1,1,82,0,0.754983," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-2 i \, B a \tan\left(d x + c\right)^{3} - {\left(3 i \, A + 3 \, B\right)} a \tan\left(d x + c\right)^{2} + 6 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a + 3 \, {\left(i \, A + B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(A - i \, B\right)} a \tan\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(-2*I*B*a*tan(d*x + c)^3 - (3*I*A + 3*B)*a*tan(d*x + c)^2 + 6*(d*x + c)*(A - I*B)*a + 3*(I*A + B)*a*log(tan(d*x + c)^2 + 1) - 6*(A - I*B)*a*tan(d*x + c))/d","A",0
2,1,68,0,0.861723," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-i \, B a \tan\left(d x + c\right)^{2} - 2 \, {\left(d x + c\right)} {\left(-i \, A - B\right)} a - {\left(A - i \, B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - {\left(2 i \, A + 2 \, B\right)} a \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(-I*B*a*tan(d*x + c)^2 - 2*(d*x + c)*(-I*A - B)*a - (A - I*B)*a*log(tan(d*x + c)^2 + 1) - (2*I*A + 2*B)*a*tan(d*x + c))/d","A",0
3,1,50,0,0.805736," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a - {\left(-i \, A - B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 i \, B a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*(A - I*B)*a - (-I*A - B)*a*log(tan(d*x + c)^2 + 1) + 2*I*B*a*tan(d*x + c))/d","A",0
4,1,49,0,0.567625," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} {\left(i \, A + B\right)} a - {\left(A - i \, B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, A a \log\left(\tan\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*(I*A + B)*a - (A - I*B)*a*log(tan(d*x + c)^2 + 1) + 2*A*a*log(tan(d*x + c)))/d","A",0
5,1,64,0,0.935485," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a + {\left(i \, A + B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(i \, A + B\right)} a \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, A a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c)*(A - I*B)*a + (I*A + B)*a*log(tan(d*x + c)^2 + 1) - 2*(I*A + B)*a*log(tan(d*x + c)) + 2*A*a/tan(d*x + c))/d","A",0
6,1,83,0,0.658491," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} {\left(-i \, A - B\right)} a + {\left(A - i \, B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(A - i \, B\right)} a \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(2 i \, A + 2 \, B\right)} a \tan\left(d x + c\right) + A a}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*(-I*A - B)*a + (A - I*B)*a*log(tan(d*x + c)^2 + 1) - 2*(A - I*B)*a*log(tan(d*x + c)) - ((2*I*A + 2*B)*a*tan(d*x + c) + A*a)/tan(d*x + c)^2)/d","A",0
7,1,103,0,0.908057," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a - 3 \, {\left(-i \, A - B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(-i \, A - B\right)} a \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, {\left(A - i \, B\right)} a \tan\left(d x + c\right)^{2} - {\left(3 i \, A + 3 \, B\right)} a \tan\left(d x + c\right) - 2 \, A a}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(d*x + c)*(A - I*B)*a - 3*(-I*A - B)*a*log(tan(d*x + c)^2 + 1) + 6*(-I*A - B)*a*log(tan(d*x + c)) + (6*(A - I*B)*a*tan(d*x + c)^2 - (3*I*A + 3*B)*a*tan(d*x + c) - 2*A*a)/tan(d*x + c)^3)/d","A",0
8,1,115,0,0.857195," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} {\left(i \, A + B\right)} a - 6 \, {\left(A - i \, B\right)} a \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(A - i \, B\right)} a \log\left(\tan\left(d x + c\right)\right) + \frac{{\left(12 i \, A + 12 \, B\right)} a \tan\left(d x + c\right)^{3} + 6 \, {\left(A - i \, B\right)} a \tan\left(d x + c\right)^{2} + {\left(-4 i \, A - 4 \, B\right)} a \tan\left(d x + c\right) - 3 \, A a}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*(I*A + B)*a - 6*(A - I*B)*a*log(tan(d*x + c)^2 + 1) + 12*(A - I*B)*a*log(tan(d*x + c)) + ((12*I*A + 12*B)*a*tan(d*x + c)^3 + 6*(A - I*B)*a*tan(d*x + c)^2 + (-4*I*A - 4*B)*a*tan(d*x + c) - 3*A*a)/tan(d*x + c)^4)/d","A",0
9,1,112,0,0.572839," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, B a^{2} \tan\left(d x + c\right)^{4} + 4 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(d x + c\right)^{3} - {\left(12 i \, A + 12 \, B\right)} a^{2} \tan\left(d x + c\right)^{2} + 24 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{2} - 12 \, {\left(-i \, A - B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 24 \, {\left(A - i \, B\right)} a^{2} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*B*a^2*tan(d*x + c)^4 + 4*(A - 2*I*B)*a^2*tan(d*x + c)^3 - (12*I*A + 12*B)*a^2*tan(d*x + c)^2 + 24*(d*x + c)*(A - I*B)*a^2 - 12*(-I*A - B)*a^2*log(tan(d*x + c)^2 + 1) - 24*(A - I*B)*a^2*tan(d*x + c))/d","A",0
10,1,94,0,0.904541," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, B a^{2} \tan\left(d x + c\right)^{3} + 3 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(d x + c\right)^{2} - 6 \, {\left(d x + c\right)} {\left(-2 i \, A - 2 \, B\right)} a^{2} - 6 \, {\left(A - i \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - {\left(12 i \, A + 12 \, B\right)} a^{2} \tan\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*B*a^2*tan(d*x + c)^3 + 3*(A - 2*I*B)*a^2*tan(d*x + c)^2 - 6*(d*x + c)*(-2*I*A - 2*B)*a^2 - 6*(A - I*B)*a^2*log(tan(d*x + c)^2 + 1) - (12*I*A + 12*B)*a^2*tan(d*x + c))/d","A",0
11,1,71,0,0.839720," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{B a^{2} \tan\left(d x + c\right)^{2} - 4 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{2} - 2 \, {\left(i \, A + B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(B*a^2*tan(d*x + c)^2 - 4*(d*x + c)*(A - I*B)*a^2 - 2*(I*A + B)*a^2*log(tan(d*x + c)^2 + 1) + 2*(A - 2*I*B)*a^2*tan(d*x + c))/d","A",0
12,1,66,0,0.725547," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} {\left(2 i \, A + 2 \, B\right)} a^{2} - {\left(A - i \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + A a^{2} \log\left(\tan\left(d x + c\right)\right) - B a^{2} \tan\left(d x + c\right)}{d}"," ",0,"((d*x + c)*(2*I*A + 2*B)*a^2 - (A - I*B)*a^2*log(tan(d*x + c)^2 + 1) + A*a^2*log(tan(d*x + c)) - B*a^2*tan(d*x + c))/d","A",0
13,1,74,0,0.852656," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{2} - {\left(-i \, A - B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - {\left(2 i \, A + B\right)} a^{2} \log\left(\tan\left(d x + c\right)\right) + \frac{A a^{2}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(2*(d*x + c)*(A - I*B)*a^2 - (-I*A - B)*a^2*log(tan(d*x + c)^2 + 1) - (2*I*A + B)*a^2*log(tan(d*x + c)) + A*a^2/tan(d*x + c))/d","A",0
14,1,94,0,0.954700," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} {\left(-2 i \, A - 2 \, B\right)} a^{2} + 2 \, {\left(A - i \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 4 \, {\left(A - i \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(4 i \, A + 2 \, B\right)} a^{2} \tan\left(d x + c\right) + A a^{2}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*(-2*I*A - 2*B)*a^2 + 2*(A - I*B)*a^2*log(tan(d*x + c)^2 + 1) - 4*(A - I*B)*a^2*log(tan(d*x + c)) - ((4*I*A + 2*B)*a^2*tan(d*x + c) + A*a^2)/tan(d*x + c)^2)/d","A",0
15,1,113,0,0.783912," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{2} + 6 \, {\left(i \, A + B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(-2 i \, A - 2 \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)\right) + \frac{12 \, {\left(A - i \, B\right)} a^{2} \tan\left(d x + c\right)^{2} - {\left(6 i \, A + 3 \, B\right)} a^{2} \tan\left(d x + c\right) - 2 \, A a^{2}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(12*(d*x + c)*(A - I*B)*a^2 + 6*(I*A + B)*a^2*log(tan(d*x + c)^2 + 1) + 6*(-2*I*A - 2*B)*a^2*log(tan(d*x + c)) + (12*(A - I*B)*a^2*tan(d*x + c)^2 - (6*I*A + 3*B)*a^2*tan(d*x + c) - 2*A*a^2)/tan(d*x + c)^3)/d","A",0
16,1,132,0,0.760333," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} {\left(2 i \, A + 2 \, B\right)} a^{2} - 12 \, {\left(A - i \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 24 \, {\left(A - i \, B\right)} a^{2} \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(-24 i \, A - 24 \, B\right)} a^{2} \tan\left(d x + c\right)^{3} - 12 \, {\left(A - i \, B\right)} a^{2} \tan\left(d x + c\right)^{2} + {\left(8 i \, A + 4 \, B\right)} a^{2} \tan\left(d x + c\right) + 3 \, A a^{2}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*(2*I*A + 2*B)*a^2 - 12*(A - I*B)*a^2*log(tan(d*x + c)^2 + 1) + 24*(A - I*B)*a^2*log(tan(d*x + c)) - ((-24*I*A - 24*B)*a^2*tan(d*x + c)^3 - 12*(A - I*B)*a^2*tan(d*x + c)^2 + (8*I*A + 4*B)*a^2*tan(d*x + c) + 3*A*a^2)/tan(d*x + c)^4)/d","A",0
17,1,134,0,0.870569," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{12 i \, B a^{3} \tan\left(d x + c\right)^{5} - {\left(-15 i \, A - 45 \, B\right)} a^{3} \tan\left(d x + c\right)^{4} + 20 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \tan\left(d x + c\right)^{3} - {\left(120 i \, A + 120 \, B\right)} a^{3} \tan\left(d x + c\right)^{2} + 240 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{3} - 60 \, {\left(-2 i \, A - 2 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 240 \, {\left(A - i \, B\right)} a^{3} \tan\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*I*B*a^3*tan(d*x + c)^5 - (-15*I*A - 45*B)*a^3*tan(d*x + c)^4 + 20*(3*A - 4*I*B)*a^3*tan(d*x + c)^3 - (120*I*A + 120*B)*a^3*tan(d*x + c)^2 + 240*(d*x + c)*(A - I*B)*a^3 - 60*(-2*I*A - 2*B)*a^3*log(tan(d*x + c)^2 + 1) - 240*(A - I*B)*a^3*tan(d*x + c))/d","A",0
18,1,116,0,1.673615," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{3 i \, B a^{3} \tan\left(d x + c\right)^{4} - {\left(-4 i \, A - 12 \, B\right)} a^{3} \tan\left(d x + c\right)^{3} + 6 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \tan\left(d x + c\right)^{2} - 12 \, {\left(d x + c\right)} {\left(-4 i \, A - 4 \, B\right)} a^{3} - 24 \, {\left(A - i \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - {\left(48 i \, A + 48 \, B\right)} a^{3} \tan\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*I*B*a^3*tan(d*x + c)^4 - (-4*I*A - 12*B)*a^3*tan(d*x + c)^3 + 6*(3*A - 4*I*B)*a^3*tan(d*x + c)^2 - 12*(d*x + c)*(-4*I*A - 4*B)*a^3 - 24*(A - I*B)*a^3*log(tan(d*x + c)^2 + 1) - (48*I*A + 48*B)*a^3*tan(d*x + c))/d","A",0
19,1,96,0,0.710469," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 i \, B a^{3} \tan\left(d x + c\right)^{3} - {\left(-3 i \, A - 9 \, B\right)} a^{3} \tan\left(d x + c\right)^{2} - 24 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{3} - 6 \, {\left(2 i \, A + 2 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \tan\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*I*B*a^3*tan(d*x + c)^3 - (-3*I*A - 9*B)*a^3*tan(d*x + c)^2 - 24*(d*x + c)*(A - I*B)*a^3 - 6*(2*I*A + 2*B)*a^3*log(tan(d*x + c)^2 + 1) + 6*(3*A - 4*I*B)*a^3*tan(d*x + c))/d","A",0
20,1,89,0,0.853945," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, B a^{3} \tan\left(d x + c\right)^{2} - 2 \, {\left(d x + c\right)} {\left(4 i \, A + 4 \, B\right)} a^{3} + 4 \, {\left(A - i \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, A a^{3} \log\left(\tan\left(d x + c\right)\right) - {\left(-2 i \, A - 6 \, B\right)} a^{3} \tan\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(I*B*a^3*tan(d*x + c)^2 - 2*(d*x + c)*(4*I*A + 4*B)*a^3 + 4*(A - I*B)*a^3*log(tan(d*x + c)^2 + 1) - 2*A*a^3*log(tan(d*x + c)) - (-2*I*A - 6*B)*a^3*tan(d*x + c))/d","A",0
21,1,86,0,0.832487," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{3} - {\left(-2 i \, A - 2 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - {\left(3 i \, A + B\right)} a^{3} \log\left(\tan\left(d x + c\right)\right) + i \, B a^{3} \tan\left(d x + c\right) + \frac{A a^{3}}{\tan\left(d x + c\right)}}{d}"," ",0,"-(4*(d*x + c)*(A - I*B)*a^3 - (-2*I*A - 2*B)*a^3*log(tan(d*x + c)^2 + 1) - (3*I*A + B)*a^3*log(tan(d*x + c)) + I*B*a^3*tan(d*x + c) + A*a^3/tan(d*x + c))/d","A",0
22,1,96,0,0.631610," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} {\left(-4 i \, A - 4 \, B\right)} a^{3} + 4 \, {\left(A - i \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(6 i \, A + 2 \, B\right)} a^{3} \tan\left(d x + c\right) + A a^{3}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*(-4*I*A - 4*B)*a^3 + 4*(A - I*B)*a^3*log(tan(d*x + c)^2 + 1) - 2*(4*A - 3*I*B)*a^3*log(tan(d*x + c)) - ((6*I*A + 2*B)*a^3*tan(d*x + c) + A*a^3)/tan(d*x + c)^2)/d","A",0
23,1,117,0,0.990320," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{24 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{3} + 6 \, {\left(2 i \, A + 2 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(-4 i \, A - 4 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \tan\left(d x + c\right)^{2} - {\left(9 i \, A + 3 \, B\right)} a^{3} \tan\left(d x + c\right) - 2 \, A a^{3}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(24*(d*x + c)*(A - I*B)*a^3 + 6*(2*I*A + 2*B)*a^3*log(tan(d*x + c)^2 + 1) + 6*(-4*I*A - 4*B)*a^3*log(tan(d*x + c)) + (6*(4*A - 3*I*B)*a^3*tan(d*x + c)^2 - (9*I*A + 3*B)*a^3*tan(d*x + c) - 2*A*a^3)/tan(d*x + c)^3)/d","A",0
24,1,134,0,0.914144," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} {\left(4 i \, A + 4 \, B\right)} a^{3} - 24 \, {\left(A - i \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 48 \, {\left(A - i \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(-48 i \, A - 48 \, B\right)} a^{3} \tan\left(d x + c\right)^{3} - 6 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \tan\left(d x + c\right)^{2} + {\left(12 i \, A + 4 \, B\right)} a^{3} \tan\left(d x + c\right) + 3 \, A a^{3}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*(4*I*A + 4*B)*a^3 - 24*(A - I*B)*a^3*log(tan(d*x + c)^2 + 1) + 48*(A - I*B)*a^3*log(tan(d*x + c)) - ((-48*I*A - 48*B)*a^3*tan(d*x + c)^3 - 6*(4*A - 3*I*B)*a^3*tan(d*x + c)^2 + (12*I*A + 4*B)*a^3*tan(d*x + c) + 3*A*a^3)/tan(d*x + c)^4)/d","A",0
25,1,153,0,0.981908," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{240 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{3} - 60 \, {\left(-2 i \, A - 2 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(4 i \, A + 4 \, B\right)} a^{3} \log\left(\tan\left(d x + c\right)\right) + \frac{240 \, {\left(A - i \, B\right)} a^{3} \tan\left(d x + c\right)^{4} + {\left(-120 i \, A - 120 \, B\right)} a^{3} \tan\left(d x + c\right)^{3} - 20 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \tan\left(d x + c\right)^{2} + {\left(45 i \, A + 15 \, B\right)} a^{3} \tan\left(d x + c\right) + 12 \, A a^{3}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(240*(d*x + c)*(A - I*B)*a^3 - 60*(-2*I*A - 2*B)*a^3*log(tan(d*x + c)^2 + 1) - 60*(4*I*A + 4*B)*a^3*log(tan(d*x + c)) + (240*(A - I*B)*a^3*tan(d*x + c)^4 + (-120*I*A - 120*B)*a^3*tan(d*x + c)^3 - 20*(4*A - 3*I*B)*a^3*tan(d*x + c)^2 + (45*I*A + 15*B)*a^3*tan(d*x + c) + 12*A*a^3)/tan(d*x + c)^5)/d","A",0
26,1,150,0,0.664816," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{10 \, B a^{4} \tan\left(d x + c\right)^{6} + 12 \, {\left(A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{5} + {\left(-60 i \, A - 105 \, B\right)} a^{4} \tan\left(d x + c\right)^{4} - 20 \, {\left(7 \, A - 8 i \, B\right)} a^{4} \tan\left(d x + c\right)^{3} + {\left(240 i \, A + 240 \, B\right)} a^{4} \tan\left(d x + c\right)^{2} - 480 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{4} + 60 \, {\left(-4 i \, A - 4 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 480 \, {\left(A - i \, B\right)} a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*B*a^4*tan(d*x + c)^6 + 12*(A - 4*I*B)*a^4*tan(d*x + c)^5 + (-60*I*A - 105*B)*a^4*tan(d*x + c)^4 - 20*(7*A - 8*I*B)*a^4*tan(d*x + c)^3 + (240*I*A + 240*B)*a^4*tan(d*x + c)^2 - 480*(d*x + c)*(A - I*B)*a^4 + 60*(-4*I*A - 4*B)*a^4*log(tan(d*x + c)^2 + 1) + 480*(A - I*B)*a^4*tan(d*x + c))/d","A",0
27,1,132,0,0.735293," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, B a^{4} \tan\left(d x + c\right)^{5} + 15 \, {\left(A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{4} + {\left(-80 i \, A - 140 \, B\right)} a^{4} \tan\left(d x + c\right)^{3} - 30 \, {\left(7 \, A - 8 i \, B\right)} a^{4} \tan\left(d x + c\right)^{2} + 60 \, {\left(d x + c\right)} {\left(-8 i \, A - 8 \, B\right)} a^{4} + 240 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + {\left(480 i \, A + 480 \, B\right)} a^{4} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*B*a^4*tan(d*x + c)^5 + 15*(A - 4*I*B)*a^4*tan(d*x + c)^4 + (-80*I*A - 140*B)*a^4*tan(d*x + c)^3 - 30*(7*A - 8*I*B)*a^4*tan(d*x + c)^2 + 60*(d*x + c)*(-8*I*A - 8*B)*a^4 + 240*(A - I*B)*a^4*log(tan(d*x + c)^2 + 1) + (480*I*A + 480*B)*a^4*tan(d*x + c))/d","A",0
28,1,113,0,1.632322," ","integrate((a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B a^{4} \tan\left(d x + c\right)^{4} + 4 \, {\left(A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{3} + {\left(-24 i \, A - 42 \, B\right)} a^{4} \tan\left(d x + c\right)^{2} + 96 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{4} + 12 \, {\left(4 i \, A + 4 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 12 \, {\left(7 \, A - 8 i \, B\right)} a^{4} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*a^4*tan(d*x + c)^4 + 4*(A - 4*I*B)*a^4*tan(d*x + c)^3 + (-24*I*A - 42*B)*a^4*tan(d*x + c)^2 + 96*(d*x + c)*(A - I*B)*a^4 + 12*(4*I*A + 4*B)*a^4*log(tan(d*x + c)^2 + 1) - 12*(7*A - 8*I*B)*a^4*tan(d*x + c))/d","A",0
29,1,106,0,0.791023," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B a^{4} \tan\left(d x + c\right)^{3} + 3 \, {\left(A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{2} + 6 \, {\left(d x + c\right)} {\left(8 i \, A + 8 \, B\right)} a^{4} - 24 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, A a^{4} \log\left(\tan\left(d x + c\right)\right) + {\left(-24 i \, A - 42 \, B\right)} a^{4} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*a^4*tan(d*x + c)^3 + 3*(A - 4*I*B)*a^4*tan(d*x + c)^2 + 6*(d*x + c)*(8*I*A + 8*B)*a^4 - 24*(A - I*B)*a^4*log(tan(d*x + c)^2 + 1) + 6*A*a^4*log(tan(d*x + c)) + (-24*I*A - 42*B)*a^4*tan(d*x + c))/d","A",0
30,1,104,0,0.881503," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B a^{4} \tan\left(d x + c\right)^{2} - 16 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{4} + 2 \, {\left(-4 i \, A - 4 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(4 i \, A + B\right)} a^{4} \log\left(\tan\left(d x + c\right)\right) + 2 \, {\left(A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right) - \frac{2 \, A a^{4}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(B*a^4*tan(d*x + c)^2 - 16*(d*x + c)*(A - I*B)*a^4 + 2*(-4*I*A - 4*B)*a^4*log(tan(d*x + c)^2 + 1) + 2*(4*I*A + B)*a^4*log(tan(d*x + c)) + 2*(A - 4*I*B)*a^4*tan(d*x + c) - 2*A*a^4/tan(d*x + c))/d","A",0
31,1,108,0,0.723532," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(d x + c\right)} {\left(-8 i \, A - 8 \, B\right)} a^{4} + 8 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(7 \, A - 4 i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)\right) + 2 \, B a^{4} \tan\left(d x + c\right) - \frac{{\left(8 i \, A + 2 \, B\right)} a^{4} \tan\left(d x + c\right) + A a^{4}}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*(d*x + c)*(-8*I*A - 8*B)*a^4 + 8*(A - I*B)*a^4*log(tan(d*x + c)^2 + 1) - 2*(7*A - 4*I*B)*a^4*log(tan(d*x + c)) + 2*B*a^4*tan(d*x + c) - ((8*I*A + 2*B)*a^4*tan(d*x + c) + A*a^4)/tan(d*x + c)^2)/d","A",0
32,1,117,0,1.054802," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{48 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{4} + 6 \, {\left(4 i \, A + 4 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(-8 i \, A - 7 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, {\left(7 \, A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{2} - {\left(12 i \, A + 3 \, B\right)} a^{4} \tan\left(d x + c\right) - 2 \, A a^{4}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(48*(d*x + c)*(A - I*B)*a^4 + 6*(4*I*A + 4*B)*a^4*log(tan(d*x + c)^2 + 1) + 6*(-8*I*A - 7*B)*a^4*log(tan(d*x + c)) + (6*(7*A - 4*I*B)*a^4*tan(d*x + c)^2 - (12*I*A + 3*B)*a^4*tan(d*x + c) - 2*A*a^4)/tan(d*x + c)^3)/d","A",0
33,1,134,0,0.754376," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)} {\left(8 i \, A + 8 \, B\right)} a^{4} - 48 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 96 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(-96 i \, A - 84 \, B\right)} a^{4} \tan\left(d x + c\right)^{3} - 6 \, {\left(7 \, A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{2} + {\left(16 i \, A + 4 \, B\right)} a^{4} \tan\left(d x + c\right) + 3 \, A a^{4}}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(d*x + c)*(8*I*A + 8*B)*a^4 - 48*(A - I*B)*a^4*log(tan(d*x + c)^2 + 1) + 96*(A - I*B)*a^4*log(tan(d*x + c)) - ((-96*I*A - 84*B)*a^4*tan(d*x + c)^3 - 6*(7*A - 4*I*B)*a^4*tan(d*x + c)^2 + (16*I*A + 4*B)*a^4*tan(d*x + c) + 3*A*a^4)/tan(d*x + c)^4)/d","A",0
34,1,153,0,0.770952," ","integrate(cot(d*x+c)^6*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{480 \, {\left(d x + c\right)} {\left(A - i \, B\right)} a^{4} - 60 \, {\left(-4 i \, A - 4 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(8 i \, A + 8 \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)\right) + \frac{480 \, {\left(A - i \, B\right)} a^{4} \tan\left(d x + c\right)^{4} + {\left(-240 i \, A - 210 \, B\right)} a^{4} \tan\left(d x + c\right)^{3} - 20 \, {\left(7 \, A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{2} + {\left(60 i \, A + 15 \, B\right)} a^{4} \tan\left(d x + c\right) + 12 \, A a^{4}}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(480*(d*x + c)*(A - I*B)*a^4 - 60*(-4*I*A - 4*B)*a^4*log(tan(d*x + c)^2 + 1) - 60*(8*I*A + 8*B)*a^4*log(tan(d*x + c)) + (480*(A - I*B)*a^4*tan(d*x + c)^4 + (-240*I*A - 210*B)*a^4*tan(d*x + c)^3 - 20*(7*A - 4*I*B)*a^4*tan(d*x + c)^2 + (60*I*A + 15*B)*a^4*tan(d*x + c) + 12*A*a^4)/tan(d*x + c)^5)/d","A",0
35,1,171,0,0.712186," ","integrate(cot(d*x+c)^7*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{60 \, {\left(d x + c\right)} {\left(-8 i \, A - 8 \, B\right)} a^{4} + 240 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 480 \, {\left(A - i \, B\right)} a^{4} \log\left(\tan\left(d x + c\right)\right) - \frac{{\left(480 i \, A + 480 \, B\right)} a^{4} \tan\left(d x + c\right)^{5} + 240 \, {\left(A - i \, B\right)} a^{4} \tan\left(d x + c\right)^{4} + {\left(-160 i \, A - 140 \, B\right)} a^{4} \tan\left(d x + c\right)^{3} - 15 \, {\left(7 \, A - 4 i \, B\right)} a^{4} \tan\left(d x + c\right)^{2} + {\left(48 i \, A + 12 \, B\right)} a^{4} \tan\left(d x + c\right) + 10 \, A a^{4}}{\tan\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(60*(d*x + c)*(-8*I*A - 8*B)*a^4 + 240*(A - I*B)*a^4*log(tan(d*x + c)^2 + 1) - 480*(A - I*B)*a^4*log(tan(d*x + c)) - ((480*I*A + 480*B)*a^4*tan(d*x + c)^5 + 240*(A - I*B)*a^4*tan(d*x + c)^4 + (-160*I*A - 140*B)*a^4*tan(d*x + c)^3 - 15*(7*A - 4*I*B)*a^4*tan(d*x + c)^2 + (48*I*A + 12*B)*a^4*tan(d*x + c) + 10*A*a^4)/tan(d*x + c)^6)/d","A",0
36,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*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
37,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*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
38,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*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
39,-2,0,0,0.000000," ","integrate((A+B*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
40,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*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
41,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*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
42,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*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
43,-2,0,0,0.000000," ","integrate(cot(d*x+c)^4*(A+B*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
44,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*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
45,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*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
46,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*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
47,-2,0,0,0.000000," ","integrate((A+B*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
48,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*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
49,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*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
50,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*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
51,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4*(A+B*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
52,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*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
53,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*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
54,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*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
55,-2,0,0,0.000000," ","integrate((A+B*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
56,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*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
57,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*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
58,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*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
59,-2,0,0,0.000000," ","integrate(tan(d*x+c)^4*(A+B*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
60,-2,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*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
61,-2,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*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
62,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*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
63,-2,0,0,0.000000," ","integrate((A+B*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
64,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*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
65,-2,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*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
66,-2,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*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
67,1,153,0,0.739805," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{105 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 60 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} B a + 84 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(A + 2 i \, B\right)} a^{2} - 140 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A + 2 i \, B\right)} a^{3} + 420 \, \sqrt{i \, a \tan\left(d x + c\right) + a} A a^{4}}{210 \, a^{4} d}"," ",0,"-1/210*(105*sqrt(2)*(A - I*B)*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))) - 60*I*(I*a*tan(d*x + c) + a)^(7/2)*B*a + 84*(I*a*tan(d*x + c) + a)^(5/2)*(A + 2*I*B)*a^2 - 140*(I*a*tan(d*x + c) + a)^(3/2)*(A + 2*I*B)*a^3 + 420*sqrt(I*a*tan(d*x + c) + a)*A*a^4)/(a^4*d)","A",0
68,1,130,0,0.791088," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(15 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 12 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} B a + 20 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A + i \, B\right)} a^{2} - 60 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a^{3}\right)}}{30 \, a^{3} d}"," ",0,"-1/30*I*(15*sqrt(2)*(A - I*B)*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))) - 12*I*(I*a*tan(d*x + c) + a)^(5/2)*B*a + 20*(I*a*tan(d*x + c) + a)^(3/2)*(A + I*B)*a^2 - 60*I*sqrt(I*a*tan(d*x + c) + a)*B*a^3)/(a^3*d)","A",0
69,1,107,0,1.115778," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(A - i \, B\right)} 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 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a + 12 \, \sqrt{i \, a \tan\left(d x + c\right) + a} A a^{2}}{6 \, a^{2} d}"," ",0,"1/6*(3*sqrt(2)*(A - I*B)*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*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a + 12*sqrt(I*a*tan(d*x + c) + a)*A*a^2)/(a^2*d)","A",0
70,1,87,0,0.775211," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{i \, {\left(\sqrt{2} {\left(A - i \, B\right)} 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) - 4 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a\right)}}{2 \, a d}"," ",0,"1/2*I*(sqrt(2)*(A - I*B)*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*I*sqrt(I*a*tan(d*x + c) + a)*B*a)/(a*d)","A",0
71,1,113,0,0.763309," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(A - i \, B\right)} \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 \, A \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)*(A - I*B)*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*A*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
72,1,145,0,0.678211," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{\sqrt{2} {\left(A - i \, B\right)} \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{{\left(A - 2 i \, B\right)} \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}{a \tan\left(d x + c\right)}\right)} a}{2 \, d}"," ",0,"-1/2*I*(sqrt(2)*(A - I*B)*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) - (A - 2*I*B)*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/(a*tan(d*x + c)))*a/d","A",0
73,1,202,0,1.231255," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{4 \, \sqrt{2} {\left(A - i \, B\right)} \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{{\left(7 \, A - 4 i \, B\right)} \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{2 \, {\left({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A - 4 i \, B\right)} + \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A + 4 i \, B\right)} 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}}\right)}}{8 \, d}"," ",0,"1/8*a^2*(4*sqrt(2)*(A - I*B)*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*A - 4*I*B)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(3/2) + 2*((I*a*tan(d*x + c) + a)^(3/2)*(A - 4*I*B) + sqrt(I*a*tan(d*x + c) + a)*(A + 4*I*B)*a)/((I*a*tan(d*x + c) + a)^2*a - 2*(I*a*tan(d*x + c) + a)*a^2 + a^3))/d","A",0
