a^{2}} - \frac{4 \, d^{\frac{5}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2}}}{8 \, d f}"," ",0,"1/8*(4*sqrt(d*tan(f*x + e))*d^3/(a^2*d*tan(f*x + e) + a^2*d) + d^3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^2 - 4*d^(5/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^2)/(d*f)","A",0
366,1,218,0,0.624828," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{a^{2} d \tan\left(f x + e\right) + a^{2} d} + \frac{4 \, d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2}} - \frac{2 \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + 2 \, \sqrt{2} d^{\frac{3}{2}} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right) + \sqrt{2} d^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right) - \sqrt{2} d^{\frac{3}{2}} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{a^{2}}}{8 \, d f}"," ",0,"-1/8*(4*sqrt(d*tan(f*x + e))*d^2/(a^2*d*tan(f*x + e) + a^2*d) + 4*d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^2 - (2*sqrt(2)*d^(3/2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + 2*sqrt(2)*d^(3/2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d)) + sqrt(2)*d^(3/2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d) - sqrt(2)*d^(3/2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d))/a^2)/(d*f)","A",0
367,1,217,0,0.473860," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, \sqrt{d \tan\left(f x + e\right)} d}{a^{2} d \tan\left(f x + e\right) + a^{2} d} - \frac{d {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a^{2}} + \frac{12 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2}}}{8 \, d f}"," ",0,"1/8*(4*sqrt(d*tan(f*x + e))*d/(a^2*d*tan(f*x + e) + a^2*d) - d*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^2 + 12*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^2)/(d*f)","A",0
368,1,230,0,0.647999," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(5 \, d \tan\left(f x + e\right) + 4 \, d\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} + \sqrt{d \tan\left(f x + e\right)} a^{2} d} + \frac{\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}}{a^{2}} + \frac{20 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2} \sqrt{d}}}{8 \, d f}"," ",0,"-1/8*(4*(5*d*tan(f*x + e) + 4*d)/((d*tan(f*x + e))^(3/2)*a^2 + sqrt(d*tan(f*x + e))*a^2*d) + (2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^2 + 20*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*sqrt(d)))/(d*f)","A",0
369,1,254,0,0.543807," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(27 \, d^{2} \tan\left(f x + e\right)^{2} + 20 \, d^{2} \tan\left(f x + e\right) - 4 \, d^{2}\right)}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{2} d + \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{2} d^{2}} + \frac{3 \, {\left(\frac{2 \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{2 \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} + \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a^{2} d} + \frac{84 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{2} d^{\frac{3}{2}}}}{24 \, d f}"," ",0,"1/24*(4*(27*d^2*tan(f*x + e)^2 + 20*d^2*tan(f*x + e) - 4*d^2)/((d*tan(f*x + e))^(5/2)*a^2*d + (d*tan(f*x + e))^(3/2)*a^2*d^2) + 3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) + sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/(a^2*d) + 84*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^2*d^(3/2)))/(d*f)","A",0
370,1,201,0,0.451012," ","integrate((d*tan(f*x+e))^(9/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{d^{6} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a^{3}} - \frac{31 \, d^{\frac{11}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3}} + \frac{16 \, \sqrt{d \tan\left(f x + e\right)} d^{5}}{a^{3}} + \frac{13 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d^{6} + 11 \, \sqrt{d \tan\left(f x + e\right)} d^{7}}{a^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}}}{8 \, d f}"," ",0,"1/8*(d^6*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^3 - 31*d^(11/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^3 + 16*sqrt(d*tan(f*x + e))*d^5/a^3 + (13*(d*tan(f*x + e))^(3/2)*d^6 + 11*sqrt(d*tan(f*x + e))*d^7)/(a^3*d^2*tan(f*x + e)^2 + 2*a^3*d^2*tan(f*x + e) + a^3*d^2))/(d*f)","A",0
371,1,184,0,0.799696," ","integrate((d*tan(f*x+e))^(7/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, d^{5} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{a^{3}} - \frac{11 \, d^{\frac{9}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3}} + \frac{9 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d^{5} + 7 \, \sqrt{d \tan\left(f x + e\right)} d^{6}}{a^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}}}{8 \, d f}"," ",0,"-1/8*(2*d^5*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/a^3 - 11*d^(9/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^3 + (9*(d*tan(f*x + e))^(3/2)*d^5 + 7*sqrt(d*tan(f*x + e))*d^6)/(a^3*d^2*tan(f*x + e)^2 + 2*a^3*d^2*tan(f*x + e) + a^3*d^2))/(d*f)","A",0
372,1,184,0,0.538125," ","integrate((d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{d^{4} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a^{3}} - \frac{d^{\frac{7}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3}} - \frac{5 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d^{4} + 3 \, \sqrt{d \tan\left(f x + e\right)} d^{5}}{a^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}}}{8 \, d f}"," ",0,"-1/8*(d^4*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^3 - d^(7/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^3 - (5*(d*tan(f*x + e))^(3/2)*d^4 + 3*sqrt(d*tan(f*x + e))*d^5)/(a^3*d^2*tan(f*x + e)^2 + 2*a^3*d^2*tan(f*x + e) + a^3*d^2))/(d*f)","A",0
373,1,184,0,0.485365," ","integrate((d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, d^{3} {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{a^{3}} - \frac{5 \, d^{\frac{5}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3}} - \frac{\left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d^{3} - \sqrt{d \tan\left(f x + e\right)} d^{4}}{a^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}}}{8 \, d f}"," ",0,"1/8*(2*d^3*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/a^3 - 5*d^(5/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^3 - ((d*tan(f*x + e))^(3/2)*d^3 - sqrt(d*tan(f*x + e))*d^4)/(a^3*d^2*tan(f*x + e)^2 + 2*a^3*d^2*tan(f*x + e) + a^3*d^2))/(d*f)","A",0
374,1,184,0,0.844178," ","integrate((d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d^{2} + 5 \, \sqrt{d \tan\left(f x + e\right)} d^{3}}{a^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}} - \frac{d^{2} {\left(\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}\right)}}{a^{3}} - \frac{d^{\frac{3}{2}} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3}}}{8 \, d f}"," ",0,"-1/8*((3*(d*tan(f*x + e))^(3/2)*d^2 + 5*sqrt(d*tan(f*x + e))*d^3)/(a^3*d^2*tan(f*x + e)^2 + 2*a^3*d^2*tan(f*x + e) + a^3*d^2) - d^2*(sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^3 - d^(3/2)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^3)/(d*f)","A",0
375,1,180,0,0.773311," ","integrate(1/(d*tan(f*x+e))^(1/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{7 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} d + 9 \, \sqrt{d \tan\left(f x + e\right)} d^{2}}{a^{3} d^{2} \tan\left(f x + e\right)^{2} + 2 \, a^{3} d^{2} \tan\left(f x + e\right) + a^{3} d^{2}} - \frac{2 \, d {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{a^{3}} + \frac{11 \, \sqrt{d} \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3}}}{8 \, d f}"," ",0,"1/8*((7*(d*tan(f*x + e))^(3/2)*d + 9*sqrt(d*tan(f*x + e))*d^2)/(a^3*d^2*tan(f*x + e)^2 + 2*a^3*d^2*tan(f*x + e) + a^3*d^2) - 2*d*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/a^3 + 11*sqrt(d)*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/a^3)/(d*f)","A",0
376,1,190,0,0.669525," ","integrate(1/(d*tan(f*x+e))^(3/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{27 \, d^{2} \tan\left(f x + e\right)^{2} + 45 \, d^{2} \tan\left(f x + e\right) + 16 \, d^{2}}{\left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} + 2 \, \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d + \sqrt{d \tan\left(f x + e\right)} a^{3} d^{2}} + \frac{\frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) + \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}} - \frac{\sqrt{2} \log\left(d \tan\left(f x + e\right) - \sqrt{2} \sqrt{d \tan\left(f x + e\right)} \sqrt{d} + d\right)}{\sqrt{d}}}{a^{3}} + \frac{31 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} \sqrt{d}}}{8 \, d f}"," ",0,"-1/8*((27*d^2*tan(f*x + e)^2 + 45*d^2*tan(f*x + e) + 16*d^2)/((d*tan(f*x + e))^(5/2)*a^3 + 2*(d*tan(f*x + e))^(3/2)*a^3*d + sqrt(d*tan(f*x + e))*a^3*d^2) + (sqrt(2)*log(d*tan(f*x + e) + sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d) - sqrt(2)*log(d*tan(f*x + e) - sqrt(2)*sqrt(d*tan(f*x + e))*sqrt(d) + d)/sqrt(d))/a^3 + 31*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*sqrt(d)))/(d*f)","A",0
377,1,210,0,0.492579," ","integrate(1/(d*tan(f*x+e))^(5/2)/(a+a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{189 \, d^{3} \tan\left(f x + e\right)^{3} + 323 \, d^{3} \tan\left(f x + e\right)^{2} + 112 \, d^{3} \tan\left(f x + e\right) - 16 \, d^{3}}{\left(d \tan\left(f x + e\right)\right)^{\frac{7}{2}} a^{3} d + 2 \, \left(d \tan\left(f x + e\right)\right)^{\frac{5}{2}} a^{3} d^{2} + \left(d \tan\left(f x + e\right)\right)^{\frac{3}{2}} a^{3} d^{3}} + \frac{6 \, {\left(\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} + 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}} + \frac{\sqrt{2} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{d} - 2 \, \sqrt{d \tan\left(f x + e\right)}\right)}}{2 \, \sqrt{d}}\right)}{\sqrt{d}}\right)}}{a^{3} d} + \frac{177 \, \arctan\left(\frac{\sqrt{d \tan\left(f x + e\right)}}{\sqrt{d}}\right)}{a^{3} d^{\frac{3}{2}}}}{24 \, d f}"," ",0,"1/24*((189*d^3*tan(f*x + e)^3 + 323*d^3*tan(f*x + e)^2 + 112*d^3*tan(f*x + e) - 16*d^3)/((d*tan(f*x + e))^(7/2)*a^3*d + 2*(d*tan(f*x + e))^(5/2)*a^3*d^2 + (d*tan(f*x + e))^(3/2)*a^3*d^3) + 6*(sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(d) + 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d) + sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(d) - 2*sqrt(d*tan(f*x + e)))/sqrt(d))/sqrt(d))/(a^3*d) + 177*arctan(sqrt(d*tan(f*x + e))/sqrt(d))/(a^3*d^(3/2)))/(d*f)","A",0
378,0,0,0,0.000000," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^5,x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \tan\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*tan(f*x + e)^5, x)","F",0
379,0,0,0,0.000000," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^3,x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*tan(f*x + e)^3, x)","F",0
380,0,0,0,0.000000," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e),x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*tan(f*x + e), x)","F",0
381,0,0,0,0.000000," ","integrate(cot(f*x+e)*(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
384,0,0,0,0.000000," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^4,x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*tan(f*x + e)^4, x)","F",0
385,0,0,0,0.000000," ","integrate((1+tan(f*x+e))^(1/2)*tan(f*x+e)^2,x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*tan(f*x + e)^2, x)","F",0
386,-2,0,0,0.000000," ","integrate((1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  1which is not of the expected type LIST","F(-2)",0
387,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*cot(f*x + e)^2, x)","F",0
388,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{\tan\left(f x + e\right) + 1} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate(sqrt(tan(f*x + e) + 1)*cot(f*x + e)^4, x)","F",0
389,-1,0,0,0.000000," ","integrate(tan(f*x+e)^5*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,0,0,0,0.000000," ","integrate(tan(f*x+e)^3*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*tan(f*x + e)^3, x)","F",0
391,0,0,0,0.000000," ","integrate(tan(f*x+e)*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*tan(f*x + e), x)","F",0
392,0,0,0,0.000000," ","integrate(cot(f*x+e)*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\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=""maxima"")","\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,-1,0,0,0.000000," ","integrate(cot(f*x+e)^5*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,0,0,0,0.000000," ","integrate(tan(f*x+e)^4*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*tan(f*x + e)^4, x)","F",0
396,0,0,0,0.000000," ","integrate(tan(f*x+e)^2*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*tan(f*x + e)^2, x)","F",0
397,-2,0,0,0.000000," ","integrate((1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  1which is not of the expected type LIST","F(-2)",0
398,0,0,0,0.000000," ","integrate(cot(f*x+e)^2*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*cot(f*x + e)^2, x)","F",0
399,0,0,0,0.000000," ","integrate(cot(f*x+e)^4*(1+tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(\tan\left(f x + e\right) + 1\right)}^{\frac{3}{2}} \cot\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((tan(f*x + e) + 1)^(3/2)*cot(f*x + e)^4, x)","F",0
400,0,0,0,0.000000," ","integrate(tan(f*x+e)^5/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{5}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(tan(f*x + e)^5/sqrt(tan(f*x + e) + 1), x)","F",0
401,0,0,0,0.000000," ","integrate(tan(f*x+e)^3/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{3}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(tan(f*x + e)^3/sqrt(tan(f*x + e) + 1), x)","F",0
402,0,0,0,0.000000," ","integrate(tan(f*x+e)/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(tan(f*x + e)/sqrt(tan(f*x + e) + 1), x)","F",0
403,0,0,0,0.000000," ","integrate(cot(f*x+e)/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
406,0,0,0,0.000000," ","integrate(tan(f*x+e)^4/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{4}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(tan(f*x + e)^4/sqrt(tan(f*x + e) + 1), x)","F",0
407,0,0,0,0.000000," ","integrate(tan(f*x+e)^2/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(f x + e\right)^{2}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(tan(f*x + e)^2/sqrt(tan(f*x + e) + 1), x)","F",0
408,-2,0,0,0.000000," ","integrate(1/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  1which is not of the expected type LIST","F(-2)",0
409,0,0,0,0.000000," ","integrate(cot(f*x+e)^2/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{2}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(cot(f*x + e)^2/sqrt(tan(f*x + e) + 1), x)","F",0
410,0,0,0,0.000000," ","integrate(cot(f*x+e)^4/(1+tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(f x + e\right)^{4}}{\sqrt{\tan\left(f x + e\right) + 1}}\,{d x}"," ",0,"integrate(cot(f*x + e)^4/sqrt(tan(f*x + e) + 1), x)","F",0
411,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+a*tan(f*x+e))^m,x, algorithm=""maxima"")","\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
412,1,81,0,0.595866," ","integrate(tan(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, b \tan\left(d x + c\right)^{5} + 15 \, a \tan\left(d x + c\right)^{4} - 20 \, b \tan\left(d x + c\right)^{3} - 30 \, a \tan\left(d x + c\right)^{2} - 60 \, {\left(d x + c\right)} b + 30 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, b \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b*tan(d*x + c)^5 + 15*a*tan(d*x + c)^4 - 20*b*tan(d*x + c)^3 - 30*a*tan(d*x + c)^2 - 60*(d*x + c)*b + 30*a*log(tan(d*x + c)^2 + 1) + 60*b*tan(d*x + c))/d","A",0
413,1,70,0,0.608501," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, b \tan\left(d x + c\right)^{4} + 4 \, a \tan\left(d x + c\right)^{3} - 6 \, b \tan\left(d x + c\right)^{2} + 12 \, {\left(d x + c\right)} a + 6 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 12 \, a \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b*tan(d*x + c)^4 + 4*a*tan(d*x + c)^3 - 6*b*tan(d*x + c)^2 + 12*(d*x + c)*a + 6*b*log(tan(d*x + c)^2 + 1) - 12*a*tan(d*x + c))/d","A",0
414,1,59,0,0.918501," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, b \tan\left(d x + c\right)^{3} + 3 \, a \tan\left(d x + c\right)^{2} + 6 \, {\left(d x + c\right)} b - 3 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, b \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*b*tan(d*x + c)^3 + 3*a*tan(d*x + c)^2 + 6*(d*x + c)*b - 3*a*log(tan(d*x + c)^2 + 1) - 6*b*tan(d*x + c))/d","A",0
415,1,47,0,0.736599," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{b \tan\left(d x + c\right)^{2} - 2 \, {\left(d x + c\right)} a - b \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(b*tan(d*x + c)^2 - 2*(d*x + c)*a - b*log(tan(d*x + c)^2 + 1) + 2*a*tan(d*x + c))/d","A",0
416,1,37,0,1.600820," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} b - a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, b \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*b - a*log(tan(d*x + c)^2 + 1) - 2*b*tan(d*x + c))/d","A",0
417,1,16,0,0.328928," ","integrate(a+b*tan(d*x+c),x, algorithm=""maxima"")","a x + \frac{b \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a*x + b*log(sec(d*x + c))/d","A",0
418,1,38,0,0.871641," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} b - a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, a \log\left(\tan\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*b - a*log(tan(d*x + c)^2 + 1) + 2*a*log(tan(d*x + c)))/d","B",0
419,1,48,0,0.869103," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} a + b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, b \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*a + b*log(tan(d*x + c)^2 + 1) - 2*b*log(tan(d*x + c)) + 2*a/tan(d*x + c))/d","A",0
420,1,58,0,0.909799," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} b - a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, a \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, b \tan\left(d x + c\right) + a}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*b - a*log(tan(d*x + c)^2 + 1) + 2*a*log(tan(d*x + c)) + (2*b*tan(d*x + c) + a)/tan(d*x + c)^2)/d","A",0
421,1,71,0,0.853812," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} a + 3 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, b \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, a \tan\left(d x + c\right)^{2} - 3 \, b \tan\left(d x + c\right) - 2 \, a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*a + 3*b*log(tan(d*x + c)^2 + 1) - 6*b*log(tan(d*x + c)) + (6*a*tan(d*x + c)^2 - 3*b*tan(d*x + c) - 2*a)/tan(d*x + c)^3)/d","A",0
422,1,82,0,0.818297," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} b - 6 \, a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, a \log\left(\tan\left(d x + c\right)\right) + \frac{12 \, b \tan\left(d x + c\right)^{3} + 6 \, a \tan\left(d x + c\right)^{2} - 4 \, b \tan\left(d x + c\right) - 3 \, a}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*b - 6*a*log(tan(d*x + c)^2 + 1) + 12*a*log(tan(d*x + c)) + (12*b*tan(d*x + c)^3 + 6*a*tan(d*x + c)^2 - 4*b*tan(d*x + c) - 3*a)/tan(d*x + c)^4)/d","A",0
423,1,93,0,1.046020," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, {\left(d x + c\right)} a + 30 \, b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, b \log\left(\tan\left(d x + c\right)\right) + \frac{60 \, a \tan\left(d x + c\right)^{4} - 30 \, b \tan\left(d x + c\right)^{3} - 20 \, a \tan\left(d x + c\right)^{2} + 15 \, b \tan\left(d x + c\right) + 12 \, a}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(d*x + c)*a + 30*b*log(tan(d*x + c)^2 + 1) - 60*b*log(tan(d*x + c)) + (60*a*tan(d*x + c)^4 - 30*b*tan(d*x + c)^3 - 20*a*tan(d*x + c)^2 + 15*b*tan(d*x + c) + 12*a)/tan(d*x + c)^5)/d","A",0
424,1,110,0,1.222631," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, b^{2} \tan\left(d x + c\right)^{5} + 15 \, a b \tan\left(d x + c\right)^{4} - 30 \, a b \tan\left(d x + c\right)^{2} + 10 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{3} + 30 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 30 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} - 30 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(6*b^2*tan(d*x + c)^5 + 15*a*b*tan(d*x + c)^4 - 30*a*b*tan(d*x + c)^2 + 10*(a^2 - b^2)*tan(d*x + c)^3 + 30*a*b*log(tan(d*x + c)^2 + 1) + 30*(a^2 - b^2)*(d*x + c) - 30*(a^2 - b^2)*tan(d*x + c))/d","A",0
425,1,91,0,0.855207," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} \tan\left(d x + c\right)^{4} + 8 \, a b \tan\left(d x + c\right)^{3} + 24 \, {\left(d x + c\right)} a b - 24 \, a b \tan\left(d x + c\right) + 6 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{12 \, d}"," ",0,"1/12*(3*b^2*tan(d*x + c)^4 + 8*a*b*tan(d*x + c)^3 + 24*(d*x + c)*a*b - 24*a*b*tan(d*x + c) + 6*(a^2 - b^2)*tan(d*x + c)^2 - 6*(a^2 - b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
426,1,78,0,0.734429," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(d x + c\right)^{3} + 3 \, a b \tan\left(d x + c\right)^{2} - 3 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 3 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{3 \, d}"," ",0,"1/3*(b^2*tan(d*x + c)^3 + 3*a*b*tan(d*x + c)^2 - 3*a*b*log(tan(d*x + c)^2 + 1) - 3*(a^2 - b^2)*(d*x + c) + 3*(a^2 - b^2)*tan(d*x + c))/d","A",0
427,1,58,0,0.848613," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} \tan\left(d x + c\right)^{2} - 4 \, {\left(d x + c\right)} a b + 4 \, a b \tan\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(b^2*tan(d*x + c)^2 - 4*(d*x + c)*a*b + 4*a*b*tan(d*x + c) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
428,1,41,0,0.847592," ","integrate((a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","a^{2} x - \frac{{\left(d x + c - \tan\left(d x + c\right)\right)} b^{2}}{d} + \frac{2 \, a b \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^2*x - (d*x + c - tan(d*x + c))*b^2/d + 2*a*b*log(sec(d*x + c))/d","A",0
429,1,49,0,0.925433," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(d x + c\right)} a b + 2 \, a^{2} \log\left(\tan\left(d x + c\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(tan(d*x + c)) - (a^2 - b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
430,1,58,0,0.587823," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, a b \log\left(\tan\left(d x + c\right)\right) + {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} + \frac{a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(a*b*log(tan(d*x + c)^2 + 1) - 2*a*b*log(tan(d*x + c)) + (a^2 - b^2)*(d*x + c) + a^2/tan(d*x + c))/d","A",0
431,1,78,0,0.823390," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c\right)} a b - {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{4 \, a b \tan\left(d x + c\right) + a^{2}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(4*(d*x + c)*a*b - (a^2 - b^2)*log(tan(d*x + c)^2 + 1) + 2*(a^2 - b^2)*log(tan(d*x + c)) + (4*a*b*tan(d*x + c) + a^2)/tan(d*x + c)^2)/d","A",0
432,1,91,0,0.510430," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, a b \log\left(\tan\left(d x + c\right)\right) + 3 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{3 \, a b \tan\left(d x + c\right) - 3 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} + a^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*a*b*log(tan(d*x + c)^2 + 1) - 6*a*b*log(tan(d*x + c)) + 3*(a^2 - b^2)*(d*x + c) - (3*a*b*tan(d*x + c) - 3*(a^2 - b^2)*tan(d*x + c)^2 + a^2)/tan(d*x + c)^3)/d","A",0
433,1,111,0,0.830038," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{24 \, {\left(d x + c\right)} a b - 6 \, {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(a^{2} - b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{24 \, a b \tan\left(d x + c\right)^{3} - 8 \, a b \tan\left(d x + c\right) + 6 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 3 \, a^{2}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(24*(d*x + c)*a*b - 6*(a^2 - b^2)*log(tan(d*x + c)^2 + 1) + 12*(a^2 - b^2)*log(tan(d*x + c)) + (24*a*b*tan(d*x + c)^3 - 8*a*b*tan(d*x + c) + 6*(a^2 - b^2)*tan(d*x + c)^2 - 3*a^2)/tan(d*x + c)^4)/d","A",0
434,1,124,0,0.816680," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{30 \, a b \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, a b \log\left(\tan\left(d x + c\right)\right) + 30 \, {\left(a^{2} - b^{2}\right)} {\left(d x + c\right)} - \frac{30 \, a b \tan\left(d x + c\right)^{3} - 30 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{4} - 15 \, a b \tan\left(d x + c\right) + 10 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 6 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"-1/30*(30*a*b*log(tan(d*x + c)^2 + 1) - 60*a*b*log(tan(d*x + c)) + 30*(a^2 - b^2)*(d*x + c) - (30*a*b*tan(d*x + c)^3 - 30*(a^2 - b^2)*tan(d*x + c)^4 - 15*a*b*tan(d*x + c) + 10*(a^2 - b^2)*tan(d*x + c)^2 - 6*a^2)/tan(d*x + c)^5)/d","A",0
435,1,137,0,0.853325," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{12 \, b^{3} \tan\left(d x + c\right)^{5} + 45 \, a b^{2} \tan\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2} + 60 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} - 30 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b^3*tan(d*x + c)^5 + 45*a*b^2*tan(d*x + c)^4 + 20*(3*a^2*b - b^3)*tan(d*x + c)^3 + 30*(a^3 - 3*a*b^2)*tan(d*x + c)^2 + 60*(3*a^2*b - b^3)*(d*x + c) - 30*(a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1) - 60*(3*a^2*b - b^3)*tan(d*x + c))/d","A",0
436,1,114,0,0.512898," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{b^{3} \tan\left(d x + c\right)^{4} + 4 \, a b^{2} \tan\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(b^3*tan(d*x + c)^4 + 4*a*b^2*tan(d*x + c)^3 + 2*(3*a^2*b - b^3)*tan(d*x + c)^2 - 4*(a^3 - 3*a*b^2)*(d*x + c) - 2*(3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1) + 4*(a^3 - 3*a*b^2)*tan(d*x + c))/d","A",0
437,1,95,0,0.836192," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, b^{3} \tan\left(d x + c\right)^{3} + 9 \, a b^{2} \tan\left(d x + c\right)^{2} - 6 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*b^3*tan(d*x + c)^3 + 9*a*b^2*tan(d*x + c)^2 - 6*(3*a^2*b - b^3)*(d*x + c) + 3*(a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1) + 6*(3*a^2*b - b^3)*tan(d*x + c))/d","A",0
438,1,78,0,0.851959," ","integrate((a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","a^{3} x - \frac{3 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b^{2}}{d} - \frac{b^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{2 \, d} + \frac{3 \, a^{2} b \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^3*x - 3*(d*x + c - tan(d*x + c))*a*b^2/d - 1/2*b^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 3*a^2*b*log(sec(d*x + c))/d","A",0
439,1,71,0,0.887846," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \log\left(\tan\left(d x + c\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(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
440,1,74,0,0.832715," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, a^{2} b \log\left(\tan\left(d x + c\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 \, a^{3}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(6*a^2*b*log(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*a^3/tan(d*x + c))/d","A",0
441,1,92,0,0.795034," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{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 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, a^{2} b \tan\left(d x + c\right) + a^{3}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(3*a^2*b - b^3)*(d*x + c) - (a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1) + 2*(a^3 - 3*a*b^2)*log(tan(d*x + c)) + (6*a^2*b*tan(d*x + c) + a^3)/tan(d*x + c)^2)/d","A",0
442,1,117,0,0.827244," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{9 \, a^{2} b \tan\left(d x + c\right) + 2 \, a^{3} - 6 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(a^3 - 3*a*b^2)*(d*x + c) + 3*(3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1) - 6*(3*a^2*b - b^3)*log(tan(d*x + c)) - (9*a^2*b*tan(d*x + c) + 2*a^3 - 6*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^3)/d","A",0
443,1,135,0,0.580585," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, a^{2} b - b^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{4 \, a^{2} b \tan\left(d x + c\right) - 4 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} + a^{3} - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{4}}}{4 \, d}"," ",0,"1/4*(4*(3*a^2*b - b^3)*(d*x + c) - 2*(a^3 - 3*a*b^2)*log(tan(d*x + c)^2 + 1) + 4*(a^3 - 3*a*b^2)*log(tan(d*x + c)) - (4*a^2*b*tan(d*x + c) - 4*(3*a^2*b - b^3)*tan(d*x + c)^3 + a^3 - 2*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^4)/d","A",0
444,1,158,0,0.875156," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{60 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)} + 30 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{60 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{4} + 45 \, a^{2} b \tan\left(d x + c\right) - 30 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} + 12 \, a^{3} - 20 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(a^3 - 3*a*b^2)*(d*x + c) + 30*(3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1) - 60*(3*a^2*b - b^3)*log(tan(d*x + c)) + (60*(a^3 - 3*a*b^2)*tan(d*x + c)^4 + 45*a^2*b*tan(d*x + c) - 30*(3*a^2*b - b^3)*tan(d*x + c)^3 + 12*a^3 - 20*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^5)/d","A",0
445,1,171,0,0.852252," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{10 \, b^{4} \tan\left(d x + c\right)^{6} + 48 \, a b^{3} \tan\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{4} + 80 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{2} + 240 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} - 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 240 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*b^4*tan(d*x + c)^6 + 48*a*b^3*tan(d*x + c)^5 + 15*(6*a^2*b^2 - b^4)*tan(d*x + c)^4 + 80*(a^3*b - a*b^3)*tan(d*x + c)^3 + 30*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c)^2 + 240*(a^3*b - a*b^3)*(d*x + c) - 30*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2 + 1) - 240*(a^3*b - a*b^3)*tan(d*x + c))/d","A",0
446,1,149,0,0.825356," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, b^{4} \tan\left(d x + c\right)^{5} + 15 \, a b^{3} \tan\left(d x + c\right)^{4} + 5 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{2} - 15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} - 30 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)}{15 \, d}"," ",0,"1/15*(3*b^4*tan(d*x + c)^5 + 15*a*b^3*tan(d*x + c)^4 + 5*(6*a^2*b^2 - b^4)*tan(d*x + c)^3 + 30*(a^3*b - a*b^3)*tan(d*x + c)^2 - 15*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c) - 30*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1) + 15*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c))/d","A",0
447,1,124,0,0.773112," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, b^{4} \tan\left(d x + c\right)^{4} + 16 \, a b^{3} \tan\left(d x + c\right)^{3} + 6 \, {\left(6 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{2} - 48 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} + 6 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 48 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*b^4*tan(d*x + c)^4 + 16*a*b^3*tan(d*x + c)^3 + 6*(6*a^2*b^2 - b^4)*tan(d*x + c)^2 - 48*(a^3*b - a*b^3)*(d*x + c) + 6*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2 + 1) + 48*(a^3*b - a*b^3)*tan(d*x + c))/d","A",0
448,1,113,0,0.758216," ","integrate((a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","a^{4} x - \frac{6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} b^{2}}{d} + \frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} b^{4}}{3 \, d} - \frac{2 \, a b^{3} {\left(\frac{1}{\sin\left(d x + c\right)^{2} - 1} - \log\left(\sin\left(d x + c\right)^{2} - 1\right)\right)}}{d} + \frac{4 \, a^{3} b \log\left(\sec\left(d x + c\right)\right)}{d}"," ",0,"a^4*x - 6*(d*x + c - tan(d*x + c))*a^2*b^2/d + 1/3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*b^4/d - 2*a*b^3*(1/(sin(d*x + c)^2 - 1) - log(sin(d*x + c)^2 - 1))/d + 4*a^3*b*log(sec(d*x + c))/d","A",0
449,1,89,0,0.776364," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{b^{4} \tan\left(d x + c\right)^{2} + 2 \, a^{4} \log\left(\tan\left(d x + c\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(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
450,1,88,0,0.553720," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{4 \, a^{3} b \log\left(\tan\left(d x + c\right)\right) + b^{4} \tan\left(d x + c\right) - \frac{a^{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)}{d}"," ",0,"(4*a^3*b*log(tan(d*x + c)) + b^4*tan(d*x + c) - a^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))/d","A",0
451,1,99,0,0.811839," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\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(\tan\left(d x + c\right)\right) + \frac{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(tan(d*x + c)) + (8*a^3*b*tan(d*x + c) + a^4)/tan(d*x + c)^2)/d","A",0
452,1,122,0,0.500937," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} + 6 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 12 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{6 \, a^{3} b \tan\left(d x + c\right) + a^{4} - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c) + 6*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1) - 12*(a^3*b - a*b^3)*log(tan(d*x + c)) - (6*a^3*b*tan(d*x + c) + a^4 - 3*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/tan(d*x + c)^3)/d","A",0
453,1,149,0,0.551277," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{48 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{16 \, a^{3} b \tan\left(d x + c\right) + 3 \, a^{4} - 48 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(48*(a^3*b - a*b^3)*(d*x + c) - 6*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2 + 1) + 12*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)) - (16*a^3*b*tan(d*x + c) + 3*a^4 - 48*(a^3*b - a*b^3)*tan(d*x + c)^3 - 6*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/tan(d*x + c)^4)/d","A",0
454,1,170,0,0.827174," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} {\left(d x + c\right)} + 30 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(a^{3} b - a b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{15 \, a^{3} b \tan\left(d x + c\right) + 15 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} + 3 \, a^{4} - 30 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} - 5 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"-1/15*(15*(a^4 - 6*a^2*b^2 + b^4)*(d*x + c) + 30*(a^3*b - a*b^3)*log(tan(d*x + c)^2 + 1) - 60*(a^3*b - a*b^3)*log(tan(d*x + c)) + (15*a^3*b*tan(d*x + c) + 15*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c)^4 + 3*a^4 - 30*(a^3*b - a*b^3)*tan(d*x + c)^3 - 5*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/tan(d*x + c)^5)/d","A",0
455,1,195,0,2.061830," ","integrate(cot(d*x+c)^7*(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{240 \, {\left(a^{3} b - a b^{3}\right)} {\left(d x + c\right)} - 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{240 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{5} + 48 \, a^{3} b \tan\left(d x + c\right) + 30 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)^{4} + 10 \, a^{4} - 80 \, {\left(a^{3} b - a b^{3}\right)} \tan\left(d x + c\right)^{3} - 15 \, {\left(a^{4} - 6 \, a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2}}{\tan\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(240*(a^3*b - a*b^3)*(d*x + c) - 30*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)^2 + 1) + 60*(a^4 - 6*a^2*b^2 + b^4)*log(tan(d*x + c)) + (240*(a^3*b - a*b^3)*tan(d*x + c)^5 + 48*a^3*b*tan(d*x + c) + 30*(a^4 - 6*a^2*b^2 + b^4)*tan(d*x + c)^4 + 10*a^4 - 80*(a^3*b - a*b^3)*tan(d*x + c)^3 - 15*(a^4 - 6*a^2*b^2)*tan(d*x + c)^2)/tan(d*x + c)^6)/d","A",0
456,1,146,0,0.806910," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{12 \, a^{6} \log\left(b \tan\left(d x + c\right) + a\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 \, {\left(a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{2} - 12 \, {\left(a^{3} - a b^{2}\right)} \tan\left(d x + c\right)}{b^{4}}}{12 \, d}"," ",0,"1/12*(12*a^6*log(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 - b^3)*tan(d*x + c)^2 - 12*(a^3 - a*b^2)*tan(d*x + c))/b^4)/d","A",0
457,1,123,0,0.994847," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{6 \, a^{5} \log\left(b \tan\left(d x + c\right) + a\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 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{b^{3}}}{6 \, d}"," ",0,"-1/6*(6*a^5*log(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 - b^2)*tan(d*x + c))/b^3)/d","A",0
458,1,99,0,0.884772," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{4} \log\left(b \tan\left(d x + c\right) + a\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(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
459,1,85,0,0.883831," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, a^{3} \log\left(b \tan\left(d x + c\right) + a\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(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
460,1,72,0,0.859524," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} \log\left(b \tan\left(d x + c\right) + a\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(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
461,1,68,0,0.821203," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(d x + c\right)} b}{a^{2} + b^{2}} - \frac{2 \, a \log\left(b \tan\left(d x + c\right) + a\right)}{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*(d*x + c)*b/(a^2 + b^2) - 2*a*log(b*tan(d*x + c) + a)/(a^2 + b^2) + a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
462,1,69,0,0.861522," ","integrate(1/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(d x + c\right)} a}{a^{2} + b^{2}} + \frac{2 \, b \log\left(b \tan\left(d x + c\right) + a\right)}{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*(d*x + c)*a/(a^2 + b^2) + 2*b*log(b*tan(d*x + c) + a)/(a^2 + b^2) - b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
463,1,84,0,0.579170," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{2} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{3} + a b^{2}} + \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(\tan\left(d x + c\right)\right)}{a}}{2 \, d}"," ",0,"-1/2*(2*b^2*log(b*tan(d*x + c) + a)/(a^3 + a*b^2) + 2*(d*x + c)*b/(a^2 + b^2) + a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*log(tan(d*x + c))/a)/d","A",0
464,1,100,0,0.506757," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{3} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + a^{2} b^{2}} - \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(\tan\left(d x + c\right)\right)}{a^{2}} - \frac{2}{a \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*b^3*log(b*tan(d*x + c) + a)/(a^4 + a^2*b^2) - 2*(d*x + c)*a/(a^2 + b^2) + b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*b*log(tan(d*x + c))/a^2 - 2/(a*tan(d*x + c)))/d","A",0
465,1,122,0,1.651159," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{4} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{5} + a^{3} b^{2}} - \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(\tan\left(d x + c\right)\right)}{a^{3}} - \frac{2 \, b \tan\left(d x + c\right) - a}{a^{2} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*b^4*log(b*tan(d*x + c) + a)/(a^5 + a^3*b^2) - 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(tan(d*x + c))/a^3 - (2*b*tan(d*x + c) - a)/(a^2*tan(d*x + c)^2))/d","A",0
466,1,145,0,0.668726," ","integrate(cot(d*x+c)^4/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, b^{5} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + a^{4} b^{2}} + \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(\tan\left(d x + c\right)\right)}{a^{4}} + \frac{3 \, a b \tan\left(d x + c\right) + 6 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 2 \, a^{2}}{a^{3} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*b^5*log(b*tan(d*x + c) + a)/(a^6 + a^4*b^2) + 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(tan(d*x + c))/a^4 + (3*a*b*tan(d*x + c) + 6*(a^2 - b^2)*tan(d*x + c)^2 - 2*a^2)/(a^3*tan(d*x + c)^3))/d","A",0
467,1,206,0,0.819622," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, a^{6}}{a^{3} b^{5} + a b^{7} + {\left(a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)} - \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(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}} - \frac{b^{2} \tan\left(d x + c\right)^{3} - 3 \, a b \tan\left(d x + c\right)^{2} + 3 \, {\left(3 \, a^{2} - b^{2}\right)} \tan\left(d x + c\right)}{b^{4}}}{3 \, d}"," ",0,"-1/3*(3*a^6/(a^3*b^5 + a*b^7 + (a^2*b^6 + b^8)*tan(d*x + c)) - 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(b*tan(d*x + c) + a)/(a^4*b^5 + 2*a^2*b^7 + b^9) - (b^2*tan(d*x + c)^3 - 3*a*b*tan(d*x + c)^2 + 3*(3*a^2 - b^2)*tan(d*x + c))/b^4)/d","A",0
468,1,180,0,0.538646," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a^{5}}{a^{3} b^{4} + a b^{6} + {\left(a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)} + \frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(3 \, a^{6} + 5 \, a^{4} b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}} + \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{b \tan\left(d x + c\right)^{2} - 4 \, a \tan\left(d x + c\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*(2*a^5/(a^3*b^4 + a*b^6 + (a^2*b^5 + b^7)*tan(d*x + c)) + 4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + 2*(3*a^6 + 5*a^4*b^2)*log(b*tan(d*x + c) + a)/(a^4*b^4 + 2*a^2*b^6 + b^8) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (b*tan(d*x + c)^2 - 4*a*tan(d*x + c))/b^3)/d","A",0
469,1,164,0,0.656233," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a^{4}}{a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)} + \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(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} - \frac{\tan\left(d x + c\right)}{b^{2}}}{d}"," ",0,"-(a^4/(a^3*b^3 + a*b^5 + (a^2*b^4 + b^6)*tan(d*x + c)) + 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(b*tan(d*x + c) + a)/(a^4*b^3 + 2*a^2*b^5 + b^7) - tan(d*x + c)/b^2)/d","A",0
470,1,155,0,0.815166," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a^{3}}{a^{3} b^{2} + a b^{4} + {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)} - \frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} - \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}}}{2 \, d}"," ",0,"1/2*(2*a^3/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(d*x + c)) - 4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) + 2*(a^4 + 3*a^2*b^2)*log(b*tan(d*x + c) + a)/(a^4*b^2 + 2*a^2*b^4 + b^6) - (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
471,1,137,0,0.980083," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, a b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \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{a^{2}}{a^{3} b + a b^{3} + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)}}{d}"," ",0,"-(2*a*b*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - 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) + a^2/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(d*x + c)))/d","A",0
472,1,139,0,0.563630," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{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 \, a}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) - 2*(a^2 - b^2)*log(b*tan(d*x + c) + a)/(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/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)))/d","A",0
473,1,131,0,0.720752," ","integrate(1/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \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{b}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)}}{d}"," ",0,"(2*a*b*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - 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) - b/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)))/d","A",0
474,1,164,0,0.784625," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, b^{2}}{a^{4} + a^{2} b^{2} + {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)} + \frac{2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + 2 \, a^{4} b^{2} + a^{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 \, \log\left(\tan\left(d x + c\right)\right)}{a^{2}}}{2 \, d}"," ",0,"-1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) - 2*b^2/(a^4 + a^2*b^2 + (a^3*b + a*b^3)*tan(d*x + c)) + 2*(3*a^2*b^2 + b^4)*log(b*tan(d*x + c) + a)/(a^6 + 2*a^4*b^2 + a^2*b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*log(tan(d*x + c))/a^2)/d","A",0
475,1,200,0,0.574206," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\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^{3} + b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}} - \frac{a^{3} + a b^{2} + {\left(a^{2} b + 2 \, b^{3}\right)} \tan\left(d x + c\right)}{{\left(a^{4} b + a^{2} b^{3}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} \tan\left(d x + c\right)} - \frac{2 \, b \log\left(\tan\left(d x + c\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^3 + b^5)*log(b*tan(d*x + c) + a)/(a^7 + 2*a^5*b^2 + a^3*b^4) - (a^3 + a*b^2 + (a^2*b + 2*b^3)*tan(d*x + c))/((a^4*b + a^2*b^3)*tan(d*x + c)^2 + (a^5 + a^3*b^2)*tan(d*x + c)) - 2*b*log(tan(d*x + c))/a^3)/d","A",0
476,1,240,0,0.687730," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(d x + c\right)} a b}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(5 \, a^{2} b^{4} + 3 \, b^{6}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} + 2 \, a^{6} b^{2} + a^{4} 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{a^{4} + a^{2} b^{2} - 2 \, {\left(2 \, a^{2} b^{2} + 3 \, b^{4}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)}{{\left(a^{5} b + a^{3} b^{3}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{6} + a^{4} b^{2}\right)} \tan\left(d x + c\right)^{2}} - \frac{2 \, {\left(a^{2} - 3 \, b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*a*b/(a^4 + 2*a^2*b^2 + b^4) - 2*(5*a^2*b^4 + 3*b^6)*log(b*tan(d*x + c) + a)/(a^8 + 2*a^6*b^2 + a^4*b^4) + (a^2 - b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (a^4 + a^2*b^2 - 2*(2*a^2*b^2 + 3*b^4)*tan(d*x + c)^2 - 3*(a^3*b + a*b^3)*tan(d*x + c))/((a^5*b + a^3*b^3)*tan(d*x + c)^3 + (a^6 + a^4*b^2)*tan(d*x + c)^2) - 2*(a^2 - 3*b^2)*log(tan(d*x + c))/a^4)/d","A",0
477,1,308,0,0.551346," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\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{2 \, {\left(6 \, a^{8} + 17 \, a^{6} b^{2} + 15 \, a^{4} b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}} - \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{7 \, a^{8} + 11 \, a^{6} b^{2} + 4 \, {\left(2 \, a^{7} b + 3 \, a^{5} b^{3}\right)} \tan\left(d x + c\right)}{a^{6} b^{5} + 2 \, a^{4} b^{7} + a^{2} b^{9} + {\left(a^{4} b^{7} + 2 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{6} + 2 \, a^{3} b^{8} + a b^{10}\right)} \tan\left(d x + c\right)} - \frac{b \tan\left(d x + c\right)^{2} - 6 \, a \tan\left(d x + c\right)}{b^{4}}}{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) - 2*(6*a^8 + 17*a^6*b^2 + 15*a^4*b^4)*log(b*tan(d*x + c) + a)/(a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11) - (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) - (7*a^8 + 11*a^6*b^2 + 4*(2*a^7*b + 3*a^5*b^3)*tan(d*x + c))/(a^6*b^5 + 2*a^4*b^7 + a^2*b^9 + (a^4*b^7 + 2*a^2*b^9 + b^11)*tan(d*x + c)^2 + 2*(a^5*b^6 + 2*a^3*b^8 + a*b^10)*tan(d*x + c)) - (b*tan(d*x + c)^2 - 6*a*tan(d*x + c))/b^4)/d","A",0
478,1,293,0,0.699057," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\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{2 \, {\left(3 \, a^{7} + 9 \, a^{5} b^{2} + 10 \, a^{3} b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}} + \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{5 \, a^{7} + 9 \, a^{5} b^{2} + 2 \, {\left(3 \, a^{6} b + 5 \, a^{4} b^{3}\right)} \tan\left(d x + c\right)}{a^{6} b^{4} + 2 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)} + \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) - 2*(3*a^7 + 9*a^5*b^2 + 10*a^3*b^4)*log(b*tan(d*x + c) + a)/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + (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) - (5*a^7 + 9*a^5*b^2 + 2*(3*a^6*b + 5*a^4*b^3)*tan(d*x + c))/(a^6*b^4 + 2*a^4*b^6 + a^2*b^8 + (a^4*b^6 + 2*a^2*b^8 + b^10)*tan(d*x + c)^2 + 2*(a^5*b^5 + 2*a^3*b^7 + a*b^9)*tan(d*x + c)) + 2*tan(d*x + c)/b^3)/d","A",0
479,1,279,0,0.856897," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\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{2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}} - \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{3 \, a^{6} + 7 \, a^{4} b^{2} + 4 \, {\left(a^{5} b + 2 \, a^{3} b^{3}\right)} \tan\left(d x + c\right)}{a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} \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) + 2*(a^6 + 3*a^4*b^2 + 6*a^2*b^4)*log(b*tan(d*x + c) + a)/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) - (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) + (3*a^6 + 7*a^4*b^2 + 4*(a^5*b + 2*a^3*b^3)*tan(d*x + c))/(a^6*b^3 + 2*a^4*b^5 + a^2*b^7 + (a^4*b^5 + 2*a^2*b^7 + b^9)*tan(d*x + c)^2 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*tan(d*x + c)))/d","A",0
480,1,262,0,0.559000," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\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{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\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{a^{5} + 5 \, a^{3} b^{2} + 2 \, {\left(a^{4} b + 3 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)}}{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) - 2*(a^3 - 3*a*b^2)*log(b*tan(d*x + c) + a)/(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) + (a^5 + 5*a^3*b^2 + 2*(a^4*b + 3*a^2*b^3)*tan(d*x + c))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + (a^4*b^4 + 2*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*tan(d*x + c)))/d","A",0
481,1,256,0,0.639886," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\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{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\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{4 \, a b^{3} \tan\left(d x + c\right) - a^{4} + 3 \, a^{2} b^{2}}{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \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) + 2*(3*a^2*b - b^3)*log(b*tan(d*x + c) + a)/(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) - (4*a*b^3*tan(d*x + c) - a^4 + 3*a^2*b^2)/(a^6*b + 2*a^4*b^3 + a^2*b^5 + (a^4*b^3 + 2*a^2*b^5 + b^7)*tan(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*tan(d*x + c)))/d","B",0
482,1,253,0,0.654636," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\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{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\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{3 \, a^{3} - a b^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} \tan\left(d x + c\right)}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)}}{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) - 2*(a^3 - 3*a*b^2)*log(b*tan(d*x + c) + a)/(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) + (3*a^3 - a*b^2 + 2*(a^2*b - b^3)*tan(d*x + c))/(a^6 + 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 + 2*a^2*b^4 + b^6)*tan(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c)))/d","A",0
483,1,248,0,0.614316," ","integrate(1/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\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{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\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{4 \, a b^{2} \tan\left(d x + c\right) + 5 \, a^{2} b + b^{3}}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \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) + 2*(3*a^2*b - b^3)*log(b*tan(d*x + c) + a)/(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) - (4*a*b^2*tan(d*x + c) + 5*a^2*b + b^3)/(a^6 + 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 + 2*a^2*b^4 + b^6)*tan(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c)))/d","B",0
484,1,290,0,0.789728," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\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{2 \, {\left(6 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} 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{7 \, a^{3} b^{2} + 3 \, a b^{4} + 2 \, {\left(3 \, a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)}{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4} + {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \tan\left(d x + c\right)} - \frac{2 \, \log\left(\tan\left(d x + c\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) + 2*(6*a^4*b^2 + 3*a^2*b^4 + b^6)*log(b*tan(d*x + c) + a)/(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*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) - (7*a^3*b^2 + 3*a*b^4 + 2*(3*a^2*b^3 + b^5)*tan(d*x + c))/(a^8 + 2*a^6*b^2 + a^4*b^4 + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*tan(d*x + c)^2 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*tan(d*x + c)) - 2*log(tan(d*x + c))/a^3)/d","A",0