74,1,249,0,0.702009," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{i \, a^{3} {\left(\frac{2 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(7 \, A - 2 i \, B\right)} - 40 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} A a + 3 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(9 \, A + 2 i \, B\right)} a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{2} - 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} - a^{5}} + \frac{24 \, \sqrt{2} {\left(A - i \, B\right)} \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{3 \, {\left(9 \, A - 14 i \, B\right)} \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)}}{48 \, d}"," ",0,"1/48*I*a^3*(2*(3*(I*a*tan(d*x + c) + a)^(5/2)*(7*A - 2*I*B) - 40*(I*a*tan(d*x + c) + a)^(3/2)*A*a + 3*sqrt(I*a*tan(d*x + c) + a)*(9*A + 2*I*B)*a^2)/((I*a*tan(d*x + c) + a)^3*a^2 - 3*(I*a*tan(d*x + c) + a)^2*a^3 + 3*(I*a*tan(d*x + c) + a)*a^4 - a^5) + 24*sqrt(2)*(A - I*B)*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) - 3*(9*A - 14*I*B)*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
75,1,153,0,0.466786," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(105 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 30 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} B a + 42 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(A + i \, B\right)} a^{2} - 70 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a^{3} + 210 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - i \, B\right)} a^{4}\right)}}{105 \, a^{3} d}"," ",0,"-1/105*I*(105*sqrt(2)*(A - I*B)*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))) - 30*I*(I*a*tan(d*x + c) + a)^(7/2)*B*a + 42*(I*a*tan(d*x + c) + a)^(5/2)*(A + I*B)*a^2 - 70*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a^3 + 210*sqrt(I*a*tan(d*x + c) + a)*(A - I*B)*a^4)/(a^3*d)","A",0
76,1,130,0,0.598268," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{15 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 6 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} B a + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} A a^{2} + 30 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - i \, B\right)} a^{3}}{15 \, a^{2} d}"," ",0,"1/15*(15*sqrt(2)*(A - I*B)*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))) - 6*I*(I*a*tan(d*x + c) + a)^(5/2)*B*a + 10*(I*a*tan(d*x + c) + a)^(3/2)*A*a^2 + 30*sqrt(I*a*tan(d*x + c) + a)*(A - I*B)*a^3)/(a^2*d)","A",0
77,1,111,0,0.694575," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{i \, {\left(3 \, \sqrt{2} {\left(A - i \, B\right)} 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 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a + 6 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - i \, B\right)} a^{2}\right)}}{3 \, a d}"," ",0,"1/3*I*(3*sqrt(2)*(A - I*B)*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*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a + 6*sqrt(I*a*tan(d*x + c) + a)*(A - I*B)*a^2)/(a*d)","A",0
78,1,130,0,0.945807," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(A - i \, B\right)} 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 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) - 2 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a}{d}"," ",0,"-(sqrt(2)*(A - I*B)*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*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)*B*a)/d","A",0
79,1,145,0,0.909651," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{2} {\left(A - i \, B\right)} \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) - {\left(3 \, A - 2 i \, B\right)} \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} A}{\tan\left(d x + c\right)}\right)} a}{2 \, d}"," ",0,"-1/2*I*(2*sqrt(2)*(A - I*B)*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*A - 2*I*B)*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)*A/tan(d*x + c))*a/d","A",0
80,1,203,0,0.852427," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\frac{8 \, \sqrt{2} {\left(A - i \, B\right)} \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{{\left(11 \, A - 12 i \, B\right)} \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({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(5 \, A - 4 i \, B\right)} - \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(3 \, A - 4 i \, B\right)} 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}}{8 \, d}"," ",0,"1/8*(8*sqrt(2)*(A - I*B)*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*A - 12*I*B)*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*a*tan(d*x + c) + a)^(3/2)*(5*A - 4*I*B) - sqrt(I*a*tan(d*x + c) + a)*(3*A - 4*I*B)*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
81,1,253,0,0.959019," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{i \, a^{3} {\left(\frac{48 \, \sqrt{2} {\left(A - i \, B\right)} \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{3 \, {\left(23 \, A - 22 i \, B\right)} \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{2 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(9 \, A - 10 i \, B\right)} - 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(5 \, A - 6 i \, B\right)} a + 3 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(7 \, A - 6 i \, B\right)} a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a - 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{2} + 3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{3} - a^{4}}\right)}}{48 \, d}"," ",0,"1/48*I*a^3*(48*sqrt(2)*(A - I*B)*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) - 3*(23*A - 22*I*B)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(3/2) + 2*(3*(I*a*tan(d*x + c) + a)^(5/2)*(9*A - 10*I*B) - 8*(I*a*tan(d*x + c) + a)^(3/2)*(5*A - 6*I*B)*a + 3*sqrt(I*a*tan(d*x + c) + a)*(7*A - 6*I*B)*a^2)/((I*a*tan(d*x + c) + a)^3*a - 3*(I*a*tan(d*x + c) + a)^2*a^2 + 3*(I*a*tan(d*x + c) + a)*a^3 - a^4))/d","A",0
82,1,176,0,0.961237," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 i \, {\left(315 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 35 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} B a + 45 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} {\left(A + i \, B\right)} a^{2} - 63 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} B a^{3} + 105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A - i \, B\right)} a^{4} + 630 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - i \, B\right)} a^{5}\right)}}{315 \, a^{3} d}"," ",0,"-2/315*I*(315*sqrt(2)*(A - I*B)*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))) - 35*I*(I*a*tan(d*x + c) + a)^(9/2)*B*a + 45*(I*a*tan(d*x + c) + a)^(7/2)*(A + I*B)*a^2 - 63*I*(I*a*tan(d*x + c) + a)^(5/2)*B*a^3 + 105*(I*a*tan(d*x + c) + a)^(3/2)*(A - I*B)*a^4 + 630*sqrt(I*a*tan(d*x + c) + a)*(A - I*B)*a^5)/(a^3*d)","A",0
83,1,153,0,0.888722," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(105 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 15 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} B a + 21 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} A a^{2} + 35 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A - i \, B\right)} a^{3} + 210 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - i \, B\right)} a^{4}\right)}}{105 \, a^{2} d}"," ",0,"2/105*(105*sqrt(2)*(A - I*B)*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))) - 15*I*(I*a*tan(d*x + c) + a)^(7/2)*B*a + 21*(I*a*tan(d*x + c) + a)^(5/2)*A*a^2 + 35*(I*a*tan(d*x + c) + a)^(3/2)*(A - I*B)*a^3 + 210*sqrt(I*a*tan(d*x + c) + a)*(A - I*B)*a^4)/(a^2*d)","A",0
84,1,134,0,0.948559," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 i \, {\left(15 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 3 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} B a + 5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A - i \, B\right)} a^{2} + 30 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - i \, B\right)} a^{3}\right)}}{15 \, a d}"," ",0,"2/15*I*(15*sqrt(2)*(A - I*B)*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))) - 3*I*(I*a*tan(d*x + c) + a)^(5/2)*B*a + 5*(I*a*tan(d*x + c) + a)^(3/2)*(A - I*B)*a^2 + 30*sqrt(I*a*tan(d*x + c) + a)*(A - I*B)*a^3)/(a*d)","A",0
85,1,154,0,0.982964," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 3 \, A 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 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a + 6 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A - 2 i \, B\right)} a^{2}}{3 \, d}"," ",0,"-1/3*(6*sqrt(2)*(A - I*B)*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))) - 3*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*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a + 6*sqrt(I*a*tan(d*x + c) + a)*(A - 2*I*B)*a^2)/d","A",0
86,1,163,0,0.744048," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(4 \, \sqrt{2} {\left(A - i \, B\right)} 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) - {\left(5 \, A - 2 i \, B\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) - 4 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a - \frac{2 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} A a}{\tan\left(d x + c\right)}\right)} a}{2 \, d}"," ",0,"-1/2*I*(4*sqrt(2)*(A - I*B)*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 - 2*I*B)*a^(3/2)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a))) - 4*I*sqrt(I*a*tan(d*x + c) + a)*B*a - 2*I*sqrt(I*a*tan(d*x + c) + a)*A*a/tan(d*x + c))*a/d","A",0
87,1,206,0,0.665856," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(16 \, \sqrt{2} {\left(A - i \, B\right)} \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) - {\left(23 \, A - 20 i \, B\right)} \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({\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(9 \, A - 4 i \, B\right)} a - \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(7 \, A - 4 i \, B\right)} 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)*(A - I*B)*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*A - 20*I*B)*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*a*tan(d*x + c) + a)^(3/2)*(9*A - 4*I*B)*a - sqrt(I*a*tan(d*x + c) + a)*(7*A - 4*I*B)*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
88,1,249,0,0.890796," ","integrate(cot(d*x+c)^4*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{96 \, \sqrt{2} {\left(A - i \, B\right)} \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{3 \, {\left(45 \, A - 46 i \, B\right)} \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(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(19 \, A - 18 i \, B\right)} - 8 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(11 \, A - 12 i \, B\right)} a + 3 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(13 \, A - 14 i \, B\right)} 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)} a^{3}}{48 \, d}"," ",0,"1/48*I*(96*sqrt(2)*(A - I*B)*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) - 3*(45*A - 46*I*B)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/sqrt(a) + 2*(3*(I*a*tan(d*x + c) + a)^(5/2)*(19*A - 18*I*B) - 8*(I*a*tan(d*x + c) + a)^(3/2)*(11*A - 12*I*B)*a + 3*sqrt(I*a*tan(d*x + c) + a)*(13*A - 14*I*B)*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))*a^3/d","A",0
89,1,293,0,0.916801," ","integrate(cot(d*x+c)^5*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{a^{4} {\left(\frac{768 \, \sqrt{2} {\left(A - i \, B\right)} \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{9 \, {\left(121 \, A - 120 i \, B\right)} \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{2 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} {\left(149 \, A - 152 i \, B\right)} - {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} {\left(1127 \, A - 1160 i \, B\right)} a + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(1049 \, A - 1016 i \, B\right)} a^{2} - 3 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(107 \, A - 104 i \, B\right)} a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} a - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} a^{2} + 6 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} a^{3} - 4 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} a^{4} + a^{5}}\right)}}{384 \, d}"," ",0,"-1/384*a^4*(768*sqrt(2)*(A - I*B)*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) - 9*(121*A - 120*I*B)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(3/2) + 2*(3*(I*a*tan(d*x + c) + a)^(7/2)*(149*A - 152*I*B) - (I*a*tan(d*x + c) + a)^(5/2)*(1127*A - 1160*I*B)*a + (I*a*tan(d*x + c) + a)^(3/2)*(1049*A - 1016*I*B)*a^2 - 3*sqrt(I*a*tan(d*x + c) + a)*(107*A - 104*I*B)*a^3)/((I*a*tan(d*x + c) + a)^4*a - 4*(I*a*tan(d*x + c) + a)^3*a^2 + 6*(I*a*tan(d*x + c) + a)^2*a^3 - 4*(I*a*tan(d*x + c) + a)*a^4 + a^5))/d","A",0
90,1,157,0,1.666033," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 24 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} B a + 40 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(A + 2 i \, B\right)} a^{2} - 120 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A + 2 i \, B\right)} a^{3} - \frac{60 \, {\left(A + i \, B\right)} a^{4}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{60 \, a^{4} d}"," ",0,"-1/60*(15*sqrt(2)*(A - I*B)*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))) - 24*I*(I*a*tan(d*x + c) + a)^(5/2)*B*a + 40*(I*a*tan(d*x + c) + a)^(3/2)*(A + 2*I*B)*a^2 - 120*sqrt(I*a*tan(d*x + c) + a)*(A + 2*I*B)*a^3 - 60*(A + I*B)*a^4/sqrt(I*a*tan(d*x + c) + a))/(a^4*d)","A",0
91,1,134,0,1.161342," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{i \, {\left(3 \, \sqrt{2} {\left(A - i \, B\right)} 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 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a + 24 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A + i \, B\right)} a^{2} + \frac{12 \, {\left(A + i \, B\right)} a^{3}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}}{12 \, a^{3} d}"," ",0,"-1/12*I*(3*sqrt(2)*(A - I*B)*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*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a + 24*sqrt(I*a*tan(d*x + c) + a)*(A + I*B)*a^2 + 12*(A + I*B)*a^3/sqrt(I*a*tan(d*x + c) + a))/(a^3*d)","A",0
92,1,110,0,0.738008," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(A - i \, B\right)} 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) - 8 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a - \frac{4 \, {\left(A + i \, B\right)} a^{2}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{4 \, a^{2} d}"," ",0,"1/4*(sqrt(2)*(A - I*B)*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))) - 8*I*sqrt(I*a*tan(d*x + c) + a)*B*a - 4*(A + I*B)*a^2/sqrt(I*a*tan(d*x + c) + a))/(a^2*d)","A",0
93,1,91,0,0.684950," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{i \, {\left(\sqrt{2} {\left(A - i \, B\right)} \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(A + i \, B\right)} a}{\sqrt{i \, a \tan\left(d x + c\right) + a}}\right)}}{4 \, a d}"," ",0,"1/4*I*(sqrt(2)*(A - I*B)*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 + I*B)*a/sqrt(I*a*tan(d*x + c) + a))/(a*d)","A",0
94,1,133,0,0.613815," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{\sqrt{2} {\left(A - i \, B\right)} \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 \, 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)}{\sqrt{a}} - \frac{4 \, {\left(A + i \, B\right)}}{\sqrt{i \, a \tan\left(d x + c\right) + a}}}{4 \, d}"," ",0,"-1/4*(sqrt(2)*(A - I*B)*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*A*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/sqrt(a) - 4*(A + I*B)/sqrt(I*a*tan(d*x + c) + a))/d","A",0
95,1,184,0,0.644755," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{\sqrt{2} {\left(A - i \, B\right)} \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 \, {\left(A + 2 i \, B\right)} \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({\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(2 \, A + i \, B\right)} - {\left(A + i \, B\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}}\right)}}{4 \, d}"," ",0,"-1/4*I*a*(sqrt(2)*(A - I*B)*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*(A + 2*I*B)*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*((I*a*tan(d*x + c) + a)*(2*A + I*B) - (A + I*B)*a)/((I*a*tan(d*x + c) + a)^(3/2)*a - sqrt(I*a*tan(d*x + c) + a)*a^2))/d","A",0
96,1,232,0,0.975209," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(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)}^{2} {\left(7 \, A + 8 i \, B\right)} - {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(13 \, A + 12 i \, B\right)} a + 4 \, {\left(A + i \, B\right)} 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} {\left(A - i \, B\right)} \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{{\left(11 \, A + 4 i \, B\right)} \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*((I*a*tan(d*x + c) + a)^2*(7*A + 8*I*B) - (I*a*tan(d*x + c) + a)*(13*A + 12*I*B)*a + 4*(A + I*B)*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)*(A - I*B)*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*A + 4*I*B)*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
97,1,160,0,2.022751," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 16 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a + 48 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A + 2 i \, B\right)} a^{2} + \frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(5 \, A + 7 i \, B\right)} a^{3} - 2 \, {\left(A + i \, B\right)} 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 - I*B)*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))) - 16*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a + 48*sqrt(I*a*tan(d*x + c) + a)*(A + 2*I*B)*a^2 + 4*(3*(I*a*tan(d*x + c) + a)*(5*A + 7*I*B)*a^3 - 2*(A + I*B)*a^4)/(I*a*tan(d*x + c) + a)^(3/2))/(a^4*d)","A",0
98,1,137,0,0.628599," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(3 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 48 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a - \frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(3 \, A + 5 i \, B\right)} a^{2} - 2 \, {\left(A + i \, B\right)} 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 - I*B)*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))) - 48*I*sqrt(I*a*tan(d*x + c) + a)*B*a - 4*(3*(I*a*tan(d*x + c) + a)*(3*A + 5*I*B)*a^2 - 2*(A + I*B)*a^3)/(I*a*tan(d*x + c) + a)^(3/2))/(a^3*d)","A",0
99,1,116,0,0.733977," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{2} {\left(A - i \, B\right)} \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)} {\left(A + 3 i \, B\right)} a - 2 \, {\left(A + i \, B\right)} 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)*(A - I*B)*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 + 3*I*B)*a - 2*(A + I*B)*a^2)/(I*a*tan(d*x + c) + a)^(3/2))/(a^2*d)","A",0
100,1,113,0,0.987916," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{3 \, \sqrt{2} {\left(A - i \, B\right)} \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 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(A - i \, B\right)} + 2 \, {\left(A + i \, B\right)} 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)*(A - I*B)*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) + a)*(A - I*B) + 2*(A + I*B)*a)/(I*a*tan(d*x + c) + a)^(3/2))/(a*d)","A",0
101,1,161,0,1.723207," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sqrt{2} {\left(A - i \, B\right)} \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 \, 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)}{a^{\frac{3}{2}}} - \frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(3 \, A + i \, B\right)} + 2 \, {\left(A + i \, B\right)} 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)*(A - I*B)*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*A*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*(3*(I*a*tan(d*x + c) + a)*(3*A + I*B) + 2*(A + I*B)*a)/((I*a*tan(d*x + c) + a)^(3/2)*a))/d","A",0
102,1,215,0,1.683491," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{4 \, {\left(3 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(7 \, A + 3 i \, B\right)} - {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(13 \, A + 7 i \, B\right)} a - 2 \, {\left(A + i \, B\right)} 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} {\left(A - i \, B\right)} \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{12 \, {\left(3 \, A + 2 i \, B\right)} \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*(3*(I*a*tan(d*x + c) + a)^2*(7*A + 3*I*B) - (I*a*tan(d*x + c) + a)*(13*A + 7*I*B)*a - 2*(A + I*B)*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)*(A - I*B)*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) + 12*(3*A + 2*I*B)*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
103,1,259,0,0.886459," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{2 \, {\left(21 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} {\left(3 \, A + 2 i \, B\right)} - {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(107 \, A + 68 i \, B\right)} a + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(17 \, A + 11 i \, B\right)} a^{2} + 4 \, {\left(A + i \, B\right)} 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} {\left(A - i \, B\right)} \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{3 \, {\left(23 \, A + 12 i \, B\right)} \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*(21*(I*a*tan(d*x + c) + a)^3*(3*A + 2*I*B) - (I*a*tan(d*x + c) + a)^2*(107*A + 68*I*B)*a + 2*(I*a*tan(d*x + c) + a)*(17*A + 11*I*B)*a^2 + 4*(A + I*B)*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)*(A - I*B)*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) + 3*(23*A + 12*I*B)*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
104,1,185,0,0.965276," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(15 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 160 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} B a + 480 \, \sqrt{i \, a \tan\left(d x + c\right) + a} {\left(A + 3 i \, B\right)} a^{2} + \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(17 \, A + 31 i \, B\right)} a^{3} - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(7 \, A + 9 i \, B\right)} a^{4} + 12 \, {\left(A + i \, B\right)} 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 - I*B)*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))) - 160*I*(I*a*tan(d*x + c) + a)^(3/2)*B*a + 480*sqrt(I*a*tan(d*x + c) + a)*(A + 3*I*B)*a^2 + 4*(15*(I*a*tan(d*x + c) + a)^2*(17*A + 31*I*B)*a^3 - 10*(I*a*tan(d*x + c) + a)*(7*A + 9*I*B)*a^4 + 12*(A + I*B)*a^5)/(I*a*tan(d*x + c) + a)^(5/2))/(a^5*d)","A",0
105,1,162,0,0.721965," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{15 \, \sqrt{2} {\left(A - i \, B\right)} 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) - 480 i \, \sqrt{i \, a \tan\left(d x + c\right) + a} B a - \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(7 \, A + 17 i \, B\right)} a^{2} - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(5 \, A + 7 i \, B\right)} a^{3} + 12 \, {\left(A + i \, B\right)} 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 - I*B)*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))) - 480*I*sqrt(I*a*tan(d*x + c) + a)*B*a - 4*(15*(I*a*tan(d*x + c) + a)^2*(7*A + 17*I*B)*a^2 - 10*(I*a*tan(d*x + c) + a)*(5*A + 7*I*B)*a^3 + 12*(A + I*B)*a^4)/(I*a*tan(d*x + c) + a)^(5/2))/(a^4*d)","A",0
106,1,141,0,0.843174," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{i \, {\left(15 \, \sqrt{2} {\left(A - i \, B\right)} \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(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(A + 7 i \, B\right)} a - 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(3 \, A + 5 i \, B\right)} a^{2} + 12 \, {\left(A + i \, B\right)} a^{3}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\right)}}{240 \, a^{3} d}"," ",0,"-1/240*I*(15*sqrt(2)*(A - I*B)*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*(15*(I*a*tan(d*x + c) + a)^2*(A + 7*I*B)*a - 10*(I*a*tan(d*x + c) + a)*(3*A + 5*I*B)*a^2 + 12*(A + I*B)*a^3)/(I*a*tan(d*x + c) + a)^(5/2))/(a^3*d)","A",0
107,1,136,0,0.748969," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{\frac{15 \, \sqrt{2} {\left(A - i \, B\right)} \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} {\left(A - i \, B\right)} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(A + 3 i \, B\right)} a - 12 \, {\left(A + i \, B\right)} 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)*(A - I*B)*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*(A - I*B) + 10*(I*a*tan(d*x + c) + a)*(A + 3*I*B)*a - 12*(A + I*B)*a^2)/(I*a*tan(d*x + c) + a)^(5/2))/(a^2*d)","A",0
108,1,139,0,0.698231," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{15 \, \sqrt{2} {\left(A - i \, B\right)} \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} {\left(A - i \, B\right)} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(A - i \, B\right)} a + 12 \, {\left(A + i \, B\right)} 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)*(A - I*B)*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*(A - I*B) + 10*(I*a*tan(d*x + c) + a)*(A - I*B)*a + 12*(A + I*B)*a^2)/((I*a*tan(d*x + c) + a)^(5/2)*a))/(a*d)","A",0
109,1,186,0,1.702851," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{15 \, \sqrt{2} {\left(A - i \, B\right)} \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{240 \, 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)}{a^{\frac{5}{2}}} - \frac{4 \, {\left(15 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(7 \, A + i \, B\right)} + 10 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(3 \, A + i \, B\right)} a + 12 \, {\left(A + i \, B\right)} a^{2}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{2}}}{240 \, d}"," ",0,"-1/240*(15*sqrt(2)*(A - I*B)*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) - 240*A*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*(15*(I*a*tan(d*x + c) + a)^2*(7*A + I*B) + 10*(I*a*tan(d*x + c) + a)*(3*A + I*B)*a + 12*(A + I*B)*a^2)/((I*a*tan(d*x + c) + a)^(5/2)*a^2))/d","A",0
110,1,240,0,0.763312," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{i \, a {\left(\frac{4 \, {\left(105 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} {\left(3 \, A + i \, B\right)} - 5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(41 \, A + 15 i \, B\right)} a - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(19 \, A + 9 i \, B\right)} a^{2} - 12 \, {\left(A + i \, B\right)} 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} {\left(A - i \, B\right)} \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{120 \, {\left(5 \, A + 2 i \, B\right)} \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*(105*(I*a*tan(d*x + c) + a)^3*(3*A + I*B) - 5*(I*a*tan(d*x + c) + a)^2*(41*A + 15*I*B)*a - 2*(I*a*tan(d*x + c) + a)*(19*A + 9*I*B)*a^2 - 12*(A + I*B)*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)*(A - I*B)*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) + 120*(5*A + 2*I*B)*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
111,1,283,0,0.763207," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","-\frac{a^{2} {\left(\frac{4 \, {\left(315 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} {\left(2 \, A + i \, B\right)} - 5 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} {\left(211 \, A + 104 i \, B\right)} a + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} {\left(337 \, A + 167 i \, B\right)} a^{2} + 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)} {\left(23 \, A + 13 i \, B\right)} a^{3} + 12 \, {\left(A + i \, B\right)} a^{4}\right)}}{{\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{9}{2}} a^{4} - 2 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{7}{2}} a^{5} + {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} a^{6}} - \frac{15 \, \sqrt{2} {\left(A - i \, B\right)} \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{9}{2}}} + \frac{30 \, {\left(43 \, A + 20 i \, B\right)} \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{9}{2}}}\right)}}{240 \, d}"," ",0,"-1/240*a^2*(4*(315*(I*a*tan(d*x + c) + a)^4*(2*A + I*B) - 5*(I*a*tan(d*x + c) + a)^3*(211*A + 104*I*B)*a + (I*a*tan(d*x + c) + a)^2*(337*A + 167*I*B)*a^2 + 2*(I*a*tan(d*x + c) + a)*(23*A + 13*I*B)*a^3 + 12*(A + I*B)*a^4)/((I*a*tan(d*x + c) + a)^(9/2)*a^4 - 2*(I*a*tan(d*x + c) + a)^(7/2)*a^5 + (I*a*tan(d*x + c) + a)^(5/2)*a^6) - 15*sqrt(2)*(A - I*B)*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^(9/2) + 30*(43*A + 20*I*B)*log((sqrt(I*a*tan(d*x + c) + a) - sqrt(a))/(sqrt(I*a*tan(d*x + c) + a) + sqrt(a)))/a^(9/2))/d","A",0
112,1,204,0,0.546427," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-120 i \, B a \tan\left(d x + c\right)^{\frac{7}{2}} - 8 \, {\left(21 i \, A + 21 \, B\right)} a \tan\left(d x + c\right)^{\frac{5}{2}} - 280 \, {\left(A - i \, B\right)} a \tan\left(d x + c\right)^{\frac{3}{2}} - 8 \, {\left(-105 i \, A - 105 \, B\right)} a \sqrt{\tan\left(d x + c\right)} - 105 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a}{420 \, d}"," ",0,"-1/420*(-120*I*B*a*tan(d*x + c)^(7/2) - 8*(21*I*A + 21*B)*a*tan(d*x + c)^(5/2) - 280*(A - I*B)*a*tan(d*x + c)^(3/2) - 8*(-105*I*A - 105*B)*a*sqrt(tan(d*x + c)) - 105*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a)/d","B",0
113,1,186,0,0.812735," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-24 i \, B a \tan\left(d x + c\right)^{\frac{5}{2}} - 8 \, {\left(5 i \, A + 5 \, B\right)} a \tan\left(d x + c\right)^{\frac{3}{2}} - 120 \, {\left(A - i \, B\right)} a \sqrt{\tan\left(d x + c\right)} - 15 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a}{60 \, d}"," ",0,"-1/60*(-24*I*B*a*tan(d*x + c)^(5/2) - 8*(5*I*A + 5*B)*a*tan(d*x + c)^(3/2) - 120*(A - I*B)*a*sqrt(tan(d*x + c)) - 15*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a)/d","B",0
114,1,170,0,1.708168," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{-8 i \, B a \tan\left(d x + c\right)^{\frac{3}{2}} - 8 \, {\left(3 i \, A + 3 \, B\right)} a \sqrt{\tan\left(d x + c\right)} + 3 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a}{12 \, d}"," ",0,"-1/12*(-8*I*B*a*tan(d*x + c)^(3/2) - 8*(3*I*A + 3*B)*a*sqrt(tan(d*x + c)) + 3*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a)/d","B",0
115,1,151,0,0.813444," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{-8 i \, B a \sqrt{\tan\left(d x + c\right)} + {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a}{4 \, d}"," ",0,"-1/4*(-8*I*B*a*sqrt(tan(d*x + c)) + (2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a)/d","B",0
116,1,151,0,0.883971," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a - \frac{8 \, A a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*((2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a - 8*A*a/sqrt(tan(d*x + c)))/d","B",0