485,1,349,0,0.498185," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\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{2 \, {\left(10 \, a^{4} b^{3} + 9 \, a^{2} b^{5} + 3 \, b^{7}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{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 \, a^{6} + 4 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + 2 \, {\left(a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(4 \, a^{5} b + 17 \, a^{3} b^{3} + 9 \, a b^{5}\right)} \tan\left(d x + c\right)}{{\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{3} + 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \tan\left(d x + c\right)} + \frac{6 \, b \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{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) - 2*(10*a^4*b^3 + 9*a^2*b^5 + 3*b^7)*log(b*tan(d*x + c) + a)/(a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^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 + 4*a^4*b^2 + 2*a^2*b^4 + 2*(a^4*b^2 + 6*a^2*b^4 + 3*b^6)*tan(d*x + c)^2 + (4*a^5*b + 17*a^3*b^3 + 9*a*b^5)*tan(d*x + c))/((a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*tan(d*x + c)^3 + 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*tan(d*x + c)^2 + (a^9 + 2*a^7*b^2 + a^5*b^4)*tan(d*x + c)) + 6*b*log(tan(d*x + c))/a^4)/d","A",0
486,1,444,0,0.680209," ","integrate(tan(d*x+c)^6/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\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{12 \, {\left(a^{9} + 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} + 5 \, a^{3} b^{6}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} b^{5} + 4 \, a^{6} b^{7} + 6 \, a^{4} b^{9} + 4 \, a^{2} b^{11} + b^{13}} - \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{13 \, a^{10} + 38 \, a^{8} b^{2} + 37 \, a^{6} b^{4} + 3 \, {\left(6 \, a^{8} b^{2} + 17 \, a^{6} b^{4} + 15 \, a^{4} b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(10 \, a^{9} b + 29 \, a^{7} b^{3} + 27 \, a^{5} b^{5}\right)} \tan\left(d x + c\right)}{a^{9} b^{5} + 3 \, a^{7} b^{7} + 3 \, a^{5} b^{9} + a^{3} b^{11} + {\left(a^{6} b^{8} + 3 \, a^{4} b^{10} + 3 \, a^{2} b^{12} + b^{14}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{7} + 3 \, a^{5} b^{9} + 3 \, a^{3} b^{11} + a b^{13}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b^{6} + 3 \, a^{6} b^{8} + 3 \, a^{4} b^{10} + a^{2} b^{12}\right)} \tan\left(d x + c\right)} - \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) + 12*(a^9 + 4*a^7*b^2 + 6*a^5*b^4 + 5*a^3*b^6)*log(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) - 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) + (13*a^10 + 38*a^8*b^2 + 37*a^6*b^4 + 3*(6*a^8*b^2 + 17*a^6*b^4 + 15*a^4*b^6)*tan(d*x + c)^2 + 3*(10*a^9*b + 29*a^7*b^3 + 27*a^5*b^5)*tan(d*x + c))/(a^9*b^5 + 3*a^7*b^7 + 3*a^5*b^9 + a^3*b^11 + (a^6*b^8 + 3*a^4*b^10 + 3*a^2*b^12 + b^14)*tan(d*x + c)^3 + 3*(a^7*b^7 + 3*a^5*b^9 + 3*a^3*b^11 + a*b^13)*tan(d*x + c)^2 + 3*(a^8*b^6 + 3*a^6*b^8 + 3*a^4*b^10 + a^2*b^12)*tan(d*x + c)) - 3*tan(d*x + c)/b^4)/d","A",0
487,1,433,0,0.588068," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\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{6 \, {\left(a^{8} + 4 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + 10 \, a^{2} b^{6}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{8} b^{4} + 4 \, a^{6} b^{6} + 6 \, a^{4} b^{8} + 4 \, a^{2} b^{10} + b^{12}} + \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{11 \, a^{9} + 34 \, a^{7} b^{2} + 47 \, a^{5} b^{4} + 6 \, {\left(3 \, a^{7} b^{2} + 9 \, a^{5} b^{4} + 10 \, a^{3} b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(9 \, a^{8} b + 28 \, a^{6} b^{3} + 35 \, a^{4} b^{5}\right)} \tan\left(d x + c\right)}{a^{9} b^{4} + 3 \, a^{7} b^{6} + 3 \, a^{5} b^{8} + a^{3} b^{10} + {\left(a^{6} b^{7} + 3 \, a^{4} b^{9} + 3 \, a^{2} b^{11} + b^{13}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{6} + 3 \, a^{5} b^{8} + 3 \, a^{3} b^{10} + a b^{12}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b^{5} + 3 \, a^{6} b^{7} + 3 \, a^{4} b^{9} + a^{2} b^{11}\right)} \tan\left(d x + c\right)}}{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) + 6*(a^8 + 4*a^6*b^2 + 5*a^4*b^4 + 10*a^2*b^6)*log(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) + 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) + (11*a^9 + 34*a^7*b^2 + 47*a^5*b^4 + 6*(3*a^7*b^2 + 9*a^5*b^4 + 10*a^3*b^6)*tan(d*x + c)^2 + 3*(9*a^8*b + 28*a^6*b^3 + 35*a^4*b^5)*tan(d*x + c))/(a^9*b^4 + 3*a^7*b^6 + 3*a^5*b^8 + a^3*b^10 + (a^6*b^7 + 3*a^4*b^9 + 3*a^2*b^11 + b^13)*tan(d*x + c)^3 + 3*(a^7*b^6 + 3*a^5*b^8 + 3*a^3*b^10 + a*b^12)*tan(d*x + c)^2 + 3*(a^8*b^5 + 3*a^6*b^7 + 3*a^4*b^9 + a^2*b^11)*tan(d*x + c)))/d","A",0
488,1,410,0,0.681000," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\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{12 \, {\left(a^{3} b - a b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\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{a^{8} + 2 \, a^{6} b^{2} + 13 \, a^{4} b^{4} + 3 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 6 \, a^{2} b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 10 \, a^{3} b^{5}\right)} \tan\left(d x + c\right)}{a^{9} b^{3} + 3 \, a^{7} b^{5} + 3 \, a^{5} b^{7} + a^{3} b^{9} + {\left(a^{6} b^{6} + 3 \, a^{4} b^{8} + 3 \, a^{2} b^{10} + b^{12}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{5} + 3 \, a^{5} b^{7} + 3 \, a^{3} b^{9} + a b^{11}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b^{4} + 3 \, a^{6} b^{6} + 3 \, a^{4} b^{8} + a^{2} b^{10}\right)} \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) + 12*(a^3*b - a*b^3)*log(b*tan(d*x + c) + a)/(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) - (a^8 + 2*a^6*b^2 + 13*a^4*b^4 + 3*(a^6*b^2 + 3*a^4*b^4 + 6*a^2*b^6)*tan(d*x + c)^2 + 3*(a^7*b + 3*a^5*b^3 + 10*a^3*b^5)*tan(d*x + c))/(a^9*b^3 + 3*a^7*b^5 + 3*a^5*b^7 + a^3*b^9 + (a^6*b^6 + 3*a^4*b^8 + 3*a^2*b^10 + b^12)*tan(d*x + c)^3 + 3*(a^7*b^5 + 3*a^5*b^7 + 3*a^3*b^9 + a*b^11)*tan(d*x + c)^2 + 3*(a^8*b^4 + 3*a^6*b^6 + 3*a^4*b^8 + a^2*b^10)*tan(d*x + c)))/d","B",0
489,1,402,0,0.478590," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\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{6 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\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{a^{7} + 14 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, {\left(a^{3} b^{4} - 3 \, a b^{6}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{6} b + 8 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \tan\left(d x + c\right)}{a^{9} b^{2} + 3 \, a^{7} b^{4} + 3 \, a^{5} b^{6} + a^{3} b^{8} + {\left(a^{6} b^{5} + 3 \, a^{4} b^{7} + 3 \, a^{2} b^{9} + b^{11}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{4} + 3 \, a^{5} b^{6} + 3 \, a^{3} b^{8} + a b^{10}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b^{3} + 3 \, a^{6} b^{5} + 3 \, a^{4} b^{7} + a^{2} b^{9}\right)} \tan\left(d x + c\right)}}{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) - 6*(a^4 - 6*a^2*b^2 + b^4)*log(b*tan(d*x + c) + a)/(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) + (a^7 + 14*a^5*b^2 - 11*a^3*b^4 + 6*(a^3*b^4 - 3*a*b^6)*tan(d*x + c)^2 + 3*(a^6*b + 8*a^4*b^3 - 9*a^2*b^5)*tan(d*x + c))/(a^9*b^2 + 3*a^7*b^4 + 3*a^5*b^6 + a^3*b^8 + (a^6*b^5 + 3*a^4*b^7 + 3*a^2*b^9 + b^11)*tan(d*x + c)^3 + 3*(a^7*b^4 + 3*a^5*b^6 + 3*a^3*b^8 + a*b^10)*tan(d*x + c)^2 + 3*(a^8*b^3 + 3*a^6*b^5 + 3*a^4*b^7 + a^2*b^9)*tan(d*x + c)))/d","B",0
490,1,389,0,0.827698," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\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{12 \, {\left(a^{3} b - a b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\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{a^{6} - 10 \, a^{4} b^{2} + a^{2} b^{4} - 3 \, {\left(3 \, a^{2} b^{4} - b^{6}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(7 \, a^{3} b^{3} - a b^{5}\right)} \tan\left(d x + c\right)}{a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7} + {\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b^{2} + 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} + a^{2} b^{8}\right)} \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) + 12*(a^3*b - a*b^3)*log(b*tan(d*x + c) + a)/(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) + (a^6 - 10*a^4*b^2 + a^2*b^4 - 3*(3*a^2*b^4 - b^6)*tan(d*x + c)^2 - 3*(7*a^3*b^3 - a*b^5)*tan(d*x + c))/(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7 + (a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*tan(d*x + c)^3 + 3*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*tan(d*x + c)^2 + 3*(a^8*b^2 + 3*a^6*b^4 + 3*a^4*b^6 + a^2*b^8)*tan(d*x + c)))/d","B",0
491,1,394,0,0.478787," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\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{6 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\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{11 \, a^{5} - 14 \, a^{3} b^{2} - a b^{4} + 6 \, {\left(a^{3} b^{2} - 3 \, a b^{4}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(5 \, a^{4} b - 12 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)}{a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6} + {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} \tan\left(d x + c\right)}}{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) - 6*(a^4 - 6*a^2*b^2 + b^4)*log(b*tan(d*x + c) + a)/(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) + (11*a^5 - 14*a^3*b^2 - a*b^4 + 6*(a^3*b^2 - 3*a*b^4)*tan(d*x + c)^2 + 3*(5*a^4*b - 12*a^2*b^3 - b^5)*tan(d*x + c))/(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6 + (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*tan(d*x + c)^3 + 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*tan(d*x + c)^2 + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*tan(d*x + c)))/d","B",0
492,1,385,0,0.563937," ","integrate(1/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\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{12 \, {\left(a^{3} b - a b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\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{13 \, a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 3 \, {\left(3 \, a^{2} b^{3} - b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(7 \, a^{3} b^{2} - a b^{4}\right)} \tan\left(d x + c\right)}{a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6} + {\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} \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) + 12*(a^3*b - a*b^3)*log(b*tan(d*x + c) + a)/(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) - (13*a^4*b + 2*a^2*b^3 + b^5 + 3*(3*a^2*b^3 - b^5)*tan(d*x + c)^2 + 3*(7*a^3*b^2 - a*b^4)*tan(d*x + c))/(a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6 + (a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*tan(d*x + c)^3 + 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*tan(d*x + c)^2 + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*tan(d*x + c)))/d","B",0
493,1,444,0,0.810730," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\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{6 \, {\left(10 \, a^{6} b^{2} + 5 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{12} + 4 \, a^{10} b^{2} + 6 \, a^{8} b^{4} + 4 \, a^{6} b^{6} + a^{4} 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{47 \, a^{6} b^{2} + 34 \, a^{4} b^{4} + 11 \, a^{2} b^{6} + 6 \, {\left(6 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(27 \, a^{5} b^{3} + 16 \, a^{3} b^{5} + 5 \, a b^{7}\right)} \tan\left(d x + c\right)}{a^{12} + 3 \, a^{10} b^{2} + 3 \, a^{8} b^{4} + a^{6} b^{6} + {\left(a^{9} b^{3} + 3 \, a^{7} b^{5} + 3 \, a^{5} b^{7} + a^{3} b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{10} b^{2} + 3 \, a^{8} b^{4} + 3 \, a^{6} b^{6} + a^{4} b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(a^{11} b + 3 \, a^{9} b^{3} + 3 \, a^{7} b^{5} + a^{5} b^{7}\right)} \tan\left(d x + c\right)} - \frac{6 \, \log\left(\tan\left(d x + c\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) + 6*(10*a^6*b^2 + 5*a^4*b^4 + 4*a^2*b^6 + b^8)*log(b*tan(d*x + c) + a)/(a^12 + 4*a^10*b^2 + 6*a^8*b^4 + 4*a^6*b^6 + a^4*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) - (47*a^6*b^2 + 34*a^4*b^4 + 11*a^2*b^6 + 6*(6*a^4*b^4 + 3*a^2*b^6 + b^8)*tan(d*x + c)^2 + 3*(27*a^5*b^3 + 16*a^3*b^5 + 5*a*b^7)*tan(d*x + c))/(a^12 + 3*a^10*b^2 + 3*a^8*b^4 + a^6*b^6 + (a^9*b^3 + 3*a^7*b^5 + 3*a^5*b^7 + a^3*b^9)*tan(d*x + c)^3 + 3*(a^10*b^2 + 3*a^8*b^4 + 3*a^6*b^6 + a^4*b^8)*tan(d*x + c)^2 + 3*(a^11*b + 3*a^9*b^3 + 3*a^7*b^5 + a^5*b^7)*tan(d*x + c)) - 6*log(tan(d*x + c))/a^4)/d","A",0
494,1,516,0,0.674542," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\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{12 \, {\left(5 \, a^{6} b^{3} + 6 \, a^{4} b^{5} + 4 \, a^{2} b^{7} + b^{9}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{13} + 4 \, a^{11} b^{2} + 6 \, a^{9} b^{4} + 4 \, a^{7} b^{6} + a^{5} 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{3 \, a^{9} + 9 \, a^{7} b^{2} + 9 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + 3 \, {\left(a^{6} b^{3} + 13 \, a^{4} b^{5} + 12 \, a^{2} b^{7} + 4 \, b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} b^{2} + 31 \, a^{5} b^{4} + 30 \, a^{3} b^{6} + 10 \, a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(9 \, a^{8} b + 64 \, a^{6} b^{3} + 65 \, a^{4} b^{5} + 22 \, a^{2} b^{7}\right)} \tan\left(d x + c\right)}{{\left(a^{10} b^{3} + 3 \, a^{8} b^{5} + 3 \, a^{6} b^{7} + a^{4} b^{9}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{11} b^{2} + 3 \, a^{9} b^{4} + 3 \, a^{7} b^{6} + a^{5} b^{8}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(a^{12} b + 3 \, a^{10} b^{3} + 3 \, a^{8} b^{5} + a^{6} b^{7}\right)} \tan\left(d x + c\right)^{2} + {\left(a^{13} + 3 \, a^{11} b^{2} + 3 \, a^{9} b^{4} + a^{7} b^{6}\right)} \tan\left(d x + c\right)} + \frac{12 \, b \log\left(\tan\left(d x + c\right)\right)}{a^{5}}}{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) - 12*(5*a^6*b^3 + 6*a^4*b^5 + 4*a^2*b^7 + b^9)*log(b*tan(d*x + c) + a)/(a^13 + 4*a^11*b^2 + 6*a^9*b^4 + 4*a^7*b^6 + a^5*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) + (3*a^9 + 9*a^7*b^2 + 9*a^5*b^4 + 3*a^3*b^6 + 3*(a^6*b^3 + 13*a^4*b^5 + 12*a^2*b^7 + 4*b^9)*tan(d*x + c)^3 + 3*(3*a^7*b^2 + 31*a^5*b^4 + 30*a^3*b^6 + 10*a*b^8)*tan(d*x + c)^2 + (9*a^8*b + 64*a^6*b^3 + 65*a^4*b^5 + 22*a^2*b^7)*tan(d*x + c))/((a^10*b^3 + 3*a^8*b^5 + 3*a^6*b^7 + a^4*b^9)*tan(d*x + c)^4 + 3*(a^11*b^2 + 3*a^9*b^4 + 3*a^7*b^6 + a^5*b^8)*tan(d*x + c)^3 + 3*(a^12*b + 3*a^10*b^3 + 3*a^8*b^5 + a^6*b^7)*tan(d*x + c)^2 + (a^13 + 3*a^11*b^2 + 3*a^9*b^4 + a^7*b^6)*tan(d*x + c)) + 12*b*log(tan(d*x + c))/a^5)/d","A",0
495,1,39,0,0.641627," ","integrate(1/(3+5*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, d x + 6 \, c - 5 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 10 \, \log\left(5 \, \tan\left(d x + c\right) + 3\right)}{68 \, d}"," ",0,"1/68*(6*d*x + 6*c - 5*log(tan(d*x + c)^2 + 1) + 10*log(5*tan(d*x + c) + 3))/d","A",0
496,1,53,0,0.679023," ","integrate(1/(3+5*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{16 \, d x + 16 \, c + \frac{170}{5 \, \tan\left(d x + c\right) + 3} + 15 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 30 \, \log\left(5 \, \tan\left(d x + c\right) + 3\right)}{1156 \, d}"," ",0,"-1/1156*(16*d*x + 16*c + 170/(5*tan(d*x + c) + 3) + 15*log(tan(d*x + c)^2 + 1) - 30*log(5*tan(d*x + c) + 3))/d","A",0
497,1,73,0,0.764575," ","integrate(1/(3+5*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{198 \, d x + 198 \, c + \frac{850 \, {\left(6 \, \tan\left(d x + c\right) + 7\right)}}{25 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 9} + 5 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 10 \, \log\left(5 \, \tan\left(d x + c\right) + 3\right)}{39304 \, d}"," ",0,"-1/39304*(198*d*x + 198*c + 850*(6*tan(d*x + c) + 7)/(25*tan(d*x + c)^2 + 30*tan(d*x + c) + 9) + 5*log(tan(d*x + c)^2 + 1) - 10*log(5*tan(d*x + c) + 3))/d","A",0
498,1,93,0,0.673092," ","integrate(1/(3+5*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{483 \, d x + 483 \, c + \frac{85 \, {\left(75 \, \tan\left(d x + c\right)^{2} + 855 \, \tan\left(d x + c\right) + 1064\right)}}{125 \, \tan\left(d x + c\right)^{3} + 225 \, \tan\left(d x + c\right)^{2} + 135 \, \tan\left(d x + c\right) + 27} - 360 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 720 \, \log\left(5 \, \tan\left(d x + c\right) + 3\right)}{1002252 \, d}"," ",0,"-1/1002252*(483*d*x + 483*c + 85*(75*tan(d*x + c)^2 + 855*tan(d*x + c) + 1064)/(125*tan(d*x + c)^3 + 225*tan(d*x + c)^2 + 135*tan(d*x + c) + 27) - 360*log(tan(d*x + c)^2 + 1) + 720*log(5*tan(d*x + c) + 3))/d","A",0
499,1,39,0,0.600648," ","integrate(1/(5+3*tan(d*x+c)),x, algorithm=""maxima"")","\frac{10 \, d x + 10 \, c - 3 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, \log\left(3 \, \tan\left(d x + c\right) + 5\right)}{68 \, d}"," ",0,"1/68*(10*d*x + 10*c - 3*log(tan(d*x + c)^2 + 1) + 6*log(3*tan(d*x + c) + 5))/d","A",0
500,1,53,0,0.683581," ","integrate(1/(5+3*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{16 \, d x + 16 \, c - \frac{102}{3 \, \tan\left(d x + c\right) + 5} - 15 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 30 \, \log\left(3 \, \tan\left(d x + c\right) + 5\right)}{1156 \, d}"," ",0,"1/1156*(16*d*x + 16*c - 102/(3*tan(d*x + c) + 5) - 15*log(tan(d*x + c)^2 + 1) + 30*log(3*tan(d*x + c) + 5))/d","A",0
501,1,73,0,0.808575," ","integrate(1/(5+3*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{10 \, d x + 10 \, c + \frac{102 \, {\left(30 \, \tan\left(d x + c\right) + 67\right)}}{9 \, \tan\left(d x + c\right)^{2} + 30 \, \tan\left(d x + c\right) + 25} + 99 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 198 \, \log\left(3 \, \tan\left(d x + c\right) + 5\right)}{39304 \, d}"," ",0,"-1/39304*(10*d*x + 10*c + 102*(30*tan(d*x + c) + 67)/(9*tan(d*x + c)^2 + 30*tan(d*x + c) + 25) + 99*log(tan(d*x + c)^2 + 1) - 198*log(3*tan(d*x + c) + 5))/d","A",0
502,1,93,0,0.585449," ","integrate(1/(5+3*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{161 \, d x + 161 \, c + \frac{17 \, {\left(891 \, \tan\left(d x + c\right)^{2} + 3735 \, \tan\left(d x + c\right) + 4328\right)}}{27 \, \tan\left(d x + c\right)^{3} + 135 \, \tan\left(d x + c\right)^{2} + 225 \, \tan\left(d x + c\right) + 125} + 120 \, \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 240 \, \log\left(3 \, \tan\left(d x + c\right) + 5\right)}{334084 \, d}"," ",0,"-1/334084*(161*d*x + 161*c + 17*(891*tan(d*x + c)^2 + 3735*tan(d*x + c) + 4328)/(27*tan(d*x + c)^3 + 135*tan(d*x + c)^2 + 225*tan(d*x + c) + 125) + 120*log(tan(d*x + c)^2 + 1) - 240*log(3*tan(d*x + c) + 5))/d","A",0
503,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^4,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^4, x)","F",0
504,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^3, x)","F",0
505,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2,x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^2, x)","F",0
506,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
507,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
508,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*cot(d*x + c), x)","F",0
509,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^2, x)","F",0
510,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^3, x)","F",0
511,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
512,0,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^3, x)","F",0
513,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^2, x)","F",0
514,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
515,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
516,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c), x)","F",0
517,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^2, x)","F",0
518,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^3, x)","F",0
519,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^2, x)","F",0
521,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
522,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
523,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c), x)","F",0
524,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^2, x)","F",0
525,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
528,0,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{5}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^5/sqrt(b*tan(d*x + c) + a), x)","F",0
529,0,0,0,0.000000," ","integrate(tan(d*x+c)^4/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{4}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^4/sqrt(b*tan(d*x + c) + a), x)","F",0
530,0,0,0,0.000000," ","integrate(tan(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{3}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^3/sqrt(b*tan(d*x + c) + a), x)","F",0
531,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/sqrt(b*tan(d*x + c) + a), x)","F",0
532,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
533,-2,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
534,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)/sqrt(b*tan(d*x + c) + a), x)","F",0
535,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/sqrt(b*tan(d*x + c) + a), x)","F",0
536,0,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{3}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^3/sqrt(b*tan(d*x + c) + a), x)","F",0
537,-1,0,0,0.000000," ","integrate(tan(d*x+c)^5/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,0,0,0,0.000000," ","integrate(tan(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{2}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^2/(b*tan(d*x + c) + a)^(3/2), x)","F",0
541,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
542,-2,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
543,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
544,0,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{2}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^2/(b*tan(d*x + c) + a)^(3/2), x)","F",0
545,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-2,0,0,0.000000," ","integrate(tan(d*x+c)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
551,-2,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
552,0,0,0,0.000000," ","integrate(cot(d*x+c)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
553,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-2,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(b-a>0)', see `assume?` for more details)Is b-a positive, negative or zero?","F(-2)",0
555,1,158,0,0.824067," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{24 \, b \tan\left(d x + c\right)^{\frac{5}{2}} - 30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 15 \, \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 15 \, \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 40 \, a \tan\left(d x + c\right)^{\frac{3}{2}} - 120 \, b \sqrt{\tan\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(24*b*tan(d*x + c)^(5/2) - 30*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 30*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 15*sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 15*sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 40*a*tan(d*x + c)^(3/2) - 120*b*sqrt(tan(d*x + c)))/d","A",0
556,1,147,0,0.428901," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 3 \, \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 3 \, \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 8 \, b \tan\left(d x + c\right)^{\frac{3}{2}} - 24 \, a \sqrt{\tan\left(d x + c\right)}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*b*tan(d*x + c)^(3/2) - 24*a*sqrt(tan(d*x + c)))/d","A",0
557,1,135,0,0.438719," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 8 \, b \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*b*sqrt(tan(d*x + c)))/d","A",0
558,1,124,0,0.459922," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/d","A",0
559,1,135,0,0.414353," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*a/sqrt(tan(d*x + c)))/d","A",0
560,1,146,0,0.418553," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 3 \, \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 3 \, \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, {\left(3 \, b \tan\left(d x + c\right) + a\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(3*b*tan(d*x + c) + a)/tan(d*x + c)^(3/2))/d","A",0
561,1,159,0,0.413421," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 15 \, \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 15 \, \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, {\left(15 \, a \tan\left(d x + c\right)^{2} - 5 \, b \tan\left(d x + c\right) - 3 \, a\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(30*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(15*a*tan(d*x + c)^2 - 5*b*tan(d*x + c) - 3*a)/tan(d*x + c)^(5/2))/d","A",0
562,1,217,0,0.443952," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{120 \, b^{2} \tan\left(d x + c\right)^{\frac{7}{2}} + 336 \, a b \tan\left(d x + c\right)^{\frac{5}{2}} - 210 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 210 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 105 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 105 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 1680 \, a b \sqrt{\tan\left(d x + c\right)} + 280 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{420 \, d}"," ",0,"1/420*(120*b^2*tan(d*x + c)^(7/2) + 336*a*b*tan(d*x + c)^(5/2) - 210*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 210*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 105*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 105*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 1680*a*b*sqrt(tan(d*x + c)) + 280*(a^2 - b^2)*tan(d*x + c)^(3/2))/d","A",0
563,1,205,0,0.630633," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{24 \, b^{2} \tan\left(d x + c\right)^{\frac{5}{2}} + 80 \, a b \tan\left(d x + c\right)^{\frac{3}{2}} - 30 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 30 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 15 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 15 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 120 \, {\left(a^{2} - b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(24*b^2*tan(d*x + c)^(5/2) + 80*a*b*tan(d*x + c)^(3/2) - 30*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 30*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 120*(a^2 - b^2)*sqrt(tan(d*x + c)))/d","A",0
564,1,186,0,0.431052," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, b^{2} \tan\left(d x + c\right)^{\frac{3}{2}} + 6 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 3 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 3 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 48 \, a b \sqrt{\tan\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(8*b^2*tan(d*x + c)^(3/2) + 6*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 3*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 3*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 48*a*b*sqrt(tan(d*x + c)))/d","A",0
565,1,173,0,0.476445," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 8 \, b^{2} \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*b^2*sqrt(tan(d*x + c)))/d","A",0
566,1,173,0,0.528452," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*a^2/sqrt(tan(d*x + c)))/d","A",0
567,1,185,0,0.460623," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 3 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 3 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, {\left(6 \, a b \tan\left(d x + c\right) + a^{2}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(6*a*b*tan(d*x + c) + a^2)/tan(d*x + c)^(3/2))/d","A",0
568,1,206,0,0.722796," ","integrate((a+b*tan(d*x+c))^2/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{30 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 30 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 15 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 15 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \frac{8 \, {\left(10 \, a b \tan\left(d x + c\right) - 15 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, a^{2}\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(30*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*(10*a*b*tan(d*x + c) - 15*(a^2 - b^2)*tan(d*x + c)^2 + 3*a^2)/tan(d*x + c)^(5/2))/d","A",0
569,1,280,0,0.670704," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{280 \, b^{3} \tan\left(d x + c\right)^{\frac{9}{2}} + 1080 \, a b^{2} \tan\left(d x + c\right)^{\frac{7}{2}} + 504 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 630 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 630 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 315 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 315 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 840 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} - 2520 \, {\left(3 \, a^{2} b - b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{1260 \, d}"," ",0,"1/1260*(280*b^3*tan(d*x + c)^(9/2) + 1080*a*b^2*tan(d*x + c)^(7/2) + 504*(3*a^2*b - b^3)*tan(d*x + c)^(5/2) - 630*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 630*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 315*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 315*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 840*(a^3 - 3*a*b^2)*tan(d*x + c)^(3/2) - 2520*(3*a^2*b - b^3)*sqrt(tan(d*x + c)))/d","A",0
570,1,258,0,0.529365," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{120 \, b^{3} \tan\left(d x + c\right)^{\frac{7}{2}} + 504 \, a b^{2} \tan\left(d x + c\right)^{\frac{5}{2}} - 210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 280 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 840 \, {\left(a^{3} - 3 \, a b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{420 \, d}"," ",0,"1/420*(120*b^3*tan(d*x + c)^(7/2) + 504*a*b^2*tan(d*x + c)^(5/2) - 210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 280*(3*a^2*b - b^3)*tan(d*x + c)^(3/2) + 840*(a^3 - 3*a*b^2)*sqrt(tan(d*x + c)))/d","A",0
571,1,238,0,0.774151," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{8 \, b^{3} \tan\left(d x + c\right)^{\frac{5}{2}} + 40 \, a b^{2} \tan\left(d x + c\right)^{\frac{3}{2}} + 10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 40 \, {\left(3 \, a^{2} b - b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{20 \, d}"," ",0,"1/20*(8*b^3*tan(d*x + c)^(5/2) + 40*a*b^2*tan(d*x + c)^(3/2) + 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 40*(3*a^2*b - b^3)*sqrt(tan(d*x + c)))/d","A",0
572,1,216,0,0.947405," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, b^{3} \tan\left(d x + c\right)^{\frac{3}{2}} + 72 \, a b^{2} \sqrt{\tan\left(d x + c\right)} + 6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{12 \, d}"," ",0,"1/12*(8*b^3*tan(d*x + c)^(3/2) + 72*a*b^2*sqrt(tan(d*x + c)) + 6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/d","A",0
573,1,214,0,0.611731," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{8 \, b^{3} \sqrt{\tan\left(d x + c\right)} - 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \frac{8 \, a^{3}}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(8*b^3*sqrt(tan(d*x + c)) - 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*a^3/sqrt(tan(d*x + c)))/d","A",0
574,1,215,0,0.741824," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, {\left(9 \, a^{2} b \tan\left(d x + c\right) + a^{3}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(9*a^2*b*tan(d*x + c) + a^3)/tan(d*x + c)^(3/2))/d","A",0
575,1,235,0,0.840966," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \frac{8 \, {\left(5 \, a^{2} b \tan\left(d x + c\right) + a^{3} - 5 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{20 \, d}"," ",0,"1/20*(10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*(5*a^2*b*tan(d*x + c) + a^3 - 5*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^(5/2))/d","A",0
576,1,259,0,0.740022," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \frac{8 \, {\left(63 \, a^{2} b \tan\left(d x + c\right) - 105 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} + 15 \, a^{3} - 35 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}\right)}}{\tan\left(d x + c\right)^{\frac{7}{2}}}}{420 \, d}"," ",0,"1/420*(210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*(63*a^2*b*tan(d*x + c) - 105*(3*a^2*b - b^3)*tan(d*x + c)^3 + 15*a^3 - 35*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^(7/2))/d","A",0
577,1,279,0,1.297603," ","integrate((a+b*tan(d*x+c))^3/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","-\frac{630 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 630 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - 315 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 315 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, {\left(315 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{4} + 135 \, a^{2} b \tan\left(d x + c\right) - 105 \, {\left(3 \, a^{2} b - b^{3}\right)} \tan\left(d x + c\right)^{3} + 35 \, a^{3} - 63 \, {\left(a^{3} - 3 \, a b^{2}\right)} \tan\left(d x + c\right)^{2}\right)}}{\tan\left(d x + c\right)^{\frac{9}{2}}}}{1260 \, d}"," ",0,"-1/1260*(630*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 630*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 315*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 315*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(315*(a^3 - 3*a*b^2)*tan(d*x + c)^4 + 135*a^2*b*tan(d*x + c) - 105*(3*a^2*b - b^3)*tan(d*x + c)^3 + 35*a^3 - 63*(a^3 - 3*a*b^2)*tan(d*x + c)^2)/tan(d*x + c)^(9/2))/d","A",0
578,1,124,0,0.860019," ","integrate((a+b*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/d","A",0
579,1,136,0,0.519612," ","integrate((a+b*tan(d*x+c))/(-tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{-\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{-\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{-\tan\left(d x + c\right)} - \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{-\tan\left(d x + c\right)} - \tan\left(d x + c\right) + 1\right)}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(-tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(-tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(-tan(d*x + c)) - tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(-tan(d*x + c)) - tan(d*x + c) + 1))/d","A",0
580,1,168,0,0.420123," ","integrate((a+b*tan(d*x+c))/(e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a - b\right)} \log\left(e \tan\left(d x + c\right) + \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a - b\right)} \log\left(e \tan\left(d x + c\right) - \sqrt{2} \sqrt{e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(e*tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a - b)*log(e*tan(d*x + c) + sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) - sqrt(2)*(a - b)*log(e*tan(d*x + c) - sqrt(2)*sqrt(e*tan(d*x + c))*sqrt(e) + e)/sqrt(e))/d","A",0
581,1,174,0,0.416518," ","integrate((a+b*tan(d*x+c))/(-e*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} + 2 \, \sqrt{-e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{\sqrt{2} {\left(\sqrt{2} \sqrt{e} - 2 \, \sqrt{-e \tan\left(d x + c\right)}\right)}}{2 \, \sqrt{e}}\right)}{\sqrt{e}} + \frac{\sqrt{2} {\left(a + b\right)} \log\left(-e \tan\left(d x + c\right) + \sqrt{2} \sqrt{-e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}} - \frac{\sqrt{2} {\left(a + b\right)} \log\left(-e \tan\left(d x + c\right) - \sqrt{2} \sqrt{-e \tan\left(d x + c\right)} \sqrt{e} + e\right)}{\sqrt{e}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2)*sqrt(e) + 2*sqrt(-e*tan(d*x + c)))/sqrt(e))/sqrt(e) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2)*sqrt(e) - 2*sqrt(-e*tan(d*x + c)))/sqrt(e))/sqrt(e) + sqrt(2)*(a + b)*log(-e*tan(d*x + c) + sqrt(2)*sqrt(-e*tan(d*x + c))*sqrt(e) + e)/sqrt(e) - sqrt(2)*(a + b)*log(-e*tan(d*x + c) - sqrt(2)*sqrt(-e*tan(d*x + c))*sqrt(e) + e)/sqrt(e))/d","A",0
582,1,225,0,0.437857," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{120 \, a^{5} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{2} b^{3} + b^{5}\right)} \sqrt{a b}} - \frac{15 \, {\left(2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{2} + b^{2}} - \frac{8 \, {\left(3 \, b^{2} \tan\left(d x + c\right)^{\frac{5}{2}} - 5 \, a b \tan\left(d x + c\right)^{\frac{3}{2}} + 15 \, {\left(a^{2} - b^{2}\right)} \sqrt{\tan\left(d x + c\right)}\right)}}{b^{3}}}{60 \, d}"," ",0,"-1/60*(120*a^5*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2*b^3 + b^5)*sqrt(a*b)) - 15*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) - 8*(3*b^2*tan(d*x + c)^(5/2) - 5*a*b*tan(d*x + c)^(3/2) + 15*(a^2 - b^2)*sqrt(tan(d*x + c)))/b^3)/d","A",0
583,1,202,0,0.475421," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{24 \, a^{4} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{2} b^{2} + b^{4}\right)} \sqrt{a b}} + \frac{3 \, {\left(2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{2} + b^{2}} + \frac{8 \, {\left(b \tan\left(d x + c\right)^{\frac{3}{2}} - 3 \, a \sqrt{\tan\left(d x + c\right)}\right)}}{b^{2}}}{12 \, d}"," ",0,"1/12*(24*a^4*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2*b^2 + b^4)*sqrt(a*b)) + 3*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) + 8*(b*tan(d*x + c)^(3/2) - 3*a*sqrt(tan(d*x + c)))/b^2)/d","A",0
584,1,185,0,0.436953," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, a^{3} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{2} b + b^{3}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{2} + b^{2}} - \frac{8 \, \sqrt{\tan\left(d x + c\right)}}{b}}{4 \, d}"," ",0,"-1/4*(8*a^3*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2*b + b^3)*sqrt(a*b)) + (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) - 8*sqrt(tan(d*x + c))/b)/d","A",0
585,1,171,0,0.621834," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, a^{2} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{2} + b^{2}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(8*a^2*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2 + b^2)*sqrt(a*b)) - (2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
586,1,170,0,0.513612," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, a b \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{2} + b^{2}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(8*a*b*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2 + b^2)*sqrt(a*b)) - (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
587,1,170,0,0.599513," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, b^{2} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{2} + b^{2}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(8*b^2*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2 + b^2)*sqrt(a*b)) + (2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
588,1,185,0,0.414430," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, b^{3} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{3} + a b^{2}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{2} + b^{2}} + \frac{8}{a \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(8*b^3*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^3 + a*b^2)*sqrt(a*b)) + (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) + 8/(a*sqrt(tan(d*x + c))))/d","A",0
589,1,201,0,0.431442," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{24 \, b^{4} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{4} + a^{2} b^{2}\right)} \sqrt{a b}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{2} + b^{2}} + \frac{8 \, {\left(3 \, b \tan\left(d x + c\right) - a\right)}}{a^{2} \tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(24*b^4*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4 + a^2*b^2)*sqrt(a*b)) - 3*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) + 8*(3*b*tan(d*x + c) - a)/(a^2*tan(d*x + c)^(3/2)))/d","A",0
590,1,223,0,0.429684," ","integrate(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{120 \, b^{5} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{5} + a^{3} b^{2}\right)} \sqrt{a b}} - \frac{15 \, {\left(2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a - b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a - b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{2} + b^{2}} - \frac{8 \, {\left(5 \, a b \tan\left(d x + c\right) + 15 \, {\left(a^{2} - b^{2}\right)} \tan\left(d x + c\right)^{2} - 3 \, a^{2}\right)}}{a^{3} \tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"-1/60*(120*b^5*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^5 + a^3*b^2)*sqrt(a*b)) - 15*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a - b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a - b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) - 8*(5*a*b*tan(d*x + c) + 15*(a^2 - b^2)*tan(d*x + c)^2 - 3*a^2)/(a^3*tan(d*x + c)^(5/2)))/d","A",0
591,1,311,0,0.516554," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{12 \, a^{4} \sqrt{\tan\left(d x + c\right)}}{a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)} - \frac{12 \, {\left(5 \, a^{6} + 9 \, a^{4} b^{2}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a b}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{8 \, {\left(b \tan\left(d x + c\right)^{\frac{3}{2}} - 6 \, a \sqrt{\tan\left(d x + c\right)}\right)}}{b^{3}}}{12 \, d}"," ",0,"-1/12*(12*a^4*sqrt(tan(d*x + c))/(a^3*b^3 + a*b^5 + (a^2*b^4 + b^6)*tan(d*x + c)) - 12*(5*a^6 + 9*a^4*b^2)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4*b^3 + 2*a^2*b^5 + b^7)*sqrt(a*b)) - 3*(2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) - 8*(b*tan(d*x + c)^(3/2) - 6*a*sqrt(tan(d*x + c)))/b^3)/d","A",0
592,1,296,0,0.440368," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, a^{3} \sqrt{\tan\left(d x + c\right)}}{a^{3} b^{2} + a b^{4} + {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)} - \frac{4 \, {\left(3 \, a^{5} + 7 \, a^{3} b^{2}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{8 \, \sqrt{\tan\left(d x + c\right)}}{b^{2}}}{4 \, d}"," ",0,"1/4*(4*a^3*sqrt(tan(d*x + c))/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(d*x + c)) - 4*(3*a^5 + 7*a^3*b^2)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4*b^2 + 2*a^2*b^4 + b^6)*sqrt(a*b)) + (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) + 8*sqrt(tan(d*x + c))/b^2)/d","A",0
593,1,277,0,0.427294," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, a^{2} \sqrt{\tan\left(d x + c\right)}}{a^{3} b + a b^{3} + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)} - \frac{4 \, {\left(a^{4} + 5 \, a^{2} b^{2}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{4 \, d}"," ",0,"-1/4*(4*a^2*sqrt(tan(d*x + c))/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(d*x + c)) - 4*(a^4 + 5*a^2*b^2)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4*b + 2*a^2*b^3 + b^5)*sqrt(a*b)) + (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
594,1,268,0,0.419699," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a b}} + \frac{4 \, a \sqrt{\tan\left(d x + c\right)}}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)} - \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{4 \, d}"," ",0,"1/4*(4*(a^3 - 3*a*b^2)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a*b)) + 4*a*sqrt(tan(d*x + c))/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)) - (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
595,1,270,0,0.509406," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(3 \, a^{2} b - b^{3}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a b}} + \frac{4 \, b \sqrt{\tan\left(d x + c\right)}}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)} - \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{4 \, d}"," ",0,"-1/4*(4*(3*a^2*b - b^3)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a*b)) + 4*b*sqrt(tan(d*x + c))/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)) - (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
596,1,277,0,0.451717," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, b^{2} \sqrt{\tan\left(d x + c\right)}}{a^{4} + a^{2} b^{2} + {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)} + \frac{4 \, {\left(5 \, a^{2} b^{2} + b^{4}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{4 \, d}"," ",0,"1/4*(4*b^2*sqrt(tan(d*x + c))/(a^4 + a^2*b^2 + (a^3*b + a*b^3)*tan(d*x + c)) + 4*(5*a^2*b^2 + b^4)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(a*b)) + (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
597,1,315,0,0.565939," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(7 \, a^{2} b^{3} + 3 \, b^{5}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{4 \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(2 \, a^{2} b + 3 \, b^{3}\right)} \tan\left(d x + c\right)\right)}}{{\left(a^{4} b + a^{2} b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(a^{5} + a^{3} b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(4*(7*a^2*b^3 + 3*b^5)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^6 + 2*a^4*b^2 + a^2*b^4)*sqrt(a*b)) + (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) + 4*(2*a^3 + 2*a*b^2 + (2*a^2*b + 3*b^3)*tan(d*x + c))/((a^4*b + a^2*b^3)*tan(d*x + c)^(3/2) + (a^5 + a^3*b^2)*sqrt(tan(d*x + c))))/d","A",0
598,1,342,0,0.620520," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{12 \, {\left(9 \, a^{2} b^{4} + 5 \, b^{6}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a b}} - \frac{4 \, {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - 3 \, {\left(4 \, a^{2} b^{2} + 5 \, b^{4}\right)} \tan\left(d x + c\right)^{2} - 10 \, {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)\right)}}{{\left(a^{5} b + a^{3} b^{3}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + {\left(a^{6} + a^{4} b^{2}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{12 \, d}"," ",0,"1/12*(12*(9*a^2*b^4 + 5*b^6)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^7 + 2*a^5*b^2 + a^3*b^4)*sqrt(a*b)) - 4*(2*a^4 + 2*a^2*b^2 - 3*(4*a^2*b^2 + 5*b^4)*tan(d*x + c)^2 - 10*(a^3*b + a*b^3)*tan(d*x + c))/((a^5*b + a^3*b^3)*tan(d*x + c)^(5/2) + (a^6 + a^4*b^2)*tan(d*x + c)^(3/2)) - 3*(2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
599,1,449,0,0.566777," ","integrate(tan(d*x+c)^(11/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(35 \, a^{8} + 102 \, a^{6} b^{2} + 99 \, a^{4} b^{4}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} \sqrt{a b}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{3 \, {\left({\left(13 \, a^{6} b + 21 \, a^{4} b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(11 \, a^{7} + 19 \, a^{5} b^{2}\right)} \sqrt{\tan\left(d x + c\right)}\right)}}{a^{6} b^{4} + 2 \, a^{4} b^{6} + a^{2} b^{8} + {\left(a^{4} b^{6} + 2 \, a^{2} b^{8} + b^{10}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{5} + 2 \, a^{3} b^{7} + a b^{9}\right)} \tan\left(d x + c\right)} + \frac{8 \, {\left(b \tan\left(d x + c\right)^{\frac{3}{2}} - 9 \, a \sqrt{\tan\left(d x + c\right)}\right)}}{b^{4}}}{12 \, d}"," ",0,"1/12*(3*(35*a^8 + 102*a^6*b^2 + 99*a^4*b^4)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*sqrt(a*b)) - 3*(2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 3*((13*a^6*b + 21*a^4*b^3)*tan(d*x + c)^(3/2) + (11*a^7 + 19*a^5*b^2)*sqrt(tan(d*x + c)))/(a^6*b^4 + 2*a^4*b^6 + a^2*b^8 + (a^4*b^6 + 2*a^2*b^8 + b^10)*tan(d*x + c)^2 + 2*(a^5*b^5 + 2*a^3*b^7 + a*b^9)*tan(d*x + c)) + 8*(b*tan(d*x + c)^(3/2) - 9*a*sqrt(tan(d*x + c)))/b^4)/d","A",0
600,1,434,0,0.470274," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{7} + 46 \, a^{5} b^{2} + 63 \, a^{3} b^{4}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(9 \, a^{5} b + 17 \, a^{3} b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(7 \, a^{6} + 15 \, a^{4} b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7} + {\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} \tan\left(d x + c\right)} - \frac{8 \, \sqrt{\tan\left(d x + c\right)}}{b^{3}}}{4 \, d}"," ",0,"-1/4*((15*a^7 + 46*a^5*b^2 + 63*a^3*b^4)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*sqrt(a*b)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((9*a^5*b + 17*a^3*b^3)*tan(d*x + c)^(3/2) + (7*a^6 + 15*a^4*b^2)*sqrt(tan(d*x + c)))/(a^6*b^3 + 2*a^4*b^5 + a^2*b^7 + (a^4*b^5 + 2*a^2*b^7 + b^9)*tan(d*x + c)^2 + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*tan(d*x + c)) - 8*sqrt(tan(d*x + c))/b^3)/d","A",0
601,1,420,0,0.543692," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{6} + 6 \, a^{4} b^{2} + 35 \, a^{2} b^{4}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left(5 \, a^{4} b + 13 \, a^{2} b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(3 \, a^{5} + 11 \, a^{3} b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*((3*a^6 + 6*a^4*b^2 + 35*a^2*b^4)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*sqrt(a*b)) + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((5*a^4*b + 13*a^2*b^3)*tan(d*x + c)^(3/2) + (3*a^5 + 11*a^3*b^2)*sqrt(tan(d*x + c)))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + (a^4*b^4 + 2*a^2*b^6 + b^8)*tan(d*x + c)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*tan(d*x + c)))/d","A",0
602,1,408,0,0.506843," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(a^{5} + 18 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(a^{3} b + 9 \, a b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} - {\left(a^{4} - 7 \, a^{2} b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*((a^5 + 18*a^3*b^2 - 15*a*b^4)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sqrt(a*b)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((a^3*b + 9*a*b^3)*tan(d*x + c)^(3/2) - (a^4 - 7*a^2*b^2)*sqrt(tan(d*x + c)))/(a^6*b + 2*a^4*b^3 + a^2*b^5 + (a^4*b^3 + 2*a^2*b^5 + b^7)*tan(d*x + c)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*tan(d*x + c)))/d","A",0
603,1,402,0,0.524551," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, a^{4} - 26 \, a^{2} b^{2} + 3 \, b^{4}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(3 \, a^{2} b - 5 \, b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(5 \, a^{3} - 3 \, a b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*((3*a^4 - 26*a^2*b^2 + 3*b^4)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a*b)) - (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((3*a^2*b - 5*b^3)*tan(d*x + c)^(3/2) + (5*a^3 - 3*a*b^2)*sqrt(tan(d*x + c)))/(a^6 + 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 + 2*a^2*b^4 + b^6)*tan(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(d*x + c)))/d","A",0
604,1,411,0,0.440364," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, a^{4} b - 18 \, a^{2} b^{3} - b^{5}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(7 \, a^{2} b^{2} - b^{4}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(9 \, a^{3} b + a b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4} + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*((15*a^4*b - 18*a^2*b^3 - b^5)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt(a*b)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((7*a^2*b^2 - b^4)*tan(d*x + c)^(3/2) + (9*a^3*b + a*b^3)*sqrt(tan(d*x + c)))/(a^7 + 2*a^5*b^2 + a^3*b^4 + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*tan(d*x + c)^2 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)*tan(d*x + c)))/d","A",0
605,1,419,0,0.426269," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(35 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, b^{6}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{{\left(11 \, a^{2} b^{3} + 3 \, b^{5}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(13 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \sqrt{\tan\left(d x + c\right)}}{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4} + {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*((35*a^4*b^2 + 6*a^2*b^4 + 3*b^6)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*sqrt(a*b)) + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((11*a^2*b^3 + 3*b^5)*tan(d*x + c)^(3/2) + (13*a^3*b^2 + 5*a*b^4)*sqrt(tan(d*x + c)))/(a^8 + 2*a^6*b^2 + a^4*b^4 + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*tan(d*x + c)^2 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*tan(d*x + c)))/d","A",0
606,1,464,0,0.780105," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(63 \, a^{4} b^{3} + 46 \, a^{2} b^{5} + 15 \, b^{7}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} \sqrt{a b}} + \frac{8 \, a^{6} + 16 \, a^{4} b^{2} + 8 \, a^{2} b^{4} + {\left(8 \, a^{4} b^{2} + 31 \, a^{2} b^{4} + 15 \, b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(16 \, a^{5} b + 49 \, a^{3} b^{3} + 25 \, a b^{5}\right)} \tan\left(d x + c\right)}{{\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} \sqrt{\tan\left(d x + c\right)}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}}{4 \, d}"," ",0,"-1/4*((63*a^4*b^3 + 46*a^2*b^5 + 15*b^7)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*sqrt(a*b)) + (8*a^6 + 16*a^4*b^2 + 8*a^2*b^4 + (8*a^4*b^2 + 31*a^2*b^4 + 15*b^6)*tan(d*x + c)^2 + (16*a^5*b + 49*a^3*b^3 + 25*a*b^5)*tan(d*x + c))/((a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*tan(d*x + c)^(5/2) + 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*tan(d*x + c)^(3/2) + (a^9 + 2*a^7*b^2 + a^5*b^4)*sqrt(tan(d*x + c))) + (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6))/d","A",0
607,1,502,0,0.617320," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(99 \, a^{4} b^{4} + 102 \, a^{2} b^{6} + 35 \, b^{8}\right)} \arctan\left(\frac{b \sqrt{\tan\left(d x + c\right)}}{\sqrt{a b}}\right)}{{\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} \sqrt{a b}} - \frac{8 \, a^{7} + 16 \, a^{5} b^{2} + 8 \, a^{3} b^{4} - 3 \, {\left(24 \, a^{4} b^{3} + 67 \, a^{2} b^{5} + 35 \, b^{7}\right)} \tan\left(d x + c\right)^{3} - {\left(136 \, a^{5} b^{2} + 335 \, a^{3} b^{4} + 175 \, a b^{6}\right)} \tan\left(d x + c\right)^{2} - 56 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \tan\left(d x + c\right)}{{\left(a^{8} b^{2} + 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} + 2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + {\left(a^{10} + 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}}}{12 \, d}"," ",0,"1/12*(3*(99*a^4*b^4 + 102*a^2*b^6 + 35*b^8)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*sqrt(a*b)) - (8*a^7 + 16*a^5*b^2 + 8*a^3*b^4 - 3*(24*a^4*b^3 + 67*a^2*b^5 + 35*b^7)*tan(d*x + c)^3 - (136*a^5*b^2 + 335*a^3*b^4 + 175*a*b^6)*tan(d*x + c)^2 - 56*(a^6*b + 2*a^4*b^3 + a^2*b^5)*tan(d*x + c))/((a^8*b^2 + 2*a^6*b^4 + a^4*b^6)*tan(d*x + c)^(7/2) + 2*(a^9*b + 2*a^7*b^3 + a^5*b^5)*tan(d*x + c)^(5/2) + (a^10 + 2*a^8*b^2 + a^6*b^4)*tan(d*x + c)^(3/2)) - 3*(2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6))/d","A",0
608,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(5/2), x)","F",0
609,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(3/2), x)","F",0
610,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*sqrt(tan(d*x + c)), x)","F",0
611,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \tan\left(d x + c\right) + a}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)/sqrt(tan(d*x + c)), x)","F",0
612,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)/tan(d*x + c)^(3/2), x)","F",0
613,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)/tan(d*x + c)^(5/2), x)","F",0
614,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)/tan(d*x + c)^(7/2), x)","F",0
615,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(5/2), x)","F",0
616,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(3/2), x)","F",0
617,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c)), x)","F",0
618,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/sqrt(tan(d*x + c)), x)","F",0
619,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(3/2), x)","F",0
620,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(5/2), x)","F",0
621,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(7/2), x)","F",0
622,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\tan\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(9/2), x)","F",0
623,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(5/2), x)","F",0
624,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(3/2), x)","F",0
625,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c)), x)","F",0
626,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/sqrt(tan(d*x + c)), x)","F",0
627,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(3/2), x)","F",0
628,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(5/2), x)","F",0
629,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(7/2), x)","F",0
630,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(9/2), x)","F",0
631,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\tan\left(d x + c\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(11/2), x)","F",0
632,0,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(7/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
633,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
634,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(3/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
635,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(b*tan(d*x + c) + a), x)","F",0
636,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*sqrt(tan(d*x + c))), x)","F",0
637,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(3/2)), x)","F",0
638,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(5/2)), x)","F",0
639,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(7/2)), x)","F",0
640,0,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(7/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
641,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
642,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\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(tan(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
643,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(b*tan(d*x + c) + a)^(3/2), x)","F",0
644,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c))), x)","F",0
645,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(3/2)), x)","F",0
646,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(5/2)), x)","F",0
647,0,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{9}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(9/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
648,0,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{7}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(7/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
649,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
650,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
651,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/(b*tan(d*x + c) + a)^(5/2), x)","F",0
652,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c))), x)","F",0
653,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(3/2)), x)","F",0
654,0,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(5/2)), x)","F",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
663,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(2+3*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{3 \, \tan\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(3*tan(d*x + c) + 2), x)","F",0
664,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-2+3*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{3 \, \tan\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(3*tan(d*x + c) - 2), x)","F",0
665,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(2-3*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{-3 \, \tan\left(d x + c\right) + 2}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(-3*tan(d*x + c) + 2), x)","F",0
666,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-2-3*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{-3 \, \tan\left(d x + c\right) - 2}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(-3*tan(d*x + c) - 2), x)","F",0
667,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(3+2*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{2 \, \tan\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(2*tan(d*x + c) + 3), x)","F",0
668,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(3-2*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{-2 \, \tan\left(d x + c\right) + 3}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(-2*tan(d*x + c) + 3), x)","F",0
669,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-3+2*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{2 \, \tan\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(2*tan(d*x + c) - 3), x)","F",0
670,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)/(-3-2*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\tan\left(d x + c\right)}}{\sqrt{-2 \, \tan\left(d x + c\right) - 3}}\,{d x}"," ",0,"integrate(sqrt(tan(d*x + c))/sqrt(-2*tan(d*x + c) - 3), x)","F",0
671,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
672,-1,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
673,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(1/3)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
674,-1,0,0,0.000000," ","integrate(1/tan(d*x+c)^(5/3)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
675,0,0,0,0.000000," ","integrate(tan(d*x+c)^(4/3)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{4}{3}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(4/3)/sqrt(b*tan(d*x + c) + a), x)","F",0
676,0,0,0,0.000000," ","integrate(tan(d*x+c)^(2/3)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{2}{3}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(2/3)/sqrt(b*tan(d*x + c) + a), x)","F",0
677,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/3)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^(1/3)/sqrt(b*tan(d*x + c) + a), x)","F",0
678,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(1/3),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(1/3)), x)","F",0
679,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(2/3),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(2/3)), x)","F",0
680,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(4/3),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(4/3)), x)","F",0
681,0,0,0,0.000000," ","integrate(tan(f*x+e)^4*(c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3)*tan(f*x + e)^4, x)","F",0
682,0,0,0,0.000000," ","integrate(tan(f*x+e)^3*(c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3)*tan(f*x + e)^3, x)","F",0
683,0,0,0,0.000000," ","integrate(tan(f*x+e)^2*(c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}} \tan\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3)*tan(f*x + e)^2, x)","F",0
684,0,0,0,0.000000," ","integrate(tan(f*x+e)*(c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}} \tan\left(f x + e\right)\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3)*tan(f*x + e), x)","F",0
685,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3), x)","F",0
686,0,0,0,0.000000," ","integrate(cot(f*x+e)*(c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","\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=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}} \cot\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(1/3)*cot(f*x + e)^2, x)","F",0
688,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/3),x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
702,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^m, x)","F",0
703,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
704,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{m}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(tan(d*x + c)^m/sqrt(b*tan(d*x + c) + a), x)","F",0
705,0,0,0,0.000000," ","integrate(tan(d*x+c)^m/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\tan\left(d x + c\right)^{m}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(tan(d*x + c)^m/(b*tan(d*x + c) + a)^(3/2), x)","F",0
706,0,0,0,0.000000," ","integrate((d*tan(f*x+e))^n*(a+b*tan(f*x+e))^m,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
715,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\int {\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
716,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
719,1,139,0,0.677808," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(-\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a + \frac{24 i \, a}{\sqrt{\tan\left(d x + c\right)}} + \frac{8 \, a}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(3*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a + 24*I*a/sqrt(tan(d*x + c)) + 8*a/tan(d*x + c)^(3/2))/d","B",0
720,1,127,0,0.475302," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(-\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a - \frac{8 \, a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*((-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a - 8*a/sqrt(tan(d*x + c)))/d","C",0
721,1,114,0,0.653375," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(-\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a}{4 \, d}"," ",0,"1/4*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a/d","C",0
722,1,127,0,0.475485," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{{\left(-\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a - 8 i \, a \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*((-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a - 8*I*a*sqrt(tan(d*x + c)))/d","B",0
723,1,142,0,0.613487," ","integrate((a+I*a*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{8 \, {\left(i \, a + \frac{3 \, a}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} - 3 \, {\left(-\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a}{12 \, d}"," ",0,"1/12*(8*(I*a + 3*a/tan(d*x + c))*tan(d*x + c)^(3/2) - 3*(-(2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a)/d","B",0
724,1,158,0,0.721301," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, {\left(-\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{2} - \frac{120 \, a^{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{40 i \, a^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{12 \, a^{2}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{30 \, d}"," ",0,"-1/30*(15*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 - 120*a^2/sqrt(tan(d*x + c)) + 40*I*a^2/tan(d*x + c)^(3/2) + 12*a^2/tan(d*x + c)^(5/2))/d","B",0
725,1,145,0,0.970574," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, {\left(\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{2} - \frac{24 i \, a^{2}}{\sqrt{\tan\left(d x + c\right)}} - \frac{4 \, a^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{6 \, d}"," ",0,"1/6*(3*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 - 24*I*a^2/sqrt(tan(d*x + c)) - 4*a^2/tan(d*x + c)^(3/2))/d","B",0
726,1,131,0,1.064380," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(-\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{2} - \frac{4 \, a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{2 \, d}"," ",0,"1/2*((-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 - 4*a^2/sqrt(tan(d*x + c)))/d","C",0
727,1,131,0,1.027289," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{2} + 4 \, a^{2} \sqrt{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 + 4*a^2*sqrt(tan(d*x + c)))/d","C",0
728,1,146,0,0.846535," ","integrate((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{3 \, {\left(-\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{2} + 4 \, {\left(a^{2} - \frac{6 i \, a^{2}}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{6 \, d}"," ",0,"-1/6*(3*(-(2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 + 4*(a^2 - 6*I*a^2/tan(d*x + c))*tan(d*x + c)^(3/2))/d","B",0
729,1,161,0,0.960034," ","integrate((a+I*a*tan(d*x+c))^2/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(3 \, a^{2} - \frac{10 i \, a^{2}}{\tan\left(d x + c\right)} - \frac{30 \, a^{2}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 15 \, {\left(\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{2}}{30 \, d}"," ",0,"-1/30*(4*(3*a^2 - 10*I*a^2/tan(d*x + c) - 30*a^2/tan(d*x + c)^2)*tan(d*x + c)^(5/2) - 15*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2)/d","B",0
730,1,158,0,0.564043," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{5 \, {\left(\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{3} + \frac{40 \, a^{3}}{\sqrt{\tan\left(d x + c\right)}} - \frac{10 i \, a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{2 \, a^{3}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{5 \, d}"," ",0,"1/5*(5*((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 + 40*a^3/sqrt(tan(d*x + c)) - 10*I*a^3/tan(d*x + c)^(3/2) - 2*a^3/tan(d*x + c)^(5/2))/d","A",0
731,1,145,0,0.726871," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, {\left(\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{3} - \frac{18 i \, a^{3}}{\sqrt{\tan\left(d x + c\right)}} - \frac{2 \, a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{3 \, d}"," ",0,"1/3*(3*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 - 18*I*a^3/sqrt(tan(d*x + c)) - 2*a^3/tan(d*x + c)^(3/2))/d","B",0
732,1,144,0,0.583487," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{3} + 2 i \, a^{3} \sqrt{\tan\left(d x + c\right)} + \frac{2 \, a^{3}}{\sqrt{\tan\left(d x + c\right)}}}{d}"," ",0,"-(((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 + 2*I*a^3*sqrt(tan(d*x + c)) + 2*a^3/sqrt(tan(d*x + c)))/d","B",0
733,1,148,0,0.958505," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(\left(2 i + 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i + 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(i - 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \left(i - 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{3} - 2 \, {\left(-i \, a^{3} - \frac{9 \, a^{3}}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{3 \, d}"," ",0,"-1/3*(3*((2*I + 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I + 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + (I - 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - (I - 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 - 2*(-I*a^3 - 9*a^3/tan(d*x + c))*tan(d*x + c)^(3/2))/d","B",0
734,1,161,0,0.942934," ","integrate((a+I*a*tan(d*x+c))^3/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{5 \, {\left(\left(2 i - 2\right) \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \left(2 i - 2\right) \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \left(i + 1\right) \, \sqrt{2} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \left(i + 1\right) \, \sqrt{2} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)} a^{3} - 2 \, {\left(i \, a^{3} + \frac{5 \, a^{3}}{\tan\left(d x + c\right)} - \frac{20 i \, a^{3}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}}}{5 \, d}"," ",0,"1/5*(5*((2*I - 2)*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + (2*I - 2)*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - (I + 1)*sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + (I + 1)*sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 - 2*(I*a^3 + 5*a^3/tan(d*x + c) - 20*I*a^3/tan(d*x + c)^2)*tan(d*x + c)^(5/2))/d","A",0
735,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
736,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
737,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
738,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
739,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
740,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
741,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
742,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
743,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
744,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
745,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
746,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
747,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
748,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
749,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
750,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
751,1,1127,0,1.384606," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(900 i + 900\right) \, \cos\left(3 \, d x + 3 \, c\right) - \left(1170 i + 1170\right) \, \cos\left(d x + c\right) + \left(900 i - 900\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(1170 i - 1170\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(-\left(900 i - 900\right) \, \cos\left(3 \, d x + 3 \, c\right) + \left(1170 i - 1170\right) \, \cos\left(d x + c\right) + \left(900 i + 900\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(1170 i + 1170\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(-\left(900 i - 900\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(900 i - 900\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(1800 i - 1800\right) \, \cos\left(2 \, d x + 2 \, c\right) - 900 i + 900\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(450 i + 450\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(450 i + 450\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i + 900\right) \, \cos\left(2 \, d x + 2 \, c\right) - 450 i - 450\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(900 i + 900\right) \, \cos\left(5 \, d x + 5 \, c\right) + \left(150 i + 150\right) \, \cos\left(3 \, d x + 3 \, c\right) + \left(390 i + 390\right) \, \cos\left(d x + c\right) + \left(900 i - 900\right) \, \sin\left(5 \, d x + 5 \, c\right) + \left(150 i - 150\right) \, \sin\left(3 \, d x + 3 \, c\right) + \left(390 i - 390\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(240 i + 240\right) \, \cos\left(d x + c\right) + \left(240 i - 240\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(240 i + 240\right) \, \cos\left(d x + c\right) + \left(240 i - 240\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(480 i + 480\right) \, \cos\left(d x + c\right) - \left(480 i - 480\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(240 i + 240\right) \, \cos\left(d x + c\right) + \left(240 i - 240\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(-\left(900 i - 900\right) \, \cos\left(5 \, d x + 5 \, c\right) - \left(150 i - 150\right) \, \cos\left(3 \, d x + 3 \, c\right) - \left(390 i - 390\right) \, \cos\left(d x + c\right) + \left(900 i + 900\right) \, \sin\left(5 \, d x + 5 \, c\right) + \left(150 i + 150\right) \, \sin\left(3 \, d x + 3 \, c\right) + \left(390 i + 390\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(240 i - 240\right) \, \cos\left(d x + c\right) + \left(240 i + 240\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(240 i - 240\right) \, \cos\left(d x + c\right) + \left(240 i + 240\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(480 i - 480\right) \, \cos\left(d x + c\right) - \left(480 i + 480\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(240 i - 240\right) \, \cos\left(d x + c\right) + \left(240 i + 240\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{900 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"1/900*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((900*I + 900)*cos(3*d*x + 3*c) - (1170*I + 1170)*cos(d*x + c) + (900*I - 900)*sin(3*d*x + 3*c) - (1170*I - 1170)*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(900*I - 900)*cos(3*d*x + 3*c) + (1170*I - 1170)*cos(d*x + c) + (900*I + 900)*sin(3*d*x + 3*c) - (1170*I + 1170)*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + ((-(900*I - 900)*cos(2*d*x + 2*c)^2 - (900*I - 900)*sin(2*d*x + 2*c)^2 + (1800*I - 1800)*cos(2*d*x + 2*c) - 900*I + 900)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(450*I + 450)*cos(2*d*x + 2*c)^2 - (450*I + 450)*sin(2*d*x + 2*c)^2 + (900*I + 900)*cos(2*d*x + 2*c) - 450*I - 450)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((900*I + 900)*cos(5*d*x + 5*c) + (150*I + 150)*cos(3*d*x + 3*c) + (390*I + 390)*cos(d*x + c) + (900*I - 900)*sin(5*d*x + 5*c) + (150*I - 150)*sin(3*d*x + 3*c) + (390*I - 390)*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((240*I + 240)*cos(d*x + c) + (240*I - 240)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((240*I + 240)*cos(d*x + c) + (240*I - 240)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(480*I + 480)*cos(d*x + c) - (480*I - 480)*sin(d*x + c))*cos(2*d*x + 2*c) + (240*I + 240)*cos(d*x + c) + (240*I - 240)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(900*I - 900)*cos(5*d*x + 5*c) - (150*I - 150)*cos(3*d*x + 3*c) - (390*I - 390)*cos(d*x + c) + (900*I + 900)*sin(5*d*x + 5*c) + (150*I + 150)*sin(3*d*x + 3*c) + (390*I + 390)*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(240*I - 240)*cos(d*x + c) + (240*I + 240)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(240*I - 240)*cos(d*x + c) + (240*I + 240)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((480*I - 480)*cos(d*x + c) - (480*I + 480)*sin(d*x + c))*cos(2*d*x + 2*c) - (240*I - 240)*cos(d*x + c) + (240*I + 240)*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
752,1,955,0,1.139359," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(36 i - 36\right) \, \cos\left(3 \, d x + 3 \, c\right) + \left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(36 i + 36\right) \, \sin\left(3 \, d x + 3 \, c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(\left(36 i + 36\right) \, \cos\left(3 \, d x + 3 \, c\right) + \left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(36 i - 36\right) \, \sin\left(3 \, d x + 3 \, c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(36 i + 36\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(36 i + 36\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(72 i + 72\right) \, \cos\left(2 \, d x + 2 \, c\right) + 36 i + 36\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(18 i - 18\right) \, \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(18 i - 18\right) \, \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(36 i - 36\right) \, \cos\left(2 \, d x + 2 \, c\right) - 18 i + 18\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i - 24\right) \, \cos\left(d x + c\right) + \left(24 i + 24\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i - 12\right) \, \cos\left(d x + c\right) - \left(12 i + 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i + 24\right) \, \cos\left(d x + c\right) - \left(24 i - 24\right) \, \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i + 12\right) \, \cos\left(d x + c\right) + \left(12 i - 12\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{36 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/36*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((36*I - 36)*cos(3*d*x + 3*c) + (12*I - 12)*cos(d*x + c) - (36*I + 36)*sin(3*d*x + 3*c) - (12*I + 12)*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((36*I + 36)*cos(3*d*x + 3*c) + (12*I + 12)*cos(d*x + c) + (36*I - 36)*sin(3*d*x + 3*c) + (12*I - 12)*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + (((36*I + 36)*cos(2*d*x + 2*c)^2 + (36*I + 36)*sin(2*d*x + 2*c)^2 - (72*I + 72)*cos(2*d*x + 2*c) + 36*I + 36)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(18*I - 18)*cos(2*d*x + 2*c)^2 - (18*I - 18)*sin(2*d*x + 2*c)^2 + (36*I - 36)*cos(2*d*x + 2*c) - 18*I + 18)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((12*I - 12)*cos(d*x + c) - (12*I + 12)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I - 12)*cos(d*x + c) - (12*I + 12)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I - 24)*cos(d*x + c) + (24*I + 24)*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I - 12)*cos(d*x + c) - (12*I + 12)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((12*I + 12)*cos(d*x + c) + (12*I - 12)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I + 12)*cos(d*x + c) + (12*I - 12)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I + 24)*cos(d*x + c) - (24*I - 24)*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I + 12)*cos(d*x + c) + (12*I - 12)*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
753,1,539,0,0.863532," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} {\left(\left(2 i - 2\right) \, \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + \left(i + 1\right) \, \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} + {\left({\left(-\left(4 i + 4\right) \, \cos\left(d x + c\right) - \left(4 i - 4\right) \, \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(\left(4 i - 4\right) \, \cos\left(d x + c\right) - \left(4 i + 4\right) \, \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/2*((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a)*((2*I - 2)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (I + 1)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))))) + ((-(4*I + 4)*cos(d*x + c) - (4*I - 4)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((4*I - 4)*cos(d*x + c) - (4*I + 4)*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
754,1,374,0,0.957724," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{a} {\left(-\left(2 i + 2\right) \, \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + \left(i - 1\right) \, \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)}}{2 \, d}"," ",0,"-1/2*sqrt(a)*(-(2*I + 2)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (I - 1)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))/d","B",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=""maxima"")","\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=""maxima"")","\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
757,1,1173,0,1.084147," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(450 i + 450\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(480 i + 480\right) \, a \cos\left(d x + c\right) + \left(450 i - 450\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(480 i - 480\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(-\left(450 i - 450\right) \, a \cos\left(3 \, d x + 3 \, c\right) + \left(480 i - 480\right) \, a \cos\left(d x + c\right) + \left(450 i + 450\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(480 i + 480\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(-\left(450 i - 450\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(450 i - 450\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i - 900\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(450 i - 450\right) \, a\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(225 i + 225\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(225 i + 225\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(450 i + 450\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(225 i + 225\right) \, a\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(450 i + 450\right) \, a \cos\left(5 \, d x + 5 \, c\right) - \left(150 i + 150\right) \, a \cos\left(3 \, d x + 3 \, c\right) + \left(60 i + 60\right) \, a \cos\left(d x + c\right) + \left(450 i - 450\right) \, a \sin\left(5 \, d x + 5 \, c\right) - \left(150 i - 150\right) \, a \sin\left(3 \, d x + 3 \, c\right) + \left(60 i - 60\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(90 i + 90\right) \, a \cos\left(d x + c\right) - \left(90 i - 90\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(90 i + 90\right) \, a \cos\left(d x + c\right) - \left(90 i - 90\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(180 i + 180\right) \, a \cos\left(d x + c\right) + \left(180 i - 180\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(90 i + 90\right) \, a \cos\left(d x + c\right) - \left(90 i - 90\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(-\left(450 i - 450\right) \, a \cos\left(5 \, d x + 5 \, c\right) + \left(150 i - 150\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(60 i - 60\right) \, a \cos\left(d x + c\right) + \left(450 i + 450\right) \, a \sin\left(5 \, d x + 5 \, c\right) - \left(150 i + 150\right) \, a \sin\left(3 \, d x + 3 \, c\right) + \left(60 i + 60\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(90 i - 90\right) \, a \cos\left(d x + c\right) - \left(90 i + 90\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(90 i - 90\right) \, a \cos\left(d x + c\right) - \left(90 i + 90\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(180 i - 180\right) \, a \cos\left(d x + c\right) + \left(180 i + 180\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(90 i - 90\right) \, a \cos\left(d x + c\right) - \left(90 i + 90\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{225 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"1/225*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((450*I + 450)*a*cos(3*d*x + 3*c) - (480*I + 480)*a*cos(d*x + c) + (450*I - 450)*a*sin(3*d*x + 3*c) - (480*I - 480)*a*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(450*I - 450)*a*cos(3*d*x + 3*c) + (480*I - 480)*a*cos(d*x + c) + (450*I + 450)*a*sin(3*d*x + 3*c) - (480*I + 480)*a*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + ((-(450*I - 450)*a*cos(2*d*x + 2*c)^2 - (450*I - 450)*a*sin(2*d*x + 2*c)^2 + (900*I - 900)*a*cos(2*d*x + 2*c) - (450*I - 450)*a)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(225*I + 225)*a*cos(2*d*x + 2*c)^2 - (225*I + 225)*a*sin(2*d*x + 2*c)^2 + (450*I + 450)*a*cos(2*d*x + 2*c) - (225*I + 225)*a)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((450*I + 450)*a*cos(5*d*x + 5*c) - (150*I + 150)*a*cos(3*d*x + 3*c) + (60*I + 60)*a*cos(d*x + c) + (450*I - 450)*a*sin(5*d*x + 5*c) - (150*I - 150)*a*sin(3*d*x + 3*c) + (60*I - 60)*a*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(90*I + 90)*a*cos(d*x + c) - (90*I - 90)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(90*I + 90)*a*cos(d*x + c) - (90*I - 90)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((180*I + 180)*a*cos(d*x + c) + (180*I - 180)*a*sin(d*x + c))*cos(2*d*x + 2*c) - (90*I + 90)*a*cos(d*x + c) - (90*I - 90)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(450*I - 450)*a*cos(5*d*x + 5*c) + (150*I - 150)*a*cos(3*d*x + 3*c) - (60*I - 60)*a*cos(d*x + c) + (450*I + 450)*a*sin(5*d*x + 5*c) - (150*I + 150)*a*sin(3*d*x + 3*c) + (60*I + 60)*a*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((90*I - 90)*a*cos(d*x + c) - (90*I + 90)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((90*I - 90)*a*cos(d*x + c) - (90*I + 90)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(180*I - 180)*a*cos(d*x + c) + (180*I + 180)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (90*I - 90)*a*cos(d*x + c) - (90*I + 90)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
758,1,989,0,0.996932," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(18 i - 18\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(6 i - 6\right) \, a \cos\left(d x + c\right) - \left(18 i + 18\right) \, a \sin\left(3 \, d x + 3 \, c\right) + \left(6 i + 6\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(\left(18 i + 18\right) \, a \cos\left(3 \, d x + 3 \, c\right) - \left(6 i + 6\right) \, a \cos\left(d x + c\right) + \left(18 i - 18\right) \, a \sin\left(3 \, d x + 3 \, c\right) - \left(6 i - 6\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(18 i + 18\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(18 i + 18\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(36 i + 36\right) \, a \cos\left(2 \, d x + 2 \, c\right) + \left(18 i + 18\right) \, a\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(9 i - 9\right) \, a \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(9 i - 9\right) \, a \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(18 i - 18\right) \, a \cos\left(2 \, d x + 2 \, c\right) - \left(9 i - 9\right) \, a\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(12 i - 12\right) \, a \cos\left(d x + c\right) - \left(12 i + 12\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i - 12\right) \, a \cos\left(d x + c\right) - \left(12 i + 12\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i - 24\right) \, a \cos\left(d x + c\right) + \left(24 i + 24\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i - 12\right) \, a \cos\left(d x + c\right) - \left(12 i + 12\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(12 i + 12\right) \, a \cos\left(d x + c\right) + \left(12 i - 12\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12 i + 12\right) \, a \cos\left(d x + c\right) + \left(12 i - 12\right) \, a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(24 i + 24\right) \, a \cos\left(d x + c\right) - \left(24 i - 24\right) \, a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(12 i + 12\right) \, a \cos\left(d x + c\right) + \left(12 i - 12\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{9 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/9*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((18*I - 18)*a*cos(3*d*x + 3*c) - (6*I - 6)*a*cos(d*x + c) - (18*I + 18)*a*sin(3*d*x + 3*c) + (6*I + 6)*a*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((18*I + 18)*a*cos(3*d*x + 3*c) - (6*I + 6)*a*cos(d*x + c) + (18*I - 18)*a*sin(3*d*x + 3*c) - (6*I - 6)*a*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + (((18*I + 18)*a*cos(2*d*x + 2*c)^2 + (18*I + 18)*a*sin(2*d*x + 2*c)^2 - (36*I + 36)*a*cos(2*d*x + 2*c) + (18*I + 18)*a)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(9*I - 9)*a*cos(2*d*x + 2*c)^2 - (9*I - 9)*a*sin(2*d*x + 2*c)^2 + (18*I - 18)*a*cos(2*d*x + 2*c) - (9*I - 9)*a)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((12*I - 12)*a*cos(d*x + c) - (12*I + 12)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I - 12)*a*cos(d*x + c) - (12*I + 12)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I - 24)*a*cos(d*x + c) + (24*I + 24)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I - 12)*a*cos(d*x + c) - (12*I + 12)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((12*I + 12)*a*cos(d*x + c) + (12*I - 12)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((12*I + 12)*a*cos(d*x + c) + (12*I - 12)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(24*I + 24)*a*cos(d*x + c) - (24*I - 24)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (12*I + 12)*a*cos(d*x + c) + (12*I - 12)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
759,1,544,0,0.995946," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{{\left(\left(2 i - 2\right) \, a \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + \left(i + 1\right) \, a \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(-\left(2 i + 2\right) \, a \cos\left(d x + c\right) - \left(2 i - 2\right) \, a \sin\left(d x + c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(\left(2 i - 2\right) \, a \cos\left(d x + c\right) - \left(2 i + 2\right) \, a \sin\left(d x + c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{{\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"(((2*I - 2)*a*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (I + 1)*a*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((-(2*I + 2)*a*cos(d*x + c) - (2*I - 2)*a*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((2*I - 2)*a*cos(d*x + c) - (2*I + 2)*a*sin(d*x + c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",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=""maxima"")","\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=""maxima"")","\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
762,1,3119,0,1.555995," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) - \left(44100 i - 44100\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + \left(26460 i - 26460\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(1260 i - 1260\right) \, a^{2} \cos\left(d x + c\right) - \left(44100 i + 44100\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) + \left(44100 i + 44100\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) - \left(26460 i + 26460\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(1260 i + 1260\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(27300 i - 27300\right) \, a^{2} \cos\left(d x + c\right) + \left(27300 i + 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(27300 i - 27300\right) \, a^{2} \cos\left(d x + c\right) + {\left(-\left(27300 i - 27300\right) \, a^{2} \cos\left(d x + c\right) + \left(27300 i + 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(27300 i + 27300\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(54600 i - 54600\right) \, a^{2} \cos\left(d x + c\right) - \left(54600 i + 54600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i + 44100\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(7 \, d x + 7 \, c\right) - \left(44100 i + 44100\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + \left(26460 i + 26460\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(1260 i + 1260\right) \, a^{2} \cos\left(d x + c\right) + \left(44100 i - 44100\right) \, a^{2} \sin\left(7 \, d x + 7 \, c\right) - \left(44100 i - 44100\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) + \left(26460 i - 26460\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(1260 i - 1260\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(27300 i + 27300\right) \, a^{2} \cos\left(d x + c\right) - \left(27300 i - 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(27300 i + 27300\right) \, a^{2} \cos\left(d x + c\right) + {\left(-\left(27300 i + 27300\right) \, a^{2} \cos\left(d x + c\right) - \left(27300 i - 27300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(27300 i - 27300\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i + 44100\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(54600 i + 54600\right) \, a^{2} \cos\left(d x + c\right) + \left(54600 i - 54600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} - \left(176400 i + 176400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + \left(264600 i + 264600\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(176400 i + 176400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(176400 i + 176400\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(88200 i + 88200\right) \, a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i + 44100\right) \, a^{2}\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(22050 i - 22050\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} - \left(22050 i - 22050\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} - \left(132300 i - 132300\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i - 44100\right) \, a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(22050 i - 22050\right) \, a^{2}\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(63840 i - 63840\right) \, a^{2} \cos\left(d x + c\right) - \left(63840 i + 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(63840 i - 63840\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i - 63840\right) \, a^{2} \cos\left(d x + c\right) - \left(63840 i + 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(63840 i + 63840\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(102900 i - 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(102900 i - 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(205800 i - 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(102900 i - 102900\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(127680 i - 127680\right) \, a^{2} \cos\left(d x + c\right) + \left(127680 i + 127680\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(44100 i + 44100\right) \, a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(102900 i + 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(102900 i + 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(205800 i + 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(102900 i + 102900\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(48300 i - 48300\right) \, a^{2} \cos\left(d x + c\right) + \left(48300 i + 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(48300 i - 48300\right) \, a^{2} \cos\left(d x + c\right) + \left(48300 i + 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(193200 i - 193200\right) \, a^{2} \cos\left(d x + c\right) - \left(193200 i + 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(289800 i - 289800\right) \, a^{2} \cos\left(d x + c\right) + \left(289800 i + 289800\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(48300 i - 48300\right) \, a^{2} \cos\left(d x + c\right) + {\left({\left(-\left(96600 i - 96600\right) \, a^{2} \cos\left(d x + c\right) + \left(96600 i + 96600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(96600 i - 96600\right) \, a^{2} \cos\left(d x + c\right) + \left(96600 i + 96600\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, a^{2} \cos\left(d x + c\right) - \left(193200 i + 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(48300 i + 48300\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, a^{2} \cos\left(d x + c\right) - \left(193200 i + 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(63840 i + 63840\right) \, a^{2} \cos\left(d x + c\right) + \left(63840 i - 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(63840 i + 63840\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i + 63840\right) \, a^{2} \cos\left(d x + c\right) + \left(63840 i - 63840\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(63840 i - 63840\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(44100 i + 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i + 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i + 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i + 44100\right) \, a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(102900 i + 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(102900 i + 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(205800 i + 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(102900 i + 102900\right) \, a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(127680 i + 127680\right) \, a^{2} \cos\left(d x + c\right) - \left(127680 i - 127680\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(44100 i - 44100\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(88200 i - 88200\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(44100 i - 44100\right) \, a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(102900 i - 102900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(102900 i - 102900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(205800 i - 205800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(102900 i - 102900\right) \, a^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(48300 i + 48300\right) \, a^{2} \cos\left(d x + c\right) - \left(48300 i - 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(48300 i + 48300\right) \, a^{2} \cos\left(d x + c\right) - \left(48300 i - 48300\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(193200 i + 193200\right) \, a^{2} \cos\left(d x + c\right) + \left(193200 i - 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(289800 i + 289800\right) \, a^{2} \cos\left(d x + c\right) - \left(289800 i - 289800\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(48300 i + 48300\right) \, a^{2} \cos\left(d x + c\right) + {\left({\left(-\left(96600 i + 96600\right) \, a^{2} \cos\left(d x + c\right) - \left(96600 i - 96600\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(96600 i + 96600\right) \, a^{2} \cos\left(d x + c\right) - \left(96600 i - 96600\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i + 193200\right) \, a^{2} \cos\left(d x + c\right) + \left(193200 i - 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(48300 i - 48300\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(193200 i + 193200\right) \, a^{2} \cos\left(d x + c\right) + \left(193200 i - 193200\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{11025 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{4} + \sin\left(2 \, d x + 2 \, c\right)^{4} - 4 \, \cos\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 6 \, \cos\left(2 \, d x + 2 \, c\right)^{2} - 4 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} d}"," ",0,"1/11025*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((44100*I - 44100)*a^2*cos(7*d*x + 7*c) - (44100*I - 44100)*a^2*cos(5*d*x + 5*c) + (26460*I - 26460)*a^2*cos(3*d*x + 3*c) - (1260*I - 1260)*a^2*cos(d*x + c) - (44100*I + 44100)*a^2*sin(7*d*x + 7*c) + (44100*I + 44100)*a^2*sin(5*d*x + 5*c) - (26460*I + 26460)*a^2*sin(3*d*x + 3*c) + (1260*I + 1260)*a^2*sin(d*x + c))*cos(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(27300*I - 27300)*a^2*cos(d*x + c) + (27300*I + 27300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (27300*I - 27300)*a^2*cos(d*x + c) + (-(27300*I - 27300)*a^2*cos(d*x + c) + (27300*I + 27300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (27300*I + 27300)*a^2*sin(d*x + c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*cos(3*d*x + 3*c) + ((54600*I - 54600)*a^2*cos(d*x + c) - (54600*I + 54600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (-(44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 - (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 + (88200*I + 88200)*a^2*cos(2*d*x + 2*c) - (44100*I + 44100)*a^2)*sin(3*d*x + 3*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((44100*I + 44100)*a^2*cos(7*d*x + 7*c) - (44100*I + 44100)*a^2*cos(5*d*x + 5*c) + (26460*I + 26460)*a^2*cos(3*d*x + 3*c) - (1260*I + 1260)*a^2*cos(d*x + c) + (44100*I - 44100)*a^2*sin(7*d*x + 7*c) - (44100*I - 44100)*a^2*sin(5*d*x + 5*c) + (26460*I - 26460)*a^2*sin(3*d*x + 3*c) - (1260*I - 1260)*a^2*sin(d*x + c))*sin(7/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(27300*I + 27300)*a^2*cos(d*x + c) - (27300*I - 27300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (27300*I + 27300)*a^2*cos(d*x + c) + (-(27300*I + 27300)*a^2*cos(d*x + c) - (27300*I - 27300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (27300*I - 27300)*a^2*sin(d*x + c) + ((44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I + 88200)*a^2*cos(2*d*x + 2*c) + (44100*I + 44100)*a^2)*cos(3*d*x + 3*c) + ((54600*I + 54600)*a^2*cos(d*x + c) + (54600*I - 54600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*sin(3*d*x + 3*c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + (((44100*I + 44100)*a^2*cos(2*d*x + 2*c)^4 + (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^4 - (176400*I + 176400)*a^2*cos(2*d*x + 2*c)^3 + (264600*I + 264600)*a^2*cos(2*d*x + 2*c)^2 - (176400*I + 176400)*a^2*cos(2*d*x + 2*c) + ((88200*I + 88200)*a^2*cos(2*d*x + 2*c)^2 - (176400*I + 176400)*a^2*cos(2*d*x + 2*c) + (88200*I + 88200)*a^2)*sin(2*d*x + 2*c)^2 + (44100*I + 44100)*a^2)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(22050*I - 22050)*a^2*cos(2*d*x + 2*c)^4 - (22050*I - 22050)*a^2*sin(2*d*x + 2*c)^4 + (88200*I - 88200)*a^2*cos(2*d*x + 2*c)^3 - (132300*I - 132300)*a^2*cos(2*d*x + 2*c)^2 + (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (-(44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (88200*I - 88200)*a^2*cos(2*d*x + 2*c) - (44100*I - 44100)*a^2)*sin(2*d*x + 2*c)^2 - (22050*I - 22050)*a^2)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((63840*I - 63840)*a^2*cos(d*x + c) - (63840*I + 63840)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (63840*I - 63840)*a^2*cos(d*x + c) + ((63840*I - 63840)*a^2*cos(d*x + c) - (63840*I + 63840)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (63840*I + 63840)*a^2*sin(d*x + c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*cos(5*d*x + 5*c) + (-(102900*I - 102900)*a^2*cos(2*d*x + 2*c)^2 - (102900*I - 102900)*a^2*sin(2*d*x + 2*c)^2 + (205800*I - 205800)*a^2*cos(2*d*x + 2*c) - (102900*I - 102900)*a^2)*cos(3*d*x + 3*c) + (-(127680*I - 127680)*a^2*cos(d*x + c) + (127680*I + 127680)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (-(44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 - (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 + (88200*I + 88200)*a^2*cos(2*d*x + 2*c) - (44100*I + 44100)*a^2)*sin(5*d*x + 5*c) + ((102900*I + 102900)*a^2*cos(2*d*x + 2*c)^2 + (102900*I + 102900)*a^2*sin(2*d*x + 2*c)^2 - (205800*I + 205800)*a^2*cos(2*d*x + 2*c) + (102900*I + 102900)*a^2)*sin(3*d*x + 3*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(48300*I - 48300)*a^2*cos(d*x + c) + (48300*I + 48300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(48300*I - 48300)*a^2*cos(d*x + c) + (48300*I + 48300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((193200*I - 193200)*a^2*cos(d*x + c) - (193200*I + 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(289800*I - 289800)*a^2*cos(d*x + c) + (289800*I + 289800)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (48300*I - 48300)*a^2*cos(d*x + c) + ((-(96600*I - 96600)*a^2*cos(d*x + c) + (96600*I + 96600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (96600*I - 96600)*a^2*cos(d*x + c) + (96600*I + 96600)*a^2*sin(d*x + c) + ((193200*I - 193200)*a^2*cos(d*x + c) - (193200*I + 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (48300*I + 48300)*a^2*sin(d*x + c) + ((193200*I - 193200)*a^2*cos(d*x + c) - (193200*I + 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((63840*I + 63840)*a^2*cos(d*x + c) + (63840*I - 63840)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (63840*I + 63840)*a^2*cos(d*x + c) + ((63840*I + 63840)*a^2*cos(d*x + c) + (63840*I - 63840)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (63840*I - 63840)*a^2*sin(d*x + c) + ((44100*I + 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I + 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I + 88200)*a^2*cos(2*d*x + 2*c) + (44100*I + 44100)*a^2)*cos(5*d*x + 5*c) + (-(102900*I + 102900)*a^2*cos(2*d*x + 2*c)^2 - (102900*I + 102900)*a^2*sin(2*d*x + 2*c)^2 + (205800*I + 205800)*a^2*cos(2*d*x + 2*c) - (102900*I + 102900)*a^2)*cos(3*d*x + 3*c) + (-(127680*I + 127680)*a^2*cos(d*x + c) - (127680*I - 127680)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((44100*I - 44100)*a^2*cos(2*d*x + 2*c)^2 + (44100*I - 44100)*a^2*sin(2*d*x + 2*c)^2 - (88200*I - 88200)*a^2*cos(2*d*x + 2*c) + (44100*I - 44100)*a^2)*sin(5*d*x + 5*c) + (-(102900*I - 102900)*a^2*cos(2*d*x + 2*c)^2 - (102900*I - 102900)*a^2*sin(2*d*x + 2*c)^2 + (205800*I - 205800)*a^2*cos(2*d*x + 2*c) - (102900*I - 102900)*a^2)*sin(3*d*x + 3*c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(48300*I + 48300)*a^2*cos(d*x + c) - (48300*I - 48300)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (-(48300*I + 48300)*a^2*cos(d*x + c) - (48300*I - 48300)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((193200*I + 193200)*a^2*cos(d*x + c) + (193200*I - 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(289800*I + 289800)*a^2*cos(d*x + c) - (289800*I - 289800)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (48300*I + 48300)*a^2*cos(d*x + c) + ((-(96600*I + 96600)*a^2*cos(d*x + c) - (96600*I - 96600)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (96600*I + 96600)*a^2*cos(d*x + c) - (96600*I - 96600)*a^2*sin(d*x + c) + ((193200*I + 193200)*a^2*cos(d*x + c) + (193200*I - 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 - (48300*I - 48300)*a^2*sin(d*x + c) + ((193200*I + 193200)*a^2*cos(d*x + c) + (193200*I - 193200)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^4 + sin(2*d*x + 2*c)^4 - 4*cos(2*d*x + 2*c)^3 + 2*(cos(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*sin(2*d*x + 2*c)^2 + 6*cos(2*d*x + 2*c)^2 - 4*cos(2*d*x + 2*c) + 1)*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*d)","B",0