117,1,169,0,1.125726," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a - \frac{8 \, {\left({\left(3 i \, A + 3 \, B\right)} a \tan\left(d x + c\right) + A a\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(3*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a - 8*((3*I*A + 3*B)*a*tan(d*x + c) + A*a)/tan(d*x + c)^(3/2))/d","B",0
118,1,187,0,0.865009," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{15 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a - \frac{8 \, {\left(15 \, {\left(A - i \, B\right)} a \tan\left(d x + c\right)^{2} - {\left(5 i \, A + 5 \, B\right)} a \tan\left(d x + c\right) - 3 \, A a\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"-1/60*(15*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a - 8*(15*(A - I*B)*a*tan(d*x + c)^2 - (5*I*A + 5*B)*a*tan(d*x + c) - 3*A*a)/tan(d*x + c)^(5/2))/d","B",0
119,1,232,0,0.738865," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{140 \, B a^{2} \tan\left(d x + c\right)^{\frac{9}{2}} + 180 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(d x + c\right)^{\frac{7}{2}} - 4 \, {\left(126 i \, A + 126 \, B\right)} a^{2} \tan\left(d x + c\right)^{\frac{5}{2}} - 840 \, {\left(A - i \, B\right)} a^{2} \tan\left(d x + c\right)^{\frac{3}{2}} - 4 \, {\left(-630 i \, A - 630 \, B\right)} a^{2} \sqrt{\tan\left(d x + c\right)} - 315 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2}}{630 \, d}"," ",0,"-1/630*(140*B*a^2*tan(d*x + c)^(9/2) + 180*(A - 2*I*B)*a^2*tan(d*x + c)^(7/2) - 4*(126*I*A + 126*B)*a^2*tan(d*x + c)^(5/2) - 840*(A - I*B)*a^2*tan(d*x + c)^(3/2) - 4*(-630*I*A - 630*B)*a^2*sqrt(tan(d*x + c)) - 315*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2)/d","A",0
120,1,212,0,0.914613," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, B a^{2} \tan\left(d x + c\right)^{\frac{7}{2}} + 84 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(d x + c\right)^{\frac{5}{2}} - 4 \, {\left(70 i \, A + 70 \, B\right)} a^{2} \tan\left(d x + c\right)^{\frac{3}{2}} - 840 \, {\left(A - i \, B\right)} a^{2} \sqrt{\tan\left(d x + c\right)} - 105 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2}}{210 \, d}"," ",0,"-1/210*(60*B*a^2*tan(d*x + c)^(7/2) + 84*(A - 2*I*B)*a^2*tan(d*x + c)^(5/2) - 4*(70*I*A + 70*B)*a^2*tan(d*x + c)^(3/2) - 840*(A - I*B)*a^2*sqrt(tan(d*x + c)) - 105*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2)/d","A",0
121,1,194,0,0.589588," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, B a^{2} \tan\left(d x + c\right)^{\frac{5}{2}} + 20 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(d x + c\right)^{\frac{3}{2}} - 4 \, {\left(30 i \, A + 30 \, B\right)} a^{2} \sqrt{\tan\left(d x + c\right)} + 15 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2}}{30 \, d}"," ",0,"-1/30*(12*B*a^2*tan(d*x + c)^(5/2) + 20*(A - 2*I*B)*a^2*tan(d*x + c)^(3/2) - 4*(30*I*A + 30*B)*a^2*sqrt(tan(d*x + c)) + 15*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2)/d","A",0
122,1,174,0,0.815771," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{4 \, B a^{2} \tan\left(d x + c\right)^{\frac{3}{2}} + 12 \, {\left(A - 2 i \, B\right)} a^{2} \sqrt{\tan\left(d x + c\right)} + 3 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2}}{6 \, d}"," ",0,"-1/6*(4*B*a^2*tan(d*x + c)^(3/2) + 12*(A - 2*I*B)*a^2*sqrt(tan(d*x + c)) + 3*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2)/d","B",0
123,1,170,0,0.738569," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{4 \, B a^{2} \sqrt{\tan\left(d x + c\right)} - {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2} + \frac{4 \, A a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{2 \, d}"," ",0,"-1/2*(4*B*a^2*sqrt(tan(d*x + c)) - (2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2 + 4*A*a^2/sqrt(tan(d*x + c)))/d","B",0
124,1,175,0,0.823517," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2} - \frac{4 \, {\left({\left(6 i \, A + 3 \, B\right)} a^{2} \tan\left(d x + c\right) + A a^{2}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{6 \, d}"," ",0,"1/6*(3*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2 - 4*((6*I*A + 3*B)*a^2*tan(d*x + c) + A*a^2)/tan(d*x + c)^(3/2))/d","B",0
125,1,195,0,0.902936," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{15 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2} - \frac{4 \, {\left(30 \, {\left(A - i \, B\right)} a^{2} \tan\left(d x + c\right)^{2} - {\left(10 i \, A + 5 \, B\right)} a^{2} \tan\left(d x + c\right) - 3 \, A a^{2}\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{30 \, d}"," ",0,"-1/30*(15*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2 - 4*(30*(A - I*B)*a^2*tan(d*x + c)^2 - (10*I*A + 5*B)*a^2*tan(d*x + c) - 3*A*a^2)/tan(d*x + c)^(5/2))/d","A",0
126,1,213,0,0.758238," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","-\frac{105 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{2} + \frac{4 \, {\left({\left(-210 i \, A - 210 \, B\right)} a^{2} \tan\left(d x + c\right)^{3} - 70 \, {\left(A - i \, B\right)} a^{2} \tan\left(d x + c\right)^{2} + {\left(42 i \, A + 21 \, B\right)} a^{2} \tan\left(d x + c\right) + 15 \, A a^{2}\right)}}{\tan\left(d x + c\right)^{\frac{7}{2}}}}{210 \, d}"," ",0,"-1/210*(105*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^2 + 4*((-210*I*A - 210*B)*a^2*tan(d*x + c)^3 - 70*(A - I*B)*a^2*tan(d*x + c)^2 + (42*I*A + 21*B)*a^2*tan(d*x + c) + 15*A*a^2)/tan(d*x + c)^(7/2))/d","A",0
127,1,232,0,0.748025," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{70 i \, B a^{3} \tan\left(d x + c\right)^{\frac{9}{2}} - 2 \, {\left(-45 i \, A - 135 \, B\right)} a^{3} \tan\left(d x + c\right)^{\frac{7}{2}} + 126 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \tan\left(d x + c\right)^{\frac{5}{2}} - 2 \, {\left(420 i \, A + 420 \, B\right)} a^{3} \tan\left(d x + c\right)^{\frac{3}{2}} - 2520 \, {\left(A - i \, B\right)} a^{3} \sqrt{\tan\left(d x + c\right)} - 315 \, {\left(\sqrt{2} {\left(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3}}{315 \, d}"," ",0,"-1/315*(70*I*B*a^3*tan(d*x + c)^(9/2) - 2*(-45*I*A - 135*B)*a^3*tan(d*x + c)^(7/2) + 126*(3*A - 4*I*B)*a^3*tan(d*x + c)^(5/2) - 2*(420*I*A + 420*B)*a^3*tan(d*x + c)^(3/2) - 2520*(A - I*B)*a^3*sqrt(tan(d*x + c)) - 315*(sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3)/d","A",0
128,1,214,0,0.773066," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{30 i \, B a^{3} \tan\left(d x + c\right)^{\frac{7}{2}} - 2 \, {\left(-21 i \, A - 63 \, B\right)} a^{3} \tan\left(d x + c\right)^{\frac{5}{2}} + 70 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \tan\left(d x + c\right)^{\frac{3}{2}} - 2 \, {\left(420 i \, A + 420 \, B\right)} a^{3} \sqrt{\tan\left(d x + c\right)} - 105 \, {\left(\sqrt{2} {\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3}}{105 \, d}"," ",0,"-1/105*(30*I*B*a^3*tan(d*x + c)^(7/2) - 2*(-21*I*A - 63*B)*a^3*tan(d*x + c)^(5/2) + 70*(3*A - 4*I*B)*a^3*tan(d*x + c)^(3/2) - 2*(420*I*A + 420*B)*a^3*sqrt(tan(d*x + c)) - 105*(sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3)/d","A",0
129,1,194,0,0.606397," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{6 i \, B a^{3} \tan\left(d x + c\right)^{\frac{5}{2}} - 2 \, {\left(-5 i \, A - 15 \, B\right)} a^{3} \tan\left(d x + c\right)^{\frac{3}{2}} + 30 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sqrt{\tan\left(d x + c\right)} + 15 \, {\left(\sqrt{2} {\left(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3}}{15 \, d}"," ",0,"-1/15*(6*I*B*a^3*tan(d*x + c)^(5/2) - 2*(-5*I*A - 15*B)*a^3*tan(d*x + c)^(3/2) + 30*(3*A - 4*I*B)*a^3*sqrt(tan(d*x + c)) + 15*(sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3)/d","A",0
130,1,188,0,1.183264," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, B a^{3} \tan\left(d x + c\right)^{\frac{3}{2}} - 2 \, {\left(-3 i \, A - 9 \, B\right)} a^{3} \sqrt{\tan\left(d x + c\right)} + 3 \, {\left(\sqrt{2} {\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3} + \frac{6 \, A a^{3}}{\sqrt{\tan\left(d x + c\right)}}}{3 \, d}"," ",0,"-1/3*(2*I*B*a^3*tan(d*x + c)^(3/2) - 2*(-3*I*A - 9*B)*a^3*sqrt(tan(d*x + c)) + 3*(sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3 + 6*A*a^3/sqrt(tan(d*x + c)))/d","A",0
131,1,187,0,0.936683," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{6 i \, B a^{3} \sqrt{\tan\left(d x + c\right)} - 3 \, {\left(\sqrt{2} {\left(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3} + \frac{2 \, {\left({\left(9 i \, A + 3 \, B\right)} a^{3} \tan\left(d x + c\right) + A a^{3}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{3 \, d}"," ",0,"-1/3*(6*I*B*a^3*sqrt(tan(d*x + c)) - 3*(sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3 + 2*((9*I*A + 3*B)*a^3*tan(d*x + c) + A*a^3)/tan(d*x + c)^(3/2))/d","A",0
132,1,195,0,0.868347," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{15 \, {\left(\sqrt{2} {\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3} + \frac{2 \, {\left(15 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \tan\left(d x + c\right)^{2} - {\left(15 i \, A + 5 \, B\right)} a^{3} \tan\left(d x + c\right) - 3 \, A a^{3}\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{15 \, d}"," ",0,"1/15*(15*(sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3 + 2*(15*(4*A - 3*I*B)*a^3*tan(d*x + c)^2 - (15*I*A + 5*B)*a^3*tan(d*x + c) - 3*A*a^3)/tan(d*x + c)^(5/2))/d","A",0
133,1,213,0,1.036491," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","-\frac{105 \, {\left(\sqrt{2} {\left(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(-\left(2 i + 2\right) \, A + \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, B\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} a^{3} + \frac{2 \, {\left({\left(-420 i \, A - 420 \, B\right)} a^{3} \tan\left(d x + c\right)^{3} - 35 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \tan\left(d x + c\right)^{2} + {\left(63 i \, A + 21 \, B\right)} a^{3} \tan\left(d x + c\right) + 15 \, A a^{3}\right)}}{\tan\left(d x + c\right)^{\frac{7}{2}}}}{105 \, d}"," ",0,"-1/105*(105*(sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I + 2)*A + (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*a^3 + 2*((-420*I*A - 420*B)*a^3*tan(d*x + c)^3 - 35*(4*A - 3*I*B)*a^3*tan(d*x + c)^2 + (63*I*A + 21*B)*a^3*tan(d*x + c) + 15*A*a^3)/tan(d*x + c)^(7/2))/d","A",0
134,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*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
135,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*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
136,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*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
137,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
138,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
139,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
140,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*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
141,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*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
142,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*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
143,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
144,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
145,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
146,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(9/2)*(A+B*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
147,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(7/2)*(A+B*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
148,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*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
149,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*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
150,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*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
151,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
152,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
153,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(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
154,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{i \, a \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(I*a*tan(d*x + c) + a)*sqrt(tan(d*x + c)), x)","F",0
156,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(I*a*tan(d*x + c) + a)/sqrt(tan(d*x + c)), x)","F",0
157,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(3/2), x)","F",0
162,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c)), x)","F",0
163,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(3/2), x)","F",0
170,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c)), x)","F",0
171,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
180,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
181,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
182,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/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
183,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/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
184,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2)/tan(d*x+c)^(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
185,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(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
186,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(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
187,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
188,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
189,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
190,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(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
191,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(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
192,-2,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(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
193,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
194,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
195,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
196,1,167,0,0.504601," ","integrate((a+I*a*tan(d*x+c))^(1/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{1}{3}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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) + 12 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}} B a\right)}}{4 \, a d}"," ",0,"-1/4*I*(2*sqrt(3)*2^(1/3)*(A - I*B)*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 - I*B)*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 - I*B)*a^(4/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 12*I*(I*a*tan(d*x + c) + a)^(1/3)*B*a)/(a*d)","A",0
197,1,210,0,0.686934," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(20 \, \sqrt{3} 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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) - 10 \cdot 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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) + 20 \cdot 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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) - 15 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{8}{3}} B a + 24 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}} {\left(A + i \, B\right)} a^{2} - 60 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} B a^{3}\right)}}{40 \, a^{3} d}"," ",0,"-1/40*I*(20*sqrt(3)*2^(2/3)*(A - I*B)*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)) - 10*2^(2/3)*(A - I*B)*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)) + 20*2^(2/3)*(A - I*B)*a^(11/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 15*I*(I*a*tan(d*x + c) + a)^(8/3)*B*a + 24*(I*a*tan(d*x + c) + a)^(5/3)*(A + I*B)*a^2 - 60*I*(I*a*tan(d*x + c) + a)^(2/3)*B*a^3)/(a^3*d)","A",0
198,1,187,0,0.793867," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{10 \, \sqrt{3} 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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) - 5 \cdot 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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) + 10 \cdot 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{3}} B a + 30 \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} A a^{2}}{20 \, a^{2} d}"," ",0,"1/20*(10*sqrt(3)*2^(2/3)*(A - I*B)*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)) - 5*2^(2/3)*(A - I*B)*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)) + 10*2^(2/3)*(A - I*B)*a^(8/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 12*I*(I*a*tan(d*x + c) + a)^(5/3)*B*a + 30*(I*a*tan(d*x + c) + a)^(2/3)*A*a^2)/(a^2*d)","A",0
199,1,168,0,0.456293," ","integrate((a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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) - 6 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} B a\right)}}{4 \, a d}"," ",0,"1/4*I*(2*sqrt(3)*2^(2/3)*(A - I*B)*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 - I*B)*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 - I*B)*a^(5/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 6*I*(I*a*tan(d*x + c) + a)^(2/3)*B*a)/(a*d)","A",0
200,1,252,0,0.438971," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{3} 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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) - 4 \, \sqrt{3} A a^{\frac{2}{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 \, A a^{\frac{2}{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 a^{\frac{2}{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^(2/3)*(A - I*B)*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 - I*B)*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 - I*B)*a^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 4*sqrt(3)*A*a^(2/3)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3)) + 2*A*a^(2/3)*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*a^(2/3)*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3)))/d","A",0
201,1,298,0,0.435450," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{6 \, \sqrt{3} 2^{\frac{2}{3}} {\left(A - i \, B\right)} \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{3 \cdot 2^{\frac{2}{3}} {\left(A - i \, B\right)} \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{6 \cdot 2^{\frac{2}{3}} {\left(A - i \, B\right)} \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{4 \, \sqrt{3} {\left(2 \, A - 3 i \, B\right)} \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{2 \, {\left(2 \, A - 3 i \, B\right)} \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{4 \, {\left(2 \, A - 3 i \, B\right)} \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 i \, {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}} A}{a \tan\left(d x + c\right)}\right)} a}{12 \, d}"," ",0,"-1/12*I*(6*sqrt(3)*2^(2/3)*(A - I*B)*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) - 3*2^(2/3)*(A - I*B)*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) + 6*2^(2/3)*(A - I*B)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3))/a^(1/3) - 4*sqrt(3)*(2*A - 3*I*B)*arctan(1/3*sqrt(3)*(2*(I*a*tan(d*x + c) + a)^(1/3) + a^(1/3))/a^(1/3))/a^(1/3) + 2*(2*A - 3*I*B)*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) - 4*(2*A - 3*I*B)*log((I*a*tan(d*x + c) + a)^(1/3) - a^(1/3))/a^(1/3) - 12*I*(I*a*tan(d*x + c) + a)^(2/3)*A/(a*tan(d*x + c)))*a/d","A",0
202,1,172,0,0.457831," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{2}{3}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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 \, {\left(A + i \, B\right)} 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 - I*B)*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 - I*B)*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 - I*B)*a^(2/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) + 12*(A + I*B)*a/(I*a*tan(d*x + c) + a)^(1/3))/(a*d)","A",0
203,1,171,0,0.429065," ","integrate((A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(2/3),x, algorithm=""maxima"")","-\frac{i \, {\left(2 \, \sqrt{3} 2^{\frac{1}{3}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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}} {\left(A - i \, B\right)} 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 \, {\left(A + i \, B\right)} 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 - I*B)*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 - I*B)*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 - I*B)*a^(1/3)*log(-2^(1/3)*a^(1/3) + (I*a*tan(d*x + c) + a)^(1/3)) - 6*(A + I*B)*a/(I*a*tan(d*x + c) + a)^(2/3))/(a*d)","A",0
204,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{4} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^4*tan(d*x + c)^m, x)","F",0
205,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{3} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^3*tan(d*x + c)^m, x)","F",0
206,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^2*tan(d*x + c)^m, x)","F",0
207,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
208,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
209,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*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: THROW: The catch RAT-ERR is undefined.","F(-2)",0
210,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*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: THROW: The catch RAT-ERR is undefined.","F(-2)",0
211,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*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: THROW: The catch RAT-ERR is undefined.","F(-2)",0
212,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^m, x)","F",0
213,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^m, x)","F",0
214,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{i \, a \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(I*a*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
215,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
216,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(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
217,-2,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(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
218,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n*tan(d*x + c)^m, x)","F",0
219,0,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
220,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
221,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*tan(d*x + c), x)","F",0
222,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n, x)","F",0
223,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*cot(d*x + c), x)","F",0
224,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
225,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
226,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n*tan(d*x + c)^(5/2), x)","F",0
227,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
228,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
229,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n/sqrt(tan(d*x + c)), x)","F",0
230,-1,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n/tan(d*x + c)^(5/2), x)","F",0
232,1,86,0,1.619977," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b \tan\left(d x + c\right)^{3} + 3 \, {\left(B a + A b\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(A a - B b\right)} {\left(d x + c\right)} - 3 \, {\left(B a + A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(A a - B b\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b*tan(d*x + c)^3 + 3*(B*a + A*b)*tan(d*x + c)^2 - 6*(A*a - B*b)*(d*x + c) - 3*(B*a + A*b)*log(tan(d*x + c)^2 + 1) + 6*(A*a - B*b)*tan(d*x + c))/d","A",0
233,1,66,0,0.904516," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B b \tan\left(d x + c\right)^{2} - 2 \, {\left(B a + A b\right)} {\left(d x + c\right)} + {\left(A a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b*tan(d*x + c)^2 - 2*(B*a + A*b)*(d*x + c) + (A*a - B*b)*log(tan(d*x + c)^2 + 1) + 2*(B*a + A*b)*tan(d*x + c))/d","A",0
234,1,50,0,0.905099," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b \tan\left(d x + c\right) + 2 \, {\left(A a - B b\right)} {\left(d x + c\right)} + {\left(B a + A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*B*b*tan(d*x + c) + 2*(A*a - B*b)*(d*x + c) + (B*a + A*b)*log(tan(d*x + c)^2 + 1))/d","A",0
235,1,52,0,1.096804," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, A a \log\left(\tan\left(d x + c\right)\right) + 2 \, {\left(B a + A b\right)} {\left(d x + c\right)} - {\left(A a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*A*a*log(tan(d*x + c)) + 2*(B*a + A*b)*(d*x + c) - (A*a - B*b)*log(tan(d*x + c)^2 + 1))/d","A",0
236,1,68,0,0.868526," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(A a - B b\right)} {\left(d x + c\right)} + {\left(B a + A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(B a + A b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, A a}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(A*a - B*b)*(d*x + c) + (B*a + A*b)*log(tan(d*x + c)^2 + 1) - 2*(B*a + A*b)*log(tan(d*x + c)) + 2*A*a/tan(d*x + c))/d","A",0
237,1,86,0,0.870346," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(B a + A b\right)} {\left(d x + c\right)} - {\left(A a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(A a - B b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{A a + 2 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(B*a + A*b)*(d*x + c) - (A*a - B*b)*log(tan(d*x + c)^2 + 1) + 2*(A*a - B*b)*log(tan(d*x + c)) + (A*a + 2*(B*a + A*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
238,1,104,0,0.876688," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(A a - B b\right)} {\left(d x + c\right)} + 3 \, {\left(B a + A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(B a + A b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{6 \, {\left(A a - B b\right)} \tan\left(d x + c\right)^{2} - 2 \, A a - 3 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(A*a - B*b)*(d*x + c) + 3*(B*a + A*b)*log(tan(d*x + c)^2 + 1) - 6*(B*a + A*b)*log(tan(d*x + c)) + (6*(A*a - B*b)*tan(d*x + c)^2 - 2*A*a - 3*(B*a + A*b)*tan(d*x + c))/tan(d*x + c)^3)/d","A",0
239,1,122,0,1.048052," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(B a + A b\right)} {\left(d x + c\right)} - 6 \, {\left(A a - B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(A a - B b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{12 \, {\left(B a + A b\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(A a - B b\right)} \tan\left(d x + c\right)^{2} - 3 \, A a - 4 \, {\left(B a + A b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(B*a + A*b)*(d*x + c) - 6*(A*a - B*b)*log(tan(d*x + c)^2 + 1) + 12*(A*a - B*b)*log(tan(d*x + c)) + (12*(B*a + A*b)*tan(d*x + c)^3 + 6*(A*a - B*b)*tan(d*x + c)^2 - 3*A*a - 4*(B*a + A*b)*tan(d*x + c))/tan(d*x + c)^4)/d","A",0
240,1,147,0,1.260809," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B b^{2} \tan\left(d x + c\right)^{4} + 4 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)^{2} - 12 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)} - 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^2*tan(d*x + c)^4 + 4*(2*B*a*b + A*b^2)*tan(d*x + c)^3 + 6*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c)^2 - 12*(A*a^2 - 2*B*a*b - A*b^2)*(d*x + c) - 6*(B*a^2 + 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) + 12*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c))/d","A",0
241,1,120,0,1.138684," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b^{2} \tan\left(d x + c\right)^{3} + 3 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{2} - 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b^2*tan(d*x + c)^3 + 3*(2*B*a*b + A*b^2)*tan(d*x + c)^2 - 6*(B*a^2 + 2*A*a*b - B*b^2)*(d*x + c) + 3*(A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1) + 6*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c))/d","A",0
242,1,91,0,0.965222," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B b^{2} \tan\left(d x + c\right)^{2} + 2 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)} + {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^2*tan(d*x + c)^2 + 2*(A*a^2 - 2*B*a*b - A*b^2)*(d*x + c) + (B*a^2 + 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) + 2*(2*B*a*b + A*b^2)*tan(d*x + c))/d","A",0
243,1,85,0,0.835078," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, A a^{2} \log\left(\tan\left(d x + c\right)\right) + 2 \, B b^{2} \tan\left(d x + c\right) + 2 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)} - {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(2*A*a^2*log(tan(d*x + c)) + 2*B*b^2*tan(d*x + c) + 2*(B*a^2 + 2*A*a*b - B*b^2)*(d*x + c) - (A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1))/d","A",0
244,1,93,0,0.889697," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)} + {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(B a^{2} + 2 \, A a b\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{2 \, A a^{2}}{\tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(A*a^2 - 2*B*a*b - A*b^2)*(d*x + c) + (B*a^2 + 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) - 2*(B*a^2 + 2*A*a*b)*log(tan(d*x + c)) + 2*A*a^2/tan(d*x + c))/d","A",0
245,1,120,0,0.841617," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)} - {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{A a^{2} + 2 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 + 2*A*a*b - B*b^2)*(d*x + c) - (A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1) + 2*(A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)) + (A*a^2 + 2*(B*a^2 + 2*A*a*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
246,1,149,0,0.975596," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{2 \, A a^{2} - 6 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(A*a^2 - 2*B*a*b - A*b^2)*(d*x + c) + 3*(B*a^2 + 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1) - 6*(B*a^2 + 2*A*a*b - B*b^2)*log(tan(d*x + c)) - (2*A*a^2 - 6*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c)^2 + 3*(B*a^2 + 2*A*a*b)*tan(d*x + c))/tan(d*x + c)^3)/d","A",0