763,1,1261,0,0.805521," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(900 i + 900\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(930 i + 930\right) \, a^{2} \cos\left(d x + c\right) + \left(900 i - 900\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(930 i - 930\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(-\left(900 i - 900\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(930 i - 930\right) \, a^{2} \cos\left(d x + c\right) + \left(900 i + 900\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(930 i + 930\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(-\left(900 i - 900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(900 i - 900\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(1800 i - 1800\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(900 i - 900\right) \, a^{2}\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(450 i + 450\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(450 i + 450\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(900 i + 900\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(450 i + 450\right) \, a^{2}\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left(\left(900 i + 900\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) - \left(750 i + 750\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) + \left(210 i + 210\right) \, a^{2} \cos\left(d x + c\right) + \left(900 i - 900\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) - \left(750 i - 750\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(210 i - 210\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(-\left(240 i + 240\right) \, a^{2} \cos\left(d x + c\right) - \left(240 i - 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(240 i + 240\right) \, a^{2} \cos\left(d x + c\right) + {\left(-\left(240 i + 240\right) \, a^{2} \cos\left(d x + c\right) - \left(240 i - 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(240 i - 240\right) \, a^{2} \sin\left(d x + c\right) + {\left(\left(480 i + 480\right) \, a^{2} \cos\left(d x + c\right) + \left(480 i - 480\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(-\left(900 i - 900\right) \, a^{2} \cos\left(5 \, d x + 5 \, c\right) + \left(750 i - 750\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(210 i - 210\right) \, a^{2} \cos\left(d x + c\right) + \left(900 i + 900\right) \, a^{2} \sin\left(5 \, d x + 5 \, c\right) - \left(750 i + 750\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(210 i + 210\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(240 i - 240\right) \, a^{2} \cos\left(d x + c\right) - \left(240 i + 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(240 i - 240\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(240 i - 240\right) \, a^{2} \cos\left(d x + c\right) - \left(240 i + 240\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(240 i + 240\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(480 i - 480\right) \, a^{2} \cos\left(d x + c\right) + \left(480 i + 480\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{225 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"1/225*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((900*I + 900)*a^2*cos(3*d*x + 3*c) - (930*I + 930)*a^2*cos(d*x + c) + (900*I - 900)*a^2*sin(3*d*x + 3*c) - (930*I - 930)*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(900*I - 900)*a^2*cos(3*d*x + 3*c) + (930*I - 930)*a^2*cos(d*x + c) + (900*I + 900)*a^2*sin(3*d*x + 3*c) - (930*I + 930)*a^2*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + ((-(900*I - 900)*a^2*cos(2*d*x + 2*c)^2 - (900*I - 900)*a^2*sin(2*d*x + 2*c)^2 + (1800*I - 1800)*a^2*cos(2*d*x + 2*c) - (900*I - 900)*a^2)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(450*I + 450)*a^2*cos(2*d*x + 2*c)^2 - (450*I + 450)*a^2*sin(2*d*x + 2*c)^2 + (900*I + 900)*a^2*cos(2*d*x + 2*c) - (450*I + 450)*a^2)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + (((900*I + 900)*a^2*cos(5*d*x + 5*c) - (750*I + 750)*a^2*cos(3*d*x + 3*c) + (210*I + 210)*a^2*cos(d*x + c) + (900*I - 900)*a^2*sin(5*d*x + 5*c) - (750*I - 750)*a^2*sin(3*d*x + 3*c) + (210*I - 210)*a^2*sin(d*x + c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((-(240*I + 240)*a^2*cos(d*x + c) - (240*I - 240)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 - (240*I + 240)*a^2*cos(d*x + c) + (-(240*I + 240)*a^2*cos(d*x + c) - (240*I - 240)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (240*I - 240)*a^2*sin(d*x + c) + ((480*I + 480)*a^2*cos(d*x + c) + (480*I - 480)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(900*I - 900)*a^2*cos(5*d*x + 5*c) + (750*I - 750)*a^2*cos(3*d*x + 3*c) - (210*I - 210)*a^2*cos(d*x + c) + (900*I + 900)*a^2*sin(5*d*x + 5*c) - (750*I + 750)*a^2*sin(3*d*x + 3*c) + (210*I + 210)*a^2*sin(d*x + c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((240*I - 240)*a^2*cos(d*x + c) - (240*I + 240)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (240*I - 240)*a^2*cos(d*x + c) + ((240*I - 240)*a^2*cos(d*x + c) - (240*I + 240)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (240*I + 240)*a^2*sin(d*x + c) + (-(480*I - 480)*a^2*cos(d*x + c) + (480*I + 480)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",0
764,1,1053,0,1.090915," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left({\left(\left(36 i - 36\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(24 i - 24\right) \, a^{2} \cos\left(d x + c\right) - \left(36 i + 36\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) + \left(24 i + 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left(\left(36 i + 36\right) \, a^{2} \cos\left(3 \, d x + 3 \, c\right) - \left(24 i + 24\right) \, a^{2} \cos\left(d x + c\right) + \left(36 i - 36\right) \, a^{2} \sin\left(3 \, d x + 3 \, c\right) - \left(24 i - 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a} + {\left({\left(\left(36 i + 36\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(36 i + 36\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(72 i + 72\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + \left(36 i + 36\right) \, a^{2}\right)} \arctan\left(2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \sin\left(d x + c\right), 2 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + 2 \, \cos\left(d x + c\right)\right) + {\left(-\left(18 i - 18\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} - \left(18 i - 18\right) \, a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(36 i - 36\right) \, a^{2} \cos\left(2 \, d x + 2 \, c\right) - \left(18 i - 18\right) \, a^{2}\right)} \log\left(4 \, \cos\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)^{2} + 4 \, \sqrt{\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1} {\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)^{2}\right)} + 8 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} {\left(\cos\left(d x + c\right) \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + \sin\left(d x + c\right) \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)}\right)\right)} {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{1}{4}} \sqrt{a} + {\left({\left({\left(\left(12 i - 12\right) \, a^{2} \cos\left(d x + c\right) - \left(12 i + 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i - 12\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(12 i - 12\right) \, a^{2} \cos\left(d x + c\right) - \left(12 i + 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12 i + 12\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(24 i - 24\right) \, a^{2} \cos\left(d x + c\right) + \left(24 i + 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right) + {\left({\left(\left(12 i + 12\right) \, a^{2} \cos\left(d x + c\right) + \left(12 i - 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i + 12\right) \, a^{2} \cos\left(d x + c\right) + {\left(\left(12 i + 12\right) \, a^{2} \cos\left(d x + c\right) + \left(12 i - 12\right) \, a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i - 12\right) \, a^{2} \sin\left(d x + c\right) + {\left(-\left(24 i + 24\right) \, a^{2} \cos\left(d x + c\right) - \left(24 i - 24\right) \, a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, d x + 2 \, c\right), \cos\left(2 \, d x + 2 \, c\right) - 1\right)\right)\right)} \sqrt{a}}{9 \, {\left(\cos\left(2 \, d x + 2 \, c\right)^{2} + \sin\left(2 \, d x + 2 \, c\right)^{2} - 2 \, \cos\left(2 \, d x + 2 \, c\right) + 1\right)}^{\frac{5}{4}} d}"," ",0,"-1/9*(sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(((36*I - 36)*a^2*cos(3*d*x + 3*c) - (24*I - 24)*a^2*cos(d*x + c) - (36*I + 36)*a^2*sin(3*d*x + 3*c) + (24*I + 24)*a^2*sin(d*x + c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + ((36*I + 36)*a^2*cos(3*d*x + 3*c) - (24*I + 24)*a^2*cos(d*x + c) + (36*I - 36)*a^2*sin(3*d*x + 3*c) - (24*I - 24)*a^2*sin(d*x + c))*sin(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a) + (((36*I + 36)*a^2*cos(2*d*x + 2*c)^2 + (36*I + 36)*a^2*sin(2*d*x + 2*c)^2 - (72*I + 72)*a^2*cos(2*d*x + 2*c) + (36*I + 36)*a^2)*arctan2(2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*sin(d*x + c), 2*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + 2*cos(d*x + c)) + (-(18*I - 18)*a^2*cos(2*d*x + 2*c)^2 - (18*I - 18)*a^2*sin(2*d*x + 2*c)^2 + (36*I - 36)*a^2*cos(2*d*x + 2*c) - (18*I - 18)*a^2)*log(4*cos(d*x + c)^2 + 4*sin(d*x + c)^2 + 4*sqrt(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)*(cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2 + sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1))^2) + 8*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*(cos(d*x + c)*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + sin(d*x + c)*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))))*(cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(1/4)*sqrt(a) + ((((12*I - 12)*a^2*cos(d*x + c) - (12*I + 12)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12*I - 12)*a^2*cos(d*x + c) + ((12*I - 12)*a^2*cos(d*x + c) - (12*I + 12)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (12*I + 12)*a^2*sin(d*x + c) + (-(24*I - 24)*a^2*cos(d*x + c) + (24*I + 24)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((12*I + 12)*a^2*cos(d*x + c) + (12*I - 12)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12*I + 12)*a^2*cos(d*x + c) + ((12*I + 12)*a^2*cos(d*x + c) + (12*I - 12)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (12*I - 12)*a^2*sin(d*x + c) + (-(24*I + 24)*a^2*cos(d*x + c) - (24*I - 24)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)))*sqrt(a))/((cos(2*d*x + 2*c)^2 + sin(2*d*x + 2*c)^2 - 2*cos(2*d*x + 2*c) + 1)^(5/4)*d)","B",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
775,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
776,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
777,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
778,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
779,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
780,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
781,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
782,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
783,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
784,-1,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
785,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
786,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
787,-2,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
788,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
792,-2,0,0,0.000000," ","integrate((d*cot(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
793,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+I*a*tan(f*x+e))^m,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
798,1,162,0,0.716569," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 15 \, \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 15 \, \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{120 \, a}{\sqrt{\tan\left(d x + c\right)}} + \frac{40 \, b}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{24 \, a}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"-1/60*(30*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 30*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 15*sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 15*sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 120*a/sqrt(tan(d*x + c)) + 40*b/tan(d*x + c)^(3/2) + 24*a/tan(d*x + c)^(5/2))/d","A",0
799,1,151,0,0.680713," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 3 \, \sqrt{2} {\left(a - b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 3 \, \sqrt{2} {\left(a - b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{24 \, b}{\sqrt{\tan\left(d x + c\right)}} - \frac{8 \, a}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*(a - b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*(a - b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 24*b/sqrt(tan(d*x + c)) - 8*a/tan(d*x + c)^(3/2))/d","A",0
800,1,139,0,0.766376," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{8 \, a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*a/sqrt(tan(d*x + c)))/d","A",0
801,1,128,0,0.510119," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a - b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a - b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a - b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a - b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
802,1,139,0,0.615429," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 8 \, b \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*b*sqrt(tan(d*x + c)))/d","A",0
803,1,152,0,0.592412," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 3 \, \sqrt{2} {\left(a - b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 3 \, \sqrt{2} {\left(a - b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 8 \, {\left(b + \frac{3 \, a}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*(a - b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*(a - b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 8*(b + 3*a/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
804,1,165,0,0.582538," ","integrate((a+b*tan(d*x+c))/cot(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, b + \frac{5 \, a}{\tan\left(d x + c\right)} - \frac{15 \, b}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + 30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 30 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 15 \, \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 15 \, \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{60 \, d}"," ",0,"1/60*(8*(3*b + 5*a/tan(d*x + c) - 15*b/tan(d*x + c)^2)*tan(d*x + c)^(5/2) + 30*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 30*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 15*sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 15*sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
805,1,221,0,0.562500," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{210 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 210 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 105 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 105 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{1680 \, a b}{\sqrt{\tan\left(d x + c\right)}} + \frac{336 \, a b}{\tan\left(d x + c\right)^{\frac{5}{2}}} - \frac{280 \, {\left(a^{2} - b^{2}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{120 \, a^{2}}{\tan\left(d x + c\right)^{\frac{7}{2}}}}{420 \, d}"," ",0,"-1/420*(210*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 210*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 105*sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 105*sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 1680*a*b/sqrt(tan(d*x + c)) + 336*a*b/tan(d*x + c)^(5/2) - 280*(a^2 - b^2)/tan(d*x + c)^(3/2) + 120*a^2/tan(d*x + c)^(7/2))/d","A",0
806,1,209,0,0.474856," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{30 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 30 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 15 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 15 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \frac{80 \, a b}{\tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{120 \, {\left(a^{2} - b^{2}\right)}}{\sqrt{\tan\left(d x + c\right)}} + \frac{24 \, a^{2}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"-1/60*(30*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 30*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 15*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 15*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 80*a*b/tan(d*x + c)^(3/2) - 120*(a^2 - b^2)/sqrt(tan(d*x + c)) + 24*a^2/tan(d*x + c)^(5/2))/d","A",0
807,1,190,0,0.608503," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 3 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 3 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{48 \, a b}{\sqrt{\tan\left(d x + c\right)}} - \frac{8 \, a^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 48*a*b/sqrt(tan(d*x + c)) - 8*a^2/tan(d*x + c)^(3/2))/d","A",0
808,1,177,0,0.512302," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{8 \, a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*a^2/sqrt(tan(d*x + c)))/d","A",0
809,1,177,0,0.749700," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 8 \, b^{2} \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*b^2*sqrt(tan(d*x + c)))/d","A",0
810,1,191,0,0.873842," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 3 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 3 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 8 \, {\left(b^{2} + \frac{6 \, a b}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 3*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 3*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*(b^2 + 6*a*b/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
811,1,212,0,0.788487," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, b^{2} + \frac{10 \, a b}{\tan\left(d x + c\right)} + \frac{15 \, {\left(a^{2} - b^{2}\right)}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + 30 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 30 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 15 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 15 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{60 \, d}"," ",0,"1/60*(8*(3*b^2 + 10*a*b/tan(d*x + c) + 15*(a^2 - b^2)/tan(d*x + c)^2)*tan(d*x + c)^(5/2) + 30*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 30*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 15*sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 15*sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
812,1,224,0,0.914182," ","integrate((a+b*tan(d*x+c))^2/cot(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{8 \, {\left(15 \, b^{2} + \frac{42 \, a b}{\tan\left(d x + c\right)} - \frac{210 \, a b}{\tan\left(d x + c\right)^{3}} + \frac{35 \, {\left(a^{2} - b^{2}\right)}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} + 210 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 210 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 105 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 105 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{420 \, d}"," ",0,"1/420*(8*(15*b^2 + 42*a*b/tan(d*x + c) - 210*a*b/tan(d*x + c)^3 + 35*(a^2 - b^2)/tan(d*x + c)^2)*tan(d*x + c)^(7/2) + 210*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 210*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 105*sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 105*sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
813,1,262,0,0.824130," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \frac{504 \, a^{2} b}{\tan\left(d x + c\right)^{\frac{5}{2}}} - \frac{840 \, {\left(3 \, a^{2} b - b^{3}\right)}}{\sqrt{\tan\left(d x + c\right)}} + \frac{120 \, a^{3}}{\tan\left(d x + c\right)^{\frac{7}{2}}} - \frac{280 \, {\left(a^{3} - 3 \, a b^{2}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{420 \, d}"," ",0,"-1/420*(210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 504*a^2*b/tan(d*x + c)^(5/2) - 840*(3*a^2*b - b^3)/sqrt(tan(d*x + c)) + 120*a^3/tan(d*x + c)^(7/2) - 280*(a^3 - 3*a*b^2)/tan(d*x + c)^(3/2))/d","A",0
814,1,240,0,0.868775," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \frac{40 \, a^{2} b}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{8 \, a^{3}}{\tan\left(d x + c\right)^{\frac{5}{2}}} - \frac{40 \, {\left(a^{3} - 3 \, a b^{2}\right)}}{\sqrt{\tan\left(d x + c\right)}}}{20 \, d}"," ",0,"-1/20*(10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 40*a^2*b/tan(d*x + c)^(3/2) + 8*a^3/tan(d*x + c)^(5/2) - 40*(a^3 - 3*a*b^2)/sqrt(tan(d*x + c)))/d","A",0
815,1,220,0,0.756819," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{72 \, a^{2} b}{\sqrt{\tan\left(d x + c\right)}} - \frac{8 \, a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 72*a^2*b/sqrt(tan(d*x + c)) - 8*a^3/tan(d*x + c)^(3/2))/d","A",0
816,1,218,0,0.942664," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{8 \, b^{3} \sqrt{\tan\left(d x + c\right)} + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{8 \, a^{3}}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(8*b^3*sqrt(tan(d*x + c)) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*a^3/sqrt(tan(d*x + c)))/d","A",0
817,1,221,0,1.013734," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 3 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - 8 \, {\left(b^{3} + \frac{9 \, a b^{2}}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*(b^3 + 9*a*b^2/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
818,1,243,0,0.733702," ","integrate((a+b*tan(d*x+c))^3/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, {\left(b^{3} + \frac{5 \, a b^{2}}{\tan\left(d x + c\right)} + \frac{5 \, {\left(3 \, a^{2} b - b^{3}\right)}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 10 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 5 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{20 \, d}"," ",0,"1/20*(8*(b^3 + 5*a*b^2/tan(d*x + c) + 5*(3*a^2*b - b^3)/tan(d*x + c)^2)*tan(d*x + c)^(5/2) - 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - 10*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 5*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
819,1,265,0,1.112311," ","integrate((a+b*tan(d*x+c))^3/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{8 \, {\left(15 \, b^{3} + \frac{63 \, a b^{2}}{\tan\left(d x + c\right)} + \frac{35 \, {\left(3 \, a^{2} b - b^{3}\right)}}{\tan\left(d x + c\right)^{2}} + \frac{105 \, {\left(a^{3} - 3 \, a b^{2}\right)}}{\tan\left(d x + c\right)^{3}}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} + 210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 210 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 105 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{420 \, d}"," ",0,"1/420*(8*(15*b^3 + 63*a*b^2/tan(d*x + c) + 35*(3*a^2*b - b^3)/tan(d*x + c)^2 + 105*(a^3 - 3*a*b^2)/tan(d*x + c)^3)*tan(d*x + c)^(7/2) + 210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 210*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 105*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
820,1,207,0,0.828832," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{24 \, b^{4} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{4} + a^{2} b^{2}\right)} \sqrt{a b}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)}}{a^{2} + b^{2}} - \frac{8 \, {\left(\frac{3 \, b}{\sqrt{\tan\left(d x + c\right)}} - \frac{a}{\tan\left(d x + c\right)^{\frac{3}{2}}}\right)}}{a^{2}}}{12 \, d}"," ",0,"-1/12*(24*b^4*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^4 + a^2*b^2)*sqrt(a*b)) - 3*(2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2) - 8*(3*b/sqrt(tan(d*x + c)) - a/tan(d*x + c)^(3/2))/a^2)/d","A",0
821,1,189,0,0.994423," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, b^{3} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{3} + a b^{2}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a - b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a - b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{2} + b^{2}} - \frac{8}{a \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(8*b^3*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^3 + a*b^2)*sqrt(a*b)) + (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a - b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a - b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2) - 8/(a*sqrt(tan(d*x + c))))/d","A",0
822,1,174,0,0.974522," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, b^{2} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{2} + b^{2}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(8*b^2*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2 + b^2)*sqrt(a*b)) + (2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
823,1,174,0,0.810135," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, a b \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{2} + b^{2}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a - b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a - b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(8*a*b*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2 + b^2)*sqrt(a*b)) - (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a - b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a - b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
824,1,175,0,0.975621," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, a^{2} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{2} + b^{2}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a - b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a + b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a + b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(8*a^2*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2 + b^2)*sqrt(a*b)) - (2*sqrt(2)*(a - b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a - b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a + b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a + b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
825,1,189,0,0.723547," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, a^{3} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{2} b + b^{3}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a - b\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a - b\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{2} + b^{2}} + \frac{8 \, \sqrt{\tan\left(d x + c\right)}}{b}}{4 \, d}"," ",0,"1/4*(8*a^3*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2*b + b^3)*sqrt(a*b)) + (2*sqrt(2)*(a + b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a + b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a - b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a - b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2) + 8*sqrt(tan(d*x + c))/b)/d","A",0
826,1,318,0,0.701532," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{12 \, b^{4}}{{\left(a^{5} b + a^{3} b^{3} + \frac{a^{6} + a^{4} b^{2}}{\tan\left(d x + c\right)}\right)} \sqrt{\tan\left(d x + c\right)}} - \frac{12 \, {\left(9 \, a^{2} b^{4} + 5 \, b^{6}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a b}} + \frac{3 \, {\left(2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{8 \, {\left(\frac{6 \, b}{\sqrt{\tan\left(d x + c\right)}} - \frac{a}{\tan\left(d x + c\right)^{\frac{3}{2}}}\right)}}{a^{3}}}{12 \, d}"," ",0,"1/12*(12*b^4/((a^5*b + a^3*b^3 + (a^6 + a^4*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))) - 12*(9*a^2*b^4 + 5*b^6)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^7 + 2*a^5*b^2 + a^3*b^4)*sqrt(a*b)) + 3*(2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) + 8*(6*b/sqrt(tan(d*x + c)) - a/tan(d*x + c)^(3/2))/a^3)/d","A",0
827,1,303,0,0.642595," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, b^{3}}{{\left(a^{4} b + a^{2} b^{3} + \frac{a^{5} + a^{3} b^{2}}{\tan\left(d x + c\right)}\right)} \sqrt{\tan\left(d x + c\right)}} - \frac{4 \, {\left(7 \, a^{2} b^{3} + 3 \, b^{5}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{8}{a^{2} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(4*b^3/((a^4*b + a^2*b^3 + (a^5 + a^3*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))) - 4*(7*a^2*b^3 + 3*b^5)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^6 + 2*a^4*b^2 + a^2*b^4)*sqrt(a*b)) - (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) + 8/(a^2*sqrt(tan(d*x + c))))/d","A",0
828,1,283,0,0.916794," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(5 \, a^{2} b^{2} + b^{4}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{a b}} - \frac{4 \, b^{2}}{{\left(a^{3} b + a b^{3} + \frac{a^{4} + a^{2} b^{2}}{\tan\left(d x + c\right)}\right)} \sqrt{\tan\left(d x + c\right)}} + \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{4 \, d}"," ",0,"-1/4*(4*(5*a^2*b^2 + b^4)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^5 + 2*a^3*b^2 + a*b^4)*sqrt(a*b)) - 4*b^2/((a^3*b + a*b^3 + (a^4 + a^2*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))) + (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
829,1,276,0,0.891876," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(3 \, a^{2} b - b^{3}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{4 \, b}{{\left(a^{2} b + b^{3} + \frac{a^{3} + a b^{2}}{\tan\left(d x + c\right)}\right)} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(4*(3*a^2*b - b^3)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a*b)) - (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) - 4*b/((a^2*b + b^3 + (a^3 + a*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))))/d","A",0
830,1,274,0,0.931221," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{4 \, a}{{\left(a^{2} b + b^{3} + \frac{a^{3} + a b^{2}}{\tan\left(d x + c\right)}\right)} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(4*(a^3 - 3*a*b^2)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^4 + 2*a^2*b^2 + b^4)*sqrt(a*b)) - (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) - 4*a/((a^2*b + b^3 + (a^3 + a*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))))/d","A",0
831,1,284,0,0.930637," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(a^{4} + 5 \, a^{2} b^{2}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sqrt{a b}} + \frac{4 \, a^{2}}{{\left(a^{2} b^{2} + b^{4} + \frac{a^{3} b + a b^{3}}{\tan\left(d x + c\right)}\right)} \sqrt{\tan\left(d x + c\right)}} - \frac{2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}}}{4 \, d}"," ",0,"-1/4*(4*(a^4 + 5*a^2*b^2)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^4*b + 2*a^2*b^3 + b^5)*sqrt(a*b)) + 4*a^2/((a^2*b^2 + b^4 + (a^3*b + a*b^3)/tan(d*x + c))*sqrt(tan(d*x + c))) - (2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 + 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^2 - 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^2 - 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4))/d","A",0
832,1,322,0,0.873008," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(3 \, a^{5} + 7 \, a^{3} b^{2}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{2} - 2 \, a b - b^{2}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{2} + 2 \, a b - b^{2}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{4 \, {\left(2 \, a^{2} b + 2 \, b^{3} + \frac{3 \, a^{3} + 2 \, a b^{2}}{\tan\left(d x + c\right)}\right)}}{\frac{a^{2} b^{3} + b^{5}}{\sqrt{\tan\left(d x + c\right)}} + \frac{a^{3} b^{2} + a b^{4}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}}{4 \, d}"," ",0,"1/4*(4*(3*a^5 + 7*a^3*b^2)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^4*b^2 + 2*a^2*b^4 + b^6)*sqrt(a*b)) - (2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^2 - 2*a*b - b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^2 + 2*a*b - b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^2 + 2*a*b - b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^4 + 2*a^2*b^2 + b^4) + 4*(2*a^2*b + 2*b^3 + (3*a^3 + 2*a*b^2)/tan(d*x + c))/((a^2*b^3 + b^5)/sqrt(tan(d*x + c)) + (a^3*b^2 + a*b^4)/tan(d*x + c)^(3/2)))/d","A",0
833,1,456,0,0.644011," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(99 \, a^{4} b^{4} + 102 \, a^{2} b^{6} + 35 \, b^{8}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} \sqrt{a b}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{3 \, {\left(\frac{19 \, a^{2} b^{5} + 11 \, b^{7}}{\sqrt{\tan\left(d x + c\right)}} + \frac{21 \, a^{3} b^{4} + 13 \, a b^{6}}{\tan\left(d x + c\right)^{\frac{3}{2}}}\right)}}{a^{8} b^{2} + 2 \, a^{6} b^{4} + a^{4} b^{6} + \frac{2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)}}{\tan\left(d x + c\right)} + \frac{a^{10} + 2 \, a^{8} b^{2} + a^{6} b^{4}}{\tan\left(d x + c\right)^{2}}} - \frac{8 \, {\left(\frac{9 \, b}{\sqrt{\tan\left(d x + c\right)}} - \frac{a}{\tan\left(d x + c\right)^{\frac{3}{2}}}\right)}}{a^{4}}}{12 \, d}"," ",0,"-1/12*(3*(99*a^4*b^4 + 102*a^2*b^6 + 35*b^8)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*sqrt(a*b)) - 3*(2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 3*((19*a^2*b^5 + 11*b^7)/sqrt(tan(d*x + c)) + (21*a^3*b^4 + 13*a*b^6)/tan(d*x + c)^(3/2))/(a^8*b^2 + 2*a^6*b^4 + a^4*b^6 + 2*(a^9*b + 2*a^7*b^3 + a^5*b^5)/tan(d*x + c) + (a^10 + 2*a^8*b^2 + a^6*b^4)/tan(d*x + c)^2) - 8*(9*b/sqrt(tan(d*x + c)) - a/tan(d*x + c)^(3/2))/a^4)/d","A",0
834,1,439,0,0.943651," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(63 \, a^{4} b^{3} + 46 \, a^{2} b^{5} + 15 \, b^{7}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{\frac{15 \, a^{2} b^{4} + 7 \, b^{6}}{\sqrt{\tan\left(d x + c\right)}} + \frac{17 \, a^{3} b^{3} + 9 \, a b^{5}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6} + \frac{2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)}}{\tan\left(d x + c\right)} + \frac{a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}}{\tan\left(d x + c\right)^{2}}} - \frac{8}{a^{3} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*((63*a^4*b^3 + 46*a^2*b^5 + 15*b^7)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*sqrt(a*b)) + (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((15*a^2*b^4 + 7*b^6)/sqrt(tan(d*x + c)) + (17*a^3*b^3 + 9*a*b^5)/tan(d*x + c)^(3/2))/(a^7*b^2 + 2*a^5*b^4 + a^3*b^6 + 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)/tan(d*x + c) + (a^9 + 2*a^7*b^2 + a^5*b^4)/tan(d*x + c)^2) - 8/(a^3*sqrt(tan(d*x + c))))/d","A",0
835,1,426,0,0.869178," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(35 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, b^{6}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{8} + 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} + a^{2} b^{6}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{\frac{11 \, a^{2} b^{3} + 3 \, b^{5}}{\sqrt{\tan\left(d x + c\right)}} + \frac{13 \, a^{3} b^{2} + 5 \, a b^{4}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + \frac{2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)}}{\tan\left(d x + c\right)} + \frac{a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}}{\tan\left(d x + c\right)^{2}}}}{4 \, d}"," ",0,"-1/4*((35*a^4*b^2 + 6*a^2*b^4 + 3*b^6)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^8 + 3*a^6*b^2 + 3*a^4*b^4 + a^2*b^6)*sqrt(a*b)) + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((11*a^2*b^3 + 3*b^5)/sqrt(tan(d*x + c)) + (13*a^3*b^2 + 5*a*b^4)/tan(d*x + c)^(3/2))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)/tan(d*x + c) + (a^8 + 2*a^6*b^2 + a^4*b^4)/tan(d*x + c)^2))/d","A",0
836,1,418,0,1.166070," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(15 \, a^{4} b - 18 \, a^{2} b^{3} - b^{5}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{7} + 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + a b^{6}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{\frac{7 \, a^{2} b^{2} - b^{4}}{\sqrt{\tan\left(d x + c\right)}} + \frac{9 \, a^{3} b + a b^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6} + \frac{2 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)}}{\tan\left(d x + c\right)} + \frac{a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}}{\tan\left(d x + c\right)^{2}}}}{4 \, d}"," ",0,"1/4*((15*a^4*b - 18*a^2*b^3 - b^5)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^7 + 3*a^5*b^2 + 3*a^3*b^4 + a*b^6)*sqrt(a*b)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((7*a^2*b^2 - b^4)/sqrt(tan(d*x + c)) + (9*a^3*b + a*b^3)/tan(d*x + c)^(3/2))/(a^5*b^2 + 2*a^3*b^4 + a*b^6 + 2*(a^6*b + 2*a^4*b^3 + a^2*b^5)/tan(d*x + c) + (a^7 + 2*a^5*b^2 + a^3*b^4)/tan(d*x + c)^2))/d","A",0
837,1,409,0,1.032413," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, a^{4} - 26 \, a^{2} b^{2} + 3 \, b^{4}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{\frac{3 \, a^{2} b - 5 \, b^{3}}{\sqrt{\tan\left(d x + c\right)}} + \frac{5 \, a^{3} - 3 \, a b^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6} + \frac{2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)}}{\tan\left(d x + c\right)} + \frac{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}}{\tan\left(d x + c\right)^{2}}}}{4 \, d}"," ",0,"-1/4*((3*a^4 - 26*a^2*b^2 + 3*b^4)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*sqrt(a*b)) - (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((3*a^2*b - 5*b^3)/sqrt(tan(d*x + c)) + (5*a^3 - 3*a*b^2)/tan(d*x + c)^(3/2))/(a^4*b^2 + 2*a^2*b^4 + b^6 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)/tan(d*x + c) + (a^6 + 2*a^4*b^2 + a^2*b^4)/tan(d*x + c)^2))/d","A",0
838,1,415,0,0.921286," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(a^{5} + 18 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{6} b + 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} + b^{7}\right)} \sqrt{a b}} - \frac{2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{\frac{a^{3} b + 9 \, a b^{3}}{\sqrt{\tan\left(d x + c\right)}} - \frac{a^{4} - 7 \, a^{2} b^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7} + \frac{2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)}}{\tan\left(d x + c\right)} + \frac{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}}{\tan\left(d x + c\right)^{2}}}}{4 \, d}"," ",0,"-1/4*((a^5 + 18*a^3*b^2 - 15*a*b^4)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^6*b + 3*a^4*b^3 + 3*a^2*b^5 + b^7)*sqrt(a*b)) - (2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((a^3*b + 9*a*b^3)/sqrt(tan(d*x + c)) - (a^4 - 7*a^2*b^2)/tan(d*x + c)^(3/2))/(a^4*b^3 + 2*a^2*b^5 + b^7 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)/tan(d*x + c) + (a^6*b + 2*a^4*b^3 + a^2*b^5)/tan(d*x + c)^2))/d","A",0
839,1,425,0,1.297040," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, a^{6} + 6 \, a^{4} b^{2} + 35 \, a^{2} b^{4}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} \sqrt{a b}} + \frac{2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} {\left(a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + b^{3}\right)} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) - \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + \sqrt{2} {\left(a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{\frac{5 \, a^{4} b + 13 \, a^{2} b^{3}}{\sqrt{\tan\left(d x + c\right)}} + \frac{3 \, a^{5} + 11 \, a^{3} b^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8} + \frac{2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)}}{\tan\left(d x + c\right)} + \frac{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}}{\tan\left(d x + c\right)^{2}}}}{4 \, d}"," ",0,"-1/4*((3*a^6 + 6*a^4*b^2 + 35*a^2*b^4)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*sqrt(a*b)) + (2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(a^3 - 3*a^2*b - 3*a*b^2 + b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(a^3 + 3*a^2*b - 3*a*b^2 - b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + ((5*a^4*b + 13*a^2*b^3)/sqrt(tan(d*x + c)) + (3*a^5 + 11*a^3*b^2)/tan(d*x + c)^(3/2))/(a^4*b^4 + 2*a^2*b^6 + b^8 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)/tan(d*x + c) + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)/tan(d*x + c)^2))/d","A",0
840,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(7/2), x)","F",0
841,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(5/2), x)","F",0
842,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(3/2), x)","F",0
843,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)*sqrt(cot(d*x + c)), x)","F",0
844,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \tan\left(d x + c\right) + a}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)/sqrt(cot(d*x + c)), x)","F",0
845,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \tan\left(d x + c\right) + a}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*tan(d*x + c) + a)/cot(d*x + c)^(3/2), x)","F",0
846,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(9/2), x)","F",0
847,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(7/2), x)","F",0
848,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(5/2), x)","F",0
849,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(3/2), x)","F",0
850,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c)), x)","F",0
851,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/sqrt(cot(d*x + c)), x)","F",0
852,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(3/2)/cot(d*x + c)^(3/2), x)","F",0
853,0,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(11/2), x)","F",0
854,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(9/2), x)","F",0
855,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(7/2), x)","F",0
856,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(5/2), x)","F",0
857,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(3/2), x)","F",0
858,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)*sqrt(cot(d*x + c)), x)","F",0
859,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/sqrt(cot(d*x + c)), x)","F",0
860,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(d*x + c) + a)^(5/2)/cot(d*x + c)^(3/2), x)","F",0
861,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
862,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\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
863,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/sqrt(b*tan(d*x + c) + a), x)","F",0
864,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*sqrt(cot(d*x + c))), x)","F",0
865,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(3/2)), x)","F",0
866,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(5/2)), x)","F",0
867,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
868,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\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
869,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^(3/2), x)","F",0
870,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c))), x)","F",0
871,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(3/2)), x)","F",0
872,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(5/2)), x)","F",0
873,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(7/2)), x)","F",0
874,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{\frac{5}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
875,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{\frac{3}{2}}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
876,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^(5/2), x)","F",0
877,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate(1/((b*tan(d*x + c) + a)^(5/2)*sqrt(cot(d*x + c))), x)","F",0
878,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(3/2)), x)","F",0
879,0,0,0,0.000000," ","integrate(1/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \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/((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(5/2)), x)","F",0
880,0,0,0,0.000000," ","integrate((d*cot(f*x+e))^n*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
890,1,45,0,0.989501," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{a^{3} c \tan\left(f x + e\right)^{3} - 3 i \, a^{3} c \tan\left(f x + e\right)^{2} - 3 \, a^{3} c \tan\left(f x + e\right)}{3 \, f}"," ",0,"-1/3*(a^3*c*tan(f*x + e)^3 - 3*I*a^3*c*tan(f*x + e)^2 - 3*a^3*c*tan(f*x + e))/f","B",0
891,1,32,0,1.015640," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{-i \, a^{2} c \tan\left(f x + e\right)^{2} - 2 \, a^{2} c \tan\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(-I*a^2*c*tan(f*x + e)^2 - 2*a^2*c*tan(f*x + e))/f","A",0
892,1,12,0,1.146785," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\frac{a c \tan\left(f x + e\right)}{f}"," ",0,"a*c*tan(f*x + e)/f","A",0
893,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
894,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
895,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
896,1,68,0,0.649777," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{6 \, a^{4} c^{2} \tan\left(f x + e\right)^{5} - 15 i \, a^{4} c^{2} \tan\left(f x + e\right)^{4} - 30 i \, a^{4} c^{2} \tan\left(f x + e\right)^{2} - 30 \, a^{4} c^{2} \tan\left(f x + e\right)}{30 \, f}"," ",0,"-1/30*(6*a^4*c^2*tan(f*x + e)^5 - 15*I*a^4*c^2*tan(f*x + e)^4 - 30*I*a^4*c^2*tan(f*x + e)^2 - 30*a^4*c^2*tan(f*x + e))/f","A",0
897,1,68,0,0.911592," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 i \, a^{3} c^{2} \tan\left(f x + e\right)^{4} + 4 \, a^{3} c^{2} \tan\left(f x + e\right)^{3} + 6 i \, a^{3} c^{2} \tan\left(f x + e\right)^{2} + 12 \, a^{3} c^{2} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*I*a^3*c^2*tan(f*x + e)^4 + 4*a^3*c^2*tan(f*x + e)^3 + 6*I*a^3*c^2*tan(f*x + e)^2 + 12*a^3*c^2*tan(f*x + e))/f","A",0
898,1,35,0,0.957239," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{a^{2} c^{2} \tan\left(f x + e\right)^{3} + 3 \, a^{2} c^{2} \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*(a^2*c^2*tan(f*x + e)^3 + 3*a^2*c^2*tan(f*x + e))/f","A",0
899,1,32,0,0.837836," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{-i \, a c^{2} \tan\left(f x + e\right)^{2} + 2 \, a c^{2} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(-I*a*c^2*tan(f*x + e)^2 + 2*a*c^2*tan(f*x + e))/f","A",0
900,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
901,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
902,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
903,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
904,1,116,0,0.784108," ","integrate((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{30 \, a^{5} c^{3} \tan\left(f x + e\right)^{7} - 70 i \, a^{5} c^{3} \tan\left(f x + e\right)^{6} + 42 \, a^{5} c^{3} \tan\left(f x + e\right)^{5} - 210 i \, a^{5} c^{3} \tan\left(f x + e\right)^{4} - 70 \, a^{5} c^{3} \tan\left(f x + e\right)^{3} - 210 i \, a^{5} c^{3} \tan\left(f x + e\right)^{2} - 210 \, a^{5} c^{3} \tan\left(f x + e\right)}{210 \, f}"," ",0,"-1/210*(30*a^5*c^3*tan(f*x + e)^7 - 70*I*a^5*c^3*tan(f*x + e)^6 + 42*a^5*c^3*tan(f*x + e)^5 - 210*I*a^5*c^3*tan(f*x + e)^4 - 70*a^5*c^3*tan(f*x + e)^3 - 210*I*a^5*c^3*tan(f*x + e)^2 - 210*a^5*c^3*tan(f*x + e))/f","A",0
905,1,100,0,0.952018," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{-10 i \, a^{4} c^{3} \tan\left(f x + e\right)^{6} - 12 \, a^{4} c^{3} \tan\left(f x + e\right)^{5} - 30 i \, a^{4} c^{3} \tan\left(f x + e\right)^{4} - 40 \, a^{4} c^{3} \tan\left(f x + e\right)^{3} - 30 i \, a^{4} c^{3} \tan\left(f x + e\right)^{2} - 60 \, a^{4} c^{3} \tan\left(f x + e\right)}{60 \, f}"," ",0,"-1/60*(-10*I*a^4*c^3*tan(f*x + e)^6 - 12*a^4*c^3*tan(f*x + e)^5 - 30*I*a^4*c^3*tan(f*x + e)^4 - 40*a^4*c^3*tan(f*x + e)^3 - 30*I*a^4*c^3*tan(f*x + e)^2 - 60*a^4*c^3*tan(f*x + e))/f","A",0
906,1,52,0,0.863995," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} c^{3} \tan\left(f x + e\right)^{5} + 10 \, a^{3} c^{3} \tan\left(f x + e\right)^{3} + 15 \, a^{3} c^{3} \tan\left(f x + e\right)}{15 \, f}"," ",0,"1/15*(3*a^3*c^3*tan(f*x + e)^5 + 10*a^3*c^3*tan(f*x + e)^3 + 15*a^3*c^3*tan(f*x + e))/f","A",0
907,1,68,0,0.835513," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{3 i \, a^{2} c^{3} \tan\left(f x + e\right)^{4} - 4 \, a^{2} c^{3} \tan\left(f x + e\right)^{3} + 6 i \, a^{2} c^{3} \tan\left(f x + e\right)^{2} - 12 \, a^{2} c^{3} \tan\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(3*I*a^2*c^3*tan(f*x + e)^4 - 4*a^2*c^3*tan(f*x + e)^3 + 6*I*a^2*c^3*tan(f*x + e)^2 - 12*a^2*c^3*tan(f*x + e))/f","A",0
908,1,45,0,1.127522," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{a c^{3} \tan\left(f x + e\right)^{3} + 3 i \, a c^{3} \tan\left(f x + e\right)^{2} - 3 \, a c^{3} \tan\left(f x + e\right)}{3 \, f}"," ",0,"-1/3*(a*c^3*tan(f*x + e)^3 + 3*I*a*c^3*tan(f*x + e)^2 - 3*a*c^3*tan(f*x + e))/f","B",0
909,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
910,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
911,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
912,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
913,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^5,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
914,1,132,0,0.876838," ","integrate((a+I*a*tan(f*x+e))^5*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\frac{105 i \, a^{5} c^{4} \tan\left(f x + e\right)^{8} + 120 \, a^{5} c^{4} \tan\left(f x + e\right)^{7} + 420 i \, a^{5} c^{4} \tan\left(f x + e\right)^{6} + 504 \, a^{5} c^{4} \tan\left(f x + e\right)^{5} + 630 i \, a^{5} c^{4} \tan\left(f x + e\right)^{4} + 840 \, a^{5} c^{4} \tan\left(f x + e\right)^{3} + 420 i \, a^{5} c^{4} \tan\left(f x + e\right)^{2} + 840 \, a^{5} c^{4} \tan\left(f x + e\right)}{840 \, f}"," ",0,"1/840*(105*I*a^5*c^4*tan(f*x + e)^8 + 120*a^5*c^4*tan(f*x + e)^7 + 420*I*a^5*c^4*tan(f*x + e)^6 + 504*a^5*c^4*tan(f*x + e)^5 + 630*I*a^5*c^4*tan(f*x + e)^4 + 840*a^5*c^4*tan(f*x + e)^3 + 420*I*a^5*c^4*tan(f*x + e)^2 + 840*a^5*c^4*tan(f*x + e))/f","A",0
915,1,68,0,0.964586," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\frac{5 \, a^{4} c^{4} \tan\left(f x + e\right)^{7} + 21 \, a^{4} c^{4} \tan\left(f x + e\right)^{5} + 35 \, a^{4} c^{4} \tan\left(f x + e\right)^{3} + 35 \, a^{4} c^{4} \tan\left(f x + e\right)}{35 \, f}"," ",0,"1/35*(5*a^4*c^4*tan(f*x + e)^7 + 21*a^4*c^4*tan(f*x + e)^5 + 35*a^4*c^4*tan(f*x + e)^3 + 35*a^4*c^4*tan(f*x + e))/f","A",0
916,1,100,0,0.824553," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\frac{-10 i \, a^{3} c^{4} \tan\left(f x + e\right)^{6} + 12 \, a^{3} c^{4} \tan\left(f x + e\right)^{5} - 30 i \, a^{3} c^{4} \tan\left(f x + e\right)^{4} + 40 \, a^{3} c^{4} \tan\left(f x + e\right)^{3} - 30 i \, a^{3} c^{4} \tan\left(f x + e\right)^{2} + 60 \, a^{3} c^{4} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(-10*I*a^3*c^4*tan(f*x + e)^6 + 12*a^3*c^4*tan(f*x + e)^5 - 30*I*a^3*c^4*tan(f*x + e)^4 + 40*a^3*c^4*tan(f*x + e)^3 - 30*I*a^3*c^4*tan(f*x + e)^2 + 60*a^3*c^4*tan(f*x + e))/f","A",0
917,1,68,0,0.630557," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","-\frac{6 \, a^{2} c^{4} \tan\left(f x + e\right)^{5} + 15 i \, a^{2} c^{4} \tan\left(f x + e\right)^{4} + 30 i \, a^{2} c^{4} \tan\left(f x + e\right)^{2} - 30 \, a^{2} c^{4} \tan\left(f x + e\right)}{30 \, f}"," ",0,"-1/30*(6*a^2*c^4*tan(f*x + e)^5 + 15*I*a^2*c^4*tan(f*x + e)^4 + 30*I*a^2*c^4*tan(f*x + e)^2 - 30*a^2*c^4*tan(f*x + e))/f","A",0
918,1,60,0,0.697301," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\frac{i \, a c^{4} \tan\left(f x + e\right)^{4} - 4 \, a c^{4} \tan\left(f x + e\right)^{3} - 6 i \, a c^{4} \tan\left(f x + e\right)^{2} + 4 \, a c^{4} \tan\left(f x + e\right)}{4 \, f}"," ",0,"1/4*(I*a*c^4*tan(f*x + e)^4 - 4*a*c^4*tan(f*x + e)^3 - 6*I*a*c^4*tan(f*x + e)^2 + 4*a*c^4*tan(f*x + e))/f","B",0
919,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
920,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
921,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
922,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
923,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^4/(a+I*a*tan(f*x+e))^5,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
924,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
925,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
926,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
927,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
928,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
929,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
930,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
931,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
932,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
933,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
934,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
935,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
936,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