247,1,175,0,0.789170," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)} - 6 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{12 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)^{3} - 3 \, A a^{2} + 6 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)^{2} - 4 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(B*a^2 + 2*A*a*b - B*b^2)*(d*x + c) - 6*(A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1) + 12*(A*a^2 - 2*B*a*b - A*b^2)*log(tan(d*x + c)) + (12*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c)^3 - 3*A*a^2 + 6*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c)^2 - 4*(B*a^2 + 2*A*a*b)*tan(d*x + c))/tan(d*x + c)^4)/d","A",0
248,1,214,0,0.765962," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, B b^{3} \tan\left(d x + c\right)^{5} + 15 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{4} + 20 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{2} - 60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} {\left(d x + c\right)} - 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*B*b^3*tan(d*x + c)^5 + 15*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^4 + 20*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c)^3 + 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^2 - 60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*(d*x + c) - 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2 + 1) + 60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*tan(d*x + c))/d","A",0
249,1,179,0,0.670163," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B b^{3} \tan\left(d x + c\right)^{4} + 4 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{2} - 12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} {\left(d x + c\right)} + 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^3*tan(d*x + c)^4 + 4*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^3 + 6*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c)^2 - 12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*(d*x + c) + 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1) + 12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c))/d","A",0
250,1,143,0,0.930240," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b^{3} \tan\left(d x + c\right)^{3} + 3 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b^3*tan(d*x + c)^3 + 3*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^2 + 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*(d*x + c) + 3*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2 + 1) + 6*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c))/d","A",0
251,1,124,0,0.963101," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B b^{3} \tan\left(d x + c\right)^{2} + 2 \, A a^{3} \log\left(\tan\left(d x + c\right)\right) + 2 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} {\left(d x + c\right)} - {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^3*tan(d*x + c)^2 + 2*A*a^3*log(tan(d*x + c)) + 2*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*(d*x + c) - (A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1) + 2*(3*B*a*b^2 + A*b^3)*tan(d*x + c))/d","A",0
252,1,125,0,0.770860," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b^{3} \tan\left(d x + c\right) - \frac{2 \, A a^{3}}{\tan\left(d x + c\right)} - 2 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} {\left(d x + c\right)} - {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \log\left(\tan\left(d x + c\right)\right)}{2 \, d}"," ",0,"1/2*(2*B*b^3*tan(d*x + c) - 2*A*a^3/tan(d*x + c) - 2*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*(d*x + c) - (B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2 + 1) + 2*(B*a^3 + 3*A*a^2*b)*log(tan(d*x + c)))/d","A",0
253,1,142,0,0.942831," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} {\left(d x + c\right)} - {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{A a^{3} + 2 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*(d*x + c) - (A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1) + 2*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*log(tan(d*x + c)) + (A*a^3 + 2*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
254,1,180,0,0.633590," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{2 \, A a^{3} - 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*(d*x + c) + 3*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2 + 1) - 6*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)) - (2*A*a^3 - 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 + 3*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/tan(d*x + c)^3)/d","A",0
255,1,215,0,0.734835," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{3 \, A a^{3} - 12 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} + 4 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*(d*x + c) - 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(tan(d*x + c)^2 + 1) + 12*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*log(tan(d*x + c)) - (3*A*a^3 - 12*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^3 - 6*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 + 4*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/tan(d*x + c)^4)/d","A",0
256,1,250,0,0.783356," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} {\left(d x + c\right)} + 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{60 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \tan\left(d x + c\right)^{4} + 12 \, A a^{3} - 30 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{3} - 20 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} + 15 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*(d*x + c) + 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)^2 + 1) - 60*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*log(tan(d*x + c)) + (60*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*tan(d*x + c)^4 + 12*A*a^3 - 30*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^3 - 20*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 + 15*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/tan(d*x + c)^5)/d","A",0
257,1,290,0,0.735974," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{10 \, B b^{4} \tan\left(d x + c\right)^{6} + 12 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{5} + 15 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)^{4} + 20 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \tan\left(d x + c\right)^{2} - 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} - 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*B*b^4*tan(d*x + c)^6 + 12*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^5 + 15*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c)^4 + 20*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*tan(d*x + c)^3 + 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*tan(d*x + c)^2 - 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*(d*x + c) - 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2 + 1) + 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*tan(d*x + c))/d","A",0
258,1,246,0,0.839705," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, B b^{4} \tan\left(d x + c\right)^{5} + 15 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} + 20 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)^{3} + 30 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)^{2} - 60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)} + 30 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \tan\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*B*b^4*tan(d*x + c)^5 + 15*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 + 20*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c)^3 + 30*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*tan(d*x + c)^2 - 60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*(d*x + c) + 30*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2 + 1) + 60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*tan(d*x + c))/d","A",0
259,1,202,0,0.861246," ","integrate((a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B b^{4} \tan\left(d x + c\right)^{4} + 4 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{3} + 6 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)^{2} + 12 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} + 6 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(4 \, B a^{3} b + 6 \, A a^{2} b^{2} - 4 \, B a b^{3} - A b^{4}\right)} \tan\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^4*tan(d*x + c)^4 + 4*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^3 + 6*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c)^2 + 12*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*(d*x + c) + 6*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2 + 1) + 12*(4*B*a^3*b + 6*A*a^2*b^2 - 4*B*a*b^3 - A*b^4)*tan(d*x + c))/d","A",0
260,1,175,0,0.651581," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b^{4} \tan\left(d x + c\right)^{3} + 6 \, A a^{4} \log\left(\tan\left(d x + c\right)\right) + 3 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{2} + 6 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)} - 3 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 6 \, {\left(6 \, B a^{2} b^{2} + 4 \, A a b^{3} - B b^{4}\right)} \tan\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*b^4*tan(d*x + c)^3 + 6*A*a^4*log(tan(d*x + c)) + 3*(4*B*a*b^3 + A*b^4)*tan(d*x + c)^2 + 6*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*(d*x + c) - 3*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2 + 1) + 6*(6*B*a^2*b^2 + 4*A*a*b^3 - B*b^4)*tan(d*x + c))/d","A",0
261,1,164,0,0.687237," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B b^{4} \tan\left(d x + c\right)^{2} - \frac{2 \, A a^{4}}{\tan\left(d x + c\right)} - 2 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} - {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \log\left(\tan\left(d x + c\right)\right) + 2 \, {\left(4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^4*tan(d*x + c)^2 - 2*A*a^4/tan(d*x + c) - 2*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*(d*x + c) - (B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2 + 1) + 2*(B*a^4 + 4*A*a^3*b)*log(tan(d*x + c)) + 2*(4*B*a*b^3 + A*b^4)*tan(d*x + c))/d","A",0
262,1,173,0,0.942585," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b^{4} \tan\left(d x + c\right) - 2 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)} + {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{A a^{4} + 2 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*B*b^4*tan(d*x + c) - 2*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*(d*x + c) + (A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2 + 1) - 2*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*log(tan(d*x + c)) - (A*a^4 + 2*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/tan(d*x + c)^2)/d","A",0
263,1,202,0,1.197393," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 6 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{2 \, A a^{4} - 6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*(d*x + c) + 3*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2 + 1) - 6*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*log(tan(d*x + c)) - (2*A*a^4 - 6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 + 3*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/tan(d*x + c)^3)/d","A",0
264,1,246,0,0.664913," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)} - 6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 12 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)\right) - \frac{3 \, A a^{4} - 12 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} - 6 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + 4 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*(d*x + c) - 6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2 + 1) + 12*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)) - (3*A*a^4 - 12*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*tan(d*x + c)^3 - 6*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 + 4*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/tan(d*x + c)^4)/d","A",0
265,1,289,0,0.758193," ","integrate(cot(d*x+c)^6*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)} + 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{12 \, A a^{4} + 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} - 30 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} - 20 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + 15 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*(d*x + c) + 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2 + 1) - 60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)) + (12*A*a^4 + 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 - 30*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*tan(d*x + c)^3 - 20*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 + 15*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/tan(d*x + c)^5)/d","A",0
266,1,333,0,1.311168," ","integrate(cot(d*x+c)^7*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)} - 30 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right) + 60 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \log\left(\tan\left(d x + c\right)\right) + \frac{60 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \tan\left(d x + c\right)^{5} + 10 \, A a^{4} + 30 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2} + 4 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{4} - 20 \, {\left(B a^{4} + 4 \, A a^{3} b - 6 \, B a^{2} b^{2} - 4 \, A a b^{3}\right)} \tan\left(d x + c\right)^{3} - 15 \, {\left(A a^{4} - 4 \, B a^{3} b - 6 \, A a^{2} b^{2}\right)} \tan\left(d x + c\right)^{2} + 12 \, {\left(B a^{4} + 4 \, A a^{3} b\right)} \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*(d*x + c) - 30*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)^2 + 1) + 60*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*log(tan(d*x + c)) + (60*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*tan(d*x + c)^5 + 10*A*a^4 + 30*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2 + 4*B*a*b^3 + A*b^4)*tan(d*x + c)^4 - 20*(B*a^4 + 4*A*a^3*b - 6*B*a^2*b^2 - 4*A*a*b^3)*tan(d*x + c)^3 - 15*(A*a^4 - 4*B*a^3*b - 6*A*a^2*b^2)*tan(d*x + c)^2 + 12*(B*a^4 + 4*A*a^3*b)*tan(d*x + c))/tan(d*x + c)^6)/d","A",0
267,1,130,0,0.777186," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a - A b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(B a^{4} - A a^{3} b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} b^{3} + b^{5}} - \frac{{\left(A a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{B b \tan\left(d x + c\right)^{2} - 2 \, {\left(B a - A b\right)} \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*(B*a - A*b)*(d*x + c)/(a^2 + b^2) + 2*(B*a^4 - A*a^3*b)*log(b*tan(d*x + c) + a)/(a^2*b^3 + b^5) - (A*a + B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + (B*b*tan(d*x + c)^2 - 2*(B*a - A*b)*tan(d*x + c))/b^2)/d","A",0
268,1,109,0,0.993801," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(A a + B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(B a^{3} - A a^{2} b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} b^{2} + b^{4}} + \frac{{\left(B a - A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, B \tan\left(d x + c\right)}{b}}{2 \, d}"," ",0,"-1/2*(2*(A*a + B*b)*(d*x + c)/(a^2 + b^2) + 2*(B*a^3 - A*a^2*b)*log(b*tan(d*x + c) + a)/(a^2*b^2 + b^4) + (B*a - A*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*B*tan(d*x + c)/b)/d","A",0
269,1,94,0,1.018397," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a - A b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{2 \, {\left(B a^{2} - A a b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} b + b^{3}} - \frac{{\left(A a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"-1/2*(2*(B*a - A*b)*(d*x + c)/(a^2 + b^2) - 2*(B*a^2 - A*a*b)*log(b*tan(d*x + c) + a)/(a^2*b + b^3) - (A*a + B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
270,1,88,0,0.485501," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a + B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{2 \, {\left(B a - A b\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} + b^{2}} + \frac{{\left(B a - A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*(A*a + B*b)*(d*x + c)/(a^2 + b^2) - 2*(B*a - A*b)*log(b*tan(d*x + c) + a)/(a^2 + b^2) + (B*a - A*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
271,1,107,0,1.097425," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a - A b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(B a b - A b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{3} + a b^{2}} - \frac{{\left(A a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, A \log\left(\tan\left(d x + c\right)\right)}{a}}{2 \, d}"," ",0,"1/2*(2*(B*a - A*b)*(d*x + c)/(a^2 + b^2) + 2*(B*a*b - A*b^2)*log(b*tan(d*x + c) + a)/(a^3 + a*b^2) - (A*a + B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*A*log(tan(d*x + c))/a)/d","A",0
272,1,131,0,0.748732," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(A a + B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} + \frac{2 \, {\left(B a b^{2} - A b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} + a^{2} b^{2}} + \frac{{\left(B a - A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, {\left(B a - A b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{2}} + \frac{2 \, A}{a \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(A*a + B*b)*(d*x + c)/(a^2 + b^2) + 2*(B*a*b^2 - A*b^3)*log(b*tan(d*x + c) + a)/(a^4 + a^2*b^2) + (B*a - A*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*(B*a - A*b)*log(tan(d*x + c))/a^2 + 2*A/(a*tan(d*x + c)))/d","A",0
273,1,158,0,0.829690," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a - A b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{2 \, {\left(B a b^{3} - A b^{4}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{5} + a^{3} b^{2}} - \frac{{\left(A a + B b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(A a^{2} + B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{3}} + \frac{A a + 2 \, {\left(B a - A b\right)} \tan\left(d x + c\right)}{a^{2} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*(B*a - A*b)*(d*x + c)/(a^2 + b^2) - 2*(B*a*b^3 - A*b^4)*log(b*tan(d*x + c) + a)/(a^5 + a^3*b^2) - (A*a + B*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(A*a^2 + B*a*b - A*b^2)*log(tan(d*x + c))/a^3 + (A*a + 2*(B*a - A*b)*tan(d*x + c))/(a^2*tan(d*x + c)^2))/d","A",0
274,1,200,0,0.914397," ","integrate(cot(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(A a + B b\right)} {\left(d x + c\right)}}{a^{2} + b^{2}} - \frac{6 \, {\left(B a b^{4} - A b^{5}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{6} + a^{4} b^{2}} + \frac{3 \, {\left(B a - A b\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{6 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{4}} - \frac{2 \, A a^{2} - 6 \, {\left(A a^{2} + B a b - A b^{2}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{2} - A a b\right)} \tan\left(d x + c\right)}{a^{3} \tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(A*a + B*b)*(d*x + c)/(a^2 + b^2) - 6*(B*a*b^4 - A*b^5)*log(b*tan(d*x + c) + a)/(a^6 + a^4*b^2) + 3*(B*a - A*b)*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 6*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*log(tan(d*x + c))/a^4 - (2*A*a^2 - 6*(A*a^2 + B*a*b - A*b^2)*tan(d*x + c)^2 + 3*(B*a^2 - A*a*b)*tan(d*x + c))/(a^3*tan(d*x + c)^3))/d","A",0
275,1,220,0,0.877241," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a^{2} - 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(2 \, B a^{5} - A a^{4} b + 4 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}} - \frac{{\left(A a^{2} + 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{4} - A a^{3} b\right)}}{a^{3} b^{3} + a b^{5} + {\left(a^{2} b^{4} + b^{6}\right)} \tan\left(d x + c\right)} + \frac{2 \, B \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*(B*a^2 - 2*A*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(2*B*a^5 - A*a^4*b + 4*B*a^3*b^2 - 3*A*a^2*b^3)*log(b*tan(d*x + c) + a)/(a^4*b^3 + 2*a^2*b^5 + b^7) - (A*a^2 + 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^4 - A*a^3*b)/(a^3*b^3 + a*b^5 + (a^2*b^4 + b^6)*tan(d*x + c)) + 2*B*tan(d*x + c)/b^2)/d","A",0
276,1,197,0,0.862559," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(A a^{2} + 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{4} + 3 \, B a^{2} b^{2} - 2 \, A a b^{3}\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(B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{3} - A a^{2} b\right)}}{a^{3} b^{2} + a b^{4} + {\left(a^{2} b^{3} + b^{5}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(A*a^2 + 2*B*a*b - A*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^4 + 3*B*a^2*b^2 - 2*A*a*b^3)*log(b*tan(d*x + c) + a)/(a^4*b^2 + 2*a^2*b^4 + b^6) + (B*a^2 - 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^3 - A*a^2*b)/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(d*x + c)))/d","A",0
277,1,185,0,0.698177," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a^{2} - 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(A a^{2} + 2 \, B a b - A 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 a^{2} + 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a^{2} - A a b\right)}}{a^{3} b + a b^{3} + {\left(a^{2} b^{2} + b^{4}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 - 2*A*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(A*a^2 + 2*B*a*b - A*b^2)*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) - (A*a^2 + 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a^2 - A*a*b)/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(d*x + c)))/d","A",0
278,1,177,0,0.860471," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a^{2} + 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a^{2} - 2 \, A a b - B 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(B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(B a - A b\right)}}{a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(A*a^2 + 2*B*a*b - A*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a^2 - 2*A*a*b - B*b^2)*log(b*tan(d*x + c) + a)/(a^4 + 2*a^2*b^2 + b^4) + (B*a^2 - 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(B*a - A*b)/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)))/d","A",0
279,1,208,0,0.883052," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a^{2} - 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(2 \, B a^{3} b - 3 \, A a^{2} b^{2} - A 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 a^{2} + 2 \, B a b - A b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(B a b - A b^{2}\right)}}{a^{4} + a^{2} b^{2} + {\left(a^{3} b + a b^{3}\right)} \tan\left(d x + c\right)} + \frac{2 \, A \log\left(\tan\left(d x + c\right)\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*(2*(B*a^2 - 2*A*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(2*B*a^3*b - 3*A*a^2*b^2 - A*b^4)*log(b*tan(d*x + c) + a)/(a^6 + 2*a^4*b^2 + a^2*b^4) - (A*a^2 + 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) - 2*(B*a*b - A*b^2)/(a^4 + a^2*b^2 + (a^3*b + a*b^3)*tan(d*x + c)) + 2*A*log(tan(d*x + c))/a^2)/d","A",0
280,1,262,0,0.897930," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(A a^{2} + 2 \, B a b - A b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(3 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3} + B a b^{4} - 2 \, A 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{{\left(B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(A a^{3} + A a b^{2} + {\left(A a^{2} b - B a b^{2} + 2 \, A 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)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} \tan\left(d x + c\right)} - \frac{2 \, {\left(B a - 2 \, A b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*(2*(A*a^2 + 2*B*a*b - A*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) + 2*(3*B*a^3*b^2 - 4*A*a^2*b^3 + B*a*b^4 - 2*A*b^5)*log(b*tan(d*x + c) + a)/(a^7 + 2*a^5*b^2 + a^3*b^4) + (B*a^2 - 2*A*a*b - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(A*a^3 + A*a*b^2 + (A*a^2*b - B*a*b^2 + 2*A*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*a - 2*A*b)*log(tan(d*x + c))/a^3)/d","A",0
281,1,325,0,0.824729," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a^{2} - 2 \, A a b - B b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(4 \, B a^{3} b^{3} - 5 \, A a^{2} b^{4} + 2 \, B a b^{5} - 3 \, A 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 a^{2} + 2 \, B a b - A 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 a^{4} + A a^{2} b^{2} + 2 \, {\left(B a^{3} b - 2 \, A a^{2} b^{2} + 2 \, B a b^{3} - 3 \, A b^{4}\right)} \tan\left(d x + c\right)^{2} + {\left(2 \, B a^{4} - 3 \, A a^{3} b + 2 \, B a^{2} b^{2} - 3 \, A 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 a^{2} + 2 \, B a b - 3 \, A b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^2 - 2*A*a*b - B*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(4*B*a^3*b^3 - 5*A*a^2*b^4 + 2*B*a*b^5 - 3*A*b^6)*log(b*tan(d*x + c) + a)/(a^8 + 2*a^6*b^2 + a^4*b^4) - (A*a^2 + 2*B*a*b - A*b^2)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + (A*a^4 + A*a^2*b^2 + 2*(B*a^3*b - 2*A*a^2*b^2 + 2*B*a*b^3 - 3*A*b^4)*tan(d*x + c)^2 + (2*B*a^4 - 3*A*a^3*b + 2*B*a^2*b^2 - 3*A*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*a^2 + 2*B*a*b - 3*A*b^2)*log(tan(d*x + c))/a^4)/d","A",0
282,1,389,0,0.830079," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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 \, B a^{7} - A a^{6} b + 9 \, B a^{5} b^{2} - 3 \, A a^{4} b^{3} + 10 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5}\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(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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{5 \, B a^{7} - 3 \, A a^{6} b + 9 \, B a^{5} b^{2} - 7 \, A a^{4} b^{3} + 2 \, {\left(3 \, B a^{6} b - 2 \, A a^{5} b^{2} + 5 \, B a^{4} b^{3} - 4 \, A a^{3} b^{4}\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 \, B \tan\left(d x + c\right)}{b^{3}}}{2 \, d}"," ",0,"1/2*(2*(A*a^3 + 3*B*a^2*b - 3*A*a*b^2 - B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(3*B*a^7 - A*a^6*b + 9*B*a^5*b^2 - 3*A*a^4*b^3 + 10*B*a^3*b^4 - 6*A*a^2*b^5)*log(b*tan(d*x + c) + a)/(a^6*b^4 + 3*a^4*b^6 + 3*a^2*b^8 + b^10) + (B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - (5*B*a^7 - 3*A*a^6*b + 9*B*a^5*b^2 - 7*A*a^4*b^3 + 2*(3*B*a^6*b - 2*A*a^5*b^2 + 5*B*a^4*b^3 - 4*A*a^3*b^4)*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*B*tan(d*x + c)/b^3)/d","A",0
283,1,366,0,0.782568," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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(B a^{6} + 3 \, B a^{4} b^{2} + A a^{3} b^{3} + 6 \, B a^{2} b^{4} - 3 \, A a b^{5}\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(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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 \, B a^{6} - A a^{5} b + 7 \, B a^{4} b^{2} - 5 \, A a^{3} b^{3} + 2 \, {\left(2 \, B a^{5} b - A a^{4} b^{2} + 4 \, B a^{3} b^{3} - 3 \, A a^{2} b^{4}\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*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(B*a^6 + 3*B*a^4*b^2 + A*a^3*b^3 + 6*B*a^2*b^4 - 3*A*a*b^5)*log(b*tan(d*x + c) + a)/(a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9) - (A*a^3 + 3*B*a^2*b - 3*A*a*b^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*B*a^6 - A*a^5*b + 7*B*a^4*b^2 - 5*A*a^3*b^3 + 2*(2*B*a^5*b - A*a^4*b^2 + 4*B*a^3*b^3 - 3*A*a^2*b^4)*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
284,1,333,0,0.876459," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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{B a^{5} + A a^{4} b + 5 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} + 2 \, {\left(B a^{4} b + 3 \, B a^{2} b^{3} - 2 \, A a b^{4}\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*(A*a^3 + 3*B*a^2*b - 3*A*a*b^2 - B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (B*a^5 + A*a^4*b + 5*B*a^3*b^2 - 3*A*a^2*b^3 + 2*(B*a^4*b + 3*B*a^2*b^3 - 2*A*a*b^4)*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
285,1,330,0,0.903843," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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 a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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{B a^{4} - 3 \, A a^{3} b - 3 \, B a^{2} b^{2} + A a b^{3} - 2 \, {\left(A a^{2} b^{2} + 2 \, B a b^{3} - A b^{4}\right)} \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)}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(A*a^3 + 3*B*a^2*b - 3*A*a*b^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) - (A*a^3 + 3*B*a^2*b - 3*A*a*b^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) + (B*a^4 - 3*A*a^3*b - 3*B*a^2*b^2 + A*a*b^3 - 2*(A*a^2*b^2 + 2*B*a*b^3 - A*b^4)*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
286,1,321,0,0.995386," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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 \, B a^{3} - 5 \, A a^{2} b - B a b^{2} - A b^{3} + 2 \, {\left(B a^{2} b - 2 \, A a b^{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*(A*a^3 + 3*B*a^2*b - 3*A*a*b^2 - B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(b*tan(d*x + c) + a)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*log(tan(d*x + c)^2 + 1)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + (3*B*a^3 - 5*A*a^2*b - B*a*b^2 - A*b^3 + 2*(B*a^2*b - 2*A*a*b^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
287,1,372,0,0.635549," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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 \, B a^{5} b - 6 \, A a^{4} b^{2} - B a^{3} b^{3} - 3 \, A a^{2} b^{4} - A 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 a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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{5 \, B a^{4} b - 7 \, A a^{3} b^{2} + B a^{2} b^{3} - 3 \, A a b^{4} + 2 \, {\left(2 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - A 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 \, A \log\left(\tan\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*(2*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(3*B*a^5*b - 6*A*a^4*b^2 - B*a^3*b^3 - 3*A*a^2*b^4 - A*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*a^3 + 3*B*a^2*b - 3*A*a*b^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) - (5*B*a^4*b - 7*A*a^3*b^2 + B*a^2*b^3 - 3*A*a*b^4 + 2*(2*B*a^3*b^2 - 3*A*a^2*b^3 - A*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*A*log(tan(d*x + c))/a^3)/d","A",0