937,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
938,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
939,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
940,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
941,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
942,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
943,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
944,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
945,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
946,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
947,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^6/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
948,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^5/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
949,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^4/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
950,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
951,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
952,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
953,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
954,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
955,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
956,1,67,0,0.913481," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 i \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} - 20 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} c + 60 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a^{3} c^{2}\right)}}{15 \, c^{2} f}"," ",0,"2/15*I*(3*(-I*c*tan(f*x + e) + c)^(5/2)*a^3 - 20*(-I*c*tan(f*x + e) + c)^(3/2)*a^3*c + 60*sqrt(-I*c*tan(f*x + e) + c)*a^3*c^2)/(c^2*f)","A",0
957,1,45,0,0.841918," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{2 i \, {\left({\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} - 6 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a^{2} c\right)}}{3 \, c f}"," ",0,"-2/3*I*((-I*c*tan(f*x + e) + c)^(3/2)*a^2 - 6*sqrt(-I*c*tan(f*x + e) + c)*a^2*c)/(c*f)","A",0
958,1,19,0,0.677641," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{2 i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a}{f}"," ",0,"2*I*sqrt(-I*c*tan(f*x + e) + c)*a/f","A",0
959,1,106,0,1.095576," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{\sqrt{2} c^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a} + \frac{4 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{2}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)} a - 2 \, a c}\right)}}{8 \, c f}"," ",0,"-1/8*I*(sqrt(2)*c^(3/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a + 4*sqrt(-I*c*tan(f*x + e) + c)*c^2/((-I*c*tan(f*x + e) + c)*a - 2*a*c))/(c*f)","A",0
960,1,153,0,0.945477," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{3 \, \sqrt{2} c^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{2}} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{2} - 10 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{3}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{2} - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{2} c + 4 \, a^{2} c^{2}}\right)}}{64 \, c f}"," ",0,"-1/64*I*(3*sqrt(2)*c^(3/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^2 + 4*(3*(-I*c*tan(f*x + e) + c)^(3/2)*c^2 - 10*sqrt(-I*c*tan(f*x + e) + c)*c^3)/((-I*c*tan(f*x + e) + c)^2*a^2 - 4*(-I*c*tan(f*x + e) + c)*a^2*c + 4*a^2*c^2))/(c*f)","A",0
961,1,192,0,1.157416," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} - 80 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} + 132 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{4}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} a^{3} - 6 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{3} c + 12 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{3} c^{2} - 8 \, a^{3} c^{3}} + \frac{15 \, \sqrt{2} c^{\frac{3}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{3}}\right)}}{768 \, c f}"," ",0,"-1/768*I*(4*(15*(-I*c*tan(f*x + e) + c)^(5/2)*c^2 - 80*(-I*c*tan(f*x + e) + c)^(3/2)*c^3 + 132*sqrt(-I*c*tan(f*x + e) + c)*c^4)/((-I*c*tan(f*x + e) + c)^3*a^3 - 6*(-I*c*tan(f*x + e) + c)^2*a^3*c + 12*(-I*c*tan(f*x + e) + c)*a^3*c^2 - 8*a^3*c^3) + 15*sqrt(2)*c^(3/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^3)/(c*f)","A",0
962,1,67,0,0.778683," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} - 84 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} c + 140 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} c^{2}\right)}}{105 \, c^{2} f}"," ",0,"2/105*I*(15*(-I*c*tan(f*x + e) + c)^(7/2)*a^3 - 84*(-I*c*tan(f*x + e) + c)^(5/2)*a^3*c + 140*(-I*c*tan(f*x + e) + c)^(3/2)*a^3*c^2)/(c^2*f)","A",0
963,1,46,0,0.575947," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} - 10 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} c\right)}}{15 \, c f}"," ",0,"-2/15*I*(3*(-I*c*tan(f*x + e) + c)^(5/2)*a^2 - 10*(-I*c*tan(f*x + e) + c)^(3/2)*a^2*c)/(c*f)","A",0
964,1,19,0,0.382269," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\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
965,1,106,0,0.876210," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{\sqrt{2} c^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a} - \frac{4 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{3}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)} a - 2 \, a c}\right)}}{4 \, c f}"," ",0,"1/4*I*(sqrt(2)*c^(5/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a - 4*sqrt(-I*c*tan(f*x + e) + c)*c^3/((-I*c*tan(f*x + e) + c)*a - 2*a*c))/(c*f)","A",0
966,1,151,0,0.571026," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{i \, {\left(\frac{\sqrt{2} c^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{2}} + \frac{4 \, {\left({\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{3} + 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{4}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{2} - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{2} c + 4 \, a^{2} c^{2}}\right)}}{32 \, c f}"," ",0,"1/32*I*(sqrt(2)*c^(5/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^2 + 4*((-I*c*tan(f*x + e) + c)^(3/2)*c^3 + 2*sqrt(-I*c*tan(f*x + e) + c)*c^4)/((-I*c*tan(f*x + e) + c)^2*a^2 - 4*(-I*c*tan(f*x + e) + c)*a^2*c + 4*a^2*c^2))/(c*f)","A",0
967,1,192,0,0.846360," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{i \, {\left(\frac{3 \, \sqrt{2} c^{\frac{5}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{3}} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{3} - 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{4} - 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{5}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} a^{3} - 6 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{3} c + 12 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{3} c^{2} - 8 \, a^{3} c^{3}}\right)}}{384 \, c f}"," ",0,"1/384*I*(3*sqrt(2)*c^(5/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^3 + 4*(3*(-I*c*tan(f*x + e) + c)^(5/2)*c^3 - 16*(-I*c*tan(f*x + e) + c)^(3/2)*c^4 - 12*sqrt(-I*c*tan(f*x + e) + c)*c^5)/((-I*c*tan(f*x + e) + c)^3*a^3 - 6*(-I*c*tan(f*x + e) + c)^2*a^3*c + 12*(-I*c*tan(f*x + e) + c)*a^3*c^2 - 8*a^3*c^3))/(c*f)","A",0
968,1,67,0,0.586458," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(35 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} a^{3} - 180 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} c + 252 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} c^{2}\right)}}{315 \, c^{2} f}"," ",0,"2/315*I*(35*(-I*c*tan(f*x + e) + c)^(9/2)*a^3 - 180*(-I*c*tan(f*x + e) + c)^(7/2)*a^3*c + 252*(-I*c*tan(f*x + e) + c)^(5/2)*a^3*c^2)/(c^2*f)","A",0
969,1,46,0,0.583983," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{2} - 14 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} c\right)}}{35 \, c f}"," ",0,"-2/35*I*(5*(-I*c*tan(f*x + e) + c)^(7/2)*a^2 - 14*(-I*c*tan(f*x + e) + c)^(5/2)*a^2*c)/(c*f)","A",0
970,1,19,0,0.315813," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a}{5 \, f}"," ",0,"2/5*I*(-I*c*tan(f*x + e) + c)^(5/2)*a/f","A",0
971,1,128,0,0.918452," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{3 \, \sqrt{2} c^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a} - \frac{4 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{4}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)} a - 2 \, a c} + \frac{4 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{3}}{a}\right)}}{2 \, c f}"," ",0,"1/2*I*(3*sqrt(2)*c^(7/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a - 4*sqrt(-I*c*tan(f*x + e) + c)*c^4/((-I*c*tan(f*x + e) + c)*a - 2*a*c) + 4*sqrt(-I*c*tan(f*x + e) + c)*c^3/a)/(c*f)","A",0
972,1,153,0,0.662972," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{3 \, \sqrt{2} c^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{2}} - \frac{4 \, {\left(5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{4} - 6 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{5}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{2} - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{2} c + 4 \, a^{2} c^{2}}\right)}}{16 \, c f}"," ",0,"-1/16*I*(3*sqrt(2)*c^(7/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^2 - 4*(5*(-I*c*tan(f*x + e) + c)^(3/2)*c^4 - 6*sqrt(-I*c*tan(f*x + e) + c)*c^5)/((-I*c*tan(f*x + e) + c)^2*a^2 - 4*(-I*c*tan(f*x + e) + c)*a^2*c + 4*a^2*c^2))/(c*f)","A",0
973,1,192,0,0.652807," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{3 \, \sqrt{2} c^{\frac{7}{2}} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{3}} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{4} + 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c^{5} - 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} c^{6}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} a^{3} - 6 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{3} c + 12 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{3} c^{2} - 8 \, a^{3} c^{3}}\right)}}{192 \, c f}"," ",0,"-1/192*I*(3*sqrt(2)*c^(7/2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^3 + 4*(3*(-I*c*tan(f*x + e) + c)^(5/2)*c^4 + 16*(-I*c*tan(f*x + e) + c)^(3/2)*c^5 - 12*sqrt(-I*c*tan(f*x + e) + c)*c^6)/((-I*c*tan(f*x + e) + c)^3*a^3 - 6*(-I*c*tan(f*x + e) + c)^2*a^3*c + 12*(-I*c*tan(f*x + e) + c)*a^3*c^2 - 8*a^3*c^3))/(c*f)","A",0
974,1,70,0,0.405921," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(\frac{12 \, a^{3} c}{\sqrt{-i \, c \tan\left(f x + e\right) + c}} - \frac{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} - 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a^{3} c}{c}\right)}}{3 \, c f}"," ",0,"-2/3*I*(12*a^3*c/sqrt(-I*c*tan(f*x + e) + c) - ((-I*c*tan(f*x + e) + c)^(3/2)*a^3 - 12*sqrt(-I*c*tan(f*x + e) + c)*a^3*c)/c)/(c*f)","A",0
975,1,45,0,0.519110," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(\sqrt{-i \, c \tan\left(f x + e\right) + c} a^{2} + \frac{2 \, a^{2} c}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}}{c f}"," ",0,"-2*I*(sqrt(-I*c*tan(f*x + e) + c)*a^2 + 2*a^2*c/sqrt(-I*c*tan(f*x + e) + c))/(c*f)","A",0
976,1,19,0,0.315224," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, a}{\sqrt{-i \, c \tan\left(f x + e\right) + c} f}"," ",0,"-2*I*a/(sqrt(-I*c*tan(f*x + e) + c)*f)","A",0
977,1,126,0,0.693985," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{3 \, \sqrt{2} \sqrt{c} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c - 4 \, c^{2}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a - 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a c}\right)}}{16 \, c f}"," ",0,"-1/16*I*(3*sqrt(2)*sqrt(c)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a + 4*(3*(-I*c*tan(f*x + e) + c)*c - 4*c^2)/((-I*c*tan(f*x + e) + c)^(3/2)*a - 2*sqrt(-I*c*tan(f*x + e) + c)*a*c))/(c*f)","A",0
978,1,169,0,0.831995," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c - 50 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{2} + 32 \, c^{3}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} c + 4 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a^{2} c^{2}} + \frac{15 \, \sqrt{2} \sqrt{c} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{2}}\right)}}{128 \, c f}"," ",0,"-1/128*I*(4*(15*(-I*c*tan(f*x + e) + c)^2*c - 50*(-I*c*tan(f*x + e) + c)*c^2 + 32*c^3)/((-I*c*tan(f*x + e) + c)^(5/2)*a^2 - 4*(-I*c*tan(f*x + e) + c)^(3/2)*a^2*c + 4*sqrt(-I*c*tan(f*x + e) + c)*a^2*c^2) + 15*sqrt(2)*sqrt(c)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^2)/(c*f)","A",0
979,1,208,0,0.919723," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} c - 560 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c^{2} + 924 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{3} - 384 \, c^{4}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} - 6 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} c + 12 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} c^{2} - 8 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a^{3} c^{3}} + \frac{105 \, \sqrt{2} \sqrt{c} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{3}}\right)}}{1536 \, c f}"," ",0,"-1/1536*I*(4*(105*(-I*c*tan(f*x + e) + c)^3*c - 560*(-I*c*tan(f*x + e) + c)^2*c^2 + 924*(-I*c*tan(f*x + e) + c)*c^3 - 384*c^4)/((-I*c*tan(f*x + e) + c)^(7/2)*a^3 - 6*(-I*c*tan(f*x + e) + c)^(5/2)*a^3*c + 12*(-I*c*tan(f*x + e) + c)^(3/2)*a^3*c^2 - 8*sqrt(-I*c*tan(f*x + e) + c)*a^3*c^3) + 105*sqrt(2)*sqrt(c)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/a^3)/(c*f)","A",0
980,1,68,0,0.647844," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(\frac{3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} a^{3}}{c} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{3} - a^{3} c\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\right)}}{3 \, c f}"," ",0,"2/3*I*(3*sqrt(-I*c*tan(f*x + e) + c)*a^3/c + 4*(3*(-I*c*tan(f*x + e) + c)*a^3 - a^3*c)/(-I*c*tan(f*x + e) + c)^(3/2))/(c*f)","A",0
981,1,44,0,0.432182," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{2} - 2 \, a^{2} c\right)}}{3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} c f}"," ",0,"2/3*I*(3*(-I*c*tan(f*x + e) + c)*a^2 - 2*a^2*c)/((-I*c*tan(f*x + e) + c)^(3/2)*c*f)","A",0
982,1,19,0,0.468508," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, a}{3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} f}"," ",0,"-2/3*I*a/((-I*c*tan(f*x + e) + c)^(3/2)*f)","A",0
983,1,141,0,0.568733," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} - 20 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c - 8 \, c^{2}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a - 2 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a c} + \frac{15 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a \sqrt{c}}\right)}}{96 \, c f}"," ",0,"-1/96*I*(4*(15*(-I*c*tan(f*x + e) + c)^2 - 20*(-I*c*tan(f*x + e) + c)*c - 8*c^2)/((-I*c*tan(f*x + e) + c)^(5/2)*a - 2*(-I*c*tan(f*x + e) + c)^(3/2)*a*c) + 15*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/(a*sqrt(c)))/(c*f)","A",0
984,1,184,0,0.476567," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} - 350 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c + 224 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{2} + 64 \, c^{3}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{2} - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} c + 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{2} c^{2}} + \frac{105 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{2} \sqrt{c}}\right)}}{768 \, c f}"," ",0,"-1/768*I*(4*(105*(-I*c*tan(f*x + e) + c)^3 - 350*(-I*c*tan(f*x + e) + c)^2*c + 224*(-I*c*tan(f*x + e) + c)*c^2 + 64*c^3)/((-I*c*tan(f*x + e) + c)^(7/2)*a^2 - 4*(-I*c*tan(f*x + e) + c)^(5/2)*a^2*c + 4*(-I*c*tan(f*x + e) + c)^(3/2)*a^2*c^2) + 105*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/(a^2*sqrt(c)))/(c*f)","A",0
985,1,223,0,0.693594," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(315 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} - 1680 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} c + 2772 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c^{2} - 1152 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{3} - 256 \, c^{4}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} a^{3} - 6 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} c + 12 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} c^{2} - 8 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} a^{3} c^{3}} + \frac{315 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{3} \sqrt{c}}\right)}}{3072 \, c f}"," ",0,"-1/3072*I*(4*(315*(-I*c*tan(f*x + e) + c)^4 - 1680*(-I*c*tan(f*x + e) + c)^3*c + 2772*(-I*c*tan(f*x + e) + c)^2*c^2 - 1152*(-I*c*tan(f*x + e) + c)*c^3 - 256*c^4)/((-I*c*tan(f*x + e) + c)^(9/2)*a^3 - 6*(-I*c*tan(f*x + e) + c)^(7/2)*a^3*c + 12*(-I*c*tan(f*x + e) + c)^(5/2)*a^3*c^2 - 8*(-I*c*tan(f*x + e) + c)^(3/2)*a^3*c^3) + 315*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/(a^3*sqrt(c)))/(c*f)","A",0
986,1,65,0,0.741830," ","integrate((a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} a^{3} - 20 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{3} c + 12 \, a^{3} c^{2}\right)}}{15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c^{2} f}"," ",0,"-2/15*I*(15*(-I*c*tan(f*x + e) + c)^2*a^3 - 20*(-I*c*tan(f*x + e) + c)*a^3*c + 12*a^3*c^2)/((-I*c*tan(f*x + e) + c)^(5/2)*c^2*f)","A",0
987,1,44,0,0.699013," ","integrate((a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} a^{2} - 6 \, a^{2} c\right)}}{15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c f}"," ",0,"2/15*I*(5*(-I*c*tan(f*x + e) + c)*a^2 - 6*a^2*c)/((-I*c*tan(f*x + e) + c)^(5/2)*c*f)","A",0
988,1,19,0,0.624585," ","integrate((a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, a}{5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} f}"," ",0,"-2/5*I*a/((-I*c*tan(f*x + e) + c)^(5/2)*f)","A",0
989,1,162,0,0.834393," ","integrate(1/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} - 140 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c - 56 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{2} - 48 \, c^{3}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a c - 2 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a c^{2}} + \frac{105 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a c^{\frac{3}{2}}}\right)}}{960 \, c f}"," ",0,"-1/960*I*(4*(105*(-I*c*tan(f*x + e) + c)^3 - 140*(-I*c*tan(f*x + e) + c)^2*c - 56*(-I*c*tan(f*x + e) + c)*c^2 - 48*c^3)/((-I*c*tan(f*x + e) + c)^(7/2)*a*c - 2*(-I*c*tan(f*x + e) + c)^(5/2)*a*c^2) + 105*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/(a*c^(3/2)))/(c*f)","A",0
990,1,205,0,1.053186," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(315 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} - 1050 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} c + 672 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c^{2} + 192 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{3} + 128 \, c^{4}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} a^{2} c - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{2} c^{2} + 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{2} c^{3}} + \frac{315 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{2} c^{\frac{3}{2}}}\right)}}{2560 \, c f}"," ",0,"-1/2560*I*(4*(315*(-I*c*tan(f*x + e) + c)^4 - 1050*(-I*c*tan(f*x + e) + c)^3*c + 672*(-I*c*tan(f*x + e) + c)^2*c^2 + 192*(-I*c*tan(f*x + e) + c)*c^3 + 128*c^4)/((-I*c*tan(f*x + e) + c)^(9/2)*a^2*c - 4*(-I*c*tan(f*x + e) + c)^(7/2)*a^2*c^2 + 4*(-I*c*tan(f*x + e) + c)^(5/2)*a^2*c^3) + 315*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/(a^2*c^(3/2)))/(c*f)","A",0
991,1,244,0,0.602652," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{4 \, {\left(3465 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{5} - 18480 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} c + 30492 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} c^{2} - 12672 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} c^{3} - 2816 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} c^{4} - 1536 \, c^{5}\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{11}{2}} a^{3} c - 6 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} a^{3} c^{2} + 12 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} a^{3} c^{3} - 8 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} a^{3} c^{4}} + \frac{3465 \, \sqrt{2} \log\left(-\frac{\sqrt{2} \sqrt{c} - \sqrt{-i \, c \tan\left(f x + e\right) + c}}{\sqrt{2} \sqrt{c} + \sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}{a^{3} c^{\frac{3}{2}}}\right)}}{30720 \, c f}"," ",0,"-1/30720*I*(4*(3465*(-I*c*tan(f*x + e) + c)^5 - 18480*(-I*c*tan(f*x + e) + c)^4*c + 30492*(-I*c*tan(f*x + e) + c)^3*c^2 - 12672*(-I*c*tan(f*x + e) + c)^2*c^3 - 2816*(-I*c*tan(f*x + e) + c)*c^4 - 1536*c^5)/((-I*c*tan(f*x + e) + c)^(11/2)*a^3*c - 6*(-I*c*tan(f*x + e) + c)^(9/2)*a^3*c^2 + 12*(-I*c*tan(f*x + e) + c)^(7/2)*a^3*c^3 - 8*(-I*c*tan(f*x + e) + c)^(5/2)*a^3*c^4) + 3465*sqrt(2)*log(-(sqrt(2)*sqrt(c) - sqrt(-I*c*tan(f*x + e) + c))/(sqrt(2)*sqrt(c) + sqrt(-I*c*tan(f*x + e) + c)))/(a^3*c^(3/2)))/(c*f)","A",0
992,1,667,0,0.828203," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(20 \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12 \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 20 i \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12 i \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(6 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 12 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 12 i \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, a^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(6 \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 12 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 12 i \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, a^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(-3 i \, a^{2} \cos\left(4 \, f x + 4 \, e\right) - 6 i \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(3 i \, a^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 i \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} \sin\left(4 \, f x + 4 \, e\right) - 6 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-4 i \, \cos\left(4 \, f x + 4 \, e\right) - 8 i \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(4 \, f x + 4 \, e\right) + 8 \, \sin\left(2 \, f x + 2 \, e\right) - 4 i\right)}}"," ",0,"(20*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 20*I*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*I*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (6*a^2*cos(4*f*x + 4*e) + 12*a^2*cos(2*f*x + 2*e) + 6*I*a^2*sin(4*f*x + 4*e) + 12*I*a^2*sin(2*f*x + 2*e) + 6*a^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (6*a^2*cos(4*f*x + 4*e) + 12*a^2*cos(2*f*x + 2*e) + 6*I*a^2*sin(4*f*x + 4*e) + 12*I*a^2*sin(2*f*x + 2*e) + 6*a^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (-3*I*a^2*cos(4*f*x + 4*e) - 6*I*a^2*cos(2*f*x + 2*e) + 3*a^2*sin(4*f*x + 4*e) + 6*a^2*sin(2*f*x + 2*e) - 3*I*a^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (3*I*a^2*cos(4*f*x + 4*e) + 6*I*a^2*cos(2*f*x + 2*e) - 3*a^2*sin(4*f*x + 4*e) - 6*a^2*sin(2*f*x + 2*e) + 3*I*a^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1))*sqrt(a)*sqrt(c)/(f*(-4*I*cos(4*f*x + 4*e) - 8*I*cos(2*f*x + 2*e) + 4*sin(4*f*x + 4*e) + 8*sin(2*f*x + 2*e) - 4*I))","B",0
993,1,447,0,1.152749," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(2 \, {\left(a \cos\left(2 \, f x + 2 \, e\right) + i \, a \sin\left(2 \, f x + 2 \, e\right) + a\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 2 \, {\left(a \cos\left(2 \, f x + 2 \, e\right) + i \, a \sin\left(2 \, f x + 2 \, e\right) + a\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 4 \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-i \, a \cos\left(2 \, f x + 2 \, e\right) + a \sin\left(2 \, f x + 2 \, e\right) - i \, a\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(i \, a \cos\left(2 \, f x + 2 \, e\right) - a \sin\left(2 \, f x + 2 \, e\right) + i \, a\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 4 i \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-2 i \, \cos\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right) - 2 i\right)}}"," ",0,"-(2*(a*cos(2*f*x + 2*e) + I*a*sin(2*f*x + 2*e) + a)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 2*(a*cos(2*f*x + 2*e) + I*a*sin(2*f*x + 2*e) + a)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 4*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-I*a*cos(2*f*x + 2*e) + a*sin(2*f*x + 2*e) - I*a)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (I*a*cos(2*f*x + 2*e) - a*sin(2*f*x + 2*e) + I*a)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 4*I*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/(f*(-2*I*cos(2*f*x + 2*e) + 2*sin(2*f*x + 2*e) - 2*I))","B",0
994,1,104,0,1.017148," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \sqrt{c} {\left(-2 i \, \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - 2 i \, \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)}}{2 \, f}"," ",0,"1/2*sqrt(a)*sqrt(c)*(-2*I*arctan2(cos(f*x + e), sin(f*x + e) + 1) - 2*I*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))/f","B",0
995,1,35,0,0.759332," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{i \, \sqrt{c} \sqrt{-i \, \tan\left(f x + e\right) + 1}}{\sqrt{a} f \sqrt{i \, \tan\left(f x + e\right) + 1}}"," ",0,"I*sqrt(c)*sqrt(-I*tan(f*x + e) + 1)/(sqrt(a)*f*sqrt(I*tan(f*x + e) + 1))","A",0
996,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
997,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
998,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
999,1,890,0,1.197858," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, a^{2} c \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 32 \, a^{2} c \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, a^{2} c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12 i \, a^{2} c \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 32 i \, a^{2} c \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 i \, a^{2} c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(6 \, a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 18 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 18 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 18 i \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 18 i \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 6 \, a^{2} c\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(6 \, a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 18 \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 18 \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 18 i \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 18 i \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 6 \, a^{2} c\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(-3 i \, a^{2} c \cos\left(6 \, f x + 6 \, e\right) - 9 i \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) - 9 i \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 9 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 9 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a^{2} c\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(3 i \, a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 9 i \, a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 9 i \, a^{2} c \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} c \sin\left(6 \, f x + 6 \, e\right) - 9 \, a^{2} c \sin\left(4 \, f x + 4 \, e\right) - 9 \, a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a^{2} c\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-12 i \, \cos\left(6 \, f x + 6 \, e\right) - 36 i \, \cos\left(4 \, f x + 4 \, e\right) - 36 i \, \cos\left(2 \, f x + 2 \, e\right) + 12 \, \sin\left(6 \, f x + 6 \, e\right) + 36 \, \sin\left(4 \, f x + 4 \, e\right) + 36 \, \sin\left(2 \, f x + 2 \, e\right) - 12 i\right)}}"," ",0,"-(12*a^2*c*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*a^2*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*a^2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*I*a^2*c*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*I*a^2*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*I*a^2*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (6*a^2*c*cos(6*f*x + 6*e) + 18*a^2*c*cos(4*f*x + 4*e) + 18*a^2*c*cos(2*f*x + 2*e) + 6*I*a^2*c*sin(6*f*x + 6*e) + 18*I*a^2*c*sin(4*f*x + 4*e) + 18*I*a^2*c*sin(2*f*x + 2*e) + 6*a^2*c)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (6*a^2*c*cos(6*f*x + 6*e) + 18*a^2*c*cos(4*f*x + 4*e) + 18*a^2*c*cos(2*f*x + 2*e) + 6*I*a^2*c*sin(6*f*x + 6*e) + 18*I*a^2*c*sin(4*f*x + 4*e) + 18*I*a^2*c*sin(2*f*x + 2*e) + 6*a^2*c)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (-3*I*a^2*c*cos(6*f*x + 6*e) - 9*I*a^2*c*cos(4*f*x + 4*e) - 9*I*a^2*c*cos(2*f*x + 2*e) + 3*a^2*c*sin(6*f*x + 6*e) + 9*a^2*c*sin(4*f*x + 4*e) + 9*a^2*c*sin(2*f*x + 2*e) - 3*I*a^2*c)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (3*I*a^2*c*cos(6*f*x + 6*e) + 9*I*a^2*c*cos(4*f*x + 4*e) + 9*I*a^2*c*cos(2*f*x + 2*e) - 3*a^2*c*sin(6*f*x + 6*e) - 9*a^2*c*sin(4*f*x + 4*e) - 9*a^2*c*sin(2*f*x + 2*e) + 3*I*a^2*c)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1))*sqrt(a)*sqrt(c)/(f*(-12*I*cos(6*f*x + 6*e) - 36*I*cos(4*f*x + 4*e) - 36*I*cos(2*f*x + 2*e) + 12*sin(6*f*x + 6*e) + 36*sin(4*f*x + 4*e) + 36*sin(2*f*x + 2*e) - 12*I))","B",0
1000,1,643,0,0.940867," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(4 \, a c \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 \, a c \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 4 i \, a c \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4 i \, a c \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(2 \, a c \cos\left(4 \, f x + 4 \, e\right) + 4 \, a c \cos\left(2 \, f x + 2 \, e\right) + 2 i \, a c \sin\left(4 \, f x + 4 \, e\right) + 4 i \, a c \sin\left(2 \, f x + 2 \, e\right) + 2 \, a c\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(2 \, a c \cos\left(4 \, f x + 4 \, e\right) + 4 \, a c \cos\left(2 \, f x + 2 \, e\right) + 2 i \, a c \sin\left(4 \, f x + 4 \, e\right) + 4 i \, a c \sin\left(2 \, f x + 2 \, e\right) + 2 \, a c\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(-i \, a c \cos\left(4 \, f x + 4 \, e\right) - 2 i \, a c \cos\left(2 \, f x + 2 \, e\right) + a c \sin\left(4 \, f x + 4 \, e\right) + 2 \, a c \sin\left(2 \, f x + 2 \, e\right) - i \, a c\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(i \, a c \cos\left(4 \, f x + 4 \, e\right) + 2 i \, a c \cos\left(2 \, f x + 2 \, e\right) - a c \sin\left(4 \, f x + 4 \, e\right) - 2 \, a c \sin\left(2 \, f x + 2 \, e\right) + i \, a c\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-4 i \, \cos\left(4 \, f x + 4 \, e\right) - 8 i \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(4 \, f x + 4 \, e\right) + 8 \, \sin\left(2 \, f x + 2 \, e\right) - 4 i\right)}}"," ",0,"-(4*a*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*a*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4*I*a*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4*I*a*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (2*a*c*cos(4*f*x + 4*e) + 4*a*c*cos(2*f*x + 2*e) + 2*I*a*c*sin(4*f*x + 4*e) + 4*I*a*c*sin(2*f*x + 2*e) + 2*a*c)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (2*a*c*cos(4*f*x + 4*e) + 4*a*c*cos(2*f*x + 2*e) + 2*I*a*c*sin(4*f*x + 4*e) + 4*I*a*c*sin(2*f*x + 2*e) + 2*a*c)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (-I*a*c*cos(4*f*x + 4*e) - 2*I*a*c*cos(2*f*x + 2*e) + a*c*sin(4*f*x + 4*e) + 2*a*c*sin(2*f*x + 2*e) - I*a*c)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (I*a*c*cos(4*f*x + 4*e) + 2*I*a*c*cos(2*f*x + 2*e) - a*c*sin(4*f*x + 4*e) - 2*a*c*sin(2*f*x + 2*e) + I*a*c)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1))*sqrt(a)*sqrt(c)/(f*(-4*I*cos(4*f*x + 4*e) - 8*I*cos(2*f*x + 2*e) + 4*sin(4*f*x + 4*e) + 8*sin(2*f*x + 2*e) - 4*I))","B",0
1001,1,259,0,0.811857," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(2 \, c \cos\left(2 \, f x + 2 \, e\right) + 2 i \, c \sin\left(2 \, f x + 2 \, e\right) + 2 \, c\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(2 \, c \cos\left(2 \, f x + 2 \, e\right) + 2 i \, c \sin\left(2 \, f x + 2 \, e\right) + 2 \, c\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + 4 \, c \cos\left(f x + e\right) - {\left(-i \, c \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) - i \, c\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left(i \, c \cos\left(2 \, f x + 2 \, e\right) - c \sin\left(2 \, f x + 2 \, e\right) + i \, c\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + 4 i \, c \sin\left(f x + e\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-2 i \, \cos\left(2 \, f x + 2 \, e\right) + 2 \, \sin\left(2 \, f x + 2 \, e\right) - 2 i\right)}}"," ",0,"-((2*c*cos(2*f*x + 2*e) + 2*I*c*sin(2*f*x + 2*e) + 2*c)*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (2*c*cos(2*f*x + 2*e) + 2*I*c*sin(2*f*x + 2*e) + 2*c)*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + 4*c*cos(f*x + e) - (-I*c*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) - I*c)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - (I*c*cos(2*f*x + 2*e) - c*sin(2*f*x + 2*e) + I*c)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + 4*I*c*sin(f*x + e))*sqrt(a)*sqrt(c)/(f*(-2*I*cos(2*f*x + 2*e) + 2*sin(2*f*x + 2*e) - 2*I))","B",0
1002,1,127,0,0.903333," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(2 i \, c \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 2 i \, c \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) - 4 i \, c \cos\left(f x + e\right) + c \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - c \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 4 \, c \sin\left(f x + e\right)\right)} \sqrt{c}}{2 \, \sqrt{a} f}"," ",0,"-1/2*(2*I*c*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 2*I*c*arctan2(cos(f*x + e), -sin(f*x + e) + 1) - 4*I*c*cos(f*x + e) + c*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - c*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 4*c*sin(f*x + e))*sqrt(c)/(sqrt(a)*f)","A",0
1003,1,35,0,1.050556," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{{\left(i \, c \cos\left(3 \, f x + 3 \, e\right) + c \sin\left(3 \, f x + 3 \, e\right)\right)} \sqrt{c}}{3 \, a^{\frac{3}{2}} f}"," ",0,"1/3*(I*c*cos(3*f*x + 3*e) + c*sin(3*f*x + 3*e))*sqrt(c)/(a^(3/2)*f)","A",0
1004,1,86,0,1.177583," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3 i \, c \cos\left(5 \, f x + 5 \, e\right) + 5 i \, c \cos\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, f x + 5 \, e\right), \cos\left(5 \, f x + 5 \, e\right)\right)\right) + 3 \, c \sin\left(5 \, f x + 5 \, e\right) + 5 \, c \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, f x + 5 \, e\right), \cos\left(5 \, f x + 5 \, e\right)\right)\right)\right)} \sqrt{c}}{30 \, a^{\frac{5}{2}} f}"," ",0,"1/30*(3*I*c*cos(5*f*x + 5*e) + 5*I*c*cos(3/5*arctan2(sin(5*f*x + 5*e), cos(5*f*x + 5*e))) + 3*c*sin(5*f*x + 5*e) + 5*c*sin(3/5*arctan2(sin(5*f*x + 5*e), cos(5*f*x + 5*e))))*sqrt(c)/(a^(5/2)*f)","A",0
1005,1,136,0,0.899714," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{{\left(15 i \, c \cos\left(7 \, f x + 7 \, e\right) + 42 i \, c \cos\left(\frac{5}{7} \, \arctan\left(\sin\left(7 \, f x + 7 \, e\right), \cos\left(7 \, f x + 7 \, e\right)\right)\right) + 35 i \, c \cos\left(\frac{3}{7} \, \arctan\left(\sin\left(7 \, f x + 7 \, e\right), \cos\left(7 \, f x + 7 \, e\right)\right)\right) + 15 \, c \sin\left(7 \, f x + 7 \, e\right) + 42 \, c \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(7 \, f x + 7 \, e\right), \cos\left(7 \, f x + 7 \, e\right)\right)\right) + 35 \, c \sin\left(\frac{3}{7} \, \arctan\left(\sin\left(7 \, f x + 7 \, e\right), \cos\left(7 \, f x + 7 \, e\right)\right)\right)\right)} \sqrt{c}}{420 \, a^{\frac{7}{2}} f}"," ",0,"1/420*(15*I*c*cos(7*f*x + 7*e) + 42*I*c*cos(5/7*arctan2(sin(7*f*x + 7*e), cos(7*f*x + 7*e))) + 35*I*c*cos(3/7*arctan2(sin(7*f*x + 7*e), cos(7*f*x + 7*e))) + 15*c*sin(7*f*x + 7*e) + 42*c*sin(5/7*arctan2(sin(7*f*x + 7*e), cos(7*f*x + 7*e))) + 35*c*sin(3/7*arctan2(sin(7*f*x + 7*e), cos(7*f*x + 7*e))))*sqrt(c)/(a^(7/2)*f)","A",0
1006,1,186,0,0.693721," ","integrate((c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","\frac{{\left(35 i \, c \cos\left(9 \, f x + 9 \, e\right) + 135 i \, c \cos\left(\frac{7}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 189 i \, c \cos\left(\frac{5}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 105 i \, c \cos\left(\frac{1}{3} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 35 \, c \sin\left(9 \, f x + 9 \, e\right) + 135 \, c \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 189 \, c \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 105 \, c \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right)\right)} \sqrt{c}}{2520 \, a^{\frac{9}{2}} f}"," ",0,"1/2520*(35*I*c*cos(9*f*x + 9*e) + 135*I*c*cos(7/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 189*I*c*cos(5/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 105*I*c*cos(1/3*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 35*c*sin(9*f*x + 9*e) + 135*c*sin(7/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 189*c*sin(5/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 105*c*sin(1/3*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))))*sqrt(c)/(a^(9/2)*f)","A",0
1007,1,1176,0,1.335290," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, a^{2} c^{2} \cos\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 44 \, a^{2} c^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 44 \, a^{2} c^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, a^{2} c^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12 i \, a^{2} c^{2} \sin\left(\frac{7}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 44 i \, a^{2} c^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 44 i \, a^{2} c^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 i \, a^{2} c^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(6 \, a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 24 \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 36 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 24 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 24 i \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 36 i \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 24 i \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, a^{2} c^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(6 \, a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 24 \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 36 \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 24 \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 24 i \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 36 i \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 24 i \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, a^{2} c^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(-3 i \, a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) - 12 i \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) - 18 i \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) - 12 i \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 12 \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 18 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 12 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a^{2} c^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(3 i \, a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 12 i \, a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 18 i \, a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 12 i \, a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) - 12 \, a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) - 18 \, a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) - 12 \, a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a^{2} c^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-16 i \, \cos\left(8 \, f x + 8 \, e\right) - 64 i \, \cos\left(6 \, f x + 6 \, e\right) - 96 i \, \cos\left(4 \, f x + 4 \, e\right) - 64 i \, \cos\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(8 \, f x + 8 \, e\right) + 64 \, \sin\left(6 \, f x + 6 \, e\right) + 96 \, \sin\left(4 \, f x + 4 \, e\right) + 64 \, \sin\left(2 \, f x + 2 \, e\right) - 16 i\right)}}"," ",0,"-(12*a^2*c^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 44*a^2*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 44*a^2*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*a^2*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*I*a^2*c^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 44*I*a^2*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 44*I*a^2*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*I*a^2*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (6*a^2*c^2*cos(8*f*x + 8*e) + 24*a^2*c^2*cos(6*f*x + 6*e) + 36*a^2*c^2*cos(4*f*x + 4*e) + 24*a^2*c^2*cos(2*f*x + 2*e) + 6*I*a^2*c^2*sin(8*f*x + 8*e) + 24*I*a^2*c^2*sin(6*f*x + 6*e) + 36*I*a^2*c^2*sin(4*f*x + 4*e) + 24*I*a^2*c^2*sin(2*f*x + 2*e) + 6*a^2*c^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (6*a^2*c^2*cos(8*f*x + 8*e) + 24*a^2*c^2*cos(6*f*x + 6*e) + 36*a^2*c^2*cos(4*f*x + 4*e) + 24*a^2*c^2*cos(2*f*x + 2*e) + 6*I*a^2*c^2*sin(8*f*x + 8*e) + 24*I*a^2*c^2*sin(6*f*x + 6*e) + 36*I*a^2*c^2*sin(4*f*x + 4*e) + 24*I*a^2*c^2*sin(2*f*x + 2*e) + 6*a^2*c^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (-3*I*a^2*c^2*cos(8*f*x + 8*e) - 12*I*a^2*c^2*cos(6*f*x + 6*e) - 18*I*a^2*c^2*cos(4*f*x + 4*e) - 12*I*a^2*c^2*cos(2*f*x + 2*e) + 3*a^2*c^2*sin(8*f*x + 8*e) + 12*a^2*c^2*sin(6*f*x + 6*e) + 18*a^2*c^2*sin(4*f*x + 4*e) + 12*a^2*c^2*sin(2*f*x + 2*e) - 3*I*a^2*c^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (3*I*a^2*c^2*cos(8*f*x + 8*e) + 12*I*a^2*c^2*cos(6*f*x + 6*e) + 18*I*a^2*c^2*cos(4*f*x + 4*e) + 12*I*a^2*c^2*cos(2*f*x + 2*e) - 3*a^2*c^2*sin(8*f*x + 8*e) - 12*a^2*c^2*sin(6*f*x + 6*e) - 18*a^2*c^2*sin(4*f*x + 4*e) - 12*a^2*c^2*sin(2*f*x + 2*e) + 3*I*a^2*c^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1))*sqrt(a)*sqrt(c)/(f*(-16*I*cos(8*f*x + 8*e) - 64*I*cos(6*f*x + 6*e) - 96*I*cos(4*f*x + 4*e) - 64*I*cos(2*f*x + 2*e) + 16*sin(8*f*x + 8*e) + 64*sin(6*f*x + 6*e) + 96*sin(4*f*x + 4*e) + 64*sin(2*f*x + 2*e) - 16*I))","B",0
1008,1,890,0,1.007395," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, a c^{2} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 32 \, a c^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, a c^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12 i \, a c^{2} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 32 i \, a c^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 i \, a c^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(6 \, a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 18 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 18 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 18 i \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 18 i \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, a c^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(6 \, a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 18 \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 18 \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 18 i \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 18 i \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, a c^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(-3 i \, a c^{2} \cos\left(6 \, f x + 6 \, e\right) - 9 i \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) - 9 i \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 9 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 9 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a c^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(3 i \, a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 9 i \, a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 9 i \, a c^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, a c^{2} \sin\left(6 \, f x + 6 \, e\right) - 9 \, a c^{2} \sin\left(4 \, f x + 4 \, e\right) - 9 \, a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a c^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-12 i \, \cos\left(6 \, f x + 6 \, e\right) - 36 i \, \cos\left(4 \, f x + 4 \, e\right) - 36 i \, \cos\left(2 \, f x + 2 \, e\right) + 12 \, \sin\left(6 \, f x + 6 \, e\right) + 36 \, \sin\left(4 \, f x + 4 \, e\right) + 36 \, \sin\left(2 \, f x + 2 \, e\right) - 12 i\right)}}"," ",0,"-(12*a*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 32*a*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*a*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*I*a*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 32*I*a*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*I*a*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (6*a*c^2*cos(6*f*x + 6*e) + 18*a*c^2*cos(4*f*x + 4*e) + 18*a*c^2*cos(2*f*x + 2*e) + 6*I*a*c^2*sin(6*f*x + 6*e) + 18*I*a*c^2*sin(4*f*x + 4*e) + 18*I*a*c^2*sin(2*f*x + 2*e) + 6*a*c^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (6*a*c^2*cos(6*f*x + 6*e) + 18*a*c^2*cos(4*f*x + 4*e) + 18*a*c^2*cos(2*f*x + 2*e) + 6*I*a*c^2*sin(6*f*x + 6*e) + 18*I*a*c^2*sin(4*f*x + 4*e) + 18*I*a*c^2*sin(2*f*x + 2*e) + 6*a*c^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (-3*I*a*c^2*cos(6*f*x + 6*e) - 9*I*a*c^2*cos(4*f*x + 4*e) - 9*I*a*c^2*cos(2*f*x + 2*e) + 3*a*c^2*sin(6*f*x + 6*e) + 9*a*c^2*sin(4*f*x + 4*e) + 9*a*c^2*sin(2*f*x + 2*e) - 3*I*a*c^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (3*I*a*c^2*cos(6*f*x + 6*e) + 9*I*a*c^2*cos(4*f*x + 4*e) + 9*I*a*c^2*cos(2*f*x + 2*e) - 3*a*c^2*sin(6*f*x + 6*e) - 9*a*c^2*sin(4*f*x + 4*e) - 9*a*c^2*sin(2*f*x + 2*e) + 3*I*a*c^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1))*sqrt(a)*sqrt(c)/(f*(-12*I*cos(6*f*x + 6*e) - 36*I*cos(4*f*x + 4*e) - 36*I*cos(2*f*x + 2*e) + 12*sin(6*f*x + 6*e) + 36*sin(4*f*x + 4*e) + 36*sin(2*f*x + 2*e) - 12*I))","B",0
1009,1,450,0,1.085628," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, c^{2} \cos\left(3 \, f x + 3 \, e\right) + 20 \, c^{2} \cos\left(f x + e\right) + 12 i \, c^{2} \sin\left(3 \, f x + 3 \, e\right) + 20 i \, c^{2} \sin\left(f x + e\right) + {\left(6 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 12 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 12 i \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, c^{2}\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + {\left(6 \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 12 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 12 i \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 6 \, c^{2}\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) - {\left(-3 i \, c^{2} \cos\left(4 \, f x + 4 \, e\right) - 6 i \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 6 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, c^{2}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - {\left(3 i \, c^{2} \cos\left(4 \, f x + 4 \, e\right) + 6 i \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) - 6 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 i \, c^{2}\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)} \sqrt{a} \sqrt{c}}{f {\left(-4 i \, \cos\left(4 \, f x + 4 \, e\right) - 8 i \, \cos\left(2 \, f x + 2 \, e\right) + 4 \, \sin\left(4 \, f x + 4 \, e\right) + 8 \, \sin\left(2 \, f x + 2 \, e\right) - 4 i\right)}}"," ",0,"-(12*c^2*cos(3*f*x + 3*e) + 20*c^2*cos(f*x + e) + 12*I*c^2*sin(3*f*x + 3*e) + 20*I*c^2*sin(f*x + e) + (6*c^2*cos(4*f*x + 4*e) + 12*c^2*cos(2*f*x + 2*e) + 6*I*c^2*sin(4*f*x + 4*e) + 12*I*c^2*sin(2*f*x + 2*e) + 6*c^2)*arctan2(cos(f*x + e), sin(f*x + e) + 1) + (6*c^2*cos(4*f*x + 4*e) + 12*c^2*cos(2*f*x + 2*e) + 6*I*c^2*sin(4*f*x + 4*e) + 12*I*c^2*sin(2*f*x + 2*e) + 6*c^2)*arctan2(cos(f*x + e), -sin(f*x + e) + 1) - (-3*I*c^2*cos(4*f*x + 4*e) - 6*I*c^2*cos(2*f*x + 2*e) + 3*c^2*sin(4*f*x + 4*e) + 6*c^2*sin(2*f*x + 2*e) - 3*I*c^2)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - (3*I*c^2*cos(4*f*x + 4*e) + 6*I*c^2*cos(2*f*x + 2*e) - 3*c^2*sin(4*f*x + 4*e) - 6*c^2*sin(2*f*x + 2*e) + 3*I*c^2)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))*sqrt(a)*sqrt(c)/(f*(-4*I*cos(4*f*x + 4*e) - 8*I*cos(2*f*x + 2*e) + 4*sin(4*f*x + 4*e) + 8*sin(2*f*x + 2*e) - 4*I))","B",0
1010,1,185,0,1.075018," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(6 i \, c^{2} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) \cos\left(f x + e\right) + 6 i \, c^{2} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) \cos\left(f x + e\right) - 8 i \, c^{2} \cos\left(f x + e\right)^{2} + 3 \, c^{2} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - 3 \, c^{2} \cos\left(f x + e\right) \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) - 8 \, c^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 i \, c^{2}\right)} \sqrt{c}}{2 \, \sqrt{a} f \cos\left(f x + e\right)}"," ",0,"-1/2*(6*I*c^2*arctan2(cos(f*x + e), sin(f*x + e) + 1)*cos(f*x + e) + 6*I*c^2*arctan2(cos(f*x + e), -sin(f*x + e) + 1)*cos(f*x + e) - 8*I*c^2*cos(f*x + e)^2 + 3*c^2*cos(f*x + e)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 3*c^2*cos(f*x + e)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 8*c^2*cos(f*x + e)*sin(f*x + e) - 2*I*c^2)*sqrt(c)/(sqrt(a)*f*cos(f*x + e))","A",0
1011,1,410,0,0.630820," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{{\left(-6 i \, c^{2} \arctan\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right), \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right) + 1\right) - 6 i \, c^{2} \arctan\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right), -\sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right) + 1\right) + 4 i \, c^{2} \cos\left(3 \, f x + 3 \, e\right) + 3 \, c^{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right) + 1\right) - 3 \, c^{2} \log\left(\cos\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right) + 1\right) + 4 \, c^{2} \sin\left(3 \, f x + 3 \, e\right) - 12 \, {\left(i \, c^{2} \cos\left(3 \, f x + 3 \, e\right) + c^{2} \sin\left(3 \, f x + 3 \, e\right)\right)} \cos\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right) + {\left(12 \, c^{2} \cos\left(3 \, f x + 3 \, e\right) - 12 i \, c^{2} \sin\left(3 \, f x + 3 \, e\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right)\right)} \sqrt{c}}{6 \, a^{\frac{3}{2}} f}"," ",0,"1/6*(-6*I*c^2*arctan2(cos(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))), sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))) + 1) - 6*I*c^2*arctan2(cos(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))), -sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))) + 1) + 4*I*c^2*cos(3*f*x + 3*e) + 3*c^2*log(cos(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e)))^2 + sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e)))^2 + 2*sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))) + 1) - 3*c^2*log(cos(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e)))^2 + sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e)))^2 - 2*sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))) + 1) + 4*c^2*sin(3*f*x + 3*e) - 12*(I*c^2*cos(3*f*x + 3*e) + c^2*sin(3*f*x + 3*e))*cos(2/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))) + (12*c^2*cos(3*f*x + 3*e) - 12*I*c^2*sin(3*f*x + 3*e))*sin(2/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))))*sqrt(c)/(a^(3/2)*f)","B",0
1012,1,39,0,0.662560," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(i \, c^{2} \cos\left(5 \, f x + 5 \, e\right) + c^{2} \sin\left(5 \, f x + 5 \, e\right)\right)} \sqrt{c}}{5 \, a^{\frac{5}{2}} f}"," ",0,"1/5*(I*c^2*cos(5*f*x + 5*e) + c^2*sin(5*f*x + 5*e))*sqrt(c)/(a^(5/2)*f)","A",0
1013,1,94,0,0.631829," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{{\left(5 i \, c^{2} \cos\left(7 \, f x + 7 \, e\right) + 7 i \, c^{2} \cos\left(\frac{5}{7} \, \arctan\left(\sin\left(7 \, f x + 7 \, e\right), \cos\left(7 \, f x + 7 \, e\right)\right)\right) + 5 \, c^{2} \sin\left(7 \, f x + 7 \, e\right) + 7 \, c^{2} \sin\left(\frac{5}{7} \, \arctan\left(\sin\left(7 \, f x + 7 \, e\right), \cos\left(7 \, f x + 7 \, e\right)\right)\right)\right)} \sqrt{c}}{70 \, a^{\frac{7}{2}} f}"," ",0,"1/70*(5*I*c^2*cos(7*f*x + 7*e) + 7*I*c^2*cos(5/7*arctan2(sin(7*f*x + 7*e), cos(7*f*x + 7*e))) + 5*c^2*sin(7*f*x + 7*e) + 7*c^2*sin(5/7*arctan2(sin(7*f*x + 7*e), cos(7*f*x + 7*e))))*sqrt(c)/(a^(7/2)*f)","A",0
1014,1,148,0,0.545721," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","\frac{{\left(35 i \, c^{2} \cos\left(9 \, f x + 9 \, e\right) + 90 i \, c^{2} \cos\left(\frac{7}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 63 i \, c^{2} \cos\left(\frac{5}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 35 \, c^{2} \sin\left(9 \, f x + 9 \, e\right) + 90 \, c^{2} \sin\left(\frac{7}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right) + 63 \, c^{2} \sin\left(\frac{5}{9} \, \arctan\left(\sin\left(9 \, f x + 9 \, e\right), \cos\left(9 \, f x + 9 \, e\right)\right)\right)\right)} \sqrt{c}}{1260 \, a^{\frac{9}{2}} f}"," ",0,"1/1260*(35*I*c^2*cos(9*f*x + 9*e) + 90*I*c^2*cos(7/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 63*I*c^2*cos(5/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 35*c^2*sin(9*f*x + 9*e) + 90*c^2*sin(7/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))) + 63*c^2*sin(5/9*arctan2(sin(9*f*x + 9*e), cos(9*f*x + 9*e))))*sqrt(c)/(a^(9/2)*f)","A",0
1015,1,202,0,0.549324," ","integrate((c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(11/2),x, algorithm=""maxima"")","\frac{{\left(105 i \, c^{2} \cos\left(11 \, f x + 11 \, e\right) + 385 i \, c^{2} \cos\left(\frac{9}{11} \, \arctan\left(\sin\left(11 \, f x + 11 \, e\right), \cos\left(11 \, f x + 11 \, e\right)\right)\right) + 495 i \, c^{2} \cos\left(\frac{7}{11} \, \arctan\left(\sin\left(11 \, f x + 11 \, e\right), \cos\left(11 \, f x + 11 \, e\right)\right)\right) + 231 i \, c^{2} \cos\left(\frac{5}{11} \, \arctan\left(\sin\left(11 \, f x + 11 \, e\right), \cos\left(11 \, f x + 11 \, e\right)\right)\right) + 105 \, c^{2} \sin\left(11 \, f x + 11 \, e\right) + 385 \, c^{2} \sin\left(\frac{9}{11} \, \arctan\left(\sin\left(11 \, f x + 11 \, e\right), \cos\left(11 \, f x + 11 \, e\right)\right)\right) + 495 \, c^{2} \sin\left(\frac{7}{11} \, \arctan\left(\sin\left(11 \, f x + 11 \, e\right), \cos\left(11 \, f x + 11 \, e\right)\right)\right) + 231 \, c^{2} \sin\left(\frac{5}{11} \, \arctan\left(\sin\left(11 \, f x + 11 \, e\right), \cos\left(11 \, f x + 11 \, e\right)\right)\right)\right)} \sqrt{c}}{9240 \, a^{\frac{11}{2}} f}"," ",0,"1/9240*(105*I*c^2*cos(11*f*x + 11*e) + 385*I*c^2*cos(9/11*arctan2(sin(11*f*x + 11*e), cos(11*f*x + 11*e))) + 495*I*c^2*cos(7/11*arctan2(sin(11*f*x + 11*e), cos(11*f*x + 11*e))) + 231*I*c^2*cos(5/11*arctan2(sin(11*f*x + 11*e), cos(11*f*x + 11*e))) + 105*c^2*sin(11*f*x + 11*e) + 385*c^2*sin(9/11*arctan2(sin(11*f*x + 11*e), cos(11*f*x + 11*e))) + 495*c^2*sin(7/11*arctan2(sin(11*f*x + 11*e), cos(11*f*x + 11*e))) + 231*c^2*sin(5/11*arctan2(sin(11*f*x + 11*e), cos(11*f*x + 11*e))))*sqrt(c)/(a^(11/2)*f)","A",0
1016,1,790,0,0.625005," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(72 \, a^{3} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 72 i \, a^{3} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(60 \, a^{3} \cos\left(4 \, f x + 4 \, e\right) + 120 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 60 i \, a^{3} \sin\left(4 \, f x + 4 \, e\right) + 120 i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 60 \, a^{3}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(60 \, a^{3} \cos\left(4 \, f x + 4 \, e\right) + 120 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 60 i \, a^{3} \sin\left(4 \, f x + 4 \, e\right) + 120 i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 60 \, a^{3}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(64 \, a^{3} \cos\left(4 \, f x + 4 \, e\right) + 128 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 64 i \, a^{3} \sin\left(4 \, f x + 4 \, e\right) + 128 i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 120 \, a^{3}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(-30 i \, a^{3} \cos\left(4 \, f x + 4 \, e\right) - 60 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 30 \, a^{3} \sin\left(4 \, f x + 4 \, e\right) + 60 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) - 30 i \, a^{3}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(30 i \, a^{3} \cos\left(4 \, f x + 4 \, e\right) + 60 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) - 30 \, a^{3} \sin\left(4 \, f x + 4 \, e\right) - 60 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 30 i \, a^{3}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(64 i \, a^{3} \cos\left(4 \, f x + 4 \, e\right) + 128 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) - 64 \, a^{3} \sin\left(4 \, f x + 4 \, e\right) - 128 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 120 i \, a^{3}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-8 i \, c \cos\left(4 \, f x + 4 \, e\right) - 16 i \, c \cos\left(2 \, f x + 2 \, e\right) + 8 \, c \sin\left(4 \, f x + 4 \, e\right) + 16 \, c \sin\left(2 \, f x + 2 \, e\right) - 8 i \, c\right)} f}"," ",0,"-(72*a^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 72*I*a^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (60*a^3*cos(4*f*x + 4*e) + 120*a^3*cos(2*f*x + 2*e) + 60*I*a^3*sin(4*f*x + 4*e) + 120*I*a^3*sin(2*f*x + 2*e) + 60*a^3)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (60*a^3*cos(4*f*x + 4*e) + 120*a^3*cos(2*f*x + 2*e) + 60*I*a^3*sin(4*f*x + 4*e) + 120*I*a^3*sin(2*f*x + 2*e) + 60*a^3)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (64*a^3*cos(4*f*x + 4*e) + 128*a^3*cos(2*f*x + 2*e) + 64*I*a^3*sin(4*f*x + 4*e) + 128*I*a^3*sin(2*f*x + 2*e) + 120*a^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-30*I*a^3*cos(4*f*x + 4*e) - 60*I*a^3*cos(2*f*x + 2*e) + 30*a^3*sin(4*f*x + 4*e) + 60*a^3*sin(2*f*x + 2*e) - 30*I*a^3)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (30*I*a^3*cos(4*f*x + 4*e) + 60*I*a^3*cos(2*f*x + 2*e) - 30*a^3*sin(4*f*x + 4*e) - 60*a^3*sin(2*f*x + 2*e) + 30*I*a^3)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (64*I*a^3*cos(4*f*x + 4*e) + 128*I*a^3*cos(2*f*x + 2*e) - 64*a^3*sin(4*f*x + 4*e) - 128*a^3*sin(2*f*x + 2*e) + 120*I*a^3)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-8*I*c*cos(4*f*x + 4*e) - 16*I*c*cos(2*f*x + 2*e) + 8*c*sin(4*f*x + 4*e) + 16*c*sin(2*f*x + 2*e) - 8*I*c)*f)","B",0
1017,1,541,0,0.568230," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left(6 \, {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 6 \, {\left(a^{2} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + a^{2}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 4 \, {\left(2 \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 i \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 \, a^{2}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-3 i \, a^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) - 3 i \, a^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(3 i \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 3 i \, a^{2}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(8 i \, a^{2} \cos\left(2 \, f x + 2 \, e\right) - 8 \, a^{2} \sin\left(2 \, f x + 2 \, e\right) + 12 i \, a^{2}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-2 i \, c \cos\left(2 \, f x + 2 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) - 2 i \, c\right)} f}"," ",0,"(6*(a^2*cos(2*f*x + 2*e) + I*a^2*sin(2*f*x + 2*e) + a^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 6*(a^2*cos(2*f*x + 2*e) + I*a^2*sin(2*f*x + 2*e) + a^2)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 4*(2*a^2*cos(2*f*x + 2*e) + 2*I*a^2*sin(2*f*x + 2*e) + 3*a^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-3*I*a^2*cos(2*f*x + 2*e) + 3*a^2*sin(2*f*x + 2*e) - 3*I*a^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (3*I*a^2*cos(2*f*x + 2*e) - 3*a^2*sin(2*f*x + 2*e) + 3*I*a^2)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (8*I*a^2*cos(2*f*x + 2*e) - 8*a^2*sin(2*f*x + 2*e) + 12*I*a^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-2*I*c*cos(2*f*x + 2*e) + 2*c*sin(2*f*x + 2*e) - 2*I*c)*f)","B",0
1018,1,319,0,0.688175," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(-2 i \, a \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 2 i \, a \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 4 i \, a \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + a \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - a \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 4 \, a \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a}}{2 \, \sqrt{c} f}"," ",0,"-1/2*(-2*I*a*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 2*I*a*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 4*I*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + a*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - a*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 4*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(sqrt(c)*f)","B",0
1019,1,25,0,0.504299," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} {\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right)}}{\sqrt{c} f}"," ",0,"sqrt(a)*(-I*cos(f*x + e) + sin(f*x + e))/(sqrt(c)*f)","A",0
1020,1,16,0,0.660997," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\sin\left(f x + e\right)}{\sqrt{a} \sqrt{c} f}"," ",0,"sin(f*x + e)/(sqrt(a)*sqrt(c)*f)","A",0
1021,-2,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1022,-2,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1023,-2,0,0,0.000000," ","integrate(1/(c-I*c*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1024,1,919,0,0.812484," ","integrate((a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(1260 \, a^{4} \cos\left(4 \, f x + 4 \, e\right) + 2520 \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 1260 i \, a^{4} \sin\left(4 \, f x + 4 \, e\right) + 2520 i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 1260 \, a^{4}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(1260 \, a^{4} \cos\left(4 \, f x + 4 \, e\right) + 2520 \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 1260 i \, a^{4} \sin\left(4 \, f x + 4 \, e\right) + 2520 i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 1260 \, a^{4}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(192 \, a^{4} \cos\left(4 \, f x + 4 \, e\right) + 384 \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 192 i \, a^{4} \sin\left(4 \, f x + 4 \, e\right) + 384 i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) - 744 \, a^{4}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(1728 \, a^{4} \cos\left(4 \, f x + 4 \, e\right) + 3456 \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 1728 i \, a^{4} \sin\left(4 \, f x + 4 \, e\right) + 3456 i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 2520 \, a^{4}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-630 i \, a^{4} \cos\left(4 \, f x + 4 \, e\right) - 1260 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 630 \, a^{4} \sin\left(4 \, f x + 4 \, e\right) + 1260 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) - 630 i \, a^{4}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(630 i \, a^{4} \cos\left(4 \, f x + 4 \, e\right) + 1260 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) - 630 \, a^{4} \sin\left(4 \, f x + 4 \, e\right) - 1260 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 630 i \, a^{4}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(-192 i \, a^{4} \cos\left(4 \, f x + 4 \, e\right) - 384 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 192 \, a^{4} \sin\left(4 \, f x + 4 \, e\right) + 384 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 744 i \, a^{4}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(1728 i \, a^{4} \cos\left(4 \, f x + 4 \, e\right) + 3456 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) - 1728 \, a^{4} \sin\left(4 \, f x + 4 \, e\right) - 3456 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 2520 i \, a^{4}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-72 i \, c^{2} \cos\left(4 \, f x + 4 \, e\right) - 144 i \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 72 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 144 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 72 i \, c^{2}\right)} f}"," ",0,"-((1260*a^4*cos(4*f*x + 4*e) + 2520*a^4*cos(2*f*x + 2*e) + 1260*I*a^4*sin(4*f*x + 4*e) + 2520*I*a^4*sin(2*f*x + 2*e) + 1260*a^4)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (1260*a^4*cos(4*f*x + 4*e) + 2520*a^4*cos(2*f*x + 2*e) + 1260*I*a^4*sin(4*f*x + 4*e) + 2520*I*a^4*sin(2*f*x + 2*e) + 1260*a^4)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (192*a^4*cos(4*f*x + 4*e) + 384*a^4*cos(2*f*x + 2*e) + 192*I*a^4*sin(4*f*x + 4*e) + 384*I*a^4*sin(2*f*x + 2*e) - 744*a^4)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (1728*a^4*cos(4*f*x + 4*e) + 3456*a^4*cos(2*f*x + 2*e) + 1728*I*a^4*sin(4*f*x + 4*e) + 3456*I*a^4*sin(2*f*x + 2*e) + 2520*a^4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-630*I*a^4*cos(4*f*x + 4*e) - 1260*I*a^4*cos(2*f*x + 2*e) + 630*a^4*sin(4*f*x + 4*e) + 1260*a^4*sin(2*f*x + 2*e) - 630*I*a^4)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (630*I*a^4*cos(4*f*x + 4*e) + 1260*I*a^4*cos(2*f*x + 2*e) - 630*a^4*sin(4*f*x + 4*e) - 1260*a^4*sin(2*f*x + 2*e) + 630*I*a^4)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (-192*I*a^4*cos(4*f*x + 4*e) - 384*I*a^4*cos(2*f*x + 2*e) + 192*a^4*sin(4*f*x + 4*e) + 384*a^4*sin(2*f*x + 2*e) + 744*I*a^4)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (1728*I*a^4*cos(4*f*x + 4*e) + 3456*I*a^4*cos(2*f*x + 2*e) - 1728*a^4*sin(4*f*x + 4*e) - 3456*a^4*sin(2*f*x + 2*e) + 2520*I*a^4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-72*I*c^2*cos(4*f*x + 4*e) - 144*I*c^2*cos(2*f*x + 2*e) + 72*c^2*sin(4*f*x + 4*e) + 144*c^2*sin(2*f*x + 2*e) - 72*I*c^2)*f)","B",0
1025,1,661,0,0.902407," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(90 \, {\left(a^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + a^{3}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 90 \, {\left(a^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + a^{3}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 24 \, {\left(a^{3} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + a^{3}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 36 \, {\left(4 \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 4 i \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 5 \, a^{3}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-45 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 45 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) - 45 i \, a^{3}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(45 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) - 45 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 45 i \, a^{3}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(-24 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) + 24 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) - 24 i \, a^{3}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(144 i \, a^{3} \cos\left(2 \, f x + 2 \, e\right) - 144 \, a^{3} \sin\left(2 \, f x + 2 \, e\right) + 180 i \, a^{3}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-18 i \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 18 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 18 i \, c^{2}\right)} f}"," ",0,"-(90*(a^3*cos(2*f*x + 2*e) + I*a^3*sin(2*f*x + 2*e) + a^3)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 90*(a^3*cos(2*f*x + 2*e) + I*a^3*sin(2*f*x + 2*e) + a^3)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 24*(a^3*cos(2*f*x + 2*e) + I*a^3*sin(2*f*x + 2*e) + a^3)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 36*(4*a^3*cos(2*f*x + 2*e) + 4*I*a^3*sin(2*f*x + 2*e) + 5*a^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-45*I*a^3*cos(2*f*x + 2*e) + 45*a^3*sin(2*f*x + 2*e) - 45*I*a^3)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (45*I*a^3*cos(2*f*x + 2*e) - 45*a^3*sin(2*f*x + 2*e) + 45*I*a^3)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (-24*I*a^3*cos(2*f*x + 2*e) + 24*a^3*sin(2*f*x + 2*e) - 24*I*a^3)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (144*I*a^3*cos(2*f*x + 2*e) - 144*a^3*sin(2*f*x + 2*e) + 180*I*a^3)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-18*I*c^2*cos(2*f*x + 2*e) + 18*c^2*sin(2*f*x + 2*e) - 18*I*c^2)*f)","B",0
1026,1,386,0,0.573702," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{{\left(-6 i \, a^{2} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 6 i \, a^{2} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 4 i \, a^{2} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12 i \, a^{2} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, a^{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 3 \, a^{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 4 \, a^{2} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12 \, a^{2} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a}}{6 \, c^{\frac{3}{2}} f}"," ",0,"1/6*(-6*I*a^2*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 6*I*a^2*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 4*I*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*I*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a^2*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 3*a^2*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 4*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(3/2)*f)","B",0
1027,1,35,0,0.655621," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{{\left(-i \, a \cos\left(3 \, f x + 3 \, e\right) + a \sin\left(3 \, f x + 3 \, e\right)\right)} \sqrt{a}}{3 \, c^{\frac{3}{2}} f}"," ",0,"1/3*(-I*a*cos(3*f*x + 3*e) + a*sin(3*f*x + 3*e))*sqrt(a)/(c^(3/2)*f)","A",0
1028,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1029,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1030,1,45,0,0.800780," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\sin\left(3 \, f x + 3 \, e\right) + 9 \, \sin\left(\frac{1}{3} \, \arctan\left(\sin\left(3 \, f x + 3 \, e\right), \cos\left(3 \, f x + 3 \, e\right)\right)\right)}{12 \, a^{\frac{3}{2}} c^{\frac{3}{2}} f}"," ",0,"1/12*(sin(3*f*x + 3*e) + 9*sin(1/3*arctan2(sin(3*f*x + 3*e), cos(3*f*x + 3*e))))/(a^(3/2)*c^(3/2)*f)","A",0
1031,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1032,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1033,1,1090,0,0.697730," ","integrate((a+I*a*tan(f*x+e))^(11/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left({\left(6300 \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 12600 \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 6300 i \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 12600 i \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 6300 \, a^{5}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + {\left(6300 \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 12600 \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 6300 i \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 12600 i \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 6300 \, a^{5}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(320 \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 640 \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 320 i \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 640 i \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 320 \, a^{5}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(1600 \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 3200 \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 1600 i \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 3200 i \, a^{5} \sin\left(2 \, f x + 2 \, e\right) - 1800 \, a^{5}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(9600 \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 19200 \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 9600 i \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 19200 i \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 12600 \, a^{5}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-3150 i \, a^{5} \cos\left(4 \, f x + 4 \, e\right) - 6300 i \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 3150 \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 6300 \, a^{5} \sin\left(2 \, f x + 2 \, e\right) - 3150 i \, a^{5}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(3150 i \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 6300 i \, a^{5} \cos\left(2 \, f x + 2 \, e\right) - 3150 \, a^{5} \sin\left(4 \, f x + 4 \, e\right) - 6300 \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 3150 i \, a^{5}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(320 i \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 640 i \, a^{5} \cos\left(2 \, f x + 2 \, e\right) - 320 \, a^{5} \sin\left(4 \, f x + 4 \, e\right) - 640 \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 320 i \, a^{5}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-1600 i \, a^{5} \cos\left(4 \, f x + 4 \, e\right) - 3200 i \, a^{5} \cos\left(2 \, f x + 2 \, e\right) + 1600 \, a^{5} \sin\left(4 \, f x + 4 \, e\right) + 3200 \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 1800 i \, a^{5}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(9600 i \, a^{5} \cos\left(4 \, f x + 4 \, e\right) + 19200 i \, a^{5} \cos\left(2 \, f x + 2 \, e\right) - 9600 \, a^{5} \sin\left(4 \, f x + 4 \, e\right) - 19200 \, a^{5} \sin\left(2 \, f x + 2 \, e\right) + 12600 i \, a^{5}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-200 i \, c^{3} \cos\left(4 \, f x + 4 \, e\right) - 400 i \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + 200 \, c^{3} \sin\left(4 \, f x + 4 \, e\right) + 400 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 200 i \, c^{3}\right)} f}"," ",0,"((6300*a^5*cos(4*f*x + 4*e) + 12600*a^5*cos(2*f*x + 2*e) + 6300*I*a^5*sin(4*f*x + 4*e) + 12600*I*a^5*sin(2*f*x + 2*e) + 6300*a^5)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + (6300*a^5*cos(4*f*x + 4*e) + 12600*a^5*cos(2*f*x + 2*e) + 6300*I*a^5*sin(4*f*x + 4*e) + 12600*I*a^5*sin(2*f*x + 2*e) + 6300*a^5)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (320*a^5*cos(4*f*x + 4*e) + 640*a^5*cos(2*f*x + 2*e) + 320*I*a^5*sin(4*f*x + 4*e) + 640*I*a^5*sin(2*f*x + 2*e) + 320*a^5)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1600*a^5*cos(4*f*x + 4*e) + 3200*a^5*cos(2*f*x + 2*e) + 1600*I*a^5*sin(4*f*x + 4*e) + 3200*I*a^5*sin(2*f*x + 2*e) - 1800*a^5)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (9600*a^5*cos(4*f*x + 4*e) + 19200*a^5*cos(2*f*x + 2*e) + 9600*I*a^5*sin(4*f*x + 4*e) + 19200*I*a^5*sin(2*f*x + 2*e) + 12600*a^5)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-3150*I*a^5*cos(4*f*x + 4*e) - 6300*I*a^5*cos(2*f*x + 2*e) + 3150*a^5*sin(4*f*x + 4*e) + 6300*a^5*sin(2*f*x + 2*e) - 3150*I*a^5)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (3150*I*a^5*cos(4*f*x + 4*e) + 6300*I*a^5*cos(2*f*x + 2*e) - 3150*a^5*sin(4*f*x + 4*e) - 6300*a^5*sin(2*f*x + 2*e) + 3150*I*a^5)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (320*I*a^5*cos(4*f*x + 4*e) + 640*I*a^5*cos(2*f*x + 2*e) - 320*a^5*sin(4*f*x + 4*e) - 640*a^5*sin(2*f*x + 2*e) + 320*I*a^5)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1600*I*a^5*cos(4*f*x + 4*e) - 3200*I*a^5*cos(2*f*x + 2*e) + 1600*a^5*sin(4*f*x + 4*e) + 3200*a^5*sin(2*f*x + 2*e) + 1800*I*a^5)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (9600*I*a^5*cos(4*f*x + 4*e) + 19200*I*a^5*cos(2*f*x + 2*e) - 9600*a^5*sin(4*f*x + 4*e) - 19200*a^5*sin(2*f*x + 2*e) + 12600*I*a^5)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-200*I*c^3*cos(4*f*x + 4*e) - 400*I*c^3*cos(2*f*x + 2*e) + 200*c^3*sin(4*f*x + 4*e) + 400*c^3*sin(2*f*x + 2*e) - 200*I*c^3)*f)","B",0
1034,1,773,0,0.585851," ","integrate((a+I*a*tan(f*x+e))^(9/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(3150 \, {\left(a^{4} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + a^{4}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 3150 \, {\left(a^{4} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + a^{4}\right)} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 360 \, {\left(a^{4} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + a^{4}\right)} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1200 \, {\left(a^{4} \cos\left(2 \, f x + 2 \, e\right) + i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + a^{4}\right)} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 900 \, {\left(6 \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 6 i \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 7 \, a^{4}\right)} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-1575 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 1575 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) - 1575 i \, a^{4}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(1575 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) - 1575 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 1575 i \, a^{4}\right)} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - {\left(360 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) - 360 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 360 i \, a^{4}\right)} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-1200 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) + 1200 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) - 1200 i \, a^{4}\right)} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(5400 i \, a^{4} \cos\left(2 \, f x + 2 \, e\right) - 5400 \, a^{4} \sin\left(2 \, f x + 2 \, e\right) + 6300 i \, a^{4}\right)} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-450 i \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + 450 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 450 i \, c^{3}\right)} f}"," ",0,"(3150*(a^4*cos(2*f*x + 2*e) + I*a^4*sin(2*f*x + 2*e) + a^4)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 3150*(a^4*cos(2*f*x + 2*e) + I*a^4*sin(2*f*x + 2*e) + a^4)*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 360*(a^4*cos(2*f*x + 2*e) + I*a^4*sin(2*f*x + 2*e) + a^4)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1200*(a^4*cos(2*f*x + 2*e) + I*a^4*sin(2*f*x + 2*e) + a^4)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 900*(6*a^4*cos(2*f*x + 2*e) + 6*I*a^4*sin(2*f*x + 2*e) + 7*a^4)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1575*I*a^4*cos(2*f*x + 2*e) + 1575*a^4*sin(2*f*x + 2*e) - 1575*I*a^4)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (1575*I*a^4*cos(2*f*x + 2*e) - 1575*a^4*sin(2*f*x + 2*e) + 1575*I*a^4)*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - (360*I*a^4*cos(2*f*x + 2*e) - 360*a^4*sin(2*f*x + 2*e) + 360*I*a^4)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1200*I*a^4*cos(2*f*x + 2*e) + 1200*a^4*sin(2*f*x + 2*e) - 1200*I*a^4)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (5400*I*a^4*cos(2*f*x + 2*e) - 5400*a^4*sin(2*f*x + 2*e) + 6300*I*a^4)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-450*I*c^3*cos(2*f*x + 2*e) + 450*c^3*sin(2*f*x + 2*e) - 450*I*c^3)*f)","B",0
1035,1,440,0,0.567982," ","integrate((a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(-30 i \, a^{3} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 30 i \, a^{3} \arctan\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right), -\sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) + 12 i \, a^{3} \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 20 i \, a^{3} \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 60 i \, a^{3} \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 15 \, a^{3} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 15 \, a^{3} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1\right) - 12 \, a^{3} \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 20 \, a^{3} \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 60 \, a^{3} \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a}}{30 \, c^{\frac{5}{2}} f}"," ",0,"-1/30*(-30*I*a^3*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 30*I*a^3*arctan2(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))), -sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) + 12*I*a^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 20*I*a^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 60*I*a^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 15*a^3*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 15*a^3*log(cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 + sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e)))^2 - 2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1) - 12*a^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 20*a^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 60*a^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(5/2)*f)","B",0
1036,1,39,0,0.532405," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(-i \, a^{2} \cos\left(5 \, f x + 5 \, e\right) + a^{2} \sin\left(5 \, f x + 5 \, e\right)\right)} \sqrt{a}}{5 \, c^{\frac{5}{2}} f}"," ",0,"1/5*(-I*a^2*cos(5*f*x + 5*e) + a^2*sin(5*f*x + 5*e))*sqrt(a)/(c^(5/2)*f)","A",0
1037,1,112,0,0.543799," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(-3 i \, a \cos\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 5 i \, a \cos\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3 \, a \sin\left(\frac{5}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 5 \, a \sin\left(\frac{3}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right)\right)} \sqrt{a}}{30 \, c^{\frac{5}{2}} f}"," ",0,"1/30*(-3*I*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*I*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(5/2)*f)","A",0
1038,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1039,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1040,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1041,1,71,0,0.563499," ","integrate(1/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{3 \, \sin\left(5 \, f x + 5 \, e\right) + 25 \, \sin\left(\frac{3}{5} \, \arctan\left(\sin\left(5 \, f x + 5 \, e\right), \cos\left(5 \, f x + 5 \, e\right)\right)\right) + 150 \, \sin\left(\frac{1}{5} \, \arctan\left(\sin\left(5 \, f x + 5 \, e\right), \cos\left(5 \, f x + 5 \, e\right)\right)\right)}{240 \, a^{\frac{5}{2}} c^{\frac{5}{2}} f}"," ",0,"1/240*(3*sin(5*f*x + 5*e) + 25*sin(3/5*arctan2(sin(5*f*x + 5*e), cos(5*f*x + 5*e))) + 150*sin(1/5*arctan2(sin(5*f*x + 5*e), cos(5*f*x + 5*e))))/(a^(5/2)*c^(5/2)*f)","A",0
1042,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(7/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1043,1,860,0,0.822317," ","integrate((a+I*a*tan(f*x+e))^4*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{3 \cdot 2^{n + 4} a^{4} c^{n} \cos\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - 3 i \cdot 2^{n + 4} a^{4} c^{n} \sin\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 48 \, {\left(a^{4} c^{n} n + 3 \, a^{4} c^{n}\right)} 2^{n} \cos\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) + 24 \, {\left(a^{4} c^{n} n^{2} + 5 \, a^{4} c^{n} n + 6 \, a^{4} c^{n}\right)} 2^{n} \cos\left(-4 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, e\right) + 8 \, {\left(a^{4} c^{n} n^{3} + 6 \, a^{4} c^{n} n^{2} + 11 \, a^{4} c^{n} n + 6 \, a^{4} c^{n}\right)} 2^{n} \cos\left(-6 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 6 \, e\right) - {\left(48 i \, a^{4} c^{n} n + 144 i \, a^{4} c^{n}\right)} 2^{n} \sin\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) - {\left(24 i \, a^{4} c^{n} n^{2} + 120 i \, a^{4} c^{n} n + 144 i \, a^{4} c^{n}\right)} 2^{n} \sin\left(-4 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, e\right) - {\left(8 i \, a^{4} c^{n} n^{3} + 48 i \, a^{4} c^{n} n^{2} + 88 i \, a^{4} c^{n} n + 48 i \, a^{4} c^{n}\right)} 2^{n} \sin\left(-6 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 6 \, e\right)}{{\left({\left(-i \, n^{4} - 6 i \, n^{3} - 11 i \, n^{2} - 6 i \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} \cos\left(6 \, f x + 6 \, e\right) + {\left(-3 i \, n^{4} - 18 i \, n^{3} - 33 i \, n^{2} - 18 i \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} \cos\left(4 \, f x + 4 \, e\right) + {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} \sin\left(6 \, f x + 6 \, e\right) + 3 \, {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} \sin\left(4 \, f x + 4 \, e\right) + {\left(-i \, n^{4} - 6 i \, n^{3} - 11 i \, n^{2} + {\left(-3 i \, n^{4} - 18 i \, n^{3} - 33 i \, n^{2} - 18 i \, n\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} \sin\left(2 \, f x + 2 \, e\right) - 6 i \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n}\right)} f}"," ",0,"(3*2^(n + 4)*a^4*c^n*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - 3*I*2^(n + 4)*a^4*c^n*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 48*(a^4*c^n*n + 3*a^4*c^n)*2^n*cos(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) + 24*(a^4*c^n*n^2 + 5*a^4*c^n*n + 6*a^4*c^n)*2^n*cos(-4*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*e) + 8*(a^4*c^n*n^3 + 6*a^4*c^n*n^2 + 11*a^4*c^n*n + 6*a^4*c^n)*2^n*cos(-6*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 6*e) - (48*I*a^4*c^n*n + 144*I*a^4*c^n)*2^n*sin(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) - (24*I*a^4*c^n*n^2 + 120*I*a^4*c^n*n + 144*I*a^4*c^n)*2^n*sin(-4*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*e) - (8*I*a^4*c^n*n^3 + 48*I*a^4*c^n*n^2 + 88*I*a^4*c^n*n + 48*I*a^4*c^n)*2^n*sin(-6*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 6*e))/(((-I*n^4 - 6*I*n^3 - 11*I*n^2 - 6*I*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*cos(6*f*x + 6*e) + (-3*I*n^4 - 18*I*n^3 - 33*I*n^2 - 18*I*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*cos(4*f*x + 4*e) + (n^4 + 6*n^3 + 11*n^2 + 6*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*sin(6*f*x + 6*e) + 3*(n^4 + 6*n^3 + 11*n^2 + 6*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*sin(4*f*x + 4*e) + (-I*n^4 - 6*I*n^3 - 11*I*n^2 + (-3*I*n^4 - 18*I*n^3 - 33*I*n^2 - 18*I*n)*cos(2*f*x + 2*e) + 3*(n^4 + 6*n^3 + 11*n^2 + 6*n)*sin(2*f*x + 2*e) - 6*I*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n))*f)","B",0
1044,1,546,0,0.874974," ","integrate((a+I*a*tan(f*x+e))^3*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{2^{n + 3} a^{3} c^{n} \cos\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - i \cdot 2^{n + 3} a^{3} c^{n} \sin\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 8 \, {\left(a^{3} c^{n} n + 2 \, a^{3} c^{n}\right)} 2^{n} \cos\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) + 4 \, {\left(a^{3} c^{n} n^{2} + 3 \, a^{3} c^{n} n + 2 \, a^{3} c^{n}\right)} 2^{n} \cos\left(-4 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, e\right) - {\left(8 i \, a^{3} c^{n} n + 16 i \, a^{3} c^{n}\right)} 2^{n} \sin\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) - {\left(4 i \, a^{3} c^{n} n^{2} + 12 i \, a^{3} c^{n} n + 8 i \, a^{3} c^{n}\right)} 2^{n} \sin\left(-4 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 4 \, e\right)}{{\left({\left(-i \, n^{3} - 3 i \, n^{2} - 2 i \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} \cos\left(4 \, f x + 4 \, e\right) + {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} \sin\left(4 \, f x + 4 \, e\right) + {\left(-i \, n^{3} - 3 i \, n^{2} + {\left(-2 i \, n^{3} - 6 i \, n^{2} - 4 i \, n\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} \sin\left(2 \, f x + 2 \, e\right) - 2 i \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n}\right)} f}"," ",0,"(2^(n + 3)*a^3*c^n*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - I*2^(n + 3)*a^3*c^n*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 8*(a^3*c^n*n + 2*a^3*c^n)*2^n*cos(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) + 4*(a^3*c^n*n^2 + 3*a^3*c^n*n + 2*a^3*c^n)*2^n*cos(-4*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*e) - (8*I*a^3*c^n*n + 16*I*a^3*c^n)*2^n*sin(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) - (4*I*a^3*c^n*n^2 + 12*I*a^3*c^n*n + 8*I*a^3*c^n)*2^n*sin(-4*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 4*e))/(((-I*n^3 - 3*I*n^2 - 2*I*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*cos(4*f*x + 4*e) + (n^3 + 3*n^2 + 2*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*sin(4*f*x + 4*e) + (-I*n^3 - 3*I*n^2 + (-2*I*n^3 - 6*I*n^2 - 4*I*n)*cos(2*f*x + 2*e) + 2*(n^3 + 3*n^2 + 2*n)*sin(2*f*x + 2*e) - 2*I*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n))*f)","B",0
1045,1,272,0,0.661684," ","integrate((a+I*a*tan(f*x+e))^2*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{2^{n + 1} a^{2} c^{n} \cos\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) - i \cdot 2^{n + 1} a^{2} c^{n} \sin\left(n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right)\right) + 2 \, {\left(a^{2} c^{n} n + a^{2} c^{n}\right)} 2^{n} \cos\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right) - {\left(2 i \, a^{2} c^{n} n + 2 i \, a^{2} c^{n}\right)} 2^{n} \sin\left(-2 \, f x + n \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right) + 1\right) - 2 \, e\right)}{{\left(-i \, n^{2} + {\left(-i \, n^{2} - i \, n\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(n^{2} + n\right)} \sin\left(2 \, f x + 2 \, e\right) - i \, n\right)} {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}^{\frac{1}{2} \, n} f}"," ",0,"(2^(n + 1)*a^2*c^n*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - I*2^(n + 1)*a^2*c^n*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + 2*(a^2*c^n*n + a^2*c^n)*2^n*cos(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e) - (2*I*a^2*c^n*n + 2*I*a^2*c^n)*2^n*sin(-2*f*x + n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1) - 2*e))/((-I*n^2 + (-I*n^2 - I*n)*cos(2*f*x + 2*e) + (n^2 + n)*sin(2*f*x + 2*e) - I*n)*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)^(1/2*n)*f)","B",0
1046,1,24,0,0.540700," ","integrate((a+I*a*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{i \, a c^{n} {\left(-i \, \tan\left(f x + e\right) + 1\right)}^{n}}{f n}"," ",0,"I*a*c^n*(-I*tan(f*x + e) + 1)^n/(f*n)","A",0
1047,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1048,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1049,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
1054,1,24,0,0.479516," ","integrate((a+I*a*tan(f*x+e))^m*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{i \, a^{m} c {\left(i \, \tan\left(f x + e\right) + 1\right)}^{m}}{f m}"," ",0,"-I*a^m*c*(I*tan(f*x + e) + 1)^m/(f*m)","A",0
1055,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1056,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1057,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1058,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1064,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1065,1,109,0,0.412114," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{2 i \, a^{3} d \tan\left(f x + e\right)^{3} + 3 \, {\left(i \, a^{3} c + 3 \, a^{3} d\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left(4 \, a^{3} c - 4 i \, a^{3} d\right)} {\left(f x + e\right)} + 12 \, {\left(-i \, a^{3} c - a^{3} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + {\left(18 \, a^{3} c - 24 i \, a^{3} d\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(2*I*a^3*d*tan(f*x + e)^3 + 3*(I*a^3*c + 3*a^3*d)*tan(f*x + e)^2 - 6*(4*a^3*c - 4*I*a^3*d)*(f*x + e) + 12*(-I*a^3*c - a^3*d)*log(tan(f*x + e)^2 + 1) + (18*a^3*c - 24*I*a^3*d)*tan(f*x + e))/f","A",0
1066,1,84,0,0.448637," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{a^{2} d \tan\left(f x + e\right)^{2} - 2 \, {\left(2 \, a^{2} c - 2 i \, a^{2} d\right)} {\left(f x + e\right)} - 2 \, {\left(i \, a^{2} c + a^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + {\left(2 \, a^{2} c - 4 i \, a^{2} d\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(a^2*d*tan(f*x + e)^2 - 2*(2*a^2*c - 2*I*a^2*d)*(f*x + e) - 2*(I*a^2*c + a^2*d)*log(tan(f*x + e)^2 + 1) + (2*a^2*c - 4*I*a^2*d)*tan(f*x + e))/f","A",0
1067,1,52,0,0.424490," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{-2 i \, a d \tan\left(f x + e\right) - 2 \, {\left(a c - i \, a d\right)} {\left(f x + e\right)} + {\left(-i \, a c - a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{2 \, f}"," ",0,"-1/2*(-2*I*a*d*tan(f*x + e) - 2*(a*c - I*a*d)*(f*x + e) + (-I*a*c - a*d)*log(tan(f*x + e)^2 + 1))/f","A",0
1068,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1069,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1070,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1071,1,181,0,0.413730," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{3 i \, a^{3} d^{2} \tan\left(f x + e\right)^{4} + 4 \, {\left(2 i \, a^{3} c d + 3 \, a^{3} d^{2}\right)} \tan\left(f x + e\right)^{3} - {\left(-6 i \, a^{3} c^{2} - 36 \, a^{3} c d + 24 i \, a^{3} d^{2}\right)} \tan\left(f x + e\right)^{2} - 12 \, {\left(4 \, a^{3} c^{2} - 8 i \, a^{3} c d - 4 \, a^{3} d^{2}\right)} {\left(f x + e\right)} - 12 \, {\left(2 i \, a^{3} c^{2} + 4 \, a^{3} c d - 2 i \, a^{3} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + {\left(36 \, a^{3} c^{2} - 96 i \, a^{3} c d - 48 \, a^{3} d^{2}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(3*I*a^3*d^2*tan(f*x + e)^4 + 4*(2*I*a^3*c*d + 3*a^3*d^2)*tan(f*x + e)^3 - (-6*I*a^3*c^2 - 36*a^3*c*d + 24*I*a^3*d^2)*tan(f*x + e)^2 - 12*(4*a^3*c^2 - 8*I*a^3*c*d - 4*a^3*d^2)*(f*x + e) - 12*(2*I*a^3*c^2 + 4*a^3*c*d - 2*I*a^3*d^2)*log(tan(f*x + e)^2 + 1) + (36*a^3*c^2 - 96*I*a^3*c*d - 48*a^3*d^2)*tan(f*x + e))/f","A",0
1072,1,145,0,0.441785," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{a^{2} d^{2} \tan\left(f x + e\right)^{3} + {\left(3 \, a^{2} c d - 3 i \, a^{2} d^{2}\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left(2 \, a^{2} c^{2} - 4 i \, a^{2} c d - 2 \, a^{2} d^{2}\right)} {\left(f x + e\right)} - 3 \, {\left(i \, a^{2} c^{2} + 2 \, a^{2} c d - i \, a^{2} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + {\left(3 \, a^{2} c^{2} - 12 i \, a^{2} c d - 6 \, a^{2} d^{2}\right)} \tan\left(f x + e\right)}{3 \, f}"," ",0,"-1/3*(a^2*d^2*tan(f*x + e)^3 + (3*a^2*c*d - 3*I*a^2*d^2)*tan(f*x + e)^2 - 3*(2*a^2*c^2 - 4*I*a^2*c*d - 2*a^2*d^2)*(f*x + e) - 3*(I*a^2*c^2 + 2*a^2*c*d - I*a^2*d^2)*log(tan(f*x + e)^2 + 1) + (3*a^2*c^2 - 12*I*a^2*c*d - 6*a^2*d^2)*tan(f*x + e))/f","A",0
1073,1,94,0,0.415036," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{-i \, a d^{2} \tan\left(f x + e\right)^{2} - 2 \, {\left(a c^{2} - 2 i \, a c d - a d^{2}\right)} {\left(f x + e\right)} + {\left(-i \, a c^{2} - 2 \, a c d + i \, a d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 2 \, {\left(-2 i \, a c d - a d^{2}\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(-I*a*d^2*tan(f*x + e)^2 - 2*(a*c^2 - 2*I*a*c*d - a*d^2)*(f*x + e) + (-I*a*c^2 - 2*a*c*d + I*a*d^2)*log(tan(f*x + e)^2 + 1) + 2*(-2*I*a*c*d - a*d^2)*tan(f*x + e))/f","A",0
1074,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1075,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1076,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^2/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1077,1,263,0,0.419914," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{12 i \, a^{3} d^{3} \tan\left(f x + e\right)^{5} + 45 \, {\left(i \, a^{3} c d^{2} + a^{3} d^{3}\right)} \tan\left(f x + e\right)^{4} - {\left(-60 i \, a^{3} c^{2} d - 180 \, a^{3} c d^{2} + 80 i \, a^{3} d^{3}\right)} \tan\left(f x + e\right)^{3} - {\left(-30 i \, a^{3} c^{3} - 270 \, a^{3} c^{2} d + 360 i \, a^{3} c d^{2} + 120 \, a^{3} d^{3}\right)} \tan\left(f x + e\right)^{2} - 60 \, {\left(4 \, a^{3} c^{3} - 12 i \, a^{3} c^{2} d - 12 \, a^{3} c d^{2} + 4 i \, a^{3} d^{3}\right)} {\left(f x + e\right)} - 60 \, {\left(2 i \, a^{3} c^{3} + 6 \, a^{3} c^{2} d - 6 i \, a^{3} c d^{2} - 2 \, a^{3} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + {\left(180 \, a^{3} c^{3} - 720 i \, a^{3} c^{2} d - 720 \, a^{3} c d^{2} + 240 i \, a^{3} d^{3}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"-1/60*(12*I*a^3*d^3*tan(f*x + e)^5 + 45*(I*a^3*c*d^2 + a^3*d^3)*tan(f*x + e)^4 - (-60*I*a^3*c^2*d - 180*a^3*c*d^2 + 80*I*a^3*d^3)*tan(f*x + e)^3 - (-30*I*a^3*c^3 - 270*a^3*c^2*d + 360*I*a^3*c*d^2 + 120*a^3*d^3)*tan(f*x + e)^2 - 60*(4*a^3*c^3 - 12*I*a^3*c^2*d - 12*a^3*c*d^2 + 4*I*a^3*d^3)*(f*x + e) - 60*(2*I*a^3*c^3 + 6*a^3*c^2*d - 6*I*a^3*c*d^2 - 2*a^3*d^3)*log(tan(f*x + e)^2 + 1) + (180*a^3*c^3 - 720*I*a^3*c^2*d - 720*a^3*c*d^2 + 240*I*a^3*d^3)*tan(f*x + e))/f","A",0
1078,1,217,0,0.520885," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{3 \, a^{2} d^{3} \tan\left(f x + e\right)^{4} + {\left(12 \, a^{2} c d^{2} - 8 i \, a^{2} d^{3}\right)} \tan\left(f x + e\right)^{3} + {\left(18 \, a^{2} c^{2} d - 36 i \, a^{2} c d^{2} - 12 \, a^{2} d^{3}\right)} \tan\left(f x + e\right)^{2} - 12 \, {\left(2 \, a^{2} c^{3} - 6 i \, a^{2} c^{2} d - 6 \, a^{2} c d^{2} + 2 i \, a^{2} d^{3}\right)} {\left(f x + e\right)} - 12 \, {\left(i \, a^{2} c^{3} + 3 \, a^{2} c^{2} d - 3 i \, a^{2} c d^{2} - a^{2} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + {\left(12 \, a^{2} c^{3} - 72 i \, a^{2} c^{2} d - 72 \, a^{2} c d^{2} + 24 i \, a^{2} d^{3}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(3*a^2*d^3*tan(f*x + e)^4 + (12*a^2*c*d^2 - 8*I*a^2*d^3)*tan(f*x + e)^3 + (18*a^2*c^2*d - 36*I*a^2*c*d^2 - 12*a^2*d^3)*tan(f*x + e)^2 - 12*(2*a^2*c^3 - 6*I*a^2*c^2*d - 6*a^2*c*d^2 + 2*I*a^2*d^3)*(f*x + e) - 12*(I*a^2*c^3 + 3*a^2*c^2*d - 3*I*a^2*c*d^2 - a^2*d^3)*log(tan(f*x + e)^2 + 1) + (12*a^2*c^3 - 72*I*a^2*c^2*d - 72*a^2*c*d^2 + 24*I*a^2*d^3)*tan(f*x + e))/f","A",0
1079,1,145,0,0.565917," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{-2 i \, a d^{3} \tan\left(f x + e\right)^{3} + 3 \, {\left(-3 i \, a c d^{2} - a d^{3}\right)} \tan\left(f x + e\right)^{2} - 6 \, {\left(a c^{3} - 3 i \, a c^{2} d - 3 \, a c d^{2} + i \, a d^{3}\right)} {\left(f x + e\right)} + 3 \, {\left(-i \, a c^{3} - 3 \, a c^{2} d + 3 i \, a c d^{2} + a d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) - {\left(18 i \, a c^{2} d + 18 \, a c d^{2} - 6 i \, a d^{3}\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(-2*I*a*d^3*tan(f*x + e)^3 + 3*(-3*I*a*c*d^2 - a*d^3)*tan(f*x + e)^2 - 6*(a*c^3 - 3*I*a*c^2*d - 3*a*c*d^2 + I*a*d^3)*(f*x + e) + 3*(-I*a*c^3 - 3*a*c^2*d + 3*I*a*c*d^2 + a*d^3)*log(tan(f*x + e)^2 + 1) - (18*I*a*c^2*d + 18*a*c*d^2 - 6*I*a*d^3)*tan(f*x + e))/f","A",0
1080,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1081,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1082,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^3/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1083,1,140,0,0.416713," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{-\frac{i \, a^{3} \tan\left(f x + e\right)}{d} + \frac{{\left(4 \, a^{3} c + 4 i \, a^{3} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{{\left(i \, a^{3} c^{3} - 3 \, a^{3} c^{2} d - 3 i \, a^{3} c d^{2} + a^{3} d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(-i \, a^{3} c + a^{3} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{f}"," ",0,"(-I*a^3*tan(f*x + e)/d + (4*a^3*c + 4*I*a^3*d)*(f*x + e)/(c^2 + d^2) + (I*a^3*c^3 - 3*a^3*c^2*d - 3*I*a^3*c*d^2 + a^3*d^3)*log(d*tan(f*x + e) + c)/(c^2*d^2 + d^4) - 2*(-I*a^3*c + a^3*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
1084,1,114,0,0.428009," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, a^{2} c + 2 i \, a^{2} d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} - \frac{{\left(a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{2} d + d^{3}} - \frac{{\left(-i \, a^{2} c + a^{2} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{f}"," ",0,"((2*a^2*c + 2*I*a^2*d)*(f*x + e)/(c^2 + d^2) - (a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)*log(d*tan(f*x + e) + c)/(c^2*d + d^3) - (-I*a^2*c + a^2*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
1085,1,90,0,0.416157," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a c + i \, a d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{2 \, {\left(-i \, a c + a d\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{2} + d^{2}} + \frac{{\left(i \, a c - a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{2 \, f}"," ",0,"1/2*(2*(a*c + I*a*d)*(f*x + e)/(c^2 + d^2) + 2*(-I*a*c + a*d)*log(d*tan(f*x + e) + c)/(c^2 + d^2) + (I*a*c - a*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","B",0
1086,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1087,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1088,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1089,1,248,0,0.423349," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, a^{3} c^{2} + 8 i \, a^{3} c d - 4 \, a^{3} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(-i \, a^{3} c^{4} - 6 i \, a^{3} c^{2} d^{2} + 8 \, a^{3} c d^{3} + 3 i \, a^{3} d^{4}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}} + \frac{{\left(4 i \, a^{3} c^{2} - 8 \, a^{3} c d - 4 i \, a^{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(-i \, a^{3} c^{3} + 3 \, a^{3} c^{2} d + 3 i \, a^{3} c d^{2} - a^{3} d^{3}\right)}}{c^{3} d^{2} + c d^{4} + {\left(c^{2} d^{3} + d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(4*a^3*c^2 + 8*I*a^3*c*d - 4*a^3*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + 2*(-I*a^3*c^4 - 6*I*a^3*c^2*d^2 + 8*a^3*c*d^3 + 3*I*a^3*d^4)*log(d*tan(f*x + e) + c)/(c^4*d^2 + 2*c^2*d^4 + d^6) + (4*I*a^3*c^2 - 8*a^3*c*d - 4*I*a^3*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(-I*a^3*c^3 + 3*a^3*c^2*d + 3*I*a^3*c*d^2 - a^3*d^3)/(c^3*d^2 + c*d^4 + (c^2*d^3 + d^5)*tan(f*x + e)))/f","A",0
1090,1,213,0,0.418135," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, a^{2} c^{2} + 4 i \, a^{2} c d - 2 \, a^{2} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(-2 i \, a^{2} c^{2} + 4 \, a^{2} c d + 2 i \, a^{2} d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(i \, a^{2} c^{2} - 2 \, a^{2} c d - i \, a^{2} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{a^{2} c^{2} + 2 i \, a^{2} c d - a^{2} d^{2}}{c^{3} d + c d^{3} + {\left(c^{2} d^{2} + d^{4}\right)} \tan\left(f x + e\right)}}{f}"," ",0,"((2*a^2*c^2 + 4*I*a^2*c*d - 2*a^2*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + (-2*I*a^2*c^2 + 4*a^2*c*d + 2*I*a^2*d^2)*log(d*tan(f*x + e) + c)/(c^4 + 2*c^2*d^2 + d^4) + (I*a^2*c^2 - 2*a^2*c*d - I*a^2*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + (a^2*c^2 + 2*I*a^2*c*d - a^2*d^2)/(c^3*d + c*d^3 + (c^2*d^2 + d^4)*tan(f*x + e)))/f","B",0
1091,1,180,0,0.762666," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a c^{2} + 2 i \, a c d - a d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(-i \, a c^{2} + 2 \, a c d + i \, a d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(i \, a c^{2} - 2 \, a c d - i \, a 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(i \, a c - a d\right)}}{c^{3} + c d^{2} + {\left(c^{2} d + d^{3}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(a*c^2 + 2*I*a*c*d - a*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + 2*(-I*a*c^2 + 2*a*c*d + I*a*d^2)*log(d*tan(f*x + e) + c)/(c^4 + 2*c^2*d^2 + d^4) + (I*a*c^2 - 2*a*c*d - I*a*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(I*a*c - a*d)/(c^3 + c*d^2 + (c^2*d + d^3)*tan(f*x + e)))/f","B",0
1092,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1093,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1094,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1095,1,404,0,0.432931," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, a^{3} c^{3} + 12 i \, a^{3} c^{2} d - 12 \, a^{3} c d^{2} - 4 i \, a^{3} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{2 \, {\left(-4 i \, a^{3} c^{3} + 12 \, a^{3} c^{2} d + 12 i \, a^{3} c d^{2} - 4 \, a^{3} d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(4 i \, a^{3} c^{3} - 12 \, a^{3} c^{2} d - 12 i \, a^{3} c d^{2} + 4 \, a^{3} 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{i \, a^{3} c^{5} + 3 \, a^{3} c^{4} d + 14 i \, a^{3} c^{3} d^{2} - 14 \, a^{3} c^{2} d^{3} - 3 i \, a^{3} c d^{4} - a^{3} d^{5} - {\left(-2 i \, a^{3} c^{4} d - 12 i \, a^{3} c^{2} d^{3} + 16 \, a^{3} c d^{4} + 6 i \, a^{3} d^{5}\right)} \tan\left(f x + e\right)}{c^{6} d^{2} + 2 \, c^{4} d^{4} + c^{2} d^{6} + {\left(c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{3} + 2 \, c^{3} d^{5} + c d^{7}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(4*a^3*c^3 + 12*I*a^3*c^2*d - 12*a^3*c*d^2 - 4*I*a^3*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + 2*(-4*I*a^3*c^3 + 12*a^3*c^2*d + 12*I*a^3*c*d^2 - 4*a^3*d^3)*log(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (4*I*a^3*c^3 - 12*a^3*c^2*d - 12*I*a^3*c*d^2 + 4*a^3*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (I*a^3*c^5 + 3*a^3*c^4*d + 14*I*a^3*c^3*d^2 - 14*a^3*c^2*d^3 - 3*I*a^3*c*d^4 - a^3*d^5 - (-2*I*a^3*c^4*d - 12*I*a^3*c^2*d^3 + 16*a^3*c*d^4 + 6*I*a^3*d^5)*tan(f*x + e))/(c^6*d^2 + 2*c^4*d^4 + c^2*d^6 + (c^4*d^4 + 2*c^2*d^6 + d^8)*tan(f*x + e)^2 + 2*(c^5*d^3 + 2*c^3*d^5 + c*d^7)*tan(f*x + e)))/f","B",0
1096,1,381,0,0.438433," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(2 \, a^{2} c^{3} + 6 i \, a^{2} c^{2} d - 6 \, a^{2} c d^{2} - 2 i \, a^{2} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{2 \, {\left(-2 i \, a^{2} c^{3} + 6 \, a^{2} c^{2} d + 6 i \, a^{2} c d^{2} - 2 \, a^{2} d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(2 i \, a^{2} c^{3} - 6 \, a^{2} c^{2} d - 6 i \, a^{2} c d^{2} + 2 \, a^{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{a^{2} c^{4} + 6 i \, a^{2} c^{3} d - 8 \, a^{2} c^{2} d^{2} - 2 i \, a^{2} c d^{3} - a^{2} d^{4} - {\left(-4 i \, a^{2} c^{2} d^{2} + 8 \, a^{2} c d^{3} + 4 i \, a^{2} d^{4}\right)} \tan\left(f x + e\right)}{c^{6} d + 2 \, c^{4} d^{3} + c^{2} d^{5} + {\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{4} + c d^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(2*a^2*c^3 + 6*I*a^2*c^2*d - 6*a^2*c*d^2 - 2*I*a^2*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + 2*(-2*I*a^2*c^3 + 6*a^2*c^2*d + 6*I*a^2*c*d^2 - 2*a^2*d^3)*log(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (2*I*a^2*c^3 - 6*a^2*c^2*d - 6*I*a^2*c*d^2 + 2*a^2*d^3)*log(tan(f*x + e)^2 + 1)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (a^2*c^4 + 6*I*a^2*c^3*d - 8*a^2*c^2*d^2 - 2*I*a^2*c*d^3 - a^2*d^4 - (-4*I*a^2*c^2*d^2 + 8*a^2*c*d^3 + 4*I*a^2*d^4)*tan(f*x + e))/(c^6*d + 2*c^4*d^3 + c^2*d^5 + (c^4*d^3 + 2*c^2*d^5 + d^7)*tan(f*x + e)^2 + 2*(c^5*d^2 + 2*c^3*d^4 + c*d^6)*tan(f*x + e)))/f","B",0