288,1,454,0,0.837038," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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 \, B a^{5} b^{2} - 10 \, A a^{4} b^{3} + 3 \, B a^{3} b^{4} - 9 \, A a^{2} b^{5} + B a b^{6} - 3 \, A 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(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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 a^{6} + 4 \, A a^{4} b^{2} + 2 \, A a^{2} b^{4} + 2 \, {\left(A a^{4} b^{2} - 3 \, B a^{3} b^{3} + 6 \, A a^{2} b^{4} - B a b^{5} + 3 \, A b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(4 \, A a^{5} b - 7 \, B a^{4} b^{2} + 17 \, A a^{3} b^{3} - 3 \, B a^{2} b^{4} + 9 \, A 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{2 \, {\left(B a - 3 \, A b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{2 \, d}"," ",0,"-1/2*(2*(A*a^3 + 3*B*a^2*b - 3*A*a*b^2 - B*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) + 2*(6*B*a^5*b^2 - 10*A*a^4*b^3 + 3*B*a^3*b^4 - 9*A*a^2*b^5 + B*a*b^6 - 3*A*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) + (B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*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*a^6 + 4*A*a^4*b^2 + 2*A*a^2*b^4 + 2*(A*a^4*b^2 - 3*B*a^3*b^3 + 6*A*a^2*b^4 - B*a*b^5 + 3*A*b^6)*tan(d*x + c)^2 + (4*A*a^5*b - 7*B*a^4*b^2 + 17*A*a^3*b^3 - 3*B*a^2*b^4 + 9*A*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)) - 2*(B*a - 3*A*b)*log(tan(d*x + c))/a^4)/d","A",0
289,1,541,0,0.838086," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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(10 \, B a^{5} b^{3} - 15 \, A a^{4} b^{4} + 9 \, B a^{3} b^{5} - 17 \, A a^{2} b^{6} + 3 \, B a b^{7} - 6 \, A b^{8}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{11} + 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} + a^{5} b^{6}} - \frac{{\left(A a^{3} + 3 \, B a^{2} b - 3 \, A a b^{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{A a^{7} + 2 \, A a^{5} b^{2} + A a^{3} b^{4} + 2 \, {\left(B a^{5} b^{2} - 3 \, A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 11 \, A a^{2} b^{5} + 3 \, B a b^{6} - 6 \, A b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(4 \, B a^{6} b - 11 \, A a^{5} b^{2} + 17 \, B a^{4} b^{3} - 33 \, A a^{3} b^{4} + 9 \, B a^{2} b^{5} - 18 \, A a b^{6}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(B a^{7} - 2 \, A a^{6} b + 2 \, B a^{5} b^{2} - 4 \, A a^{4} b^{3} + B a^{3} b^{4} - 2 \, A 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)^{4} + 2 \, {\left(a^{9} b + 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{10} + 2 \, a^{8} b^{2} + a^{6} b^{4}\right)} \tan\left(d x + c\right)^{2}} + \frac{2 \, {\left(A a^{2} + 3 \, B a b - 6 \, A b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{5}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*b^3)*(d*x + c)/(a^6 + 3*a^4*b^2 + 3*a^2*b^4 + b^6) - 2*(10*B*a^5*b^3 - 15*A*a^4*b^4 + 9*B*a^3*b^5 - 17*A*a^2*b^6 + 3*B*a*b^7 - 6*A*b^8)*log(b*tan(d*x + c) + a)/(a^11 + 3*a^9*b^2 + 3*a^7*b^4 + a^5*b^6) - (A*a^3 + 3*B*a^2*b - 3*A*a*b^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) + (A*a^7 + 2*A*a^5*b^2 + A*a^3*b^4 + 2*(B*a^5*b^2 - 3*A*a^4*b^3 + 6*B*a^3*b^4 - 11*A*a^2*b^5 + 3*B*a*b^6 - 6*A*b^7)*tan(d*x + c)^3 + (4*B*a^6*b - 11*A*a^5*b^2 + 17*B*a^4*b^3 - 33*A*a^3*b^4 + 9*B*a^2*b^5 - 18*A*a*b^6)*tan(d*x + c)^2 + 2*(B*a^7 - 2*A*a^6*b + 2*B*a^5*b^2 - 4*A*a^4*b^3 + B*a^3*b^4 - 2*A*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)^4 + 2*(a^9*b + 2*a^7*b^3 + a^5*b^5)*tan(d*x + c)^3 + (a^10 + 2*a^8*b^2 + a^6*b^4)*tan(d*x + c)^2) + 2*(A*a^2 + 3*B*a*b - 6*A*b^2)*log(tan(d*x + c))/a^5)/d","A",0
290,1,583,0,1.189850," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{6 \, {\left(B a^{8} + 4 \, B a^{6} b^{2} + 5 \, B a^{4} b^{4} + 4 \, A a^{3} b^{5} + 10 \, B a^{2} b^{6} - 4 \, A a b^{7}\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(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B 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 \, B a^{9} - 2 \, A a^{8} b + 34 \, B a^{7} b^{2} - 4 \, A a^{6} b^{3} + 47 \, B a^{5} b^{4} - 26 \, A a^{4} b^{5} + 6 \, {\left(3 \, B a^{7} b^{2} - A a^{6} b^{3} + 9 \, B a^{5} b^{4} - 3 \, A a^{4} b^{5} + 10 \, B a^{3} b^{6} - 6 \, A a^{2} b^{7}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(9 \, B a^{8} b - 2 \, A a^{7} b^{2} + 28 \, B a^{6} b^{3} - 6 \, A a^{5} b^{4} + 35 \, B a^{4} b^{5} - 20 \, A a^{3} b^{6}\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*(6*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 6*(B*a^8 + 4*B*a^6*b^2 + 5*B*a^4*b^4 + 4*A*a^3*b^5 + 10*B*a^2*b^6 - 4*A*a*b^7)*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*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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*B*a^9 - 2*A*a^8*b + 34*B*a^7*b^2 - 4*A*a^6*b^3 + 47*B*a^5*b^4 - 26*A*a^4*b^5 + 6*(3*B*a^7*b^2 - A*a^6*b^3 + 9*B*a^5*b^4 - 3*A*a^4*b^5 + 10*B*a^3*b^6 - 6*A*a^2*b^7)*tan(d*x + c)^2 + 3*(9*B*a^8*b - 2*A*a^7*b^2 + 28*B*a^6*b^3 - 6*A*a^5*b^4 + 35*B*a^4*b^5 - 20*A*a^3*b^6)*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
291,1,550,0,0.796308," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{6 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A 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 a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A 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{2 \, B a^{8} + A a^{7} b + 4 \, B a^{6} b^{2} + 14 \, A a^{5} b^{3} + 26 \, B a^{4} b^{4} - 11 \, A a^{3} b^{5} + 6 \, {\left(B a^{6} b^{2} + 3 \, B a^{4} b^{4} + A a^{3} b^{5} + 6 \, B a^{2} b^{6} - 3 \, A a b^{7}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{7} b + A a^{6} b^{2} + 6 \, B a^{5} b^{3} + 8 \, A a^{4} b^{4} + 20 \, B a^{3} b^{5} - 9 \, A a^{2} b^{6}\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)}}{6 \, d}"," ",0,"1/6*(6*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 6*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*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*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*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) - (2*B*a^8 + A*a^7*b + 4*B*a^6*b^2 + 14*A*a^5*b^3 + 26*B*a^4*b^4 - 11*A*a^3*b^5 + 6*(B*a^6*b^2 + 3*B*a^4*b^4 + A*a^3*b^5 + 6*B*a^2*b^6 - 3*A*a*b^7)*tan(d*x + c)^2 + 3*(2*B*a^7*b + A*a^6*b^2 + 6*B*a^5*b^3 + 8*A*a^4*b^4 + 20*B*a^3*b^5 - 9*A*a^2*b^6)*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","A",0
292,1,526,0,0.659966," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B 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(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B 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{B a^{7} + 2 \, A a^{6} b + 14 \, B a^{5} b^{2} - 20 \, A a^{4} b^{3} - 11 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5} + 6 \, {\left(B a^{3} b^{4} - 3 \, A a^{2} b^{5} - 3 \, B a b^{6} + A b^{7}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(B a^{6} b + 8 \, B a^{4} b^{3} - 14 \, A a^{3} b^{4} - 9 \, B a^{2} b^{5} + 2 \, A a b^{6}\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*(6*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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) + (B*a^7 + 2*A*a^6*b + 14*B*a^5*b^2 - 20*A*a^4*b^3 - 11*B*a^3*b^4 + 2*A*a^2*b^5 + 6*(B*a^3*b^4 - 3*A*a^2*b^5 - 3*B*a*b^6 + A*b^7)*tan(d*x + c)^2 + 3*(B*a^6*b + 8*B*a^4*b^3 - 14*A*a^3*b^4 - 9*B*a^2*b^5 + 2*A*a*b^6)*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
293,1,523,0,0.958176," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{6 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A 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 a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A 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{2 \, B a^{6} - 11 \, A a^{5} b - 20 \, B a^{4} b^{2} + 14 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} + A a b^{5} - 6 \, {\left(A a^{3} b^{3} + 3 \, B a^{2} b^{4} - 3 \, A a b^{5} - B b^{6}\right)} \tan\left(d x + c\right)^{2} - 3 \, {\left(5 \, A a^{4} b^{2} + 14 \, B a^{3} b^{3} - 12 \, A a^{2} b^{4} - 2 \, B a b^{5} - A b^{6}\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)}}{6 \, d}"," ",0,"-1/6*(6*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 6*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*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*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*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) + (2*B*a^6 - 11*A*a^5*b - 20*B*a^4*b^2 + 14*A*a^3*b^3 + 2*B*a^2*b^4 + A*a*b^5 - 6*(A*a^3*b^3 + 3*B*a^2*b^4 - 3*A*a*b^5 - B*b^6)*tan(d*x + c)^2 - 3*(5*A*a^4*b^2 + 14*B*a^3*b^3 - 12*A*a^2*b^4 - 2*B*a*b^5 - A*b^6)*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
294,1,514,0,0.848290," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B 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(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B 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 \, B a^{5} - 26 \, A a^{4} b - 14 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3} - B a b^{4} - 2 \, A b^{5} + 6 \, {\left(B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 3 \, B a b^{4} + A b^{5}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(5 \, B a^{4} b - 14 \, A a^{3} b^{2} - 12 \, B a^{2} b^{3} + 2 \, A a b^{4} - B 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*(6*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*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*B*a^5 - 26*A*a^4*b - 14*B*a^3*b^2 - 4*A*a^2*b^3 - B*a*b^4 - 2*A*b^5 + 6*(B*a^3*b^2 - 3*A*a^2*b^3 - 3*B*a*b^4 + A*b^5)*tan(d*x + c)^2 + 3*(5*B*a^4*b - 14*A*a^3*b^2 - 12*B*a^2*b^3 + 2*A*a*b^4 - B*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
295,1,580,0,1.090586," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{6 \, {\left(4 \, B a^{7} b - 10 \, A a^{6} b^{2} - 4 \, B a^{5} b^{3} - 5 \, A a^{4} b^{4} - 4 \, A a^{2} b^{6} - A 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 a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A 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{26 \, B a^{7} b - 47 \, A a^{6} b^{2} + 4 \, B a^{5} b^{3} - 34 \, A a^{4} b^{4} + 2 \, B a^{3} b^{5} - 11 \, A a^{2} b^{6} + 6 \, {\left(3 \, B a^{5} b^{3} - 6 \, A a^{4} b^{4} - B a^{3} b^{5} - 3 \, A a^{2} b^{6} - A b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(14 \, B a^{6} b^{2} - 27 \, A a^{5} b^{3} - 2 \, B a^{4} b^{4} - 16 \, A a^{3} b^{5} - 5 \, A 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 \, A \log\left(\tan\left(d x + c\right)\right)}{a^{4}}}{6 \, d}"," ",0,"1/6*(6*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 6*(4*B*a^7*b - 10*A*a^6*b^2 - 4*B*a^5*b^3 - 5*A*a^4*b^4 - 4*A*a^2*b^6 - A*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*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*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) - (26*B*a^7*b - 47*A*a^6*b^2 + 4*B*a^5*b^3 - 34*A*a^4*b^4 + 2*B*a^3*b^5 - 11*A*a^2*b^6 + 6*(3*B*a^5*b^3 - 6*A*a^4*b^4 - B*a^3*b^5 - 3*A*a^2*b^6 - A*b^8)*tan(d*x + c)^2 + 3*(14*B*a^6*b^2 - 27*A*a^5*b^3 - 2*B*a^4*b^4 - 16*A*a^3*b^5 - 5*A*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*A*log(tan(d*x + c))/a^4)/d","A",0
296,1,698,0,0.913307," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{6 \, {\left(10 \, B a^{7} b^{2} - 20 \, A a^{6} b^{3} + 5 \, B a^{5} b^{4} - 24 \, A a^{4} b^{5} + 4 \, B a^{3} b^{6} - 16 \, A a^{2} b^{7} + B a b^{8} - 4 \, A 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{3 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} + \frac{6 \, A a^{9} + 18 \, A a^{7} b^{2} + 18 \, A a^{5} b^{4} + 6 \, A a^{3} b^{6} + 6 \, {\left(A a^{6} b^{3} - 6 \, B a^{5} b^{4} + 13 \, A a^{4} b^{5} - 3 \, B a^{3} b^{6} + 12 \, A a^{2} b^{7} - B a b^{8} + 4 \, A b^{9}\right)} \tan\left(d x + c\right)^{3} + 3 \, {\left(6 \, A a^{7} b^{2} - 27 \, B a^{6} b^{3} + 62 \, A a^{5} b^{4} - 16 \, B a^{4} b^{5} + 60 \, A a^{3} b^{6} - 5 \, B a^{2} b^{7} + 20 \, A a b^{8}\right)} \tan\left(d x + c\right)^{2} + {\left(18 \, A a^{8} b - 47 \, B a^{7} b^{2} + 128 \, A a^{6} b^{3} - 34 \, B a^{5} b^{4} + 130 \, A a^{4} b^{5} - 11 \, B a^{3} b^{6} + 44 \, A 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{6 \, {\left(B a - 4 \, A b\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{5}}}{6 \, d}"," ",0,"-1/6*(6*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + 6*(10*B*a^7*b^2 - 20*A*a^6*b^3 + 5*B*a^5*b^4 - 24*A*a^4*b^5 + 4*B*a^3*b^6 - 16*A*a^2*b^7 + B*a*b^8 - 4*A*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) + 3*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*log(tan(d*x + c)^2 + 1)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) + (6*A*a^9 + 18*A*a^7*b^2 + 18*A*a^5*b^4 + 6*A*a^3*b^6 + 6*(A*a^6*b^3 - 6*B*a^5*b^4 + 13*A*a^4*b^5 - 3*B*a^3*b^6 + 12*A*a^2*b^7 - B*a*b^8 + 4*A*b^9)*tan(d*x + c)^3 + 3*(6*A*a^7*b^2 - 27*B*a^6*b^3 + 62*A*a^5*b^4 - 16*B*a^4*b^5 + 60*A*a^3*b^6 - 5*B*a^2*b^7 + 20*A*a*b^8)*tan(d*x + c)^2 + (18*A*a^8*b - 47*B*a^7*b^2 + 128*A*a^6*b^3 - 34*B*a^5*b^4 + 130*A*a^4*b^5 - 11*B*a^3*b^6 + 44*A*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)) - 6*(B*a - 4*A*b)*log(tan(d*x + c))/a^5)/d","A",0
297,1,815,0,0.979000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} {\left(d x + c\right)}}{a^{8} + 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} + 4 \, a^{2} b^{6} + b^{8}} - \frac{6 \, {\left(20 \, B a^{7} b^{3} - 35 \, A a^{6} b^{4} + 24 \, B a^{5} b^{5} - 56 \, A a^{4} b^{6} + 16 \, B a^{3} b^{7} - 39 \, A a^{2} b^{8} + 4 \, B a b^{9} - 10 \, A b^{10}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{14} + 4 \, a^{12} b^{2} + 6 \, a^{10} b^{4} + 4 \, a^{8} b^{6} + a^{6} b^{8}} - \frac{3 \, {\left(A a^{4} + 4 \, B a^{3} b - 6 \, A a^{2} b^{2} - 4 \, B a b^{3} + A 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{3 \, A a^{10} + 9 \, A a^{8} b^{2} + 9 \, A a^{6} b^{4} + 3 \, A a^{4} b^{6} + 6 \, {\left(B a^{7} b^{3} - 4 \, A a^{6} b^{4} + 13 \, B a^{5} b^{5} - 27 \, A a^{4} b^{6} + 12 \, B a^{3} b^{7} - 29 \, A a^{2} b^{8} + 4 \, B a b^{9} - 10 \, A b^{10}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(6 \, B a^{8} b^{2} - 23 \, A a^{7} b^{3} + 62 \, B a^{6} b^{4} - 134 \, A a^{5} b^{5} + 60 \, B a^{4} b^{6} - 145 \, A a^{3} b^{7} + 20 \, B a^{2} b^{8} - 50 \, A a b^{9}\right)} \tan\left(d x + c\right)^{3} + {\left(18 \, B a^{9} b - 63 \, A a^{8} b^{2} + 128 \, B a^{7} b^{3} - 296 \, A a^{6} b^{4} + 130 \, B a^{5} b^{5} - 319 \, A a^{4} b^{6} + 44 \, B a^{3} b^{7} - 110 \, A a^{2} b^{8}\right)} \tan\left(d x + c\right)^{2} + 3 \, {\left(2 \, B a^{10} - 5 \, A a^{9} b + 6 \, B a^{8} b^{2} - 15 \, A a^{7} b^{3} + 6 \, B a^{6} b^{4} - 15 \, A a^{5} b^{5} + 2 \, B a^{4} b^{6} - 5 \, A a^{3} b^{7}\right)} \tan\left(d x + c\right)}{{\left(a^{11} b^{3} + 3 \, a^{9} b^{5} + 3 \, a^{7} b^{7} + a^{5} b^{9}\right)} \tan\left(d x + c\right)^{5} + 3 \, {\left(a^{12} b^{2} + 3 \, a^{10} b^{4} + 3 \, a^{8} b^{6} + a^{6} b^{8}\right)} \tan\left(d x + c\right)^{4} + 3 \, {\left(a^{13} b + 3 \, a^{11} b^{3} + 3 \, a^{9} b^{5} + a^{7} b^{7}\right)} \tan\left(d x + c\right)^{3} + {\left(a^{14} + 3 \, a^{12} b^{2} + 3 \, a^{10} b^{4} + a^{8} b^{6}\right)} \tan\left(d x + c\right)^{2}} + \frac{6 \, {\left(A a^{2} + 4 \, B a b - 10 \, A b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{6}}}{6 \, d}"," ",0,"-1/6*(6*(B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*(d*x + c)/(a^8 + 4*a^6*b^2 + 6*a^4*b^4 + 4*a^2*b^6 + b^8) - 6*(20*B*a^7*b^3 - 35*A*a^6*b^4 + 24*B*a^5*b^5 - 56*A*a^4*b^6 + 16*B*a^3*b^7 - 39*A*a^2*b^8 + 4*B*a*b^9 - 10*A*b^10)*log(b*tan(d*x + c) + a)/(a^14 + 4*a^12*b^2 + 6*a^10*b^4 + 4*a^8*b^6 + a^6*b^8) - 3*(A*a^4 + 4*B*a^3*b - 6*A*a^2*b^2 - 4*B*a*b^3 + A*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) + (3*A*a^10 + 9*A*a^8*b^2 + 9*A*a^6*b^4 + 3*A*a^4*b^6 + 6*(B*a^7*b^3 - 4*A*a^6*b^4 + 13*B*a^5*b^5 - 27*A*a^4*b^6 + 12*B*a^3*b^7 - 29*A*a^2*b^8 + 4*B*a*b^9 - 10*A*b^10)*tan(d*x + c)^4 + 3*(6*B*a^8*b^2 - 23*A*a^7*b^3 + 62*B*a^6*b^4 - 134*A*a^5*b^5 + 60*B*a^4*b^6 - 145*A*a^3*b^7 + 20*B*a^2*b^8 - 50*A*a*b^9)*tan(d*x + c)^3 + (18*B*a^9*b - 63*A*a^8*b^2 + 128*B*a^7*b^3 - 296*A*a^6*b^4 + 130*B*a^5*b^5 - 319*A*a^4*b^6 + 44*B*a^3*b^7 - 110*A*a^2*b^8)*tan(d*x + c)^2 + 3*(2*B*a^10 - 5*A*a^9*b + 6*B*a^8*b^2 - 15*A*a^7*b^3 + 6*B*a^6*b^4 - 15*A*a^5*b^5 + 2*B*a^4*b^6 - 5*A*a^3*b^7)*tan(d*x + c))/((a^11*b^3 + 3*a^9*b^5 + 3*a^7*b^7 + a^5*b^9)*tan(d*x + c)^5 + 3*(a^12*b^2 + 3*a^10*b^4 + 3*a^8*b^6 + a^6*b^8)*tan(d*x + c)^4 + 3*(a^13*b + 3*a^11*b^3 + 3*a^9*b^5 + a^7*b^7)*tan(d*x + c)^3 + (a^14 + 3*a^12*b^2 + 3*a^10*b^4 + a^8*b^6)*tan(d*x + c)^2) + 6*(A*a^2 + 4*B*a*b - 10*A*b^2)*log(tan(d*x + c))/a^6)/d","A",0
298,1,30,0,1.088497," ","integrate(tan(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B \tan\left(d x + c\right)^{2} - B \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*(B*tan(d*x + c)^2 - B*log(tan(d*x + c)^2 + 1))/d","A",0
299,1,22,0,0.929737," ","integrate(tan(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c\right)} B - B \tan\left(d x + c\right)}{d}"," ",0,"-((d*x + c)*B - B*tan(d*x + c))/d","A",0
300,1,17,0,1.157938," ","integrate(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{2 \, d}"," ",0,"1/2*B*log(tan(d*x + c)^2 + 1)/d","A",0
301,1,10,0,1.158482," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)} B}{d}"," ",0,"(d*x + c)*B/d","C",0
302,1,29,0,0.948597," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{B \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, B \log\left(\tan\left(d x + c\right)\right)}{2 \, d}"," ",0,"-1/2*(B*log(tan(d*x + c)^2 + 1) - 2*B*log(tan(d*x + c)))/d","B",0
303,1,23,0,0.963474," ","integrate(cot(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c\right)} B + \frac{B}{\tan\left(d x + c\right)}}{d}"," ",0,"-((d*x + c)*B + B/tan(d*x + c))/d","A",0
304,1,40,0,0.901009," ","integrate(cot(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{B \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, B \log\left(\tan\left(d x + c\right)\right) - \frac{B}{\tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(B*log(tan(d*x + c)^2 + 1) - 2*B*log(tan(d*x + c)) - B/tan(d*x + c)^2)/d","A",0
305,1,38,0,1.212762," ","integrate(cot(d*x+c)^4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(d x + c\right)} B + \frac{3 \, B \tan\left(d x + c\right)^{2} - B}{\tan\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*(d*x + c)*B + (3*B*tan(d*x + c)^2 - B)/tan(d*x + c)^3)/d","A",0
306,1,104,0,0.947243," ","integrate(tan(d*x+c)^4*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, B 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)} B a}{a^{2} + b^{2}} - \frac{B b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{B b \tan\left(d x + c\right)^{2} - 2 \, B a \tan\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*B*a^4*log(b*tan(d*x + c) + a)/(a^2*b^3 + b^5) + 2*(d*x + c)*B*a/(a^2 + b^2) - B*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + (B*b*tan(d*x + c)^2 - 2*B*a*tan(d*x + c))/b^2)/d","A",0
307,1,89,0,0.568010," ","integrate(tan(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, B 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 b}{a^{2} + b^{2}} + \frac{B a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, B \tan\left(d x + c\right)}{b}}{2 \, d}"," ",0,"-1/2*(2*B*a^3*log(b*tan(d*x + c) + a)/(a^2*b^2 + b^4) + 2*(d*x + c)*B*b/(a^2 + b^2) + B*a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*B*tan(d*x + c)/b)/d","A",0
308,1,75,0,0.636330," ","integrate(tan(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, B 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)} B a}{a^{2} + b^{2}} + \frac{B b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}}}{2 \, d}"," ",0,"1/2*(2*B*a^2*log(b*tan(d*x + c) + a)/(a^2*b + b^3) - 2*(d*x + c)*B*a/(a^2 + b^2) + B*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
309,1,71,0,0.635543," ","integrate(tan(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(d x + c\right)} B b}{a^{2} + b^{2}} - \frac{2 \, B a \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} + b^{2}} + \frac{B 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*b/(a^2 + b^2) - 2*B*a*log(b*tan(d*x + c) + a)/(a^2 + b^2) + B*a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
310,1,72,0,0.555021," ","integrate((a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(d x + c\right)} B a}{a^{2} + b^{2}} + \frac{2 \, B b \log\left(b \tan\left(d x + c\right) + a\right)}{a^{2} + b^{2}} - \frac{B 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)*B*a/(a^2 + b^2) + 2*B*b*log(b*tan(d*x + c) + a)/(a^2 + b^2) - B*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2))/d","A",0
311,1,88,0,0.591446," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, B 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 b}{a^{2} + b^{2}} + \frac{B a \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 \, d}"," ",0,"-1/2*(2*B*b^2*log(b*tan(d*x + c) + a)/(a^3 + a*b^2) + 2*(d*x + c)*B*b/(a^2 + b^2) + B*a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*B*log(tan(d*x + c))/a)/d","A",0
312,1,105,0,0.441023," ","integrate(cot(d*x+c)^2*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, B 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)} B a}{a^{2} + b^{2}} + \frac{B b \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} - \frac{2 \, B b \log\left(\tan\left(d x + c\right)\right)}{a^{2}} - \frac{2 \, B}{a \tan\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*B*b^3*log(b*tan(d*x + c) + a)/(a^4 + a^2*b^2) - 2*(d*x + c)*B*a/(a^2 + b^2) + B*b*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) - 2*B*b*log(tan(d*x + c))/a^2 - 2*B/(a*tan(d*x + c)))/d","A",0
313,1,130,0,0.502979," ","integrate(cot(d*x+c)^3*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, B 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 b}{a^{2} + b^{2}} - \frac{B a \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{2} + b^{2}} + \frac{2 \, {\left(B a^{2} - B b^{2}\right)} \log\left(\tan\left(d x + c\right)\right)}{a^{3}} - \frac{2 \, B b \tan\left(d x + c\right) - B a}{a^{2} \tan\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*B*b^4*log(b*tan(d*x + c) + a)/(a^5 + a^3*b^2) - 2*(d*x + c)*B*b/(a^2 + b^2) - B*a*log(tan(d*x + c)^2 + 1)/(a^2 + b^2) + 2*(B*a^2 - B*b^2)*log(tan(d*x + c))/a^3 - (2*B*b*tan(d*x + c) - B*a)/(a^2*tan(d*x + c)^2))/d","A",0
314,1,35,0,0.502524," ","integrate((3+tan(d*x+c))/(2-tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, d x + 2 \, c + \log\left(\tan\left(d x + c\right)^{2} + 1\right) - 2 \, \log\left(\tan\left(d x + c\right) - 2\right)}{2 \, d}"," ",0,"1/2*(2*d*x + 2*c + log(tan(d*x + c)^2 + 1) - 2*log(tan(d*x + c) - 2))/d","A",0
315,1,95,0,0.500913," ","integrate((b*B/a+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(d x + c\right)} B b}{a^{2} + b^{2}} - \frac{2 \, {\left(B a^{2} - B b^{2}\right)} \log\left(b \tan\left(d x + c\right) + a\right)}{a^{3} + a b^{2}} + \frac{{\left(B a^{2} - B b^{2}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{3} + a b^{2}}}{2 \, d}"," ",0,"1/2*(4*(d*x + c)*B*b/(a^2 + b^2) - 2*(B*a^2 - B*b^2)*log(b*tan(d*x + c) + a)/(a^3 + a*b^2) + (B*a^2 - B*b^2)*log(tan(d*x + c)^2 + 1)/(a^3 + a*b^2))/d","A",0
316,1,161,0,0.427121," ","integrate((a+b*tan(d*x+c))/(b+a*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(a^{3} - 3 \, a b^{2}\right)} {\left(d x + c\right)}}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} - \frac{2 \, {\left(3 \, a^{2} b - b^{3}\right)} \log\left(a \tan\left(d x + c\right) + b\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(3 \, a^{2} b - b^{3}\right)} \log\left(\tan\left(d x + c\right)^{2} + 1\right)}{a^{4} + 2 \, a^{2} b^{2} + b^{4}} + \frac{2 \, {\left(a^{2} - b^{2}\right)}}{a^{2} b + b^{3} + {\left(a^{3} + a b^{2}\right)} \tan\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(a^3 - 3*a*b^2)*(d*x + c)/(a^4 + 2*a^2*b^2 + b^4) - 2*(3*a^2*b - b^3)*log(a*tan(d*x + c) + b)/(a^4 + 2*a^2*b^2 + b^4) + (3*a^2*b - b^3)*log(tan(d*x + c)^2 + 1)/(a^4 + 2*a^2*b^2 + b^4) + 2*(a^2 - b^2)/(a^2*b + b^3 + (a^3 + a*b^2)*tan(d*x + c)))/d","A",0
317,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^3, x)","F",0
318,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^2, x)","F",0
319,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c), x)","F",0
320,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*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
321,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c), x)","F",0
322,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^2, x)","F",0
323,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^3, x)","F",0
324,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^4, x)","F",0
325,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^2, x)","F",0
326,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \tan\left(d x + c\right)\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^(3/2)*tan(d*x + c), x)","F",0
327,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*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
328,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c), x)","F",0
329,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^2, x)","F",0
330,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^3, x)","F",0
331,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-2,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*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
335,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*cot(d*x + c), x)","F",0
336,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
338,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
339,-1,0,0,0.000000," ","integrate(cot(d*x+c)^5*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
340,-2,0,0,0.000000," ","integrate((-a+b*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
341,-2,0,0,0.000000," ","integrate((-a+b*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
342,-2,0,0,0.000000," ","integrate((-a+b*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
343,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{2}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^2/sqrt(b*tan(d*x + c) + a), x)","F",0
345,0,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)/sqrt(b*tan(d*x + c) + a), x)","F",0
346,-2,0,0,0.000000," ","integrate((A+B*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
347,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)/sqrt(b*tan(d*x + c) + a), x)","F",0
348,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)^{2}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)^2/sqrt(b*tan(d*x + c) + a), x)","F",0
349,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)^{3}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)^3/sqrt(b*tan(d*x + c) + a), x)","F",0
350,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
352,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
353,-2,0,0,0.000000," ","integrate((A+B*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
354,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
355,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
356,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,-1,0,0,0.000000," ","integrate(tan(d*x+c)^4*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
358,-1,0,0,0.000000," ","integrate(tan(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
359,-1,0,0,0.000000," ","integrate(tan(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
360,-1,0,0,0.000000," ","integrate(tan(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-2,0,0,0.000000," ","integrate((A+B*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
362,0,0,0,0.000000," ","integrate(cot(d*x+c)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
363,-1,0,0,0.000000," ","integrate(cot(d*x+c)^2*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate(cot(d*x+c)^3*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,-2,0,0,0.000000," ","integrate((a*B+b*B*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
366,-2,0,0,0.000000," ","integrate((a*B+b*B*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
367,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,-2,0,0,0.000000," ","integrate((a*B+b*B*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
369,-1,0,0,0.000000," ","integrate(cot(d*x+c)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
370,-2,0,0,0.000000," ","integrate((-a+b*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
371,-2,0,0,0.000000," ","integrate((-a+b*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
372,-2,0,0,0.000000," ","integrate((-a+b*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