1097,1,325,0,0.430730," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a c^{3} + 3 i \, a c^{2} d - 3 \, a c d^{2} - i \, a d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{2 \, {\left(-i \, a c^{3} + 3 \, a c^{2} d + 3 i \, a c d^{2} - a d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(i \, a c^{3} - 3 \, a c^{2} d - 3 i \, a 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{3 i \, a c^{3} - 5 \, a c^{2} d - i \, a c d^{2} - a d^{3} - {\left(-2 i \, a c^{2} d + 4 \, a c d^{2} + 2 i \, a d^{3}\right)} \tan\left(f x + e\right)}{c^{6} + 2 \, c^{4} d^{2} + c^{2} d^{4} + {\left(c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d + 2 \, c^{3} d^{3} + c d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(a*c^3 + 3*I*a*c^2*d - 3*a*c*d^2 - I*a*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + 2*(-I*a*c^3 + 3*a*c^2*d + 3*I*a*c*d^2 - a*d^3)*log(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (I*a*c^3 - 3*a*c^2*d - 3*I*a*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) + (3*I*a*c^3 - 5*a*c^2*d - I*a*c*d^2 - a*d^3 - (-2*I*a*c^2*d + 4*a*c*d^2 + 2*I*a*d^3)*tan(f*x + e))/(c^6 + 2*c^4*d^2 + c^2*d^4 + (c^4*d^2 + 2*c^2*d^4 + d^6)*tan(f*x + e)^2 + 2*(c^5*d + 2*c^3*d^3 + c*d^5)*tan(f*x + e)))/f","B",0
1098,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1099,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1100,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1101,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*sqrt(d*tan(f*x + e) + c), x)","F",0
1102,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*sqrt(d*tan(f*x + e) + c), x)","F",0
1103,1,4437,0,1.275889," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{{\left({\left(-8 i \, \sqrt{2} a \cos\left(2 \, f x + 2 \, e\right) + 8 \, \sqrt{2} a \sin\left(2 \, f x + 2 \, e\right) - 8 i \, \sqrt{2} a\right)} \arctan\left(-2 \, d \cos\left(2 \, f x + 2 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) - {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left(\sqrt{2} \sqrt{-c + \sqrt{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) - \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)}, 2 \, c \cos\left(2 \, f x + 2 \, e\right) + 2 \, d \sin\left(2 \, f x + 2 \, e\right) + {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) + \sqrt{2} \sqrt{-c + \sqrt{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)} + 2 \, c\right) - {\left(4 \, \sqrt{2} a \cos\left(2 \, f x + 2 \, e\right) + 4 i \, \sqrt{2} a \sin\left(2 \, f x + 2 \, e\right) + 4 \, \sqrt{2} a\right)} \log\left(8 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{2} + d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 8 \, c d \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{2} + d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sqrt{4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)} \sqrt{c^{2} + d^{2}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)^{2}\right)} + 4 \, c^{2} + 4 \, {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left({\left({\left(\sqrt{2} c \cos\left(2 \, f x + 2 \, e\right) + \sqrt{2} d \sin\left(2 \, f x + 2 \, e\right) + \sqrt{2} c\right)} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) - {\left(\sqrt{2} d \cos\left(2 \, f x + 2 \, e\right) - \sqrt{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)} \sqrt{c + \sqrt{c^{2} + d^{2}}} + {\left({\left(\sqrt{2} d \cos\left(2 \, f x + 2 \, e\right) - \sqrt{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) + {\left(\sqrt{2} c \cos\left(2 \, f x + 2 \, e\right) + \sqrt{2} d \sin\left(2 \, f x + 2 \, e\right) + \sqrt{2} c\right)} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)} \sqrt{-c + \sqrt{c^{2} + d^{2}}}\right)}\right)\right)} \sqrt{c + \sqrt{c^{2} + d^{2}}} - {\left({\left(8 \, \sqrt{2} a \cos\left(2 \, f x + 2 \, e\right) + 8 i \, \sqrt{2} a \sin\left(2 \, f x + 2 \, e\right) + 8 \, \sqrt{2} a\right)} \arctan\left(-2 \, d \cos\left(2 \, f x + 2 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) - {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left(\sqrt{2} \sqrt{-c + \sqrt{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) - \sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)}, 2 \, c \cos\left(2 \, f x + 2 \, e\right) + 2 \, d \sin\left(2 \, f x + 2 \, e\right) + {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left(\sqrt{2} \sqrt{c + \sqrt{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) + \sqrt{2} \sqrt{-c + \sqrt{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)} + 2 \, c\right) - {\left(4 i \, \sqrt{2} a \cos\left(2 \, f x + 2 \, e\right) - 4 \, \sqrt{2} a \sin\left(2 \, f x + 2 \, e\right) + 4 i \, \sqrt{2} a\right)} \log\left(8 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{2} + d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 8 \, c d \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{2} + d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, \sqrt{4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)} \sqrt{c^{2} + d^{2}} {\left(\cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)^{2}\right)} + 4 \, c^{2} + 4 \, {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left({\left({\left(\sqrt{2} c \cos\left(2 \, f x + 2 \, e\right) + \sqrt{2} d \sin\left(2 \, f x + 2 \, e\right) + \sqrt{2} c\right)} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) - {\left(\sqrt{2} d \cos\left(2 \, f x + 2 \, e\right) - \sqrt{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)} \sqrt{c + \sqrt{c^{2} + d^{2}}} + {\left({\left(\sqrt{2} d \cos\left(2 \, f x + 2 \, e\right) - \sqrt{2} c \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) + {\left(\sqrt{2} c \cos\left(2 \, f x + 2 \, e\right) + \sqrt{2} d \sin\left(2 \, f x + 2 \, e\right) + \sqrt{2} c\right)} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)} \sqrt{-c + \sqrt{c^{2} + d^{2}}}\right)}\right)\right)} \sqrt{-c + \sqrt{c^{2} + d^{2}}} + {\left(4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(4 \, f x + 4 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} + d^{2} + 2 \, {\left(2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) - 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + c^{2} - d^{2}\right)} \cos\left(4 \, f x + 4 \, e\right) + 4 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right) + c^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(4 \, f x + 4 \, e\right)\right)}^{\frac{1}{4}} {\left(32 \, a \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right) + 32 i \, a \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(4 \, f x + 4 \, e\right) + c \sin\left(4 \, f x + 4 \, e\right) + 2 \, c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(4 \, f x + 4 \, e\right) + 2 \, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(4 \, f x + 4 \, e\right) + c\right)\right)\right)}}{f {\left(-16 i \, \cos\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(2 \, f x + 2 \, e\right) - 16 i\right)}}"," ",0,"(((-8*I*sqrt(2)*a*cos(2*f*x + 2*e) + 8*sqrt(2)*a*sin(2*f*x + 2*e) - 8*I*sqrt(2)*a)*arctan2(-2*d*cos(2*f*x + 2*e) + 2*c*sin(2*f*x + 2*e) - (4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(sqrt(2)*sqrt(-c + sqrt(c^2 + d^2))*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) - sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))), 2*c*cos(2*f*x + 2*e) + 2*d*sin(2*f*x + 2*e) + (4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) + sqrt(2)*sqrt(-c + sqrt(c^2 + d^2))*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))) + 2*c) - (4*sqrt(2)*a*cos(2*f*x + 2*e) + 4*I*sqrt(2)*a*sin(2*f*x + 2*e) + 4*sqrt(2)*a)*log(8*c^2*cos(2*f*x + 2*e) + 4*(c^2 + d^2)*cos(2*f*x + 2*e)^2 + 8*c*d*sin(2*f*x + 2*e) + 4*(c^2 + d^2)*sin(2*f*x + 2*e)^2 + 4*sqrt(4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))*sqrt(c^2 + d^2)*(cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))^2 + sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))^2) + 4*c^2 + 4*(4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(((sqrt(2)*c*cos(2*f*x + 2*e) + sqrt(2)*d*sin(2*f*x + 2*e) + sqrt(2)*c)*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) - (sqrt(2)*d*cos(2*f*x + 2*e) - sqrt(2)*c*sin(2*f*x + 2*e))*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)))*sqrt(c + sqrt(c^2 + d^2)) + ((sqrt(2)*d*cos(2*f*x + 2*e) - sqrt(2)*c*sin(2*f*x + 2*e))*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) + (sqrt(2)*c*cos(2*f*x + 2*e) + sqrt(2)*d*sin(2*f*x + 2*e) + sqrt(2)*c)*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)))*sqrt(-c + sqrt(c^2 + d^2)))))*sqrt(c + sqrt(c^2 + d^2)) - ((8*sqrt(2)*a*cos(2*f*x + 2*e) + 8*I*sqrt(2)*a*sin(2*f*x + 2*e) + 8*sqrt(2)*a)*arctan2(-2*d*cos(2*f*x + 2*e) + 2*c*sin(2*f*x + 2*e) - (4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(sqrt(2)*sqrt(-c + sqrt(c^2 + d^2))*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) - sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))), 2*c*cos(2*f*x + 2*e) + 2*d*sin(2*f*x + 2*e) + (4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(sqrt(2)*sqrt(c + sqrt(c^2 + d^2))*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) + sqrt(2)*sqrt(-c + sqrt(c^2 + d^2))*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))) + 2*c) - (4*I*sqrt(2)*a*cos(2*f*x + 2*e) - 4*sqrt(2)*a*sin(2*f*x + 2*e) + 4*I*sqrt(2)*a)*log(8*c^2*cos(2*f*x + 2*e) + 4*(c^2 + d^2)*cos(2*f*x + 2*e)^2 + 8*c*d*sin(2*f*x + 2*e) + 4*(c^2 + d^2)*sin(2*f*x + 2*e)^2 + 4*sqrt(4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))*sqrt(c^2 + d^2)*(cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))^2 + sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))^2) + 4*c^2 + 4*(4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(((sqrt(2)*c*cos(2*f*x + 2*e) + sqrt(2)*d*sin(2*f*x + 2*e) + sqrt(2)*c)*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) - (sqrt(2)*d*cos(2*f*x + 2*e) - sqrt(2)*c*sin(2*f*x + 2*e))*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)))*sqrt(c + sqrt(c^2 + d^2)) + ((sqrt(2)*d*cos(2*f*x + 2*e) - sqrt(2)*c*sin(2*f*x + 2*e))*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) + (sqrt(2)*c*cos(2*f*x + 2*e) + sqrt(2)*d*sin(2*f*x + 2*e) + sqrt(2)*c)*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)))*sqrt(-c + sqrt(c^2 + d^2)))))*sqrt(-c + sqrt(c^2 + d^2)) + (4*c^2*cos(2*f*x + 2*e)^2 + 4*c^2*sin(2*f*x + 2*e)^2 + (c^2 + d^2)*cos(4*f*x + 4*e)^2 + 4*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*sin(4*f*x + 4*e)^2 + 4*c*d*sin(2*f*x + 2*e) + c^2 + d^2 + 2*(2*c^2*cos(2*f*x + 2*e) - 2*c*d*sin(2*f*x + 2*e) + c^2 - d^2)*cos(4*f*x + 4*e) + 4*(c*d*cos(2*f*x + 2*e) + c^2*sin(2*f*x + 2*e) + c*d)*sin(4*f*x + 4*e))^(1/4)*(32*a*cos(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c)) + 32*I*a*sin(1/2*arctan2(-d*cos(4*f*x + 4*e) + c*sin(4*f*x + 4*e) + 2*c*sin(2*f*x + 2*e) + d, c*cos(4*f*x + 4*e) + 2*c*cos(2*f*x + 2*e) + d*sin(4*f*x + 4*e) + c))))/(f*(-16*I*cos(2*f*x + 2*e) + 16*sin(2*f*x + 2*e) - 16*I))","B",0
1104,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1105,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1106,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1107,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{3} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3*(d*tan(f*x + e) + c)^(3/2), x)","F",0
1108,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(i \, a \tan\left(f x + e\right) + a\right)}^{2} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2*(d*tan(f*x + e) + c)^(3/2), x)","F",0
1109,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1111,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1112,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1113,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1115,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1116,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1117,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1118,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1119,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{3}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^3/sqrt(d*tan(f*x + e) + c), x)","F",0
1120,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/sqrt(d*tan(f*x + e) + c), x)","F",0
1121,1,6484,0,0.780210," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2 \, c^{2} + 2 \, d^{2}} {\left(2 \, a \arctan\left(\frac{d^{2} \cos\left(2 \, f x + 2 \, e\right) - c d \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} d \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)}{d^{2}}, -\frac{c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) - {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right) + c}{d}\right) - i \, a \log\left(\frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + \sqrt{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)^{2} + \sqrt{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)^{2} + c^{2} - \frac{2 \, {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(c d \cos\left(2 \, f x + 2 \, e\right) + d^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)}{d} + \frac{2 \, {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(d^{2} \cos\left(2 \, f x + 2 \, e\right) - c d \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)}{d}}{d^{2}}\right)\right)} \sqrt{c + \sqrt{c^{2} + d^{2}}} - \sqrt{2 \, c^{2} + 2 \, d^{2}} {\left(-2 i \, a \arctan\left(\frac{d^{2} \cos\left(2 \, f x + 2 \, e\right) - c d \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} d \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)}{d^{2}}, -\frac{c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) - {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right) + c}{d}\right) - a \log\left(\frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, c d \sin\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + \sqrt{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)^{2} + \sqrt{{\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)^{2} + c^{2} - \frac{2 \, {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(c d \cos\left(2 \, f x + 2 \, e\right) + d^{2} \sin\left(2 \, f x + 2 \, e\right) + c d\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)}{d} + \frac{2 \, {\left({\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(2 \, f x + 2 \, e\right)^{4} + c^{4} + 2 \, c^{2} d^{2} + d^{4} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{3} + 4 \, {\left(c^{3} d + c d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{3} + 2 \, {\left(3 \, c^{4} + 2 \, c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4} + {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left(c^{4} + c^{2} d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(c^{3} d + c d^{3} + {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 2 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left(d^{2} \cos\left(2 \, f x + 2 \, e\right) - c d \sin\left(2 \, f x + 2 \, e\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(2 \, f x + 2 \, e\right)^{2} - c d \sin\left(2 \, f x + 2 \, e\right)^{2} + c d \cos\left(2 \, f x + 2 \, e\right) - {\left(c^{2} + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)\right)}}{d^{2}}, \frac{2 \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(2 \, c d \cos\left(2 \, f x + 2 \, e\right) + c d\right)} \sin\left(2 \, f x + 2 \, e\right)}{d^{2}}\right)\right)}{d}}{d^{2}}\right)\right)} \sqrt{-c + \sqrt{c^{2} + d^{2}}}}{4 \, {\left(c^{2} + d^{2}\right)} f}"," ",0,"-1/4*(sqrt(2*c^2 + 2*d^2)*(2*a*arctan2((d^2*cos(2*f*x + 2*e) - c*d*sin(2*f*x + 2*e) + ((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*d*sin(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2)))/d^2, -(c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) - ((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2)) + c)/d) - I*a*log((2*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*cos(2*f*x + 2*e)^2 + 2*c*d*sin(2*f*x + 2*e) + (c^2 + d^2)*sin(2*f*x + 2*e)^2 + sqrt((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))*cos(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))^2 + sqrt((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))*sin(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))^2 + c^2 - 2*((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*(c*d*cos(2*f*x + 2*e) + d^2*sin(2*f*x + 2*e) + c*d)*cos(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))/d + 2*((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*(d^2*cos(2*f*x + 2*e) - c*d*sin(2*f*x + 2*e))*sin(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))/d)/d^2))*sqrt(c + sqrt(c^2 + d^2)) - sqrt(2*c^2 + 2*d^2)*(-2*I*a*arctan2((d^2*cos(2*f*x + 2*e) - c*d*sin(2*f*x + 2*e) + ((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*d*sin(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2)))/d^2, -(c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) - ((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2)) + c)/d) - a*log((2*c^2*cos(2*f*x + 2*e) + (c^2 + d^2)*cos(2*f*x + 2*e)^2 + 2*c*d*sin(2*f*x + 2*e) + (c^2 + d^2)*sin(2*f*x + 2*e)^2 + sqrt((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))*cos(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))^2 + sqrt((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))*sin(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))^2 + c^2 - 2*((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*(c*d*cos(2*f*x + 2*e) + d^2*sin(2*f*x + 2*e) + c*d)*cos(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))/d + 2*((c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^4 + (c^4 + 2*c^2*d^2 + d^4)*sin(2*f*x + 2*e)^4 + c^4 + 2*c^2*d^2 + d^4 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e)^3 + 4*(c^3*d + c*d^3)*sin(2*f*x + 2*e)^3 + 2*(3*c^4 + 2*c^2*d^2 - d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + 2*c^2*d^2 + d^4 + (c^4 + 2*c^2*d^2 + d^4)*cos(2*f*x + 2*e)^2 + 2*(c^4 + c^2*d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e)^2 + 4*(c^4 + c^2*d^2)*cos(2*f*x + 2*e) + 4*(c^3*d + c*d^3 + (c^3*d + c*d^3)*cos(2*f*x + 2*e)^2 + 2*(c^3*d + c*d^3)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))^(1/4)*(d^2*cos(2*f*x + 2*e) - c*d*sin(2*f*x + 2*e))*sin(1/2*arctan2(-2*(c*d*cos(2*f*x + 2*e)^2 - c*d*sin(2*f*x + 2*e)^2 + c*d*cos(2*f*x + 2*e) - (c^2 + (c^2 - d^2)*cos(2*f*x + 2*e))*sin(2*f*x + 2*e))/d^2, (2*c^2*cos(2*f*x + 2*e) + (c^2 - d^2)*cos(2*f*x + 2*e)^2 - (c^2 - d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(2*c*d*cos(2*f*x + 2*e) + c*d)*sin(2*f*x + 2*e))/d^2))/d)/d^2))*sqrt(-c + sqrt(c^2 + d^2)))/((c^2 + d^2)*f)","B",0
1122,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1123,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1124,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1125,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{2}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^2/(d*tan(f*x + e) + c)^(3/2), x)","F",0
1127,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((-(2*c*d^4)/((c^2-d^2)^2>0)', see `assume?` for more details)Is ((-(2*c*d^4)/((c^2-d^2)^2                                    +4*c^2*d^2))    -(2*c^3*d^2)/((c^2-d^2)^2                                     +4*c^2*d^2)    +(c*d^2*(c^2-d^2))     /((c^2-d^2)^2+4*c^2*d^2)    +(c^3*(c^2-d^2))     /((c^2-d^2)^2+4*c^2*d^2)    +(2*c*d^2)/(d^2+c^2)    -(2*c^3)/(d^2+c^2)+c)    ^2    -((2*c^2*d^3)/((c^2-d^2)^2                                      +4*c^2*d^2)     +(d^3*(c^2-d^2))      /((c^2-d^2)^2+4*c^2*d^2)     +(c^2*d*(c^2-d^2))      /((c^2-d^2)^2+4*c^2*d^2)     +(2*c^4*d)/((c^2-d^2)^2                                    +4*c^2*d^2)     -(4*c^2*d)/(d^2+c^2)+d)     ^2 positive, negative or zero?","F(-2)",0
1128,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1129,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1130,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1131,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1132,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1133,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((-(2*c*d^4)/((c^2-d^2)^2>0)', see `assume?` for more details)Is ((-(2*c*d^4)/((c^2-d^2)^2                                    +4*c^2*d^2))    -(2*c^3*d^2)/((c^2-d^2)^2                                     +4*c^2*d^2)    +(c*d^2*(c^2-d^2))     /((c^2-d^2)^2+4*c^2*d^2)    +(c^3*(c^2-d^2))     /((c^2-d^2)^2+4*c^2*d^2)    +(2*c*d^2)/(d^2+c^2)    -(2*c^3)/(d^2+c^2)+c)    ^2    -((2*c^2*d^3)/((c^2-d^2)^2                                      +4*c^2*d^2)     +(d^3*(c^2-d^2))      /((c^2-d^2)^2+4*c^2*d^2)     +(c^2*d*(c^2-d^2))      /((c^2-d^2)^2+4*c^2*d^2)     +(2*c^4*d)/((c^2-d^2)^2                                    +4*c^2*d^2)     -(4*c^2*d)/(d^2+c^2)+d)     ^2 positive, negative or zero?","F(-2)",0
1134,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1135,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^2/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1136,-2,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^3/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: Error executing code in Maxima: expt: undefined: 0 to a negative exponent.","F(-2)",0
1137,-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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(3*d-c>0)', see `assume?` for more details)Is 3*d-c positive, negative or zero?","F(-2)",0
1138,-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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(3*d-c>0)', see `assume?` for more details)Is 3*d-c positive, negative or zero?","F(-2)",0
1139,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(f x + e\right) + a} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)*sqrt(d*tan(f*x + e) + c), x)","F",0
1140,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1143,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(3*d-c>0)', see `assume?` for more details)Is 3*d-c positive, negative or zero?","F(-2)",0
1144,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(3*d-c>0)', see `assume?` for more details)Is 3*d-c positive, negative or zero?","F(-2)",0
1145,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(3/2), x)","F",0
1146,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \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((d*tan(f*x + e) + c)^(3/2)/sqrt(I*a*tan(f*x + e) + a), x)","F",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1149,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(3*d-c>0)', see `assume?` for more details)Is 3*d-c positive, negative or zero?","F(-2)",0
1150,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(3*d-c>0)', see `assume?` for more details)Is 3*d-c positive, negative or zero?","F(-2)",0
1151,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \sqrt{i \, a \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(I*a*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(5/2), x)","F",0
1152,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \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((d*tan(f*x + e) + c)^(5/2)/sqrt(I*a*tan(f*x + e) + a), x)","F",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1155,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((d^2-2*c*d-c^2)>0)', see `assume?` for more details)Is (d^2-2*c*d-c^2)    *(d^2+2*c*d-c^2)    positive, negative or zero?","F(-2)",0
1156,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((d^2-2*c*d-c^2)>0)', see `assume?` for more details)Is (d^2-2*c*d-c^2)    *(d^2+2*c*d-c^2)    positive, negative or zero?","F(-2)",0
1157,1,3634,0,1.507382," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2 \, c^{2} + 2 \, d^{2}} {\left(2 \, \sqrt{2} \arctan\left(\frac{\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right) + {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}, -\frac{\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right) - {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right) - i \, \sqrt{2} \log\left(\frac{{\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right) + 2 \, {\left(\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right)\right)} \sqrt{a} \sqrt{c + \sqrt{c^{2} + d^{2}}} - \sqrt{2 \, c^{2} + 2 \, d^{2}} {\left(-2 i \, \sqrt{2} \arctan\left(\frac{\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right) + {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}, -\frac{\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right) - {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right) - \sqrt{2} \log\left(\frac{{\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right) + 2 \, {\left(\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right)\right)} \sqrt{a} \sqrt{-c + \sqrt{c^{2} + d^{2}}}}{4 \, {\left(c^{2} + d^{2}\right)} f}"," ",0,"-1/4*(sqrt(2*c^2 + 2*d^2)*(2*sqrt(2)*arctan2((sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e) + (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2), -(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e) - (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)) - I*sqrt(2)*log(((c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*cos(f*x + e)^2 + (c^2 + d^2)*sin(f*x + e)^2 - 2*(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))) + 2*(sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)))*sqrt(a)*sqrt(c + sqrt(c^2 + d^2)) - sqrt(2*c^2 + 2*d^2)*(-2*I*sqrt(2)*arctan2((sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e) + (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2), -(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e) - (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)) - sqrt(2)*log(((c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*cos(f*x + e)^2 + (c^2 + d^2)*sin(f*x + e)^2 - 2*(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))) + 2*(sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)))*sqrt(a)*sqrt(-c + sqrt(c^2 + d^2)))/((c^2 + d^2)*f)","B",0
1158,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{i \, a \tan\left(f x + e\right) + a} \sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(f*x + e) + a)*sqrt(d*tan(f*x + e) + c)), x)","F",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1161,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume((d^2-2*c*d-c^2)>0)', see `assume?` for more details)Is (d^2-2*c*d-c^2)    *(d^2+2*c*d-c^2)    positive, negative or zero?","F(-2)",0
1162,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1163,1,8482,0,2.005707," ","integrate((a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(-8 i \, \sqrt{2} c^{2} d - 8 i \, \sqrt{2} d^{3}\right)} \cos\left(f x + e\right) + 8 \, {\left(\sqrt{2} c^{2} d + \sqrt{2} d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a} + {\left({\left(c^{2} + d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(\sqrt{c^{2} + d^{2}} {\left({\left(2 i \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) - 2 \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \arctan\left(\frac{\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right) + {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}, -\frac{\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right) - {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right) + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + i \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \log\left(\frac{{\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right) + 2 \, {\left(\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right)\right)} \sqrt{a} + {\left({\left(-4 i \, \sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + 4 \, \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \arctan\left(\frac{\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right) + {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}, -\frac{\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right) - {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right) - 2 \, {\left(\sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + i \, \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \log\left(\frac{{\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right) + 2 \, {\left(\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right)\right)} \sqrt{a}\right)} \sqrt{2 \, c^{2} + 2 \, d^{2}} \sqrt{c + \sqrt{c^{2} + d^{2}}} + {\left(\sqrt{c^{2} + d^{2}} {\left(2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + i \, \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \arctan\left(\frac{\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right) + {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}, -\frac{\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right) - {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right) + {\left(-i \, \sqrt{2} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + \sqrt{2} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \log\left(\frac{{\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right) + 2 \, {\left(\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right)\right)} \sqrt{a} + {\left(4 \, {\left(\sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + i \, \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \arctan\left(\frac{\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right) + {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}, -\frac{\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right) - {\left(c^{2} + d^{2}\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right) + {\left(-2 i \, \sqrt{2} c \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + 2 \, \sqrt{2} c \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} \log\left(\frac{{\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \sqrt{\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)^{2} + {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(\sqrt{c^{2} + d^{2}} c \cos\left(f x + e\right) + \sqrt{c^{2} + d^{2}} d \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right) + 2 \, {\left(\sqrt{c^{2} + d^{2}} d \cos\left(f x + e\right) - \sqrt{c^{2} + d^{2}} c \sin\left(f x + e\right)\right)} \left(\frac{{\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{4} + 8 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} + d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)^{\frac{1}{4}} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(c d \cos\left(f x + e\right)^{2} - c d \sin\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right)\right)}}{c^{2} + d^{2}}, \frac{4 \, c d \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{2} - d^{2}\right)} \sin\left(f x + e\right)^{2} + c^{2} + d^{2}}{c^{2} + d^{2}}\right)\right)}{c^{2} + d^{2}}\right)\right)} \sqrt{a}\right)} \sqrt{2 \, c^{2} + 2 \, d^{2}} \sqrt{-c + \sqrt{c^{2} + d^{2}}}\right)}}{{\left({\left(c^{2} + d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, c d \sin\left(2 \, f x + 2 \, e\right) + {\left(c^{2} + d^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + c^{2} + d^{2} + 2 \, {\left(c^{2} - d^{2}\right)} \cos\left(2 \, f x + 2 \, e\right)\right)}^{\frac{1}{4}} {\left({\left(-4 i \, c^{4} - 8 i \, c^{2} d^{2} - 4 i \, d^{4}\right)} \cos\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right) + 4 \, {\left(c^{4} + 2 \, c^{2} d^{2} + d^{4}\right)} \sin\left(\frac{1}{2} \, \arctan\left(-d \cos\left(2 \, f x + 2 \, e\right) + c \sin\left(2 \, f x + 2 \, e\right) + d, c \cos\left(2 \, f x + 2 \, e\right) + d \sin\left(2 \, f x + 2 \, e\right) + c\right)\right)\right)} f}"," ",0,"-(((-8*I*sqrt(2)*c^2*d - 8*I*sqrt(2)*d^3)*cos(f*x + e) + 8*(sqrt(2)*c^2*d + sqrt(2)*d^3)*sin(f*x + e))*sqrt(a) + ((c^2 + d^2)*cos(2*f*x + 2*e)^2 + 4*c*d*sin(2*f*x + 2*e) + (c^2 + d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(c^2 - d^2)*cos(2*f*x + 2*e))^(1/4)*((sqrt(c^2 + d^2)*((2*I*sqrt(2)*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) - 2*sqrt(2)*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*arctan2((sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e) + (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2), -(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e) - (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)) + (sqrt(2)*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + I*sqrt(2)*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*log(((c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*cos(f*x + e)^2 + (c^2 + d^2)*sin(f*x + e)^2 - 2*(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))) + 2*(sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)))*sqrt(a) + ((-4*I*sqrt(2)*c*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + 4*sqrt(2)*c*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*arctan2((sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e) + (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2), -(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e) - (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)) - 2*(sqrt(2)*c*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + I*sqrt(2)*c*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*log(((c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*cos(f*x + e)^2 + (c^2 + d^2)*sin(f*x + e)^2 - 2*(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))) + 2*(sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)))*sqrt(a))*sqrt(2*c^2 + 2*d^2)*sqrt(c + sqrt(c^2 + d^2)) + (sqrt(c^2 + d^2)*(2*(sqrt(2)*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + I*sqrt(2)*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*arctan2((sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e) + (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2), -(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e) - (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)) + (-I*sqrt(2)*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + sqrt(2)*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*log(((c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*cos(f*x + e)^2 + (c^2 + d^2)*sin(f*x + e)^2 - 2*(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))) + 2*(sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)))*sqrt(a) + (4*(sqrt(2)*c*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + I*sqrt(2)*c*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*arctan2((sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e) + (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2), -(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e) - (c^2 + d^2)*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)) + (-2*I*sqrt(2)*c*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + 2*sqrt(2)*c*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*log(((c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*sqrt(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2)))^2 + (c^2 + d^2)*cos(f*x + e)^2 + (c^2 + d^2)*sin(f*x + e)^2 - 2*(sqrt(c^2 + d^2)*c*cos(f*x + e) + sqrt(c^2 + d^2)*d*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*cos(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))) + 2*(sqrt(c^2 + d^2)*d*cos(f*x + e) - sqrt(c^2 + d^2)*c*sin(f*x + e))*(((c^2 + d^2)*cos(f*x + e)^4 + (c^2 + d^2)*sin(f*x + e)^4 + 8*c*d*cos(f*x + e)*sin(f*x + e) + 2*(c^2 - d^2)*cos(f*x + e)^2 + 2*((c^2 + d^2)*cos(f*x + e)^2 - c^2 + d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))^(1/4)*sin(1/2*arctan2(-2*(c*d*cos(f*x + e)^2 - c*d*sin(f*x + e)^2 - (c^2 - d^2)*cos(f*x + e)*sin(f*x + e))/(c^2 + d^2), (4*c*d*cos(f*x + e)*sin(f*x + e) + (c^2 - d^2)*cos(f*x + e)^2 - (c^2 - d^2)*sin(f*x + e)^2 + c^2 + d^2)/(c^2 + d^2))))/(c^2 + d^2)))*sqrt(a))*sqrt(2*c^2 + 2*d^2)*sqrt(-c + sqrt(c^2 + d^2))))/(((c^2 + d^2)*cos(2*f*x + 2*e)^2 + 4*c*d*sin(2*f*x + 2*e) + (c^2 + d^2)*sin(2*f*x + 2*e)^2 + c^2 + d^2 + 2*(c^2 - d^2)*cos(2*f*x + 2*e))^(1/4)*((-4*I*c^4 - 8*I*c^2*d^2 - 4*I*d^4)*cos(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)) + 4*(c^4 + 2*c^2*d^2 + d^4)*sin(1/2*arctan2(-d*cos(2*f*x + 2*e) + c*sin(2*f*x + 2*e) + d, c*cos(2*f*x + 2*e) + d*sin(2*f*x + 2*e) + c)))*f)","B",0
1164,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{i \, a \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(3/2)), x)","F",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1167,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((-(2*c*d^4)/((c^2-d^2)^2>0)', see `assume?` for more details)Is ((-(2*c*d^4)/((c^2-d^2)^2                                    +4*c^2*d^2))    -(2*c^3*d^2)/((c^2-d^2)^2                                     +4*c^2*d^2)    +(c*d^2*(c^2-d^2))     /((c^2-d^2)^2+4*c^2*d^2)    +(c^3*(c^2-d^2))     /((c^2-d^2)^2+4*c^2*d^2)    +(3*c*d^2)/(d^2+c^2)    -c^3/(d^2+c^2))    ^2    -((2*c^2*d^3)/((c^2-d^2)^2                                      +4*c^2*d^2)     +(d^3*(c^2-d^2))      /((c^2-d^2)^2+4*c^2*d^2)     +(c^2*d*(c^2-d^2))      /((c^2-d^2)^2+4*c^2*d^2)     +(2*c^4*d)/((c^2-d^2)^2                                    +4*c^2*d^2)     +d^3/(d^2+c^2)     -(3*c^2*d)/(d^2+c^2))     ^2 positive, negative or zero?","F(-2)",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1170,0,0,0,0.000000," ","integrate(1/(a+I*a*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{i \, a \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(I*a*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(5/2)), x)","F",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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1178,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1179,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^n/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1186,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(d \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((d*tan(f*x + e) + c)^(3/2)*(I*a*tan(f*x + e) + a)^m, x)","F",0
1187,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{d \tan\left(f x + e\right) + c} {\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*tan(f*x + e) + c)*(I*a*tan(f*x + e) + a)^m, x)","F",0
1188,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/sqrt(d*tan(f*x + e) + c), x)","F",0
1189,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^(3/2), x)","F",0
1190,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((I*a*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^(5/2), x)","F",0
1191,1,148,0,0.900272," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, b^{3} d \tan\left(f x + e\right)^{3} + 3 \, {\left(b^{3} c + 3 \, a b^{2} d\right)} \tan\left(f x + e\right)^{2} + 6 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c - {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\left(f x + e\right)} + 3 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c + {\left(a^{3} - 3 \, a b^{2}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 6 \, {\left(3 \, a b^{2} c + {\left(3 \, a^{2} b - b^{3}\right)} d\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*b^3*d*tan(f*x + e)^3 + 3*(b^3*c + 3*a*b^2*d)*tan(f*x + e)^2 + 6*((a^3 - 3*a*b^2)*c - (3*a^2*b - b^3)*d)*(f*x + e) + 3*((3*a^2*b - b^3)*c + (a^3 - 3*a*b^2)*d)*log(tan(f*x + e)^2 + 1) + 6*(3*a*b^2*c + (3*a^2*b - b^3)*d)*tan(f*x + e))/f","A",0
1192,1,92,0,0.897542," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{b^{2} d \tan\left(f x + e\right)^{2} - 2 \, {\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} {\left(f x + e\right)} + {\left(2 \, a b c + {\left(a^{2} - b^{2}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 2 \, {\left(b^{2} c + 2 \, a b d\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(b^2*d*tan(f*x + e)^2 - 2*(2*a*b*d - (a^2 - b^2)*c)*(f*x + e) + (2*a*b*c + (a^2 - b^2)*d)*log(tan(f*x + e)^2 + 1) + 2*(b^2*c + 2*a*b*d)*tan(f*x + e))/f","A",0
1193,1,50,0,0.944130," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, b d \tan\left(f x + e\right) + 2 \, {\left(a c - b d\right)} {\left(f x + e\right)} + {\left(b c + a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{2 \, f}"," ",0,"1/2*(2*b*d*tan(f*x + e) + 2*(a*c - b*d)*(f*x + e) + (b*c + a*d)*log(tan(f*x + e)^2 + 1))/f","A",0
1194,1,89,0,0.764415," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a c + b d\right)} {\left(f x + e\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(b c - a d\right)} \log\left(b \tan\left(f x + e\right) + a\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}}}{2 \, f}"," ",0,"1/2*(2*(a*c + b*d)*(f*x + e)/(a^2 + b^2) + 2*(b*c - a*d)*log(b*tan(f*x + e) + a)/(a^2 + b^2) - (b*c - a*d)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2))/f","A",0
1195,1,180,0,0.764720," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(2 \, a b d + {\left(a^{2} - b^{2}\right)} c\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, a b c - {\left(a^{2} - b^{2}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a b c - {\left(a^{2} - b^{2}\right)} 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(b c - a d\right)}}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(2*a*b*d + (a^2 - b^2)*c)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*a*b*c - (a^2 - b^2)*d)*log(b*tan(f*x + e) + a)/(a^4 + 2*a^2*b^2 + b^4) - (2*a*b*c - (a^2 - b^2)*d)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(b*c - a*d)/(a^3 + a*b^2 + (a^2*b + b^3)*tan(f*x + e)))/f","A",0
1196,1,333,0,0.727476," ","integrate((c+d*tan(f*x+e))/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c + {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c - {\left(a^{3} - 3 \, a b^{2}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c - {\left(a^{3} - 3 \, a b^{2}\right)} 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{{\left(5 \, a^{2} b + b^{3}\right)} c - {\left(3 \, a^{3} - a b^{2}\right)} d + 2 \, {\left(2 \, a b^{2} c - {\left(a^{2} b - b^{3}\right)} d\right)} \tan\left(f x + e\right)}{a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4} + {\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c + (3*a^2*b - b^3)*d)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*((3*a^2*b - b^3)*c - (a^3 - 3*a*b^2)*d)*log(b*tan(f*x + e) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((3*a^2*b - b^3)*c - (a^3 - 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) - ((5*a^2*b + b^3)*c - (3*a^3 - a*b^2)*d + 2*(2*a*b^2*c - (a^2*b - b^3)*d)*tan(f*x + e))/(a^6 + 2*a^4*b^2 + a^2*b^4 + (a^4*b^2 + 2*a^2*b^4 + b^6)*tan(f*x + e)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*tan(f*x + e)))/f","A",0
1197,1,253,0,0.581611," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, b^{3} d^{2} \tan\left(f x + e\right)^{4} + 4 \, {\left(2 \, b^{3} c d + 3 \, a b^{2} d^{2}\right)} \tan\left(f x + e\right)^{3} + 6 \, {\left(b^{3} c^{2} + 6 \, a b^{2} c d + {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} + 12 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{2} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} {\left(f x + e\right)} + 6 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d - {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 12 \, {\left(3 \, a b^{2} c^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d + {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*b^3*d^2*tan(f*x + e)^4 + 4*(2*b^3*c*d + 3*a*b^2*d^2)*tan(f*x + e)^3 + 6*(b^3*c^2 + 6*a*b^2*c*d + (3*a^2*b - b^3)*d^2)*tan(f*x + e)^2 + 12*((a^3 - 3*a*b^2)*c^2 - 2*(3*a^2*b - b^3)*c*d - (a^3 - 3*a*b^2)*d^2)*(f*x + e) + 6*((3*a^2*b - b^3)*c^2 + 2*(a^3 - 3*a*b^2)*c*d - (3*a^2*b - b^3)*d^2)*log(tan(f*x + e)^2 + 1) + 12*(3*a*b^2*c^2 + 2*(3*a^2*b - b^3)*c*d + (a^3 - 3*a*b^2)*d^2)*tan(f*x + e))/f","A",0
1198,1,159,0,0.823322," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{b^{2} d^{2} \tan\left(f x + e\right)^{3} + 3 \, {\left(b^{2} c d + a b d^{2}\right)} \tan\left(f x + e\right)^{2} - 3 \, {\left(4 \, a b c d - {\left(a^{2} - b^{2}\right)} c^{2} + {\left(a^{2} - b^{2}\right)} d^{2}\right)} {\left(f x + e\right)} + 3 \, {\left(a b c^{2} - a b d^{2} + {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 3 \, {\left(b^{2} c^{2} + 4 \, a b c d + {\left(a^{2} - b^{2}\right)} d^{2}\right)} \tan\left(f x + e\right)}{3 \, f}"," ",0,"1/3*(b^2*d^2*tan(f*x + e)^3 + 3*(b^2*c*d + a*b*d^2)*tan(f*x + e)^2 - 3*(4*a*b*c*d - (a^2 - b^2)*c^2 + (a^2 - b^2)*d^2)*(f*x + e) + 3*(a*b*c^2 - a*b*d^2 + (a^2 - b^2)*c*d)*log(tan(f*x + e)^2 + 1) + 3*(b^2*c^2 + 4*a*b*c*d + (a^2 - b^2)*d^2)*tan(f*x + e))/f","A",0
1199,1,91,0,0.858086," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{b d^{2} \tan\left(f x + e\right)^{2} + 2 \, {\left(a c^{2} - 2 \, b c d - a d^{2}\right)} {\left(f x + e\right)} + {\left(b c^{2} + 2 \, a c d - b d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 2 \, {\left(2 \, b c d + a d^{2}\right)} \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(b*d^2*tan(f*x + e)^2 + 2*(a*c^2 - 2*b*c*d - a*d^2)*(f*x + e) + (b*c^2 + 2*a*c*d - b*d^2)*log(tan(f*x + e)^2 + 1) + 2*(2*b*c*d + a*d^2)*tan(f*x + e))/f","A",0
1200,1,123,0,0.882773," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\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{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{2} b + b^{3}} - \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}}}{2 \, f}"," ",0,"1/2*(2*(a*c^2 + 2*b*c*d - a*d^2)*(f*x + e)/(a^2 + b^2) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(b*tan(f*x + e) + a)/(a^2*b + b^3) - (b*c^2 - 2*a*c*d - b*d^2)*log(tan(f*x + e)^2 + 1)/(a^2 + b^2))/f","A",0
1201,1,230,0,0.834465," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, a b c d + {\left(a^{2} - b^{2}\right)} c^{2} - {\left(a^{2} - b^{2}\right)} d^{2}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(a b c^{2} - a b d^{2} - {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(a b c^{2} - a b d^{2} - {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{a^{3} b + a b^{3} + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(f x + e\right)}}{f}"," ",0,"((4*a*b*c*d + (a^2 - b^2)*c^2 - (a^2 - b^2)*d^2)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + 2*(a*b*c^2 - a*b*d^2 - (a^2 - b^2)*c*d)*log(b*tan(f*x + e) + a)/(a^4 + 2*a^2*b^2 + b^4) - (a*b*c^2 - a*b*d^2 - (a^2 - b^2)*c*d)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(f*x + e)))/f","A",0
1202,1,431,0,0.907863," ","integrate((c+d*tan(f*x+e))^2/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d - {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d - {\left(3 \, a^{2} b - b^{3}\right)} 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{{\left(5 \, a^{2} b^{2} + b^{4}\right)} c^{2} - 2 \, {\left(3 \, a^{3} b - a b^{3}\right)} c d + {\left(a^{4} - 3 \, a^{2} b^{2}\right)} d^{2} + 4 \, {\left(a b^{3} c^{2} - a b^{3} d^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c d\right)} \tan\left(f x + e\right)}{a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c^2 + 2*(3*a^2*b - b^3)*c*d - (a^3 - 3*a*b^2)*d^2)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*((3*a^2*b - b^3)*c^2 - 2*(a^3 - 3*a*b^2)*c*d - (3*a^2*b - b^3)*d^2)*log(b*tan(f*x + e) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((3*a^2*b - b^3)*c^2 - 2*(a^3 - 3*a*b^2)*c*d - (3*a^2*b - 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) - ((5*a^2*b^2 + b^4)*c^2 - 2*(3*a^3*b - a*b^3)*c*d + (a^4 - 3*a^2*b^2)*d^2 + 4*(a*b^3*c^2 - a*b^3*d^2 - (a^2*b^2 - b^4)*c*d)*tan(f*x + e))/(a^6*b + 2*a^4*b^3 + a^2*b^5 + (a^4*b^3 + 2*a^2*b^5 + b^7)*tan(f*x + e)^2 + 2*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*tan(f*x + e)))/f","B",0
1203,1,375,0,0.886521," ","integrate((a+b*tan(f*x+e))^3*(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{12 \, b^{3} d^{3} \tan\left(f x + e\right)^{5} + 45 \, {\left(b^{3} c d^{2} + a b^{2} d^{3}\right)} \tan\left(f x + e\right)^{4} + 20 \, {\left(3 \, b^{3} c^{2} d + 9 \, a b^{2} c d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)^{3} + 30 \, {\left(b^{3} c^{3} + 9 \, a b^{2} c^{2} d + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} + 60 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{3} - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} + {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\left(f x + e\right)} + 30 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} - {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 60 \, {\left(3 \, a b^{2} c^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d + 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*b^3*d^3*tan(f*x + e)^5 + 45*(b^3*c*d^2 + a*b^2*d^3)*tan(f*x + e)^4 + 20*(3*b^3*c^2*d + 9*a*b^2*c*d^2 + (3*a^2*b - b^3)*d^3)*tan(f*x + e)^3 + 30*(b^3*c^3 + 9*a*b^2*c^2*d + 3*(3*a^2*b - b^3)*c*d^2 + (a^3 - 3*a*b^2)*d^3)*tan(f*x + e)^2 + 60*((a^3 - 3*a*b^2)*c^3 - 3*(3*a^2*b - b^3)*c^2*d - 3*(a^3 - 3*a*b^2)*c*d^2 + (3*a^2*b - b^3)*d^3)*(f*x + e) + 30*((3*a^2*b - b^3)*c^3 + 3*(a^3 - 3*a*b^2)*c^2*d - 3*(3*a^2*b - b^3)*c*d^2 - (a^3 - 3*a*b^2)*d^3)*log(tan(f*x + e)^2 + 1) + 60*(3*a*b^2*c^3 + 3*(3*a^2*b - b^3)*c^2*d + 3*(a^3 - 3*a*b^2)*c*d^2 - (3*a^2*b - b^3)*d^3)*tan(f*x + e))/f","A",0
1204,1,246,0,0.615533," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{3 \, b^{2} d^{3} \tan\left(f x + e\right)^{4} + 4 \, {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} \tan\left(f x + e\right)^{3} + 6 \, {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + {\left(a^{2} - b^{2}\right)} d^{3}\right)} \tan\left(f x + e\right)^{2} - 12 \, {\left(6 \, a b c^{2} d - 2 \, a b d^{3} - {\left(a^{2} - b^{2}\right)} c^{3} + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} {\left(f x + e\right)} + 6 \, {\left(2 \, a b c^{3} - 6 \, a b c d^{2} + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d - {\left(a^{2} - b^{2}\right)} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 12 \, {\left(b^{2} c^{3} + 6 \, a b c^{2} d - 2 \, a b d^{3} + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*b^2*d^3*tan(f*x + e)^4 + 4*(3*b^2*c*d^2 + 2*a*b*d^3)*tan(f*x + e)^3 + 6*(3*b^2*c^2*d + 6*a*b*c*d^2 + (a^2 - b^2)*d^3)*tan(f*x + e)^2 - 12*(6*a*b*c^2*d - 2*a*b*d^3 - (a^2 - b^2)*c^3 + 3*(a^2 - b^2)*c*d^2)*(f*x + e) + 6*(2*a*b*c^3 - 6*a*b*c*d^2 + 3*(a^2 - b^2)*c^2*d - (a^2 - b^2)*d^3)*log(tan(f*x + e)^2 + 1) + 12*(b^2*c^3 + 6*a*b*c^2*d - 2*a*b*d^3 + 3*(a^2 - b^2)*c*d^2)*tan(f*x + e))/f","A",0
1205,1,143,0,0.913067," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{2 \, b d^{3} \tan\left(f x + e\right)^{3} + 3 \, {\left(3 \, b c d^{2} + a d^{3}\right)} \tan\left(f x + e\right)^{2} + 6 \, {\left(a c^{3} - 3 \, b c^{2} d - 3 \, a c d^{2} + b d^{3}\right)} {\left(f x + e\right)} + 3 \, {\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) + 6 \, {\left(3 \, b c^{2} d + 3 \, a c d^{2} - b d^{3}\right)} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*b*d^3*tan(f*x + e)^3 + 3*(3*b*c*d^2 + a*d^3)*tan(f*x + e)^2 + 6*(a*c^3 - 3*b*c^2*d - 3*a*c*d^2 + b*d^3)*(f*x + e) + 3*(b*c^3 + 3*a*c^2*d - 3*b*c*d^2 - a*d^3)*log(tan(f*x + e)^2 + 1) + 6*(3*b*c^2*d + 3*a*c*d^2 - b*d^3)*tan(f*x + e))/f","A",0
1206,1,171,0,0.945607," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\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{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(b \tan\left(f x + e\right) + a\right)}{a^{2} b^{2} + b^{4}} - \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}}}{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) + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(b*tan(f*x + e) + a)/(a^2*b^2 + b^4) - (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))/f","A",0
1207,1,308,0,0.804765," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(6 \, a b c^{2} d - 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} {\left(f x + e\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, a b^{3} c^{3} - 6 \, a b^{3} c d^{2} - 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d + {\left(a^{4} + 3 \, a^{2} b^{2}\right)} d^{3}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}} - \frac{{\left(2 \, a b c^{3} - 6 \, a b c d^{2} - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d + {\left(a^{2} - b^{2}\right)} 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(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}}{a^{3} b^{2} + a b^{4} + {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(6*a*b*c^2*d - 2*a*b*d^3 + (a^2 - b^2)*c^3 - 3*(a^2 - b^2)*c*d^2)*(f*x + e)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*a*b^3*c^3 - 6*a*b^3*c*d^2 - 3*(a^2*b^2 - b^4)*c^2*d + (a^4 + 3*a^2*b^2)*d^3)*log(b*tan(f*x + e) + a)/(a^4*b^2 + 2*a^2*b^4 + b^6) - (2*a*b*c^3 - 6*a*b*c*d^2 - 3*(a^2 - b^2)*c^2*d + (a^2 - b^2)*d^3)*log(tan(f*x + e)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(f*x + e)))/f","A",0
1208,1,533,0,0.807732," ","integrate((c+d*tan(f*x+e))^3/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} + \frac{2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}} - \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} 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{{\left(5 \, a^{2} b^{3} + b^{5}\right)} c^{3} - 3 \, {\left(3 \, a^{3} b^{2} - a b^{4}\right)} c^{2} d + 3 \, {\left(a^{4} b - 3 \, a^{2} b^{3}\right)} c d^{2} + {\left(a^{5} + 5 \, a^{3} b^{2}\right)} d^{3} + 2 \, {\left(2 \, a b^{4} c^{3} - 6 \, a b^{4} c d^{2} - 3 \, {\left(a^{2} b^{3} - b^{5}\right)} c^{2} d + {\left(a^{4} b + 3 \, a^{2} b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)}{a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6} + {\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c^3 + 3*(3*a^2*b - b^3)*c^2*d - 3*(a^3 - 3*a*b^2)*c*d^2 - (3*a^2*b - b^3)*d^3)*(f*x + e)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*((3*a^2*b - b^3)*c^3 - 3*(a^3 - 3*a*b^2)*c^2*d - 3*(3*a^2*b - b^3)*c*d^2 + (a^3 - 3*a*b^2)*d^3)*log(b*tan(f*x + e) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - ((3*a^2*b - b^3)*c^3 - 3*(a^3 - 3*a*b^2)*c^2*d - 3*(3*a^2*b - b^3)*c*d^2 + (a^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) - ((5*a^2*b^3 + b^5)*c^3 - 3*(3*a^3*b^2 - a*b^4)*c^2*d + 3*(a^4*b - 3*a^2*b^3)*c*d^2 + (a^5 + 5*a^3*b^2)*d^3 + 2*(2*a*b^4*c^3 - 6*a*b^4*c*d^2 - 3*(a^2*b^3 - b^5)*c^2*d + (a^4*b + 3*a^2*b^3)*d^3)*tan(f*x + e))/(a^6*b^2 + 2*a^4*b^4 + a^2*b^6 + (a^4*b^4 + 2*a^2*b^6 + b^8)*tan(f*x + e)^2 + 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*tan(f*x + e)))/f","B",0