373,1,6480,0,1.362940," ","integrate((1+I*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2 \, a^{2} + 2 \, b^{2}} \sqrt{a + \sqrt{a^{2} + b^{2}}} {\left(2 \, \arctan\left(\frac{b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} b \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)}{b^{2}}, -\frac{a \cos\left(2 \, d x + 2 \, c\right) + b \sin\left(2 \, d x + 2 \, c\right) - {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right) + a}{b}\right) - i \, \log\left(\frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)^{2} + \sqrt{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)^{2} + a^{2} - \frac{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} {\left(a b \cos\left(2 \, d x + 2 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right) + a b\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)}{b} + \frac{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} {\left(b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)}{b}}{b^{2}}\right)\right)} - \sqrt{2 \, a^{2} + 2 \, b^{2}} \sqrt{-a + \sqrt{a^{2} + b^{2}}} {\left(-2 i \, \arctan\left(\frac{b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} b \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)}{b^{2}}, -\frac{a \cos\left(2 \, d x + 2 \, c\right) + b \sin\left(2 \, d x + 2 \, c\right) - {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right) + a}{b}\right) - \log\left(\frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, a b \sin\left(2 \, d x + 2 \, c\right) + {\left(a^{2} + b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \sqrt{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)^{2} + \sqrt{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)^{2} + a^{2} - \frac{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} {\left(a b \cos\left(2 \, d x + 2 \, c\right) + b^{2} \sin\left(2 \, d x + 2 \, c\right) + a b\right)} \cos\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)}{b} + \frac{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + 2 \, {\left(3 \, a^{4} + 2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a^{3} b + a b^{3} + {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}^{\frac{1}{4}} {\left(b^{2} \cos\left(2 \, d x + 2 \, c\right) - a b \sin\left(2 \, d x + 2 \, c\right)\right)} \sin\left(\frac{1}{2} \, \arctan\left(-\frac{2 \, {\left(a b \cos\left(2 \, d x + 2 \, c\right)^{2} - a b \sin\left(2 \, d x + 2 \, c\right)^{2} + a b \cos\left(2 \, d x + 2 \, c\right) - {\left(a^{2} + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)}}{b^{2}}, \frac{2 \, a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(a^{2} - b^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} - {\left(a^{2} - b^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, a b \cos\left(2 \, d x + 2 \, c\right) + a b\right)} \sin\left(2 \, d x + 2 \, c\right)}{b^{2}}\right)\right)}{b}}{b^{2}}\right)\right)}}{4 \, {\left(a^{2} + b^{2}\right)} d}"," ",0,"-1/4*(sqrt(2*a^2 + 2*b^2)*sqrt(a + sqrt(a^2 + b^2))*(2*arctan2((b^2*cos(2*d*x + 2*c) - a*b*sin(2*d*x + 2*c) + ((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*b*sin(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2)))/b^2, -(a*cos(2*d*x + 2*c) + b*sin(2*d*x + 2*c) - ((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*cos(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2)) + a)/b) - I*log((2*a^2*cos(2*d*x + 2*c) + (a^2 + b^2)*cos(2*d*x + 2*c)^2 + 2*a*b*sin(2*d*x + 2*c) + (a^2 + b^2)*sin(2*d*x + 2*c)^2 + sqrt((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))*cos(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))^2 + sqrt((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))*sin(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))^2 + a^2 - 2*((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*(a*b*cos(2*d*x + 2*c) + b^2*sin(2*d*x + 2*c) + a*b)*cos(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))/b + 2*((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*(b^2*cos(2*d*x + 2*c) - a*b*sin(2*d*x + 2*c))*sin(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))/b)/b^2)) - sqrt(2*a^2 + 2*b^2)*sqrt(-a + sqrt(a^2 + b^2))*(-2*I*arctan2((b^2*cos(2*d*x + 2*c) - a*b*sin(2*d*x + 2*c) + ((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*b*sin(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2)))/b^2, -(a*cos(2*d*x + 2*c) + b*sin(2*d*x + 2*c) - ((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*cos(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2)) + a)/b) - log((2*a^2*cos(2*d*x + 2*c) + (a^2 + b^2)*cos(2*d*x + 2*c)^2 + 2*a*b*sin(2*d*x + 2*c) + (a^2 + b^2)*sin(2*d*x + 2*c)^2 + sqrt((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))*cos(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))^2 + sqrt((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))*sin(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))^2 + a^2 - 2*((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*(a*b*cos(2*d*x + 2*c) + b^2*sin(2*d*x + 2*c) + a*b)*cos(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))/b + 2*((a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^4 + (a^4 + 2*a^2*b^2 + b^4)*sin(2*d*x + 2*c)^4 + a^4 + 2*a^2*b^2 + b^4 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c)^3 + 4*(a^3*b + a*b^3)*sin(2*d*x + 2*c)^3 + 2*(3*a^4 + 2*a^2*b^2 - b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cos(2*d*x + 2*c)^2 + 2*(a^4 + a^2*b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + 4*(a^4 + a^2*b^2)*cos(2*d*x + 2*c) + 4*(a^3*b + a*b^3 + (a^3*b + a*b^3)*cos(2*d*x + 2*c)^2 + 2*(a^3*b + a*b^3)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))^(1/4)*(b^2*cos(2*d*x + 2*c) - a*b*sin(2*d*x + 2*c))*sin(1/2*arctan2(-2*(a*b*cos(2*d*x + 2*c)^2 - a*b*sin(2*d*x + 2*c)^2 + a*b*cos(2*d*x + 2*c) - (a^2 + (a^2 - b^2)*cos(2*d*x + 2*c))*sin(2*d*x + 2*c))/b^2, (2*a^2*cos(2*d*x + 2*c) + (a^2 - b^2)*cos(2*d*x + 2*c)^2 - (a^2 - b^2)*sin(2*d*x + 2*c)^2 + a^2 + b^2 + 2*(2*a*b*cos(2*d*x + 2*c) + a*b)*sin(2*d*x + 2*c))/b^2))/b)/b^2)))/((a^2 + b^2)*d)","B",0
374,-2,0,0,0.000000," ","integrate((1-I*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
375,0,0,0,0.000000," ","integrate((3+tan(x))/(4+3*tan(x))^(1/2),x, algorithm=""maxima"")","\int \frac{\tan\left(x\right) + 3}{\sqrt{3 \, \tan\left(x\right) + 4}}\,{d x}"," ",0,"integrate((tan(x) + 3)/sqrt(3*tan(x) + 4), x)","F",0
376,0,0,0,0.000000," ","integrate((1-3*tan(x))/(4+3*tan(x))^(1/2),x, algorithm=""maxima"")","-\int \frac{3 \, \tan\left(x\right) - 1}{\sqrt{3 \, \tan\left(x\right) + 4}}\,{d x}"," ",0,"-integrate((3*tan(x) - 1)/sqrt(3*tan(x) + 4), x)","F",0
377,0,0,0,0.000000," ","integrate((4-3*tan(b*x+a))/(4+3*tan(b*x+a))^(1/2),x, algorithm=""maxima"")","-\int \frac{3 \, \tan\left(b x + a\right) - 4}{\sqrt{3 \, \tan\left(b x + a\right) + 4}}\,{d x}"," ",0,"-integrate((3*tan(b*x + a) - 4)/sqrt(3*tan(b*x + a) + 4), x)","F",0
378,1,227,0,0.551789," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{120 \, B b \tan\left(d x + c\right)^{\frac{7}{2}} + 168 \, {\left(B a + A b\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 210 \, \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} b\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({\left(A - B\right)} a - {\left(A + B\right)} b\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({\left(A + B\right)} a + {\left(A - B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 105 \, \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 280 \, {\left(A a - B b\right)} \tan\left(d x + c\right)^{\frac{3}{2}} - 840 \, {\left(B a + A b\right)} \sqrt{\tan\left(d x + c\right)}}{420 \, d}"," ",0,"1/420*(120*B*b*tan(d*x + c)^(7/2) + 168*(B*a + A*b)*tan(d*x + c)^(5/2) - 210*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 210*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 105*sqrt(2)*((A + B)*a + (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 105*sqrt(2)*((A + B)*a + (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 280*(A*a - B*b)*tan(d*x + c)^(3/2) - 840*(B*a + A*b)*sqrt(tan(d*x + c)))/d","A",0
379,1,210,0,0.672806," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{24 \, B b \tan\left(d x + c\right)^{\frac{5}{2}} - 30 \, \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 40 \, {\left(B a + A b\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 120 \, {\left(A a - B b\right)} \sqrt{\tan\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(24*B*b*tan(d*x + c)^(5/2) - 30*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 30*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*((A - B)*a - (A + B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*((A - B)*a - (A + B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 40*(B*a + A*b)*tan(d*x + c)^(3/2) + 120*(A*a - B*b)*sqrt(tan(d*x + c)))/d","A",0
380,1,192,0,0.580413," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, B b \tan\left(d x + c\right)^{\frac{3}{2}} + 6 \, \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 24 \, {\left(B a + A b\right)} \sqrt{\tan\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(8*B*b*tan(d*x + c)^(3/2) + 6*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A + B)*a + (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 3*sqrt(2)*((A + B)*a + (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 24*(B*a + A*b)*sqrt(tan(d*x + c)))/d","A",0
381,1,174,0,0.664608," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 8 \, B b \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a - (A + B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a - (A + B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*B*b*sqrt(tan(d*x + c)))/d","A",0
382,1,174,0,0.866532," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, A a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a + (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a + (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*A*a/sqrt(tan(d*x + c)))/d","A",0
383,1,192,0,0.477765," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} b\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, {\left(A a + 3 \, {\left(B a + A b\right)} \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)*a + (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*((A - B)*a - (A + B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*((A - B)*a - (A + B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(A*a + 3*(B*a + A*b)*tan(d*x + c))/tan(d*x + c)^(3/2))/d","A",0
384,1,211,0,0.449977," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{30 \, \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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 \, {\left(A a - B b\right)} \tan\left(d x + c\right)^{2} - 3 \, A a - 5 \, {\left(B a + A b\right)} \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(30*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*((A + B)*a + (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*((A + B)*a + (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(15*(A*a - B*b)*tan(d*x + c)^2 - 3*A*a - 5*(B*a + A*b)*tan(d*x + c))/tan(d*x + c)^(5/2))/d","A",0
385,1,329,0,0.905085," ","integrate(tan(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{280 \, B b^{2} \tan\left(d x + c\right)^{\frac{9}{2}} + 360 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} + 504 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 630 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} b^{2}\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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} b^{2}\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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} b^{2}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 315 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 840 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} - 2520 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{1260 \, d}"," ",0,"1/1260*(280*B*b^2*tan(d*x + c)^(9/2) + 360*(2*B*a*b + A*b^2)*tan(d*x + c)^(7/2) + 504*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c)^(5/2) - 630*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 630*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 315*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 315*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 840*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c)^(3/2) - 2520*(B*a^2 + 2*A*a*b - B*b^2)*sqrt(tan(d*x + c)))/d","A",0
386,1,302,0,0.878132," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{120 \, B b^{2} \tan\left(d x + c\right)^{\frac{7}{2}} + 168 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 210 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 280 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 840 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{420 \, d}"," ",0,"1/420*(120*B*b^2*tan(d*x + c)^(7/2) + 168*(2*B*a*b + A*b^2)*tan(d*x + c)^(5/2) - 210*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 210*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 105*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 105*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 280*(B*a^2 + 2*A*a*b - B*b^2)*tan(d*x + c)^(3/2) + 840*(A*a^2 - 2*B*a*b - A*b^2)*sqrt(tan(d*x + c)))/d","A",0
387,1,275,0,0.708792," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{24 \, B b^{2} \tan\left(d x + c\right)^{\frac{5}{2}} + 30 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 40 \, {\left(2 \, B a b + A b^{2}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 120 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(24*B*b^2*tan(d*x + c)^(5/2) + 30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 40*(2*B*a*b + A*b^2)*tan(d*x + c)^(3/2) + 120*(B*a^2 + 2*A*a*b - B*b^2)*sqrt(tan(d*x + c)))/d","A",0
388,1,248,0,0.593597," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, B b^{2} \tan\left(d x + c\right)^{\frac{3}{2}} + 6 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} b^{2}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 24 \, {\left(2 \, B a b + A b^{2}\right)} \sqrt{\tan\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(8*B*b^2*tan(d*x + c)^(3/2) + 6*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 24*(2*B*a*b + A*b^2)*sqrt(tan(d*x + c)))/d","A",0
389,1,240,0,0.446122," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{8 \, B b^{2} \sqrt{\tan\left(d x + c\right)} - 2 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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 a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(8*B*b^2*sqrt(tan(d*x + c)) - 2*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 2*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*A*a^2/sqrt(tan(d*x + c)))/d","A",0
390,1,248,0,0.539432," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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(A a^{2} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} \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)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*(A*a^2 + 3*(B*a^2 + 2*A*a*b)*tan(d*x + c))/tan(d*x + c)^(3/2))/d","A",0
391,1,276,0,0.972147," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{30 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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(3 \, A a^{2} - 15 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \tan\left(d x + c\right)^{2} + 5 \, {\left(B a^{2} + 2 \, A a b\right)} \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*(3*A*a^2 - 15*(A*a^2 - 2*B*a*b - A*b^2)*tan(d*x + c)^2 + 5*(B*a^2 + 2*A*a*b)*tan(d*x + c))/tan(d*x + c)^(5/2))/d","A",0
392,1,398,0,0.821977," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{280 \, B b^{3} \tan\left(d x + c\right)^{\frac{9}{2}} + 360 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} + 504 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 630 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 840 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 2520 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{1260 \, d}"," ",0,"1/1260*(280*B*b^3*tan(d*x + c)^(9/2) + 360*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^(7/2) + 504*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c)^(5/2) - 630*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 630*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 315*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 315*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 840*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*tan(d*x + c)^(3/2) + 2520*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2 + B*b^3)*sqrt(tan(d*x + c)))/d","A",0
393,1,363,0,0.524404," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{120 \, B b^{3} \tan\left(d x + c\right)^{\frac{7}{2}} + 168 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + 210 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 840 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{420 \, d}"," ",0,"1/420*(120*B*b^3*tan(d*x + c)^(7/2) + 168*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^(5/2) + 210*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 210*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 105*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 105*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 280*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*tan(d*x + c)^(3/2) + 840*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)*sqrt(tan(d*x + c)))/d","A",0
394,1,327,0,0.444289," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{24 \, B b^{3} \tan\left(d x + c\right)^{\frac{5}{2}} + 30 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} b^{3}\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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} b^{3}\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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 15 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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 \, B a b^{2} + A b^{3}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 120 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(24*B*b^3*tan(d*x + c)^(5/2) + 30*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 15*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 15*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 40*(3*B*a*b^2 + A*b^3)*tan(d*x + c)^(3/2) + 120*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)*sqrt(tan(d*x + c)))/d","A",0
395,1,310,0,0.478240," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{8 \, B b^{3} \tan\left(d x + c\right)^{\frac{3}{2}} - \frac{24 \, A a^{3}}{\sqrt{\tan\left(d x + c\right)}} - 6 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} b^{3}\right)} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 24 \, {\left(3 \, B a b^{2} + A b^{3}\right)} \sqrt{\tan\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(8*B*b^3*tan(d*x + c)^(3/2) - 24*A*a^3/sqrt(tan(d*x + c)) - 6*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 6*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 24*(3*B*a*b^2 + A*b^3)*sqrt(tan(d*x + c)))/d","A",0
396,1,310,0,0.440191," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{24 \, B b^{3} \sqrt{\tan\left(d x + c\right)} - 6 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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(A a^{3} + 3 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(24*B*b^3*sqrt(tan(d*x + c)) - 6*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) - 6*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 3*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*(A*a^3 + 3*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/tan(d*x + c)^(3/2))/d","A",0
397,1,327,0,0.635417," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{30 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} b^{3}\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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} b^{3}\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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} b^{3}\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + 15 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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(3 \, A a^{3} - 15 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)} \tan\left(d x + c\right)^{2} + 5 \, {\left(B a^{3} + 3 \, A a^{2} b\right)} \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(30*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - 15*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 15*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*(3*A*a^3 - 15*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)*tan(d*x + c)^2 + 5*(B*a^3 + 3*A*a^2*b)*tan(d*x + c))/tan(d*x + c)^(5/2))/d","A",0
398,1,258,0,0.571249," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(B a^{4} - A a^{3} b\right)} \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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left({\left(A + B\right)} a - {\left(A - B\right)} 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 b \tan\left(d x + c\right)^{\frac{3}{2}} - 3 \, {\left(B a - A b\right)} \sqrt{\tan\left(d x + c\right)}\right)}}{b^{2}}}{12 \, d}"," ",0,"1/12*(24*(B*a^4 - A*a^3*b)*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)*a + (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a - (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a - (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) + 8*(B*b*tan(d*x + c)^(3/2) - 3*(B*a - A*b)*sqrt(tan(d*x + c)))/b^2)/d","A",0
399,1,234,0,0.574463," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(B a^{3} - A a^{2} b\right)} \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{8 \, B \sqrt{\tan\left(d x + c\right)}}{b} + \frac{2 \, \sqrt{2} {\left({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left({\left(A - B\right)} a + {\left(A + B\right)} 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*a^3 - A*a^2*b)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2*b + b^3)*sqrt(a*b)) - 8*B*sqrt(tan(d*x + c))/b + (2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a + (A + B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a + (A + B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
400,1,216,0,0.725018," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(B a^{2} - A a b\right)} \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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left({\left(A + B\right)} a - {\left(A - B\right)} 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*a^2 - A*a*b)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2 + b^2)*sqrt(a*b)) + (2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a - (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a - (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
401,1,217,0,0.657922," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(B a b - A b^{2}\right)} \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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left({\left(A - B\right)} a + {\left(A + B\right)} 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*a*b - A*b^2)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^2 + b^2)*sqrt(a*b)) - (2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a + (A + B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a + (A + B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
402,1,235,0,0.629501," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(B a b^{2} - A b^{3}\right)} \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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} {\left({\left(A + B\right)} a - {\left(A - B\right)} 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}{a \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(8*(B*a*b^2 - A*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)*a + (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a - (A - B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a - (A - B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) - 8*A/(a*sqrt(tan(d*x + c))))/d","A",0
403,1,256,0,0.960051," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(B a b^{3} - A b^{4}\right)} \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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} b\right)} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} {\left({\left(A - B\right)} a + {\left(A + B\right)} 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(A a + 3 \, {\left(B a - A b\right)} \tan\left(d x + c\right)\right)}}{a^{2} \tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(24*(B*a*b^3 - A*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)*a - (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a + (A + B)*b)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a + (A + B)*b)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/(a^2 + b^2) + 8*(A*a + 3*(B*a - A*b)*tan(d*x + c))/(a^2*tan(d*x + c)^(3/2)))/d","A",0
404,1,377,0,0.945957," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(3 \, B a^{5} - A a^{4} b + 7 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\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{4 \, {\left(B a^{3} - A a^{2} b\right)} \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{2 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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 \, B \sqrt{\tan\left(d x + c\right)}}{b^{2}}}{4 \, d}"," ",0,"-1/4*(4*(3*B*a^5 - A*a^4*b + 7*B*a^3*b^2 - 5*A*a^2*b^3)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4*b^2 + 2*a^2*b^4 + b^6)*sqrt(a*b)) - 4*(B*a^3 - A*a^2*b)*sqrt(tan(d*x + c))/(a^3*b^2 + a*b^4 + (a^2*b^3 + b^5)*tan(d*x + c)) + (2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (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*sqrt(tan(d*x + c))/b^2)/d","A",0
405,1,354,0,1.206124," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(B a^{4} + A a^{3} b + 5 \, B a^{2} b^{2} - 3 \, A a b^{3}\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{4 \, {\left(B a^{2} - A a b\right)} \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{2 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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*a^4 + A*a^3*b + 5*B*a^2*b^2 - 3*A*a*b^3)*arctan(b*sqrt(tan(d*x + c))/sqrt(a*b))/((a^4*b + 2*a^2*b^3 + b^5)*sqrt(a*b)) - 4*(B*a^2 - A*a*b)*sqrt(tan(d*x + c))/(a^3*b + a*b^3 + (a^2*b^2 + b^4)*tan(d*x + c)) - (2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (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
406,1,341,0,0.709229," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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 \, {\left(B a - A b\right)} \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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*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*a - A*b)*sqrt(tan(d*x + c))/(a^3 + a*b^2 + (a^2*b + b^3)*tan(d*x + c)) + (2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (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
407,1,356,0,0.932494," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(3 \, B a^{3} b - 5 \, A a^{2} b^{2} - B a b^{3} - A 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{4 \, {\left(B a b - A b^{2}\right)} \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{2 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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*B*a^3*b - 5*A*a^2*b^2 - B*a*b^3 - A*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)) + 4*(B*a*b - A*b^2)*sqrt(tan(d*x + c))/(a^4 + a^2*b^2 + (a^3*b + a*b^3)*tan(d*x + c)) - (2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (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
408,1,396,0,1.243478," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(5 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3} + B a b^{4} - 3 \, A 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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 a^{3} + 2 \, A a b^{2} + {\left(2 \, A a^{2} b - B a b^{2} + 3 \, A 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*(5*B*a^3*b^2 - 7*A*a^2*b^3 + B*a*b^4 - 3*A*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 - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (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*a^3 + 2*A*a*b^2 + (2*A*a^2*b - B*a*b^2 + 3*A*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
409,1,449,0,0.890794," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left(7 \, B a^{3} b^{3} - 9 \, A a^{2} b^{4} + 3 \, B a b^{5} - 5 \, A 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 a^{4} + 2 \, A a^{2} b^{2} + 3 \, {\left(2 \, B a^{3} b - 4 \, A a^{2} b^{2} + 3 \, B a b^{3} - 5 \, A b^{4}\right)} \tan\left(d x + c\right)^{2} + 2 \, {\left(3 \, B a^{4} - 5 \, A a^{3} b + 3 \, B a^{2} b^{2} - 5 \, A 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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*(7*B*a^3*b^3 - 9*A*a^2*b^4 + 3*B*a*b^5 - 5*A*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*a^4 + 2*A*a^2*b^2 + 3*(2*B*a^3*b - 4*A*a^2*b^2 + 3*B*a*b^3 - 5*A*b^4)*tan(d*x + c)^2 + 2*(3*B*a^4 - 5*A*a^3*b + 3*B*a^2*b^2 - 5*A*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 + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (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
410,1,571,0,1.061157," ","integrate(tan(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, B a^{7} - 3 \, A a^{6} b + 46 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + 63 \, B a^{3} b^{4} - 35 \, A a^{2} b^{5}\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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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 \, B a^{5} b - 5 \, A a^{4} b^{2} + 17 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(7 \, B a^{6} - 3 \, A a^{5} b + 15 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3}\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 \, B \sqrt{\tan\left(d x + c\right)}}{b^{3}}}{4 \, d}"," ",0,"-1/4*((15*B*a^7 - 3*A*a^6*b + 46*B*a^5*b^2 - 6*A*a^4*b^3 + 63*B*a^3*b^4 - 35*A*a^2*b^5)*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 + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*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*B*a^5*b - 5*A*a^4*b^2 + 17*B*a^3*b^3 - 13*A*a^2*b^4)*tan(d*x + c)^(3/2) + (7*B*a^6 - 3*A*a^5*b + 15*B*a^4*b^2 - 11*A*a^3*b^3)*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*B*sqrt(tan(d*x + c))/b^3)/d","A",0
411,1,551,0,1.226533," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, B a^{6} + A a^{5} b + 6 \, B a^{4} b^{2} + 18 \, A a^{3} b^{3} + 35 \, B a^{2} b^{4} - 15 \, A a b^{5}\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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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 \, B a^{4} b - A a^{3} b^{2} + 13 \, B a^{2} b^{3} - 9 \, A a b^{4}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(3 \, B a^{5} + A a^{4} b + 11 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}\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*B*a^6 + A*a^5*b + 6*B*a^4*b^2 + 18*A*a^3*b^3 + 35*B*a^2*b^4 - 15*A*a*b^5)*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 - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*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*B*a^4*b - A*a^3*b^2 + 13*B*a^2*b^3 - 9*A*a*b^4)*tan(d*x + c)^(3/2) + (3*B*a^5 + A*a^4*b + 11*B*a^3*b^2 - 7*A*a^2*b^3)*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
412,1,538,0,0.955673," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(B a^{5} + 3 \, A a^{4} b + 18 \, B a^{3} b^{2} - 26 \, A a^{2} b^{3} - 15 \, B a b^{4} + 3 \, A b^{5}\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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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(B a^{3} b + 3 \, A a^{2} b^{2} + 9 \, B a b^{3} - 5 \, A b^{4}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} - {\left(B a^{4} - 5 \, A a^{3} b - 7 \, B a^{2} b^{2} + 3 \, A a b^{3}\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*((B*a^5 + 3*A*a^4*b + 18*B*a^3*b^2 - 26*A*a^2*b^3 - 15*B*a*b^4 + 3*A*b^5)*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 + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*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) + ((B*a^3*b + 3*A*a^2*b^2 + 9*B*a*b^3 - 5*A*b^4)*tan(d*x + c)^(3/2) - (B*a^4 - 5*A*a^3*b - 7*B*a^2*b^2 + 3*A*a*b^3)*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
413,1,537,0,0.913109," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, B a^{5} - 15 \, A a^{4} b - 26 \, B a^{3} b^{2} + 18 \, A a^{2} b^{3} + 3 \, B a b^{4} + A 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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 \, B a^{3} b - 7 \, A a^{2} b^{2} - 5 \, B a b^{3} + A b^{4}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(5 \, B a^{4} - 9 \, A a^{3} b - 3 \, B a^{2} b^{2} - A 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*((3*B*a^5 - 15*A*a^4*b - 26*B*a^3*b^2 + 18*A*a^2*b^3 + 3*B*a*b^4 + A*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 - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*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*B*a^3*b - 7*A*a^2*b^2 - 5*B*a*b^3 + A*b^4)*tan(d*x + c)^(3/2) + (5*B*a^4 - 9*A*a^3*b - 3*B*a^2*b^2 - A*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
414,1,551,0,1.040355," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(15 \, B a^{5} b - 35 \, A a^{4} b^{2} - 18 \, B a^{3} b^{3} - 6 \, A a^{2} b^{4} - B a b^{5} - 3 \, A 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3} - B a b^{4} - 3 \, A b^{5}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + {\left(9 \, B a^{4} b - 13 \, A a^{3} b^{2} + B a^{2} b^{3} - 5 \, A 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*((15*B*a^5*b - 35*A*a^4*b^2 - 18*B*a^3*b^3 - 6*A*a^2*b^4 - B*a*b^5 - 3*A*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 + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*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*B*a^3*b^2 - 11*A*a^2*b^3 - B*a*b^4 - 3*A*b^5)*tan(d*x + c)^(3/2) + (9*B*a^4*b - 13*A*a^3*b^2 + B*a^2*b^3 - 5*A*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
415,1,607,0,0.482198," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(35 \, B a^{5} b^{2} - 63 \, A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 46 \, A a^{2} b^{5} + 3 \, B a b^{6} - 15 \, A 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 a^{6} + 16 \, A a^{4} b^{2} + 8 \, A a^{2} b^{4} + {\left(8 \, A a^{4} b^{2} - 11 \, B a^{3} b^{3} + 31 \, A a^{2} b^{4} - 3 \, B a b^{5} + 15 \, A b^{6}\right)} \tan\left(d x + c\right)^{2} + {\left(16 \, A a^{5} b - 13 \, B a^{4} b^{2} + 49 \, A a^{3} b^{3} - 5 \, B a^{2} b^{4} + 25 \, A 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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*((35*B*a^5*b^2 - 63*A*a^4*b^3 + 6*B*a^3*b^4 - 46*A*a^2*b^5 + 3*B*a*b^6 - 15*A*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*a^6 + 16*A*a^4*b^2 + 8*A*a^2*b^4 + (8*A*a^4*b^2 - 11*B*a^3*b^3 + 31*A*a^2*b^4 - 3*B*a*b^5 + 15*A*b^6)*tan(d*x + c)^2 + (16*A*a^5*b - 13*B*a^4*b^2 + 49*A*a^3*b^3 - 5*B*a^2*b^4 + 25*A*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 - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*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
416,1,123,0,0.859696," ","integrate(tan(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, B \tan\left(d x + c\right)^{\frac{3}{2}} - 3 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} B}{12 \, d}"," ",0,"1/12*(8*B*tan(d*x + c)^(3/2) - 3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*B)/d","A",0
417,1,123,0,0.908050," ","integrate(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} B \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} B \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} B \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} B \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)*B*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*B*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*B*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*B*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 8*B*sqrt(tan(d*x + c)))/d","A",0
418,1,109,0,0.543982," ","integrate(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} B}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*B/d","A",0
419,1,112,0,0.545536," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} B \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} B \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + \sqrt{2} B \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - \sqrt{2} B \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)*B*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*B*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + sqrt(2)*B*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - sqrt(2)*B*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))/d","A",0
420,1,122,0,0.922927," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) - \sqrt{2} \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \sqrt{2} \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right)\right)} B + \frac{8 \, B}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) - sqrt(2)*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + sqrt(2)*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1))*B + 8*B/sqrt(tan(d*x + c)))/d","A",0
421,1,124,0,0.901012," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} B \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 6 \, \sqrt{2} B \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - 2 \, \sqrt{\tan\left(d x + c\right)}\right)}\right) + 3 \, \sqrt{2} B \log\left(\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) - 3 \, \sqrt{2} B \log\left(-\sqrt{2} \sqrt{\tan\left(d x + c\right)} + \tan\left(d x + c\right) + 1\right) + \frac{8 \, B}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(6*sqrt(2)*B*arctan(1/2*sqrt(2)*(sqrt(2) + 2*sqrt(tan(d*x + c)))) + 6*sqrt(2)*B*arctan(-1/2*sqrt(2)*(sqrt(2) - 2*sqrt(tan(d*x + c)))) + 3*sqrt(2)*B*log(sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) - 3*sqrt(2)*B*log(-sqrt(2)*sqrt(tan(d*x + c)) + tan(d*x + c) + 1) + 8*B/tan(d*x + c)^(3/2))/d","A",0
422,1,188,0,0.727346," ","integrate(tan(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, B 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{{\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)} B}{a^{2} + b^{2}} - \frac{8 \, B \sqrt{\tan\left(d x + c\right)}}{b}}{4 \, d}"," ",0,"-1/4*(8*B*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))*B/(a^2 + b^2) - 8*B*sqrt(tan(d*x + c))/b)/d","A",0
423,1,173,0,0.829527," ","integrate(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{8 \, B 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{{\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)} B}{a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(8*B*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))*B/(a^2 + b^2))/d","A",0
424,1,172,0,0.719317," ","integrate(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, B 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{{\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)} B}{a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(8*B*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))*B/(a^2 + b^2))/d","A",0
425,1,172,0,2.040423," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{8 \, B 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{{\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)} B}{a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(8*B*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))*B/(a^2 + b^2))/d","A",0
426,1,188,0,0.862682," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{8 \, B 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{{\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)} B}{a^{2} + b^{2}} + \frac{8 \, B}{a \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(8*B*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))*B/(a^2 + b^2) + 8*B/(a*sqrt(tan(d*x + c))))/d","A",0
427,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*tan(d*x+c)^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(3/2), x)","F",0
428,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*sqrt(tan(d*x + c)), x)","F",0
429,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a}}{\sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)/sqrt(tan(d*x + c)), x)","F",0
430,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a}}{\tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)/tan(d*x + c)^(5/2), x)","F",0
432,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
433,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
434,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^(3/2), x)","F",0
435,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c)), x)","F",0
436,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)/sqrt(tan(d*x + c)), x)","F",0
437,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(5/2), x)","F",0
439,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)/tan(d*x + c)^(9/2), x)","F",0
441,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^(3/2), x)","F",0
443,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c)), x)","F",0
444,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)/sqrt(tan(d*x + c)), x)","F",0
445,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(5/2), x)","F",0
447,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(9/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(11/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/tan(d*x+c)^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(3/2*b*B/a+B*tan(d*x+c))/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{1}{2} \, \int \frac{{\left(2 \, B \tan\left(d x + c\right) + \frac{3 \, B b}{a}\right)} {\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,"1/2*integrate((2*B*tan(d*x + c) + 3*B*b/a)*(b*tan(d*x + c) + a)^(5/2)/tan(d*x + c)^(5/2), x)","F",0
452,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^(3/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
453,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{\tan\left(d x + c\right)}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(tan(d*x + c))/sqrt(b*tan(d*x + c) + a), x)","F",0
454,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{\sqrt{b \tan\left(d x + c\right) + a} \sqrt{\tan\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(sqrt(b*tan(d*x + c) + a)*sqrt(tan(d*x + c))), x)","F",0
455,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(3/2)), x)","F",0
456,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{\sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^(5/2)), x)","F",0
457,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2)/tan(d*x+c)^(7/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*tan(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
459,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{\tan\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(tan(d*x + c))/(b*tan(d*x + c) + a)^(3/2), x)","F",0
460,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c))), x)","F",0
461,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(tan(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*tan(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
464,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*tan(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
465,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{\tan\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(tan(d*x + c))/(b*tan(d*x + c) + a)^(5/2), x)","F",0
466,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(5/2)*sqrt(tan(d*x + c))), x)","F",0
467,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/tan(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \tan\left(d x + c\right) + B a\right)} \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((B*b*tan(d*x + c) + B*a)*tan(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
470,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \tan\left(d x + c\right) + B a\right)} \sqrt{\tan\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*tan(d*x + c) + B*a)*sqrt(tan(d*x + c))/(b*tan(d*x + c) + a)^(3/2), x)","F",0
471,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B b \tan\left(d x + c\right) + B a}{{\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*b*tan(d*x + c) + B*a)/((b*tan(d*x + c) + a)^(3/2)*sqrt(tan(d*x + c))), x)","F",0
472,-1,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/tan(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(2/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^(2/3), x)","F",0
474,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/3)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^(1/3), x)","F",0
475,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/3),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(b*tan(d*x + c) + a)^(1/3), x)","F",0
476,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(2/3),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(b*tan(d*x + c) + a)^(2/3), x)","F",0
477,0,0,0,0.000000," ","integrate((-tan(f*x+e)+I)/(c+d*tan(f*x+e))^(1/3),x, algorithm=""maxima"")","-\int \frac{\tan\left(f x + e\right) - i}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"-integrate((tan(f*x + e) - I)/(d*tan(f*x + e) + c)^(1/3), x)","F",0
478,0,0,0,0.000000," ","integrate((d-c*tan(f*x+e))/(c+d*tan(f*x+e))^(2/3),x, algorithm=""maxima"")","-\int \frac{c \tan\left(f x + e\right) - d}{{\left(d \tan\left(f x + e\right) + c\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"-integrate((c*tan(f*x + e) - d)/(d*tan(f*x + e) + c)^(2/3), x)","F",0
479,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^4*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{4} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^4*tan(d*x + c)^m, x)","F",0
480,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{3} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^3*tan(d*x + c)^m, x)","F",0
481,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{2} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^2*tan(d*x + c)^m, x)","F",0
482,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
483,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{b \tan\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a), x)","F",0
484,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{{\left(b \tan\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a)^2, x)","F",0
485,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{{\left(b \tan\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a)^3, x)","F",0
486,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{{\left(b \tan\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a)^4, x)","F",0
487,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^(5/2)*tan(d*x + c)^m, x)","F",0
488,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*tan(d*x + c)^m, x)","F",0
489,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*tan(d*x + c)^m, x)","F",0
490,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/sqrt(b*tan(d*x + c) + a), x)","F",0
491,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a)^(3/2), x)","F",0
492,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \tan\left(d x + c\right)^{m}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*tan(d*x + c)^m/(b*tan(d*x + c) + a)^(5/2), x)","F",0
493,0,0,0,0.000000," ","integrate(tan(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n} \tan\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^n*tan(d*x + c)^m, x)","F",0
494,0,0,0,0.000000," ","integrate(tan(d*x+c)^4*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*tan(d*x + c)^4, x)","F",0
495,0,0,0,0.000000," ","integrate(tan(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*tan(d*x + c)^3, x)","F",0
496,0,0,0,0.000000," ","integrate(tan(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*tan(d*x + c)^2, x)","F",0
497,0,0,0,0.000000," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*tan(d*x + c), x)","F",0
498,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^n, x)","F",0
499,0,0,0,0.000000," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*cot(d*x + c), x)","F",0
500,0,0,0,0.000000," ","integrate(cot(d*x+c)^2*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*cot(d*x + c)^2, x)","F",0
501,0,0,0,0.000000," ","integrate(cot(d*x+c)^3*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*cot(d*x + c)^3, x)","F",0
502,1,190,0,1.092678," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{15 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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 + \frac{120 \, {\left(A - i \, B\right)} a}{\sqrt{\tan\left(d x + c\right)}} - \frac{8 \, {\left(5 i \, A + 5 \, B\right)} a}{\tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{24 \, A a}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{60 \, d}"," ",0,"1/60*(15*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a + 120*(A - I*B)*a/sqrt(tan(d*x + c)) - 8*(5*I*A + 5*B)*a/tan(d*x + c)^(3/2) - 24*A*a/tan(d*x + c)^(5/2))/d","B",0
503,1,174,0,1.029379," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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 + \frac{8 \, {\left(3 i \, A + 3 \, B\right)} a}{\sqrt{\tan\left(d x + c\right)}} + \frac{8 \, A a}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"-1/12*(3*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a + 8*(3*I*A + 3*B)*a/sqrt(tan(d*x + c)) + 8*A*a/tan(d*x + c)^(3/2))/d","B",0
504,1,155,0,0.431005," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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 + \frac{8 \, A a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*((2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a + 8*A*a/sqrt(tan(d*x + c)))/d","B",0
505,1,155,0,0.974364," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{8 i \, B a \sqrt{\tan\left(d x + c\right)} + {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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}{4 \, d}"," ",0,"1/4*(8*I*B*a*sqrt(tan(d*x + c)) + (2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a)/d","B",0
506,1,176,0,1.001445," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, {\left(i \, B a + \frac{{\left(3 i \, A + 3 \, B\right)} a}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}} + 3 \, {\left(2 \, \sqrt{2} {\left(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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}{12 \, d}"," ",0,"1/12*(8*(I*B*a + (3*I*A + 3*B)*a/tan(d*x + c))*tan(d*x + c)^(3/2) + 3*(2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((I - 1)*A + (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a)/d","B",0
507,1,192,0,0.988212," ","integrate((a+I*a*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{8 \, {\left(-3 i \, B a + \frac{{\left(-5 i \, A - 5 \, B\right)} a}{\tan\left(d x + c\right)} - \frac{15 \, {\left(A - i \, B\right)} a}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + 15 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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}{60 \, d}"," ",0,"-1/60*(8*(-3*I*B*a + (-5*I*A - 5*B)*a/tan(d*x + c) - 15*(A - I*B)*a/tan(d*x + c)^2)*tan(d*x + c)^(5/2) + 15*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a)/d","B",0
508,1,198,0,0.836038," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{15 \, {\left(2 \, \sqrt{2} {\left(-\left(i - 1\right) \, A - \left(i + 1\right) \, 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(-\left(i - 1\right) \, A - \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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} - \frac{120 \, {\left(A - i \, B\right)} a^{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{4 \, {\left(10 i \, A + 5 \, B\right)} a^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{12 \, A a^{2}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{30 \, d}"," ",0,"-1/30*(15*(2*sqrt(2)*(-(I - 1)*A - (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I - 1)*A - (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 - 120*(A - I*B)*a^2/sqrt(tan(d*x + c)) + 4*(10*I*A + 5*B)*a^2/tan(d*x + c)^(3/2) + 12*A*a^2/tan(d*x + c)^(5/2))/d","A",0
509,1,180,0,0.818343," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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} + \frac{4 \, {\left(6 i \, A + 3 \, B\right)} a^{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{4 \, A a^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{6 \, d}"," ",0,"-1/6*(3*(2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 + 4*(6*I*A + 3*B)*a^2/sqrt(tan(d*x + c)) + 4*A*a^2/tan(d*x + c)^(3/2))/d","B",0
510,1,174,0,1.038287," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, B a^{2} \sqrt{\tan\left(d x + c\right)} - {\left(2 \, \sqrt{2} {\left(-\left(i - 1\right) \, A - \left(i + 1\right) \, 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(-\left(i - 1\right) \, A - \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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} + \frac{4 \, A a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{2 \, d}"," ",0,"-1/2*(4*B*a^2*sqrt(tan(d*x + c)) - (2*sqrt(2)*(-(I - 1)*A - (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I - 1)*A - (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 + 4*A*a^2/sqrt(tan(d*x + c)))/d","B",0
511,1,180,0,2.077187," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, \sqrt{2} {\left(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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} - 4 \, {\left(B a^{2} + \frac{3 \, {\left(A - 2 i \, B\right)} 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*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I + 1)*A + (I - 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2 - 4*(B*a^2 + 3*(A - 2*I*B)*a^2/tan(d*x + c))*tan(d*x + c)^(3/2))/d","B",0
512,1,200,0,1.713544," ","integrate((a+I*a*tan(d*x+c))^2*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{4 \, {\left(3 \, B a^{2} + \frac{5 \, {\left(A - 2 i \, B\right)} a^{2}}{\tan\left(d x + c\right)} + \frac{{\left(-30 i \, A - 30 \, B\right)} a^{2}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} + 15 \, {\left(2 \, \sqrt{2} {\left(-\left(i - 1\right) \, A - \left(i + 1\right) \, 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(-\left(i - 1\right) \, A - \left(i + 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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}}{30 \, d}"," ",0,"-1/30*(4*(3*B*a^2 + 5*(A - 2*I*B)*a^2/tan(d*x + c) + (-30*I*A - 30*B)*a^2/tan(d*x + c)^2)*tan(d*x + c)^(5/2) + 15*(2*sqrt(2)*(-(I - 1)*A - (I + 1)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*(-(I - 1)*A - (I + 1)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^2)/d","A",0
513,1,218,0,1.661177," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{105 \, {\left(\sqrt{2} {\left(\left(2 i + 2\right) \, A - \left(2 i - 2\right) \, 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(\left(2 i + 2\right) \, A - \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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^{3} + \frac{2 \, {\left(-420 i \, A - 420 \, B\right)} a^{3}}{\sqrt{\tan\left(d x + c\right)}} - \frac{70 \, {\left(4 \, A - 3 i \, B\right)} a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{2 \, {\left(63 i \, A + 21 \, B\right)} a^{3}}{\tan\left(d x + c\right)^{\frac{5}{2}}} + \frac{30 \, A a^{3}}{\tan\left(d x + c\right)^{\frac{7}{2}}}}{105 \, d}"," ",0,"-1/105*(105*(sqrt(2)*((2*I + 2)*A - (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + sqrt(2)*((2*I + 2)*A - (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 + 2*(-420*I*A - 420*B)*a^3/sqrt(tan(d*x + c)) - 70*(4*A - 3*I*B)*a^3/tan(d*x + c)^(3/2) + 2*(63*I*A + 21*B)*a^3/tan(d*x + c)^(5/2) + 30*A*a^3/tan(d*x + c)^(7/2))/d","A",0
514,1,198,0,1.109293," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{15 \, {\left(\sqrt{2} {\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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^{3} - \frac{30 \, {\left(4 \, A - 3 i \, B\right)} a^{3}}{\sqrt{\tan\left(d x + c\right)}} + \frac{2 \, {\left(15 i \, A + 5 \, B\right)} a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{6 \, A a^{3}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{15 \, d}"," ",0,"-1/15*(15*(sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 - 30*(4*A - 3*I*B)*a^3/sqrt(tan(d*x + c)) + 2*(15*I*A + 5*B)*a^3/tan(d*x + c)^(3/2) + 6*A*a^3/tan(d*x + c)^(5/2))/d","A",0
515,1,192,0,0.946952," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{-6 i \, B a^{3} \sqrt{\tan\left(d x + c\right)} + 3 \, {\left(\sqrt{2} {\left(\left(2 i + 2\right) \, A - \left(2 i - 2\right) \, 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(\left(2 i + 2\right) \, A - \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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^{3} - \frac{2 \, {\left(9 i \, A + 3 \, B\right)} a^{3}}{\sqrt{\tan\left(d x + c\right)}} - \frac{2 \, A a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{3 \, d}"," ",0,"1/3*(-6*I*B*a^3*sqrt(tan(d*x + c)) + 3*(sqrt(2)*((2*I + 2)*A - (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + sqrt(2)*((2*I + 2)*A - (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 - 2*(9*I*A + 3*B)*a^3/sqrt(tan(d*x + c)) - 2*A*a^3/tan(d*x + c)^(3/2))/d","A",0
516,1,194,0,1.189414," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(\sqrt{2} {\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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^{3} - \frac{6 \, A a^{3}}{\sqrt{\tan\left(d x + c\right)}} + 2 \, {\left(-i \, B a^{3} + \frac{{\left(-3 i \, A - 9 \, B\right)} a^{3}}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{3 \, d}"," ",0,"1/3*(3*(sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 - 6*A*a^3/sqrt(tan(d*x + c)) + 2*(-I*B*a^3 + (-3*I*A - 9*B)*a^3/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
517,1,200,0,1.109693," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{15 \, {\left(\sqrt{2} {\left(\left(2 i + 2\right) \, A - \left(2 i - 2\right) \, 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(\left(2 i + 2\right) \, A - \left(2 i - 2\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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(\left(i - 1\right) \, A + \left(i + 1\right) \, 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^{3} + 2 \, {\left(3 i \, B a^{3} + \frac{{\left(5 i \, A + 15 \, B\right)} a^{3}}{\tan\left(d x + c\right)} + \frac{15 \, {\left(3 \, A - 4 i \, B\right)} a^{3}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}}}{15 \, d}"," ",0,"-1/15*(15*(sqrt(2)*((2*I + 2)*A - (2*I - 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + sqrt(2)*((2*I + 2)*A - (2*I - 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((I - 1)*A + (I + 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((I - 1)*A + (I + 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3 + 2*(3*I*B*a^3 + (5*I*A + 15*B)*a^3/tan(d*x + c) + 15*(3*A - 4*I*B)*a^3/tan(d*x + c)^2)*tan(d*x + c)^(5/2))/d","A",0
518,1,219,0,0.799937," ","integrate((a+I*a*tan(d*x+c))^3*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(15 i \, B a^{3} + \frac{{\left(21 i \, A + 63 \, B\right)} a^{3}}{\tan\left(d x + c\right)} + \frac{35 \, {\left(3 \, A - 4 i \, B\right)} a^{3}}{\tan\left(d x + c\right)^{2}} + \frac{{\left(-420 i \, A - 420 \, B\right)} a^{3}}{\tan\left(d x + c\right)^{3}}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} + 105 \, {\left(\sqrt{2} {\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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(-\left(i + 1\right) \, A + \left(i - 1\right) \, 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^{3}}{105 \, d}"," ",0,"-1/105*(2*(15*I*B*a^3 + (21*I*A + 63*B)*a^3/tan(d*x + c) + 35*(3*A - 4*I*B)*a^3/tan(d*x + c)^2 + (-420*I*A - 420*B)*a^3/tan(d*x + c)^3)*tan(d*x + c)^(7/2) + 105*(sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + sqrt(2)*(-(2*I - 2)*A - (2*I + 2)*B)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*(-(I + 1)*A + (I - 1)*B)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*a^3)/d","A",0
519,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*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
520,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*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
521,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*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
522,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
523,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
524,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
525,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*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
526,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*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
527,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
528,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
529,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
530,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*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
531,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*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
532,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
533,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
534,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
535,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