1209,1,224,0,0.831685," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c + 4 \, {\left(a^{3} b - a b^{3}\right)} d\right)} {\left(f x + e\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(d \tan\left(f x + e\right) + c\right)}{c^{2} d^{3} + d^{5}} + \frac{{\left(4 \, {\left(a^{3} b - a b^{3}\right)} c - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}} + \frac{b^{4} d \tan\left(f x + e\right)^{2} - 2 \, {\left(b^{4} c - 4 \, a b^{3} d\right)} \tan\left(f x + e\right)}{d^{2}}}{2 \, f}"," ",0,"1/2*(2*((a^4 - 6*a^2*b^2 + b^4)*c + 4*(a^3*b - a*b^3)*d)*(f*x + e)/(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(d*tan(f*x + e) + c)/(c^2*d^3 + d^5) + (4*(a^3*b - a*b^3)*c - (a^4 - 6*a^2*b^2 + b^4)*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2) + (b^4*d*tan(f*x + e)^2 - 2*(b^4*c - 4*a*b^3*d)*tan(f*x + e))/d^2)/f","A",0
1210,1,174,0,0.844682," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{3} \tan\left(f x + e\right)}{d} + \frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c + {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\left(f x + e\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(d \tan\left(f x + e\right) + c\right)}{c^{2} d^{2} + d^{4}} + \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c - {\left(a^{3} - 3 \, a b^{2}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{2 \, f}"," ",0,"1/2*(2*b^3*tan(f*x + e)/d + 2*((a^3 - 3*a*b^2)*c + (3*a^2*b - b^3)*d)*(f*x + e)/(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(d*tan(f*x + e) + c)/(c^2*d^2 + d^4) + ((3*a^2*b - b^3)*c - (a^3 - 3*a*b^2)*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
1211,1,123,0,0.827145," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(2 \, a b d + {\left(a^{2} - b^{2}\right)} c\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} + \frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{2} d + d^{3}} + \frac{{\left(2 \, a b c - {\left(a^{2} - b^{2}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{2} + d^{2}}}{2 \, f}"," ",0,"1/2*(2*(2*a*b*d + (a^2 - b^2)*c)*(f*x + e)/(c^2 + d^2) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(d*tan(f*x + e) + c)/(c^2*d + d^3) + (2*a*b*c - (a^2 - b^2)*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
1212,1,88,0,0.868729," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a c + b d\right)} {\left(f x + e\right)}}{c^{2} + d^{2}} - \frac{2 \, {\left(b c - a d\right)} \log\left(d \tan\left(f x + e\right) + c\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}}}{2 \, f}"," ",0,"1/2*(2*(a*c + b*d)*(f*x + e)/(c^2 + d^2) - 2*(b*c - a*d)*log(d*tan(f*x + e) + c)/(c^2 + d^2) + (b*c - a*d)*log(tan(f*x + e)^2 + 1)/(c^2 + d^2))/f","A",0
1213,1,176,0,0.824526," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{2} b + b^{3}\right)} c - {\left(a^{3} + a b^{2}\right)} d} - \frac{2 \, d^{2} \log\left(d \tan\left(f x + e\right) + c\right)}{b c^{3} - a c^{2} d + b c d^{2} - a d^{3}} + \frac{2 \, {\left(a c - b d\right)} {\left(f x + e\right)}}{{\left(a^{2} + b^{2}\right)} c^{2} + {\left(a^{2} + b^{2}\right)} d^{2}} - \frac{{\left(b c + a d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{2} + b^{2}\right)} c^{2} + {\left(a^{2} + b^{2}\right)} d^{2}}}{2 \, f}"," ",0,"1/2*(2*b^2*log(b*tan(f*x + e) + a)/((a^2*b + b^3)*c - (a^3 + a*b^2)*d) - 2*d^2*log(d*tan(f*x + e) + c)/(b*c^3 - a*c^2*d + b*c*d^2 - a*d^3) + 2*(a*c - b*d)*(f*x + e)/((a^2 + b^2)*c^2 + (a^2 + b^2)*d^2) - (b*c + a*d)*log(tan(f*x + e)^2 + 1)/((a^2 + b^2)*c^2 + (a^2 + b^2)*d^2))/f","A",0
1214,1,384,0,0.835043," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{2 \, d^{3} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{2} c^{4} - 2 \, a b c^{3} d - 2 \, a b c d^{3} + a^{2} d^{4} + {\left(a^{2} + b^{2}\right)} c^{2} d^{2}} - \frac{2 \, {\left(2 \, a b d - {\left(a^{2} - b^{2}\right)} c\right)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}} - \frac{2 \, b^{2}}{{\left(a^{3} b + a b^{3}\right)} c - {\left(a^{4} + a^{2} b^{2}\right)} d + {\left({\left(a^{2} b^{2} + b^{4}\right)} c - {\left(a^{3} b + a b^{3}\right)} d\right)} \tan\left(f x + e\right)} + \frac{2 \, {\left(2 \, a b^{3} c - {\left(3 \, a^{2} b^{2} + b^{4}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{4} b^{2} + 2 \, a^{2} b^{4} + b^{6}\right)} c^{2} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c d + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2}} - \frac{{\left(2 \, a b c + {\left(a^{2} - b^{2}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}}{2 \, f}"," ",0,"1/2*(2*d^3*log(d*tan(f*x + e) + c)/(b^2*c^4 - 2*a*b*c^3*d - 2*a*b*c*d^3 + a^2*d^4 + (a^2 + b^2)*c^2*d^2) - 2*(2*a*b*d - (a^2 - b^2)*c)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2) - 2*b^2/((a^3*b + a*b^3)*c - (a^4 + a^2*b^2)*d + ((a^2*b^2 + b^4)*c - (a^3*b + a*b^3)*d)*tan(f*x + e)) + 2*(2*a*b^3*c - (3*a^2*b^2 + b^4)*d)*log(b*tan(f*x + e) + a)/((a^4*b^2 + 2*a^2*b^4 + b^6)*c^2 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*c*d + (a^6 + 2*a^4*b^2 + a^2*b^4)*d^2) - (2*a*b*c + (a^2 - b^2)*d)*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2))/f","B",0
1215,1,801,0,1.030012," ","integrate(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{2 \, d^{4} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c d^{4} - a^{3} d^{5} + {\left(3 \, a^{2} b + b^{3}\right)} c^{3} d^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} d^{3}} - \frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c - {\left(3 \, a^{2} b - b^{3}\right)} d\right)} {\left(f x + e\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{2}} + \frac{2 \, {\left(8 \, a^{3} b^{3} c d - {\left(3 \, a^{2} b^{4} - b^{6}\right)} c^{2} - {\left(6 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{6} b^{3} + 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} + b^{9}\right)} c^{3} - 3 \, {\left(a^{7} b^{2} + 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} + a b^{8}\right)} c^{2} d + 3 \, {\left(a^{8} b + 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} + a^{2} b^{7}\right)} c d^{2} - {\left(a^{9} + 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{3}} + \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c + {\left(a^{3} - 3 \, a b^{2}\right)} d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{2}} + \frac{{\left(5 \, a^{2} b^{3} + b^{5}\right)} c - {\left(7 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d + 2 \, {\left(2 \, a b^{4} c - {\left(3 \, a^{2} b^{3} + b^{5}\right)} d\right)} \tan\left(f x + e\right)}{{\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} - 2 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c d + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d^{2} + {\left({\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{2} - 2 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c d + {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} d^{2}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{2} - 2 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c d + {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} d^{2}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(2*d^4*log(d*tan(f*x + e) + c)/(b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c*d^4 - a^3*d^5 + (3*a^2*b + b^3)*c^3*d^2 - (a^3 + 3*a*b^2)*c^2*d^3) - 2*((a^3 - 3*a*b^2)*c - (3*a^2*b - b^3)*d)*(f*x + e)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^2) + 2*(8*a^3*b^3*c*d - (3*a^2*b^4 - b^6)*c^2 - (6*a^4*b^2 + 3*a^2*b^4 + b^6)*d^2)*log(b*tan(f*x + e) + a)/((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*c^3 - 3*(a^7*b^2 + 3*a^5*b^4 + 3*a^3*b^6 + a*b^8)*c^2*d + 3*(a^8*b + 3*a^6*b^3 + 3*a^4*b^5 + a^2*b^7)*c*d^2 - (a^9 + 3*a^7*b^2 + 3*a^5*b^4 + a^3*b^6)*d^3) + ((3*a^2*b - b^3)*c + (a^3 - 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)*c^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^2) + ((5*a^2*b^3 + b^5)*c - (7*a^3*b^2 + 3*a*b^4)*d + 2*(2*a*b^4*c - (3*a^2*b^3 + b^5)*d)*tan(f*x + e))/((a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2 - 2*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d + (a^8 + 2*a^6*b^2 + a^4*b^4)*d^2 + ((a^4*b^4 + 2*a^2*b^6 + b^8)*c^2 - 2*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c*d + (a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*d^2)*tan(f*x + e)^2 + 2*((a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^2 - 2*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c*d + (a^7*b + 2*a^5*b^3 + a^3*b^5)*d^2)*tan(f*x + e)))/f","B",0
1216,1,374,0,0.891440," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{b^{4} \tan\left(f x + e\right)}{d^{2}} + \frac{{\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{2} + 8 \, {\left(a^{3} b - a b^{3}\right)} c d - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} {\left(f x + e\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 d^{5} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} c^{2} d^{3} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c d^{4}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}} + \frac{{\left(2 \, {\left(a^{3} b - a b^{3}\right)} c^{2} - {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d - 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{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}}{c^{3} d^{3} + c d^{5} + {\left(c^{2} d^{4} + d^{6}\right)} \tan\left(f x + e\right)}}{f}"," ",0,"(b^4*tan(f*x + e)/d^2 + ((a^4 - 6*a^2*b^2 + b^4)*c^2 + 8*(a^3*b - a*b^3)*c*d - (a^4 - 6*a^2*b^2 + b^4)*d^2)*(f*x + e)/(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*d^5 + 2*(a^3*b - 3*a*b^3)*c^2*d^3 - (a^4 - 6*a^2*b^2)*c*d^4)*log(d*tan(f*x + e) + c)/(c^4*d^3 + 2*c^2*d^5 + d^7) + (2*(a^3*b - a*b^3)*c^2 - (a^4 - 6*a^2*b^2 + b^4)*c*d - 2*(a^3*b - a*b^3)*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - (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)/(c^3*d^3 + c*d^5 + (c^2*d^4 + d^6)*tan(f*x + e)))/f","A",0
1217,1,310,0,0.725844," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{2} + 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{2 \, {\left(b^{3} c^{4} + 3 \, a^{2} b d^{4} - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}} + \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c^{2} - 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d - {\left(3 \, a^{2} b - b^{3}\right)} 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^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)}}{c^{3} d^{2} + c d^{4} + {\left(c^{2} d^{3} + d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c^2 + 2*(3*a^2*b - b^3)*c*d - (a^3 - 3*a*b^2)*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) + 2*(b^3*c^4 + 3*a^2*b*d^4 - 3*(a^2*b - b^3)*c^2*d^2 + 2*(a^3 - 3*a*b^2)*c*d^3)*log(d*tan(f*x + e) + c)/(c^4*d^2 + 2*c^2*d^4 + d^6) + ((3*a^2*b - b^3)*c^2 - 2*(a^3 - 3*a*b^2)*c*d - (3*a^2*b - b^3)*d^2)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) + 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)/(c^3*d^2 + c*d^4 + (c^2*d^3 + d^5)*tan(f*x + e)))/f","A",0
1218,1,229,0,0.940521," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, a b c d + {\left(a^{2} - b^{2}\right)} c^{2} - {\left(a^{2} - b^{2}\right)} d^{2}\right)} {\left(f x + e\right)}}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{2 \, {\left(a b c^{2} - a b d^{2} - {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} + \frac{{\left(a b c^{2} - a b d^{2} - {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{c^{4} + 2 \, c^{2} d^{2} + d^{4}} - \frac{b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}}{c^{3} d + c d^{3} + {\left(c^{2} d^{2} + d^{4}\right)} \tan\left(f x + e\right)}}{f}"," ",0,"((4*a*b*c*d + (a^2 - b^2)*c^2 - (a^2 - b^2)*d^2)*(f*x + e)/(c^4 + 2*c^2*d^2 + d^4) - 2*(a*b*c^2 - a*b*d^2 - (a^2 - b^2)*c*d)*log(d*tan(f*x + e) + c)/(c^4 + 2*c^2*d^2 + d^4) + (a*b*c^2 - a*b*d^2 - (a^2 - b^2)*c*d)*log(tan(f*x + e)^2 + 1)/(c^4 + 2*c^2*d^2 + d^4) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)/(c^3*d + c*d^3 + (c^2*d^2 + d^4)*tan(f*x + e)))/f","A",0
1219,1,177,0,0.790542," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\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{2 \, {\left(b c^{2} - 2 \, a c d - b d^{2}\right)} \log\left(d \tan\left(f x + e\right) + c\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 - a d\right)}}{c^{3} + c d^{2} + {\left(c^{2} d + d^{3}\right)} \tan\left(f x + e\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) - 2*(b*c^2 - 2*a*c*d - b*d^2)*log(d*tan(f*x + e) + c)/(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 - a*d)/(c^3 + c*d^2 + (c^2*d + d^3)*tan(f*x + e)))/f","A",0
1220,1,384,0,0.754410," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, b^{3} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{2} b^{2} + b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c d + {\left(a^{4} + a^{2} b^{2}\right)} d^{2}} + \frac{2 \, {\left(a c^{2} - 2 \, b c d - a d^{2}\right)} {\left(f x + e\right)}}{{\left(a^{2} + b^{2}\right)} c^{4} + 2 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} + {\left(a^{2} + b^{2}\right)} d^{4}} + \frac{2 \, d^{2}}{b c^{4} - a c^{3} d + b c^{2} d^{2} - a c d^{3} + {\left(b c^{3} d - a c^{2} d^{2} + b c d^{3} - a d^{4}\right)} \tan\left(f x + e\right)} - \frac{2 \, {\left(3 \, b c^{2} d^{2} - 2 \, a c d^{3} + b d^{4}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{2} c^{6} - 2 \, a b c^{5} d - 4 \, a b c^{3} d^{3} - 2 \, a b c d^{5} + a^{2} d^{6} + {\left(a^{2} + 2 \, b^{2}\right)} c^{4} d^{2} + {\left(2 \, a^{2} + b^{2}\right)} c^{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)}{{\left(a^{2} + b^{2}\right)} c^{4} + 2 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} + {\left(a^{2} + b^{2}\right)} d^{4}}}{2 \, f}"," ",0,"1/2*(2*b^3*log(b*tan(f*x + e) + a)/((a^2*b^2 + b^4)*c^2 - 2*(a^3*b + a*b^3)*c*d + (a^4 + a^2*b^2)*d^2) + 2*(a*c^2 - 2*b*c*d - a*d^2)*(f*x + e)/((a^2 + b^2)*c^4 + 2*(a^2 + b^2)*c^2*d^2 + (a^2 + b^2)*d^4) + 2*d^2/(b*c^4 - a*c^3*d + b*c^2*d^2 - a*c*d^3 + (b*c^3*d - a*c^2*d^2 + b*c*d^3 - a*d^4)*tan(f*x + e)) - 2*(3*b*c^2*d^2 - 2*a*c*d^3 + b*d^4)*log(d*tan(f*x + e) + c)/(b^2*c^6 - 2*a*b*c^5*d - 4*a*b*c^3*d^3 - 2*a*b*c*d^5 + a^2*d^6 + (a^2 + 2*b^2)*c^4*d^2 + (2*a^2 + b^2)*c^2*d^4) - (b*c^2 + 2*a*c*d - b*d^2)*log(tan(f*x + e)^2 + 1)/((a^2 + b^2)*c^4 + 2*(a^2 + b^2)*c^2*d^2 + (a^2 + b^2)*d^4))/f","B",0
1221,1,878,0,0.799434," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, a b c d - {\left(a^{2} - b^{2}\right)} c^{2} + {\left(a^{2} - b^{2}\right)} d^{2}\right)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}} - \frac{2 \, {\left(a b^{4} c - {\left(2 \, a^{2} b^{3} + b^{5}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} c^{3} - 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} c^{2} d + 3 \, {\left(a^{6} b + 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} c d^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{3}} - \frac{2 \, {\left(2 \, b c^{2} d^{3} - a c d^{4} + b d^{5}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{3} c^{7} - 3 \, a b^{2} c^{6} d + 3 \, a^{2} b c d^{6} - a^{3} d^{7} + {\left(3 \, a^{2} b + 2 \, b^{3}\right)} c^{5} d^{2} - {\left(a^{3} + 6 \, a b^{2}\right)} c^{4} d^{3} + {\left(6 \, a^{2} b + b^{3}\right)} c^{3} d^{4} - {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c^{2} d^{5}} + \frac{{\left(a b c^{2} - a b d^{2} + {\left(a^{2} - b^{2}\right)} c d\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}} + \frac{b^{3} c^{3} + b^{3} c d^{2} + {\left(a^{3} + a b^{2}\right)} d^{3} + {\left(b^{3} c^{2} d + {\left(a^{2} b + 2 \, b^{3}\right)} d^{3}\right)} \tan\left(f x + e\right)}{{\left(a^{3} b^{2} + a b^{4}\right)} c^{5} - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{4} d + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c^{3} d^{2} - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} c^{2} d^{3} + {\left(a^{5} + a^{3} b^{2}\right)} c d^{4} + {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{4} d - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{3} d^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} d^{3} - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} c d^{4} + {\left(a^{4} b + a^{2} b^{3}\right)} d^{5}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(a^{2} b^{3} + b^{5}\right)} c^{5} - {\left(a^{3} b^{2} + a b^{4}\right)} c^{4} d - {\left(a^{4} b - b^{5}\right)} c^{3} d^{2} + {\left(a^{5} - a b^{4}\right)} c^{2} d^{3} - {\left(a^{4} b + a^{2} b^{3}\right)} c d^{4} + {\left(a^{5} + a^{3} b^{2}\right)} d^{5}\right)} \tan\left(f x + e\right)}}{f}"," ",0,"-((4*a*b*c*d - (a^2 - b^2)*c^2 + (a^2 - b^2)*d^2)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*c^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4) - 2*(a*b^4*c - (2*a^2*b^3 + b^5)*d)*log(b*tan(f*x + e) + a)/((a^4*b^3 + 2*a^2*b^5 + b^7)*c^3 - 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*c^2*d + 3*(a^6*b + 2*a^4*b^3 + a^2*b^5)*c*d^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^3) - 2*(2*b*c^2*d^3 - a*c*d^4 + b*d^5)*log(d*tan(f*x + e) + c)/(b^3*c^7 - 3*a*b^2*c^6*d + 3*a^2*b*c*d^6 - a^3*d^7 + (3*a^2*b + 2*b^3)*c^5*d^2 - (a^3 + 6*a*b^2)*c^4*d^3 + (6*a^2*b + b^3)*c^3*d^4 - (2*a^3 + 3*a*b^2)*c^2*d^5) + (a*b*c^2 - a*b*d^2 + (a^2 - b^2)*c*d)*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4) + (b^3*c^3 + b^3*c*d^2 + (a^3 + a*b^2)*d^3 + (b^3*c^2*d + (a^2*b + 2*b^3)*d^3)*tan(f*x + e))/((a^3*b^2 + a*b^4)*c^5 - 2*(a^4*b + a^2*b^3)*c^4*d + (a^5 + 2*a^3*b^2 + a*b^4)*c^3*d^2 - 2*(a^4*b + a^2*b^3)*c^2*d^3 + (a^5 + a^3*b^2)*c*d^4 + ((a^2*b^3 + b^5)*c^4*d - 2*(a^3*b^2 + a*b^4)*c^3*d^2 + (a^4*b + 2*a^2*b^3 + b^5)*c^2*d^3 - 2*(a^3*b^2 + a*b^4)*c*d^4 + (a^4*b + a^2*b^3)*d^5)*tan(f*x + e)^2 + ((a^2*b^3 + b^5)*c^5 - (a^3*b^2 + a*b^4)*c^4*d - (a^4*b - b^5)*c^3*d^2 + (a^5 - a*b^4)*c^2*d^3 - (a^4*b + a^2*b^3)*c*d^4 + (a^5 + a^3*b^2)*d^5)*tan(f*x + e)))/f","B",0
1222,1,1833,0,0.719629," ","integrate(1/(a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{2} - 2 \, {\left(3 \, a^{2} b - b^{3}\right)} c d - {\left(a^{3} - 3 \, a b^{2}\right)} d^{2}\right)} {\left(f x + e\right)}}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{4} + 2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}} + \frac{2 \, {\left({\left(3 \, a^{2} b^{5} - b^{7}\right)} c^{2} - 2 \, {\left(5 \, a^{3} b^{4} + a b^{6}\right)} c d + {\left(10 \, a^{4} b^{3} + 9 \, a^{2} b^{5} + 3 \, b^{7}\right)} d^{2}\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{6} b^{4} + 3 \, a^{4} b^{6} + 3 \, a^{2} b^{8} + b^{10}\right)} c^{4} - 4 \, {\left(a^{7} b^{3} + 3 \, a^{5} b^{5} + 3 \, a^{3} b^{7} + a b^{9}\right)} c^{3} d + 6 \, {\left(a^{8} b^{2} + 3 \, a^{6} b^{4} + 3 \, a^{4} b^{6} + a^{2} b^{8}\right)} c^{2} d^{2} - 4 \, {\left(a^{9} b + 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} + a^{3} b^{7}\right)} c d^{3} + {\left(a^{10} + 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} + a^{4} b^{6}\right)} d^{4}} - \frac{2 \, {\left(5 \, b c^{2} d^{4} - 2 \, a c d^{5} + 3 \, b d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{4} c^{8} - 4 \, a b^{3} c^{7} d - 4 \, a^{3} b c d^{7} + a^{4} d^{8} + 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} c^{6} d^{2} - 4 \, {\left(a^{3} b + 2 \, a b^{3}\right)} c^{5} d^{3} + {\left(a^{4} + 12 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{4} - 4 \, {\left(2 \, a^{3} b + a b^{3}\right)} c^{3} d^{5} + 2 \, {\left(a^{4} + 3 \, a^{2} b^{2}\right)} c^{2} d^{6}} - \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d - {\left(3 \, a^{2} b - b^{3}\right)} d^{2}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{4} + 2 \, {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} + {\left(a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + b^{6}\right)} d^{4}} - \frac{{\left(5 \, a^{2} b^{4} + b^{6}\right)} c^{4} - {\left(9 \, a^{3} b^{3} + 5 \, a b^{5}\right)} c^{3} d + {\left(5 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} - {\left(9 \, a^{3} b^{3} + 5 \, a b^{5}\right)} c d^{3} - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{4} + 2 \, {\left(2 \, a b^{5} c^{3} d + 2 \, a b^{5} c d^{3} - 2 \, {\left(2 \, a^{2} b^{4} + b^{6}\right)} c^{2} d^{2} - {\left(a^{4} b^{2} + 6 \, a^{2} b^{4} + 3 \, b^{6}\right)} d^{4}\right)} \tan\left(f x + e\right)^{2} + {\left(4 \, a b^{5} c^{4} - 3 \, {\left(a^{2} b^{4} + b^{6}\right)} c^{3} d - {\left(9 \, a^{3} b^{3} + a b^{5}\right)} c^{2} d^{2} - 3 \, {\left(a^{2} b^{4} + b^{6}\right)} c d^{3} - {\left(4 \, a^{5} b + 17 \, a^{3} b^{3} + 9 \, a b^{5}\right)} d^{4}\right)} \tan\left(f x + e\right)}{{\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{6} - 3 \, {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} c^{5} d + {\left(3 \, a^{8} b + 7 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{4} d^{2} - {\left(a^{9} + 5 \, a^{7} b^{2} + 7 \, a^{5} b^{4} + 3 \, a^{3} b^{6}\right)} c^{3} d^{3} + 3 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c^{2} d^{4} - {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} c d^{5} + {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{5} d - 3 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{4} d^{2} + {\left(3 \, a^{6} b^{3} + 7 \, a^{4} b^{5} + 5 \, a^{2} b^{7} + b^{9}\right)} c^{3} d^{3} - {\left(a^{7} b^{2} + 5 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + 3 \, a b^{8}\right)} c^{2} d^{4} + 3 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c d^{5} - {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} d^{6}\right)} \tan\left(f x + e\right)^{3} + {\left({\left(a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}\right)} c^{6} - {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{5} d - {\left(3 \, a^{6} b^{3} + 5 \, a^{4} b^{5} + a^{2} b^{7} - b^{9}\right)} c^{4} d^{2} + {\left(5 \, a^{7} b^{2} + 9 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} c^{3} d^{3} - {\left(2 \, a^{8} b + 7 \, a^{6} b^{3} + 8 \, a^{4} b^{5} + 3 \, a^{2} b^{7}\right)} c^{2} d^{4} + 5 \, {\left(a^{7} b^{2} + 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} c d^{5} - 2 \, {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)} c^{6} - 5 \, {\left(a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}\right)} c^{5} d + {\left(3 \, a^{7} b^{2} + 8 \, a^{5} b^{4} + 7 \, a^{3} b^{6} + 2 \, a b^{8}\right)} c^{4} d^{2} + {\left(a^{8} b - 3 \, a^{6} b^{3} - 9 \, a^{4} b^{5} - 5 \, a^{2} b^{7}\right)} c^{3} d^{3} - {\left(a^{9} - a^{7} b^{2} - 5 \, a^{5} b^{4} - 3 \, a^{3} b^{6}\right)} c^{2} d^{4} + {\left(a^{8} b + 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} c d^{5} - {\left(a^{9} + 2 \, a^{7} b^{2} + a^{5} b^{4}\right)} d^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c^2 - 2*(3*a^2*b - b^3)*c*d - (a^3 - 3*a*b^2)*d^2)*(f*x + e)/((a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^4 + 2*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4) + 2*((3*a^2*b^5 - b^7)*c^2 - 2*(5*a^3*b^4 + a*b^6)*c*d + (10*a^4*b^3 + 9*a^2*b^5 + 3*b^7)*d^2)*log(b*tan(f*x + e) + a)/((a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10)*c^4 - 4*(a^7*b^3 + 3*a^5*b^5 + 3*a^3*b^7 + a*b^9)*c^3*d + 6*(a^8*b^2 + 3*a^6*b^4 + 3*a^4*b^6 + a^2*b^8)*c^2*d^2 - 4*(a^9*b + 3*a^7*b^3 + 3*a^5*b^5 + a^3*b^7)*c*d^3 + (a^10 + 3*a^8*b^2 + 3*a^6*b^4 + a^4*b^6)*d^4) - 2*(5*b*c^2*d^4 - 2*a*c*d^5 + 3*b*d^6)*log(d*tan(f*x + e) + c)/(b^4*c^8 - 4*a*b^3*c^7*d - 4*a^3*b*c*d^7 + a^4*d^8 + 2*(3*a^2*b^2 + b^4)*c^6*d^2 - 4*(a^3*b + 2*a*b^3)*c^5*d^3 + (a^4 + 12*a^2*b^2 + b^4)*c^4*d^4 - 4*(2*a^3*b + a*b^3)*c^3*d^5 + 2*(a^4 + 3*a^2*b^2)*c^2*d^6) - ((3*a^2*b - b^3)*c^2 + 2*(a^3 - 3*a*b^2)*c*d - (3*a^2*b - 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)*c^4 + 2*(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*c^2*d^2 + (a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6)*d^4) - ((5*a^2*b^4 + b^6)*c^4 - (9*a^3*b^3 + 5*a*b^5)*c^3*d + (5*a^2*b^4 + b^6)*c^2*d^2 - (9*a^3*b^3 + 5*a*b^5)*c*d^3 - 2*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^4 + 2*(2*a*b^5*c^3*d + 2*a*b^5*c*d^3 - 2*(2*a^2*b^4 + b^6)*c^2*d^2 - (a^4*b^2 + 6*a^2*b^4 + 3*b^6)*d^4)*tan(f*x + e)^2 + (4*a*b^5*c^4 - 3*(a^2*b^4 + b^6)*c^3*d - (9*a^3*b^3 + a*b^5)*c^2*d^2 - 3*(a^2*b^4 + b^6)*c*d^3 - (4*a^5*b + 17*a^3*b^3 + 9*a*b^5)*d^4)*tan(f*x + e))/((a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c^6 - 3*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*c^5*d + (3*a^8*b + 7*a^6*b^3 + 5*a^4*b^5 + a^2*b^7)*c^4*d^2 - (a^9 + 5*a^7*b^2 + 7*a^5*b^4 + 3*a^3*b^6)*c^3*d^3 + 3*(a^8*b + 2*a^6*b^3 + a^4*b^5)*c^2*d^4 - (a^9 + 2*a^7*b^2 + a^5*b^4)*c*d^5 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^5*d - 3*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^4*d^2 + (3*a^6*b^3 + 7*a^4*b^5 + 5*a^2*b^7 + b^9)*c^3*d^3 - (a^7*b^2 + 5*a^5*b^4 + 7*a^3*b^6 + 3*a*b^8)*c^2*d^4 + 3*(a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c*d^5 - (a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*d^6)*tan(f*x + e)^3 + ((a^4*b^5 + 2*a^2*b^7 + b^9)*c^6 - (a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^5*d - (3*a^6*b^3 + 5*a^4*b^5 + a^2*b^7 - b^9)*c^4*d^2 + (5*a^7*b^2 + 9*a^5*b^4 + 3*a^3*b^6 - a*b^8)*c^3*d^3 - (2*a^8*b + 7*a^6*b^3 + 8*a^4*b^5 + 3*a^2*b^7)*c^2*d^4 + 5*(a^7*b^2 + 2*a^5*b^4 + a^3*b^6)*c*d^5 - 2*(a^8*b + 2*a^6*b^3 + a^4*b^5)*d^6)*tan(f*x + e)^2 + (2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)*c^6 - 5*(a^6*b^3 + 2*a^4*b^5 + a^2*b^7)*c^5*d + (3*a^7*b^2 + 8*a^5*b^4 + 7*a^3*b^6 + 2*a*b^8)*c^4*d^2 + (a^8*b - 3*a^6*b^3 - 9*a^4*b^5 - 5*a^2*b^7)*c^3*d^3 - (a^9 - a^7*b^2 - 5*a^5*b^4 - 3*a^3*b^6)*c^2*d^4 + (a^8*b + 2*a^6*b^3 + a^4*b^5)*c*d^5 - (a^9 + 2*a^7*b^2 + a^5*b^4)*d^6)*tan(f*x + e)))/f","B",0
1223,1,640,0,0.994762," ","integrate((a+b*tan(f*x+e))^4/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{3} + 12 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c d^{2} - 4 \, {\left(a^{3} b - a b^{3}\right)} d^{3}\right)} {\left(f x + e\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 \, {\left(a^{3} b - a b^{3}\right)} c^{3} d^{3} + 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 2 \, b^{4}\right)} c^{2} d^{4} + 12 \, {\left(a^{3} b - a b^{3}\right)} c d^{5} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} d^{3} + 3 \, c^{4} d^{5} + 3 \, c^{2} d^{7} + d^{9}} + \frac{{\left(4 \, {\left(a^{3} b - a b^{3}\right)} c^{3} - 3 \, {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} c^{2} d - 12 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} + {\left(a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} 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{3 \, b^{4} c^{6} - 4 \, a b^{3} c^{5} d - 4 \, a^{3} b c d^{5} - a^{4} d^{6} - {\left(6 \, a^{2} b^{2} - 7 \, b^{4}\right)} c^{4} d^{2} + 4 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} c^{3} d^{3} - {\left(5 \, a^{4} - 18 \, a^{2} b^{2}\right)} c^{2} d^{4} + 4 \, {\left(b^{4} c^{5} d - 2 \, a b^{3} c^{4} d^{2} + 2 \, b^{4} c^{3} d^{3} - 2 \, a^{3} b d^{6} + 2 \, {\left(a^{3} b - 3 \, a b^{3}\right)} c^{2} d^{4} - {\left(a^{4} - 6 \, a^{2} b^{2}\right)} c d^{5}\right)} \tan\left(f x + e\right)}{c^{6} d^{3} + 2 \, c^{4} d^{5} + c^{2} d^{7} + {\left(c^{4} d^{5} + 2 \, c^{2} d^{7} + d^{9}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{4} + 2 \, c^{3} d^{6} + c d^{8}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^4 - 6*a^2*b^2 + b^4)*c^3 + 12*(a^3*b - a*b^3)*c^2*d - 3*(a^4 - 6*a^2*b^2 + b^4)*c*d^2 - 4*(a^3*b - a*b^3)*d^3)*(f*x + e)/(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 - a*b^3)*c^3*d^3 + 3*(a^4 - 6*a^2*b^2 + 2*b^4)*c^2*d^4 + 12*(a^3*b - a*b^3)*c*d^5 - (a^4 - 6*a^2*b^2)*d^6)*log(d*tan(f*x + e) + c)/(c^6*d^3 + 3*c^4*d^5 + 3*c^2*d^7 + d^9) + (4*(a^3*b - a*b^3)*c^3 - 3*(a^4 - 6*a^2*b^2 + b^4)*c^2*d - 12*(a^3*b - a*b^3)*c*d^2 + (a^4 - 6*a^2*b^2 + 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) + (3*b^4*c^6 - 4*a*b^3*c^5*d - 4*a^3*b*c*d^5 - a^4*d^6 - (6*a^2*b^2 - 7*b^4)*c^4*d^2 + 4*(3*a^3*b - 5*a*b^3)*c^3*d^3 - (5*a^4 - 18*a^2*b^2)*c^2*d^4 + 4*(b^4*c^5*d - 2*a*b^3*c^4*d^2 + 2*b^4*c^3*d^3 - 2*a^3*b*d^6 + 2*(a^3*b - 3*a*b^3)*c^2*d^4 - (a^4 - 6*a^2*b^2)*c*d^5)*tan(f*x + e))/(c^6*d^3 + 2*c^4*d^5 + c^2*d^7 + (c^4*d^5 + 2*c^2*d^7 + d^9)*tan(f*x + e)^2 + 2*(c^5*d^4 + 2*c^3*d^6 + c*d^8)*tan(f*x + e)))/f","A",0
1224,1,528,0,0.954216," ","integrate((a+b*tan(f*x+e))^3/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left({\left(a^{3} - 3 \, a b^{2}\right)} c^{3} + 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c^{2} d - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{2} - {\left(3 \, a^{2} b - b^{3}\right)} d^{3}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left({\left(3 \, a^{2} b - b^{3}\right)} c^{3} - 3 \, {\left(a^{3} - 3 \, a b^{2}\right)} c^{2} d - 3 \, {\left(3 \, a^{2} b - b^{3}\right)} c d^{2} + {\left(a^{3} - 3 \, a b^{2}\right)} 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{b^{3} c^{5} + 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c d^{4} + a^{3} d^{5} - {\left(9 \, a^{2} b - 5 \, b^{3}\right)} c^{3} d^{2} + {\left(5 \, a^{3} - 9 \, a b^{2}\right)} c^{2} d^{3} + 2 \, {\left(b^{3} c^{4} d + 3 \, a^{2} b d^{5} - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2}\right)} c d^{4}\right)} \tan\left(f x + e\right)}{c^{6} d^{2} + 2 \, c^{4} d^{4} + c^{2} d^{6} + {\left(c^{4} d^{4} + 2 \, c^{2} d^{6} + d^{8}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{3} + 2 \, c^{3} d^{5} + c d^{7}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*((a^3 - 3*a*b^2)*c^3 + 3*(3*a^2*b - b^3)*c^2*d - 3*(a^3 - 3*a*b^2)*c*d^2 - (3*a^2*b - b^3)*d^3)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*((3*a^2*b - b^3)*c^3 - 3*(a^3 - 3*a*b^2)*c^2*d - 3*(3*a^2*b - b^3)*c*d^2 + (a^3 - 3*a*b^2)*d^3)*log(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + ((3*a^2*b - b^3)*c^3 - 3*(a^3 - 3*a*b^2)*c^2*d - 3*(3*a^2*b - b^3)*c*d^2 + (a^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) - (b^3*c^5 + 3*a*b^2*c^4*d + 3*a^2*b*c*d^4 + a^3*d^5 - (9*a^2*b - 5*b^3)*c^3*d^2 + (5*a^3 - 9*a*b^2)*c^2*d^3 + 2*(b^3*c^4*d + 3*a^2*b*d^5 - 3*(a^2*b - b^3)*c^2*d^3 + 2*(a^3 - 3*a*b^2)*c*d^4)*tan(f*x + e))/(c^6*d^2 + 2*c^4*d^4 + c^2*d^6 + (c^4*d^4 + 2*c^2*d^6 + d^8)*tan(f*x + e)^2 + 2*(c^5*d^3 + 2*c^3*d^5 + c*d^7)*tan(f*x + e)))/f","B",0
1225,1,416,0,0.986669," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(6 \, a b c^{2} d - 2 \, a b d^{3} + {\left(a^{2} - b^{2}\right)} c^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} {\left(f x + e\right)}}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} - \frac{2 \, {\left(2 \, a b c^{3} - 6 \, a b c d^{2} - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d + {\left(a^{2} - b^{2}\right)} d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{c^{6} + 3 \, c^{4} d^{2} + 3 \, c^{2} d^{4} + d^{6}} + \frac{{\left(2 \, a b c^{3} - 6 \, a b c d^{2} - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d + {\left(a^{2} - b^{2}\right)} 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{b^{2} c^{4} - 6 \, a b c^{3} d + 2 \, a b c d^{3} + a^{2} d^{4} + {\left(5 \, a^{2} - 3 \, b^{2}\right)} c^{2} d^{2} - 4 \, {\left(a b c^{2} d^{2} - a b d^{4} - {\left(a^{2} - b^{2}\right)} c d^{3}\right)} \tan\left(f x + e\right)}{c^{6} d + 2 \, c^{4} d^{3} + c^{2} d^{5} + {\left(c^{4} d^{3} + 2 \, c^{2} d^{5} + d^{7}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d^{2} + 2 \, c^{3} d^{4} + c d^{6}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*(6*a*b*c^2*d - 2*a*b*d^3 + (a^2 - b^2)*c^3 - 3*(a^2 - b^2)*c*d^2)*(f*x + e)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) - 2*(2*a*b*c^3 - 6*a*b*c*d^2 - 3*(a^2 - b^2)*c^2*d + (a^2 - b^2)*d^3)*log(d*tan(f*x + e) + c)/(c^6 + 3*c^4*d^2 + 3*c^2*d^4 + d^6) + (2*a*b*c^3 - 6*a*b*c*d^2 - 3*(a^2 - b^2)*c^2*d + (a^2 - 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) - (b^2*c^4 - 6*a*b*c^3*d + 2*a*b*c*d^3 + a^2*d^4 + (5*a^2 - 3*b^2)*c^2*d^2 - 4*(a*b*c^2*d^2 - a*b*d^4 - (a^2 - b^2)*c*d^3)*tan(f*x + e))/(c^6*d + 2*c^4*d^3 + c^2*d^5 + (c^4*d^3 + 2*c^2*d^5 + d^7)*tan(f*x + e)^2 + 2*(c^5*d^2 + 2*c^3*d^4 + c*d^6)*tan(f*x + e)))/f","A",0
1226,1,321,0,0.663961," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\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{2 \, {\left(b c^{3} - 3 \, a c^{2} d - 3 \, b c d^{2} + a d^{3}\right)} \log\left(d \tan\left(f x + e\right) + c\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{3 \, b c^{3} - 5 \, a c^{2} d - b c d^{2} - a d^{3} + 2 \, {\left(b c^{2} d - 2 \, a c d^{2} - b d^{3}\right)} \tan\left(f x + e\right)}{c^{6} + 2 \, c^{4} d^{2} + c^{2} d^{4} + {\left(c^{4} d^{2} + 2 \, c^{2} d^{4} + d^{6}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(c^{5} d + 2 \, c^{3} d^{3} + c d^{5}\right)} \tan\left(f x + e\right)}}{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) - 2*(b*c^3 - 3*a*c^2*d - 3*b*c*d^2 + a*d^3)*log(d*tan(f*x + e) + c)/(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) + (3*b*c^3 - 5*a*c^2*d - b*c*d^2 - a*d^3 + 2*(b*c^2*d - 2*a*c*d^2 - b*d^3)*tan(f*x + e))/(c^6 + 2*c^4*d^2 + c^2*d^4 + (c^4*d^2 + 2*c^2*d^4 + d^6)*tan(f*x + e)^2 + 2*(c^5*d + 2*c^3*d^3 + c*d^5)*tan(f*x + e)))/f","A",0
1227,1,799,0,0.748748," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, b^{4} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{2} b^{3} + b^{5}\right)} c^{3} - 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} c^{2} d + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} c d^{2} - {\left(a^{5} + a^{3} b^{2}\right)} 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)}}{{\left(a^{2} + b^{2}\right)} c^{6} + 3 \, {\left(a^{2} + b^{2}\right)} c^{4} d^{2} + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{4} + {\left(a^{2} + b^{2}\right)} d^{6}} - \frac{2 \, {\left(6 \, b^{2} c^{4} d^{2} - 8 \, a b c^{3} d^{3} + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{4} - {\left(a^{2} - b^{2}\right)} d^{6}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{3} c^{9} - 3 \, a b^{2} c^{8} d + 3 \, a^{2} b c d^{8} - a^{3} d^{9} + 3 \, {\left(a^{2} b + b^{3}\right)} c^{7} d^{2} - {\left(a^{3} + 9 \, a b^{2}\right)} c^{6} d^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} c^{5} d^{4} - 3 \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{4} d^{5} + {\left(9 \, a^{2} b + b^{3}\right)} c^{3} d^{6} - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{7}} - \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)}{{\left(a^{2} + b^{2}\right)} c^{6} + 3 \, {\left(a^{2} + b^{2}\right)} c^{4} d^{2} + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{4} + {\left(a^{2} + b^{2}\right)} d^{6}} + \frac{7 \, b c^{3} d^{2} - 5 \, a c^{2} d^{3} + 3 \, b c d^{4} - a d^{5} + 2 \, {\left(3 \, b c^{2} d^{3} - 2 \, a c d^{4} + b d^{5}\right)} \tan\left(f x + e\right)}{b^{2} c^{8} - 2 \, a b c^{7} d - 4 \, a b c^{5} d^{3} - 2 \, a b c^{3} d^{5} + a^{2} c^{2} d^{6} + {\left(a^{2} + 2 \, b^{2}\right)} c^{6} d^{2} + {\left(2 \, a^{2} + b^{2}\right)} c^{4} d^{4} + {\left(b^{2} c^{6} d^{2} - 2 \, a b c^{5} d^{3} - 4 \, a b c^{3} d^{5} - 2 \, a b c d^{7} + a^{2} d^{8} + {\left(a^{2} + 2 \, b^{2}\right)} c^{4} d^{4} + {\left(2 \, a^{2} + b^{2}\right)} c^{2} d^{6}\right)} \tan\left(f x + e\right)^{2} + 2 \, {\left(b^{2} c^{7} d - 2 \, a b c^{6} d^{2} - 4 \, a b c^{4} d^{4} - 2 \, a b c^{2} d^{6} + a^{2} c d^{7} + {\left(a^{2} + 2 \, b^{2}\right)} c^{5} d^{3} + {\left(2 \, a^{2} + b^{2}\right)} c^{3} d^{5}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"1/2*(2*b^4*log(b*tan(f*x + e) + a)/((a^2*b^3 + b^5)*c^3 - 3*(a^3*b^2 + a*b^4)*c^2*d + 3*(a^4*b + a^2*b^3)*c*d^2 - (a^5 + a^3*b^2)*d^3) + 2*(a*c^3 - 3*b*c^2*d - 3*a*c*d^2 + b*d^3)*(f*x + e)/((a^2 + b^2)*c^6 + 3*(a^2 + b^2)*c^4*d^2 + 3*(a^2 + b^2)*c^2*d^4 + (a^2 + b^2)*d^6) - 2*(6*b^2*c^4*d^2 - 8*a*b*c^3*d^3 + 3*(a^2 + b^2)*c^2*d^4 - (a^2 - b^2)*d^6)*log(d*tan(f*x + e) + c)/(b^3*c^9 - 3*a*b^2*c^8*d + 3*a^2*b*c*d^8 - a^3*d^9 + 3*(a^2*b + b^3)*c^7*d^2 - (a^3 + 9*a*b^2)*c^6*d^3 + 3*(3*a^2*b + b^3)*c^5*d^4 - 3*(a^3 + 3*a*b^2)*c^4*d^5 + (9*a^2*b + b^3)*c^3*d^6 - 3*(a^3 + a*b^2)*c^2*d^7) - (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)*c^6 + 3*(a^2 + b^2)*c^4*d^2 + 3*(a^2 + b^2)*c^2*d^4 + (a^2 + b^2)*d^6) + (7*b*c^3*d^2 - 5*a*c^2*d^3 + 3*b*c*d^4 - a*d^5 + 2*(3*b*c^2*d^3 - 2*a*c*d^4 + b*d^5)*tan(f*x + e))/(b^2*c^8 - 2*a*b*c^7*d - 4*a*b*c^5*d^3 - 2*a*b*c^3*d^5 + a^2*c^2*d^6 + (a^2 + 2*b^2)*c^6*d^2 + (2*a^2 + b^2)*c^4*d^4 + (b^2*c^6*d^2 - 2*a*b*c^5*d^3 - 4*a*b*c^3*d^5 - 2*a*b*c*d^7 + a^2*d^8 + (a^2 + 2*b^2)*c^4*d^4 + (2*a^2 + b^2)*c^2*d^6)*tan(f*x + e)^2 + 2*(b^2*c^7*d - 2*a*b*c^6*d^2 - 4*a*b*c^4*d^4 - 2*a*b*c^2*d^6 + a^2*c*d^7 + (a^2 + 2*b^2)*c^5*d^3 + (2*a^2 + b^2)*c^3*d^5)*tan(f*x + e)))/f","B",0
1228,1,1849,0,0.623560," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(6 \, a b c^{2} d - 2 \, a b d^{3} - {\left(a^{2} - b^{2}\right)} c^{3} + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2}\right)} {\left(f x + e\right)}}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{6}} - \frac{2 \, {\left(2 \, a b^{5} c - {\left(5 \, a^{2} b^{4} + 3 \, b^{6}\right)} d\right)} \log\left(b \tan\left(f x + e\right) + a\right)}{{\left(a^{4} b^{4} + 2 \, a^{2} b^{6} + b^{8}\right)} c^{4} - 4 \, {\left(a^{5} b^{3} + 2 \, a^{3} b^{5} + a b^{7}\right)} c^{3} d + 6 \, {\left(a^{6} b^{2} + 2 \, a^{4} b^{4} + a^{2} b^{6}\right)} c^{2} d^{2} - 4 \, {\left(a^{7} b + 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} c d^{3} + {\left(a^{8} + 2 \, a^{6} b^{2} + a^{4} b^{4}\right)} d^{4}} - \frac{2 \, {\left(10 \, b^{2} c^{4} d^{3} - 10 \, a b c^{3} d^{4} - 2 \, a b c d^{6} + 3 \, {\left(a^{2} + 3 \, b^{2}\right)} c^{2} d^{5} - {\left(a^{2} - 3 \, b^{2}\right)} d^{7}\right)} \log\left(d \tan\left(f x + e\right) + c\right)}{b^{4} c^{10} - 4 \, a b^{3} c^{9} d - 4 \, a^{3} b c d^{9} + a^{4} d^{10} + 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} c^{8} d^{2} - 4 \, {\left(a^{3} b + 3 \, a b^{3}\right)} c^{7} d^{3} + {\left(a^{4} + 18 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{6} d^{4} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{5} d^{5} + {\left(3 \, a^{4} + 18 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{6} - 4 \, {\left(3 \, a^{3} b + a b^{3}\right)} c^{3} d^{7} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c^{2} d^{8}} + \frac{{\left(2 \, a b c^{3} - 6 \, a b c d^{2} + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d - {\left(a^{2} - b^{2}\right)} d^{3}\right)} \log\left(\tan\left(f x + e\right)^{2} + 1\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{6} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{4} d^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{6}} + \frac{2 \, b^{4} c^{6} + 4 \, b^{4} c^{4} d^{2} + 9 \, {\left(a^{3} b + a b^{3}\right)} c^{3} d^{3} - {\left(5 \, a^{4} + 5 \, a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} d^{4} + 5 \, {\left(a^{3} b + a b^{3}\right)} c d^{5} - {\left(a^{4} + a^{2} b^{2}\right)} d^{6} + 2 \, {\left(b^{4} c^{4} d^{2} + 2 \, {\left(2 \, a^{2} b^{2} + 3 \, b^{4}\right)} c^{2} d^{4} - 2 \, {\left(a^{3} b + a b^{3}\right)} c d^{5} + {\left(2 \, a^{2} b^{2} + 3 \, b^{4}\right)} d^{6}\right)} \tan\left(f x + e\right)^{2} + {\left(4 \, b^{4} c^{5} d + {\left(9 \, a^{2} b^{2} + 17 \, b^{4}\right)} c^{3} d^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d^{4} - {\left(4 \, a^{4} - a^{2} b^{2} - 9 \, b^{4}\right)} c d^{5} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{6}\right)} \tan\left(f x + e\right)}{{\left(a^{3} b^{3} + a b^{5}\right)} c^{9} - 3 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c^{8} d + {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} c^{7} d^{2} - {\left(a^{6} + 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} c^{6} d^{3} + {\left(6 \, a^{5} b + 7 \, a^{3} b^{3} + a b^{5}\right)} c^{5} d^{4} - {\left(2 \, a^{6} + 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} c^{4} d^{5} + 3 \, {\left(a^{5} b + a^{3} b^{3}\right)} c^{3} d^{6} - {\left(a^{6} + a^{4} b^{2}\right)} c^{2} d^{7} + {\left({\left(a^{2} b^{4} + b^{6}\right)} c^{7} d^{2} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{6} d^{3} + {\left(3 \, a^{4} b^{2} + 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} c^{5} d^{4} - {\left(a^{5} b + 7 \, a^{3} b^{3} + 6 \, a b^{5}\right)} c^{4} d^{5} + {\left(6 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + b^{6}\right)} c^{3} d^{6} - {\left(2 \, a^{5} b + 5 \, a^{3} b^{3} + 3 \, a b^{5}\right)} c^{2} d^{7} + 3 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} c d^{8} - {\left(a^{5} b + a^{3} b^{3}\right)} d^{9}\right)} \tan\left(f x + e\right)^{3} + {\left(2 \, {\left(a^{2} b^{4} + b^{6}\right)} c^{8} d - 5 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{7} d^{2} + {\left(3 \, a^{4} b^{2} + 7 \, a^{2} b^{4} + 4 \, b^{6}\right)} c^{6} d^{3} + {\left(a^{5} b - 9 \, a^{3} b^{3} - 10 \, a b^{5}\right)} c^{5} d^{4} - {\left(a^{6} - 5 \, a^{4} b^{2} - 8 \, a^{2} b^{4} - 2 \, b^{6}\right)} c^{4} d^{5} + {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} - 5 \, a b^{5}\right)} c^{3} d^{6} - {\left(2 \, a^{6} - a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} c^{2} d^{7} + {\left(a^{5} b + a^{3} b^{3}\right)} c d^{8} - {\left(a^{6} + a^{4} b^{2}\right)} d^{9}\right)} \tan\left(f x + e\right)^{2} + {\left({\left(a^{2} b^{4} + b^{6}\right)} c^{9} - {\left(a^{3} b^{3} + a b^{5}\right)} c^{8} d - {\left(3 \, a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{7} d^{2} + {\left(5 \, a^{5} b + 3 \, a^{3} b^{3} - 2 \, a b^{5}\right)} c^{6} d^{3} - {\left(2 \, a^{6} + 8 \, a^{4} b^{2} + 5 \, a^{2} b^{4} - b^{6}\right)} c^{5} d^{4} + {\left(10 \, a^{5} b + 9 \, a^{3} b^{3} - a b^{5}\right)} c^{4} d^{5} - {\left(4 \, a^{6} + 7 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} c^{3} d^{6} + 5 \, {\left(a^{5} b + a^{3} b^{3}\right)} c^{2} d^{7} - 2 \, {\left(a^{6} + a^{4} b^{2}\right)} c d^{8}\right)} \tan\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(2*(6*a*b*c^2*d - 2*a*b*d^3 - (a^2 - b^2)*c^3 + 3*(a^2 - b^2)*c*d^2)*(f*x + e)/((a^4 + 2*a^2*b^2 + b^4)*c^6 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^4 + (a^4 + 2*a^2*b^2 + b^4)*d^6) - 2*(2*a*b^5*c - (5*a^2*b^4 + 3*b^6)*d)*log(b*tan(f*x + e) + a)/((a^4*b^4 + 2*a^2*b^6 + b^8)*c^4 - 4*(a^5*b^3 + 2*a^3*b^5 + a*b^7)*c^3*d + 6*(a^6*b^2 + 2*a^4*b^4 + a^2*b^6)*c^2*d^2 - 4*(a^7*b + 2*a^5*b^3 + a^3*b^5)*c*d^3 + (a^8 + 2*a^6*b^2 + a^4*b^4)*d^4) - 2*(10*b^2*c^4*d^3 - 10*a*b*c^3*d^4 - 2*a*b*c*d^6 + 3*(a^2 + 3*b^2)*c^2*d^5 - (a^2 - 3*b^2)*d^7)*log(d*tan(f*x + e) + c)/(b^4*c^10 - 4*a*b^3*c^9*d - 4*a^3*b*c*d^9 + a^4*d^10 + 3*(2*a^2*b^2 + b^4)*c^8*d^2 - 4*(a^3*b + 3*a*b^3)*c^7*d^3 + (a^4 + 18*a^2*b^2 + 3*b^4)*c^6*d^4 - 12*(a^3*b + a*b^3)*c^5*d^5 + (3*a^4 + 18*a^2*b^2 + b^4)*c^4*d^6 - 4*(3*a^3*b + a*b^3)*c^3*d^7 + 3*(a^4 + 2*a^2*b^2)*c^2*d^8) + (2*a*b*c^3 - 6*a*b*c*d^2 + 3*(a^2 - b^2)*c^2*d - (a^2 - b^2)*d^3)*log(tan(f*x + e)^2 + 1)/((a^4 + 2*a^2*b^2 + b^4)*c^6 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^4*d^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d^4 + (a^4 + 2*a^2*b^2 + b^4)*d^6) + (2*b^4*c^6 + 4*b^4*c^4*d^2 + 9*(a^3*b + a*b^3)*c^3*d^3 - (5*a^4 + 5*a^2*b^2 - 2*b^4)*c^2*d^4 + 5*(a^3*b + a*b^3)*c*d^5 - (a^4 + a^2*b^2)*d^6 + 2*(b^4*c^4*d^2 + 2*(2*a^2*b^2 + 3*b^4)*c^2*d^4 - 2*(a^3*b + a*b^3)*c*d^5 + (2*a^2*b^2 + 3*b^4)*d^6)*tan(f*x + e)^2 + (4*b^4*c^5*d + (9*a^2*b^2 + 17*b^4)*c^3*d^3 + 3*(a^3*b + a*b^3)*c^2*d^4 - (4*a^4 - a^2*b^2 - 9*b^4)*c*d^5 + 3*(a^3*b + a*b^3)*d^6)*tan(f*x + e))/((a^3*b^3 + a*b^5)*c^9 - 3*(a^4*b^2 + a^2*b^4)*c^8*d + (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*c^7*d^2 - (a^6 + 7*a^4*b^2 + 6*a^2*b^4)*c^6*d^3 + (6*a^5*b + 7*a^3*b^3 + a*b^5)*c^5*d^4 - (2*a^6 + 5*a^4*b^2 + 3*a^2*b^4)*c^4*d^5 + 3*(a^5*b + a^3*b^3)*c^3*d^6 - (a^6 + a^4*b^2)*c^2*d^7 + ((a^2*b^4 + b^6)*c^7*d^2 - 3*(a^3*b^3 + a*b^5)*c^6*d^3 + (3*a^4*b^2 + 5*a^2*b^4 + 2*b^6)*c^5*d^4 - (a^5*b + 7*a^3*b^3 + 6*a*b^5)*c^4*d^5 + (6*a^4*b^2 + 7*a^2*b^4 + b^6)*c^3*d^6 - (2*a^5*b + 5*a^3*b^3 + 3*a*b^5)*c^2*d^7 + 3*(a^4*b^2 + a^2*b^4)*c*d^8 - (a^5*b + a^3*b^3)*d^9)*tan(f*x + e)^3 + (2*(a^2*b^4 + b^6)*c^8*d - 5*(a^3*b^3 + a*b^5)*c^7*d^2 + (3*a^4*b^2 + 7*a^2*b^4 + 4*b^6)*c^6*d^3 + (a^5*b - 9*a^3*b^3 - 10*a*b^5)*c^5*d^4 - (a^6 - 5*a^4*b^2 - 8*a^2*b^4 - 2*b^6)*c^4*d^5 + (2*a^5*b - 3*a^3*b^3 - 5*a*b^5)*c^3*d^6 - (2*a^6 - a^4*b^2 - 3*a^2*b^4)*c^2*d^7 + (a^5*b + a^3*b^3)*c*d^8 - (a^6 + a^4*b^2)*d^9)*tan(f*x + e)^2 + ((a^2*b^4 + b^6)*c^9 - (a^3*b^3 + a*b^5)*c^8*d - (3*a^4*b^2 + a^2*b^4 - 2*b^6)*c^7*d^2 + (5*a^5*b + 3*a^3*b^3 - 2*a*b^5)*c^6*d^3 - (2*a^6 + 8*a^4*b^2 + 5*a^2*b^4 - b^6)*c^5*d^4 + (10*a^5*b + 9*a^3*b^3 - a*b^5)*c^4*d^5 - (4*a^6 + 7*a^4*b^2 + 3*a^2*b^4)*c^3*d^6 + 5*(a^5*b + a^3*b^3)*c^2*d^7 - 2*(a^6 + a^4*b^2)*c*d^8)*tan(f*x + e)))/f","B",0
1229,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{3} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^3*sqrt(d*tan(f*x + e) + c), x)","F",0
1230,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*sqrt(d*tan(f*x + e) + c), x)","F",0
1231,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",0
1232,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1233,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1234,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{2} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2*(d*tan(f*x + e) + c)^(3/2), x)","F",0
1237,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",0
1238,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1239,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1240,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1243,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",0
1244,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1245,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1246,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{2}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^2/sqrt(d*tan(f*x + e) + c), x)","F",0
1250,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",0
1251,-2,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1256,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",0
1257,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1258,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^2/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1262,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(d-c>0)', see `assume?` for more details)Is d-c positive, negative or zero?","F(-2)",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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(a*d-b*c>0)', see `assume?` for more details)Is a*d-b*c positive or negative?","F(-2)",0
1265,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(5/2)*sqrt(d*tan(f*x + e) + c), x)","F",0
1266,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(3/2)*sqrt(d*tan(f*x + e) + c), x)","F",0
1267,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right) + a} \sqrt{d \tan\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e) + a)*sqrt(d*tan(f*x + e) + c), x)","F",0
1268,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1269,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1270,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1271,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(3/2)*(d*tan(f*x + e) + c)^(3/2), x)","F",0
1272,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(3/2), x)","F",0
1273,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{b \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(3/2)/sqrt(b*tan(f*x + e) + a), x)","F",0
1274,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1275,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1276,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(3/2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1277,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(3/2)*(d*tan(f*x + e) + c)^(5/2), x)","F",0
1278,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)*(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \sqrt{b \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate(sqrt(b*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(5/2), x)","F",0
1279,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{b \tan\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(5/2)/sqrt(b*tan(f*x + e) + a), x)","F",0
1280,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(5/2)/(b*tan(f*x + e) + a)^(3/2), x)","F",0
1281,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1282,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(5/2)/(a+b*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1283,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(5/2)/sqrt(d*tan(f*x + e) + c), x)","F",0
1284,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(3/2)/sqrt(d*tan(f*x + e) + c), x)","F",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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","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=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","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=""maxima"")","\int \frac{1}{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*tan(f*x + e) + a)^(3/2)*sqrt(d*tan(f*x + e) + c)), x)","F",0
1288,0,0,0,0.000000," ","integrate(1/(c+d*tan(f*x+e))^(1/2)/(a+b*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(1/((b*tan(f*x + e) + a)^(5/2)*sqrt(d*tan(f*x + e) + c)), x)","F",0
1289,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(7/2)/(d*tan(f*x + e) + c)^(3/2), x)","F",0
1290,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(5/2)/(d*tan(f*x + e) + c)^(3/2), x)","F",0
1291,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1292,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1293,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(3/2)), x)","F",0
1294,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1295,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(f*x + e) + a)^(5/2)*(d*tan(f*x + e) + c)^(3/2)), x)","F",0
1296,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(9/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(7/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^(7/2)/(d*tan(f*x + e) + c)^(5/2), x)","F",0
1298,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1299,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1300,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1301,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(1/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \tan\left(f x + e\right) + a} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*tan(f*x + e) + a)*(d*tan(f*x + e) + c)^(5/2)), x)","F",0
1302,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(3/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((b*tan(f*x + e) + a)^(3/2)*(d*tan(f*x + e) + c)^(5/2)), x)","F",0
1303,-2,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e))^(5/2)/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(((2*b*d+2*a*c)^2>0)', see `assume?` for more details)Is ((2*b*d+2*a*c)^2    -4*((a*c-b*d)^2       -((-a*d)-b*c)        *(a*d+b*c)))    ^2 positive or zero?","F(-2)",0
1304,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^n,x, algorithm=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m*(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((d*tan(f*x + e) + c)^(3/2)*(b*tan(f*x + e) + a)^m, x)","F",0
1313,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))^(1/2)*(a+b*tan(f*x+e))^m,x, algorithm=""maxima"")","\int \sqrt{d \tan\left(f x + e\right) + c} {\left(b \tan\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate(sqrt(d*tan(f*x + e) + c)*(b*tan(f*x + e) + a)^m, x)","F",0
1314,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \tan\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m/sqrt(d*tan(f*x + e) + c), x)","F",0
1315,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^(3/2), x)","F",0
1316,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))^m/(c+d*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(b \tan\left(f x + e\right) + a\right)}^{m}}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((b*tan(f*x + e) + a)^m/(d*tan(f*x + e) + c)^(5/2), x)","F",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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,-2,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
1322,-2,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",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=""maxima"")","\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,-1,0,0,0.000000," ","integrate((c*(d*tan(f*x+e))^p)^n*(a+b*tan(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\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