536,1,1389,0,2.229920," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),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(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(1170 i + 1170\right) \, A - \left(750 i - 750\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(900 i - 900\right) \, A - \left(900 i + 900\right) \, B\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(1170 i - 1170\right) \, A + \left(750 i + 750\right) \, B\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(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(1170 i - 1170\right) \, A - \left(750 i + 750\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(1170 i + 1170\right) \, A - \left(750 i - 750\right) \, B\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(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(1800 i - 1800\right) \, A - \left(1800 i + 1800\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\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(\left(450 i + 450\right) \, A - \left(450 i - 450\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(450 i + 450\right) \, A - \left(450 i - 450\right) \, B\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(450 i + 450\right) \, A - \left(450 i - 450\right) \, B\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(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(150 i + 150\right) \, A - \left(750 i - 750\right) \, B\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(390 i + 390\right) \, A - \left(150 i - 150\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(900 i - 900\right) \, A - \left(900 i + 900\right) \, B\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(150 i - 150\right) \, A + \left(750 i + 750\right) \, B\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(390 i - 390\right) \, A + \left(150 i + 150\right) \, B\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(-\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(240 i - 240\right) \, A + \left(600 i + 600\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(240 i - 240\right) \, A + \left(600 i + 600\right) \, B\right)} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(480 i + 480\right) \, A + \left(1200 i - 1200\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(480 i - 480\right) \, A - \left(1200 i + 1200\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(240 i - 240\right) \, A + \left(600 i + 600\right) \, B\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(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(150 i - 150\right) \, A - \left(750 i + 750\right) \, B\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(390 i - 390\right) \, A - \left(150 i + 150\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(150 i + 150\right) \, A - \left(750 i - 750\right) \, B\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(390 i + 390\right) \, A - \left(150 i - 150\right) \, B\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(\left(240 i - 240\right) \, A - \left(600 i + 600\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(240 i - 240\right) \, A - \left(600 i + 600\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(480 i - 480\right) \, A + \left(1200 i + 1200\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(480 i + 480\right) \, A + \left(1200 i - 1200\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(240 i - 240\right) \, A - \left(600 i + 600\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\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)*A + (900*I - 900)*B)*cos(3*d*x + 3*c) + ((1170*I + 1170)*A - (750*I - 750)*B)*cos(d*x + c) + (-(900*I - 900)*A - (900*I + 900)*B)*sin(3*d*x + 3*c) + ((1170*I - 1170)*A + (750*I + 750)*B)*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 + (900*I + 900)*B)*cos(3*d*x + 3*c) + (-(1170*I - 1170)*A - (750*I + 750)*B)*cos(d*x + c) + (-(900*I + 900)*A + (900*I - 900)*B)*sin(3*d*x + 3*c) + ((1170*I + 1170)*A - (750*I - 750)*B)*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 + (900*I + 900)*B)*cos(2*d*x + 2*c)^2 + ((900*I - 900)*A + (900*I + 900)*B)*sin(2*d*x + 2*c)^2 + (-(1800*I - 1800)*A - (1800*I + 1800)*B)*cos(2*d*x + 2*c) + (900*I - 900)*A + (900*I + 900)*B)*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 - (450*I - 450)*B)*cos(2*d*x + 2*c)^2 + ((450*I + 450)*A - (450*I - 450)*B)*sin(2*d*x + 2*c)^2 + (-(900*I + 900)*A + (900*I - 900)*B)*cos(2*d*x + 2*c) + (450*I + 450)*A - (450*I - 450)*B)*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 + (900*I - 900)*B)*cos(5*d*x + 5*c) + (-(150*I + 150)*A - (750*I - 750)*B)*cos(3*d*x + 3*c) + (-(390*I + 390)*A - (150*I - 150)*B)*cos(d*x + c) + (-(900*I - 900)*A - (900*I + 900)*B)*sin(5*d*x + 5*c) + (-(150*I - 150)*A + (750*I + 750)*B)*sin(3*d*x + 3*c) + (-(390*I - 390)*A + (150*I + 150)*B)*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 - (600*I - 600)*B)*cos(d*x + c) + (-(240*I - 240)*A + (600*I + 600)*B)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(240*I + 240)*A - (600*I - 600)*B)*cos(d*x + c) + (-(240*I - 240)*A + (600*I + 600)*B)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((480*I + 480)*A + (1200*I - 1200)*B)*cos(d*x + c) + ((480*I - 480)*A - (1200*I + 1200)*B)*sin(d*x + c))*cos(2*d*x + 2*c) + (-(240*I + 240)*A - (600*I - 600)*B)*cos(d*x + c) + (-(240*I - 240)*A + (600*I + 600)*B)*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((900*I - 900)*A + (900*I + 900)*B)*cos(5*d*x + 5*c) + ((150*I - 150)*A - (750*I + 750)*B)*cos(3*d*x + 3*c) + ((390*I - 390)*A - (150*I + 150)*B)*cos(d*x + c) + (-(900*I + 900)*A + (900*I - 900)*B)*sin(5*d*x + 5*c) + (-(150*I + 150)*A - (750*I - 750)*B)*sin(3*d*x + 3*c) + (-(390*I + 390)*A - (150*I - 150)*B)*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 - (600*I + 600)*B)*cos(d*x + c) + (-(240*I + 240)*A - (600*I - 600)*B)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((240*I - 240)*A - (600*I + 600)*B)*cos(d*x + c) + (-(240*I + 240)*A - (600*I - 600)*B)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((-(480*I - 480)*A + (1200*I + 1200)*B)*cos(d*x + c) + ((480*I + 480)*A + (1200*I - 1200)*B)*sin(d*x + c))*cos(2*d*x + 2*c) + ((240*I - 240)*A - (600*I + 600)*B)*cos(d*x + c) + (-(240*I + 240)*A - (600*I - 600)*B)*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
537,1,1145,0,1.836047," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),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(\left(36 i - 36\right) \, A + \left(36 i + 36\right) \, B\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(12 i - 12\right) \, A - \left(36 i + 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(36 i + 36\right) \, A + \left(36 i - 36\right) \, B\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(12 i + 12\right) \, A - \left(36 i - 36\right) \, B\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(\left(36 i + 36\right) \, A - \left(36 i - 36\right) \, B\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(12 i + 12\right) \, A + \left(36 i - 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(36 i - 36\right) \, A + \left(36 i + 36\right) \, B\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(12 i - 12\right) \, A - \left(36 i + 36\right) \, B\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(\left(36 i + 36\right) \, A - \left(36 i - 36\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(36 i + 36\right) \, A - \left(36 i - 36\right) \, B\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(72 i + 72\right) \, A + \left(72 i - 72\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right) + \left(36 i + 36\right) \, A - \left(36 i - 36\right) \, B\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(-\left(18 i - 18\right) \, A - \left(18 i + 18\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(18 i - 18\right) \, A - \left(18 i + 18\right) \, B\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(36 i - 36\right) \, A + \left(36 i + 36\right) \, B\right)} \cos\left(2 \, d x + 2 \, c\right) - \left(18 i - 18\right) \, A - \left(18 i + 18\right) \, B\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(\left(12 i - 12\right) \, A + \left(36 i + 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(12 i + 12\right) \, A + \left(36 i - 36\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(12 i - 12\right) \, A + \left(36 i + 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(12 i + 12\right) \, A + \left(36 i - 36\right) \, B\right)} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(24 i - 24\right) \, A - \left(72 i + 72\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(24 i + 24\right) \, A - \left(72 i - 72\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(12 i - 12\right) \, A + \left(36 i + 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(12 i + 12\right) \, A + \left(36 i - 36\right) \, B\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(\left(12 i + 12\right) \, A - \left(36 i - 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(12 i - 12\right) \, A + \left(36 i + 36\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(12 i + 12\right) \, A - \left(36 i - 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(12 i - 12\right) \, A + \left(36 i + 36\right) \, B\right)} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(24 i + 24\right) \, A + \left(72 i - 72\right) \, B\right)} \cos\left(d x + c\right) + {\left(-\left(24 i - 24\right) \, A - \left(72 i + 72\right) \, B\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(12 i + 12\right) \, A - \left(36 i - 36\right) \, B\right)} \cos\left(d x + c\right) + {\left(\left(12 i - 12\right) \, A + \left(36 i + 36\right) \, B\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)*A + (36*I + 36)*B)*cos(3*d*x + 3*c) + ((12*I - 12)*A - (36*I + 36)*B)*cos(d*x + c) + (-(36*I + 36)*A + (36*I - 36)*B)*sin(3*d*x + 3*c) + (-(12*I + 12)*A - (36*I - 36)*B)*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 - (36*I - 36)*B)*cos(3*d*x + 3*c) + ((12*I + 12)*A + (36*I - 36)*B)*cos(d*x + c) + ((36*I - 36)*A + (36*I + 36)*B)*sin(3*d*x + 3*c) + ((12*I - 12)*A - (36*I + 36)*B)*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 - (36*I - 36)*B)*cos(2*d*x + 2*c)^2 + ((36*I + 36)*A - (36*I - 36)*B)*sin(2*d*x + 2*c)^2 + (-(72*I + 72)*A + (72*I - 72)*B)*cos(2*d*x + 2*c) + (36*I + 36)*A - (36*I - 36)*B)*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 - (18*I + 18)*B)*cos(2*d*x + 2*c)^2 + (-(18*I - 18)*A - (18*I + 18)*B)*sin(2*d*x + 2*c)^2 + ((36*I - 36)*A + (36*I + 36)*B)*cos(2*d*x + 2*c) - (18*I - 18)*A - (18*I + 18)*B)*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 + (36*I + 36)*B)*cos(d*x + c) + (-(12*I + 12)*A + (36*I - 36)*B)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((12*I - 12)*A + (36*I + 36)*B)*cos(d*x + c) + (-(12*I + 12)*A + (36*I - 36)*B)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((-(24*I - 24)*A - (72*I + 72)*B)*cos(d*x + c) + ((24*I + 24)*A - (72*I - 72)*B)*sin(d*x + c))*cos(2*d*x + 2*c) + ((12*I - 12)*A + (36*I + 36)*B)*cos(d*x + c) + (-(12*I + 12)*A + (36*I - 36)*B)*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 - (36*I - 36)*B)*cos(d*x + c) + ((12*I - 12)*A + (36*I + 36)*B)*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((12*I + 12)*A - (36*I - 36)*B)*cos(d*x + c) + ((12*I - 12)*A + (36*I + 36)*B)*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((-(24*I + 24)*A + (72*I - 72)*B)*cos(d*x + c) + (-(24*I - 24)*A - (72*I + 72)*B)*sin(d*x + c))*cos(2*d*x + 2*c) + ((12*I + 12)*A - (36*I - 36)*B)*cos(d*x + c) + ((12*I - 12)*A + (36*I + 36)*B)*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
538,1,555,0,1.592941," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left({\left(-\left(2 i - 2\right) \, A - \left(2 i + 2\right) \, B\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(i + 1\right) \, A + \left(i - 1\right) \, B\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(4 i + 4\right) \, A \cos\left(d x + c\right) + \left(4 i - 4\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(4 i - 4\right) \, A \cos\left(d x + c\right) + \left(4 i + 4\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}}{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*(((-(2*I - 2)*A - (2*I + 2)*B)*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 + (I - 1)*B)*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) + (((4*I + 4)*A*cos(d*x + c) + (4*I - 4)*A*sin(d*x + c))*cos(1/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (-(4*I - 4)*A*cos(d*x + c) + (4*I + 4)*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
539,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{i \, a \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(I*a*tan(d*x + c) + a)*sqrt(cot(d*x + c)), x)","F",0
540,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{i \, a \tan\left(d x + c\right) + a}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(I*a*tan(d*x + c) + a)/sqrt(cot(d*x + c)), x)","F",0
541,1,3719,0,7.072320," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),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(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \cos\left(7 \, d x + 7 \, c\right) + {\left(-\left(176400 i - 176400\right) \, A - \left(529200 i + 529200\right) \, B\right)} a \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(167580 i - 167580\right) \, A + \left(255780 i + 255780\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(59220 i - 59220\right) \, A - \left(79380 i + 79380\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a \sin\left(7 \, d x + 7 \, c\right) + {\left(\left(176400 i + 176400\right) \, A - \left(529200 i - 529200\right) \, B\right)} a \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(167580 i + 167580\right) \, A + \left(255780 i - 255780\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(59220 i + 59220\right) \, A - \left(79380 i - 79380\right) \, B\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(-\left(236880 i - 236880\right) \, A - \left(199920 i + 199920\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(236880 i + 236880\right) \, A - \left(199920 i - 199920\right) \, B\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 - \left(199920 i + 199920\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left(-\left(236880 i - 236880\right) \, A - \left(199920 i + 199920\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(236880 i + 236880\right) \, A - \left(199920 i - 199920\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(236880 i + 236880\right) \, A - \left(199920 i - 199920\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(705600 i - 705600\right) \, A - \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(\left(473760 i - 473760\right) \, A + \left(399840 i + 399840\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(473760 i + 473760\right) \, A + \left(399840 i - 399840\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(705600 i + 705600\right) \, A - \left(705600 i - 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a\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(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \cos\left(7 \, d x + 7 \, c\right) + {\left(-\left(176400 i + 176400\right) \, A + \left(529200 i - 529200\right) \, B\right)} a \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(167580 i + 167580\right) \, A - \left(255780 i - 255780\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(59220 i + 59220\right) \, A + \left(79380 i - 79380\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \sin\left(7 \, d x + 7 \, c\right) + {\left(-\left(176400 i - 176400\right) \, A - \left(529200 i + 529200\right) \, B\right)} a \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(167580 i - 167580\right) \, A + \left(255780 i + 255780\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(59220 i - 59220\right) \, A - \left(79380 i + 79380\right) \, B\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(-\left(236880 i + 236880\right) \, A + \left(199920 i - 199920\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(236880 i - 236880\right) \, A - \left(199920 i + 199920\right) \, B\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 + \left(199920 i - 199920\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left(-\left(236880 i + 236880\right) \, A + \left(199920 i - 199920\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(236880 i - 236880\right) \, A - \left(199920 i + 199920\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(236880 i - 236880\right) \, A - \left(199920 i + 199920\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(705600 i + 705600\right) \, A + \left(705600 i - 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(\left(473760 i + 473760\right) \, A - \left(399840 i - 399840\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(473760 i - 473760\right) \, A + \left(399840 i + 399840\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(705600 i - 705600\right) \, A - \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a\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(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(1411200 i + 1411200\right) \, A + \left(1411200 i - 1411200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(\left(2116800 i + 2116800\right) \, A - \left(2116800 i - 2116800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(1411200 i + 1411200\right) \, A + \left(1411200 i - 1411200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(\left(705600 i + 705600\right) \, A - \left(705600 i - 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(1411200 i + 1411200\right) \, A + \left(1411200 i - 1411200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(705600 i + 705600\right) \, A - \left(705600 i - 705600\right) \, B\right)} a\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\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(-\left(176400 i - 176400\right) \, A - \left(176400 i + 176400\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(176400 i - 176400\right) \, A - \left(176400 i + 176400\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(705600 i - 705600\right) \, A + \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(1058400 i - 1058400\right) \, A - \left(1058400 i + 1058400\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(705600 i - 705600\right) \, A + \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(352800 i - 352800\right) \, A - \left(352800 i + 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(705600 i - 705600\right) \, A + \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(352800 i - 352800\right) \, A - \left(352800 i + 352800\right) \, B\right)} a\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(176400 i - 176400\right) \, A - \left(176400 i + 176400\right) \, B\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(\left(524580 i - 524580\right) \, A + \left(496860 i + 496860\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(524580 i + 524580\right) \, A + \left(496860 i - 496860\right) \, B\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 + \left(496860 i + 496860\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left(\left(524580 i - 524580\right) \, A + \left(496860 i + 496860\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(524580 i + 524580\right) \, A + \left(496860 i - 496860\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(524580 i + 524580\right) \, A + \left(496860 i - 496860\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(705600 i - 705600\right) \, A - \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(823200 i - 823200\right) \, A - \left(823200 i + 823200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(823200 i - 823200\right) \, A - \left(823200 i + 823200\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1646400 i - 1646400\right) \, A + \left(1646400 i + 1646400\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(823200 i - 823200\right) \, A - \left(823200 i + 823200\right) \, B\right)} a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(-\left(1049160 i - 1049160\right) \, A - \left(993720 i + 993720\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(1049160 i + 1049160\right) \, A - \left(993720 i - 993720\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(705600 i + 705600\right) \, A - \left(705600 i - 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(352800 i + 352800\right) \, A + \left(352800 i - 352800\right) \, B\right)} a\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(\left(823200 i + 823200\right) \, A - \left(823200 i - 823200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(823200 i + 823200\right) \, A - \left(823200 i - 823200\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(1646400 i + 1646400\right) \, A + \left(1646400 i - 1646400\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(823200 i + 823200\right) \, A - \left(823200 i - 823200\right) \, B\right)} a\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(-\left(349440 i - 349440\right) \, A - \left(423360 i + 423360\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(349440 i + 349440\right) \, A - \left(423360 i - 423360\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(-\left(349440 i - 349440\right) \, A - \left(423360 i + 423360\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(349440 i + 349440\right) \, A - \left(423360 i - 423360\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(\left(1397760 i - 1397760\right) \, A + \left(1693440 i + 1693440\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(1397760 i + 1397760\right) \, A + \left(1693440 i - 1693440\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left({\left(-\left(2096640 i - 2096640\right) \, A - \left(2540160 i + 2540160\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(2096640 i + 2096640\right) \, A - \left(2540160 i - 2540160\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(349440 i - 349440\right) \, A - \left(423360 i + 423360\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left({\left(-\left(698880 i - 698880\right) \, A - \left(846720 i + 846720\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(698880 i + 698880\right) \, A - \left(846720 i - 846720\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(698880 i - 698880\right) \, A - \left(846720 i + 846720\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(698880 i + 698880\right) \, A - \left(846720 i - 846720\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(1397760 i - 1397760\right) \, A + \left(1693440 i + 1693440\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(1397760 i + 1397760\right) \, A + \left(1693440 i - 1693440\right) \, B\right)} a \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(\left(349440 i + 349440\right) \, A - \left(423360 i - 423360\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(1397760 i - 1397760\right) \, A + \left(1693440 i + 1693440\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(1397760 i + 1397760\right) \, A + \left(1693440 i - 1693440\right) \, B\right)} a \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(\left(524580 i + 524580\right) \, A - \left(496860 i - 496860\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(524580 i - 524580\right) \, A + \left(496860 i + 496860\right) \, B\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 - \left(496860 i - 496860\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left(\left(524580 i + 524580\right) \, A - \left(496860 i - 496860\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(524580 i - 524580\right) \, A + \left(496860 i + 496860\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(524580 i - 524580\right) \, A + \left(496860 i + 496860\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(705600 i + 705600\right) \, A + \left(705600 i - 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(352800 i + 352800\right) \, A - \left(352800 i - 352800\right) \, B\right)} a\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(823200 i + 823200\right) \, A + \left(823200 i - 823200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(823200 i + 823200\right) \, A + \left(823200 i - 823200\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1646400 i + 1646400\right) \, A - \left(1646400 i - 1646400\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(823200 i + 823200\right) \, A + \left(823200 i - 823200\right) \, B\right)} a\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(-\left(1049160 i + 1049160\right) \, A + \left(993720 i - 993720\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(1049160 i - 1049160\right) \, A - \left(993720 i + 993720\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(705600 i - 705600\right) \, A - \left(705600 i + 705600\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(352800 i - 352800\right) \, A + \left(352800 i + 352800\right) \, B\right)} a\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(823200 i - 823200\right) \, A - \left(823200 i + 823200\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(823200 i - 823200\right) \, A - \left(823200 i + 823200\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(1646400 i - 1646400\right) \, A + \left(1646400 i + 1646400\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(823200 i - 823200\right) \, A - \left(823200 i + 823200\right) \, B\right)} a\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(-\left(349440 i + 349440\right) \, A + \left(423360 i - 423360\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(349440 i - 349440\right) \, A - \left(423360 i + 423360\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(-\left(349440 i + 349440\right) \, A + \left(423360 i - 423360\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(349440 i - 349440\right) \, A - \left(423360 i + 423360\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(\left(1397760 i + 1397760\right) \, A - \left(1693440 i - 1693440\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(1397760 i - 1397760\right) \, A + \left(1693440 i + 1693440\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left({\left(-\left(2096640 i + 2096640\right) \, A + \left(2540160 i - 2540160\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(2096640 i - 2096640\right) \, A - \left(2540160 i + 2540160\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(349440 i + 349440\right) \, A + \left(423360 i - 423360\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left({\left(-\left(698880 i + 698880\right) \, A + \left(846720 i - 846720\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(698880 i - 698880\right) \, A - \left(846720 i + 846720\right) \, B\right)} a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(698880 i + 698880\right) \, A + \left(846720 i - 846720\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(698880 i - 698880\right) \, A - \left(846720 i + 846720\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(1397760 i + 1397760\right) \, A - \left(1693440 i - 1693440\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(1397760 i - 1397760\right) \, A + \left(1693440 i + 1693440\right) \, B\right)} a \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(-\left(349440 i - 349440\right) \, A - \left(423360 i + 423360\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(1397760 i + 1397760\right) \, A - \left(1693440 i - 1693440\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(1397760 i - 1397760\right) \, A + \left(1693440 i + 1693440\right) \, B\right)} a \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}}{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 + (352800*I + 352800)*B)*a*cos(7*d*x + 7*c) + (-(176400*I - 176400)*A - (529200*I + 529200)*B)*a*cos(5*d*x + 5*c) + ((167580*I - 167580)*A + (255780*I + 255780)*B)*a*cos(3*d*x + 3*c) + ((59220*I - 59220)*A - (79380*I + 79380)*B)*a*cos(d*x + c) + (-(352800*I + 352800)*A + (352800*I - 352800)*B)*a*sin(7*d*x + 7*c) + ((176400*I + 176400)*A - (529200*I - 529200)*B)*a*sin(5*d*x + 5*c) + (-(167580*I + 167580)*A + (255780*I - 255780)*B)*a*sin(3*d*x + 3*c) + (-(59220*I + 59220)*A - (79380*I - 79380)*B)*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 - (199920*I + 199920)*B)*a*cos(d*x + c) + ((236880*I + 236880)*A - (199920*I - 199920)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(236880*I - 236880)*A - (199920*I + 199920)*B)*a*cos(d*x + c) + ((-(236880*I - 236880)*A - (199920*I + 199920)*B)*a*cos(d*x + c) + ((236880*I + 236880)*A - (199920*I - 199920)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((236880*I + 236880)*A - (199920*I - 199920)*B)*a*sin(d*x + c) + (((352800*I - 352800)*A + (352800*I + 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a*sin(2*d*x + 2*c)^2 + (-(705600*I - 705600)*A - (705600*I + 705600)*B)*a*cos(2*d*x + 2*c) + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a)*cos(3*d*x + 3*c) + (((473760*I - 473760)*A + (399840*I + 399840)*B)*a*cos(d*x + c) + (-(473760*I + 473760)*A + (399840*I - 399840)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(352800*I + 352800)*A + (352800*I - 352800)*B)*a*cos(2*d*x + 2*c)^2 + (-(352800*I + 352800)*A + (352800*I - 352800)*B)*a*sin(2*d*x + 2*c)^2 + ((705600*I + 705600)*A - (705600*I - 705600)*B)*a*cos(2*d*x + 2*c) + (-(352800*I + 352800)*A + (352800*I - 352800)*B)*a)*sin(3*d*x + 3*c))*cos(3/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((352800*I + 352800)*A - (352800*I - 352800)*B)*a*cos(7*d*x + 7*c) + (-(176400*I + 176400)*A + (529200*I - 529200)*B)*a*cos(5*d*x + 5*c) + ((167580*I + 167580)*A - (255780*I - 255780)*B)*a*cos(3*d*x + 3*c) + ((59220*I + 59220)*A + (79380*I - 79380)*B)*a*cos(d*x + c) + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a*sin(7*d*x + 7*c) + (-(176400*I - 176400)*A - (529200*I + 529200)*B)*a*sin(5*d*x + 5*c) + ((167580*I - 167580)*A + (255780*I + 255780)*B)*a*sin(3*d*x + 3*c) + ((59220*I - 59220)*A - (79380*I + 79380)*B)*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 + (199920*I - 199920)*B)*a*cos(d*x + c) + (-(236880*I - 236880)*A - (199920*I + 199920)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(236880*I + 236880)*A + (199920*I - 199920)*B)*a*cos(d*x + c) + ((-(236880*I + 236880)*A + (199920*I - 199920)*B)*a*cos(d*x + c) + (-(236880*I - 236880)*A - (199920*I + 199920)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(236880*I - 236880)*A - (199920*I + 199920)*B)*a*sin(d*x + c) + (((352800*I + 352800)*A - (352800*I - 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((352800*I + 352800)*A - (352800*I - 352800)*B)*a*sin(2*d*x + 2*c)^2 + (-(705600*I + 705600)*A + (705600*I - 705600)*B)*a*cos(2*d*x + 2*c) + ((352800*I + 352800)*A - (352800*I - 352800)*B)*a)*cos(3*d*x + 3*c) + (((473760*I + 473760)*A - (399840*I - 399840)*B)*a*cos(d*x + c) + ((473760*I - 473760)*A + (399840*I + 399840)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (((352800*I - 352800)*A + (352800*I + 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a*sin(2*d*x + 2*c)^2 + (-(705600*I - 705600)*A - (705600*I + 705600)*B)*a*cos(2*d*x + 2*c) + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a)*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) + ((((352800*I + 352800)*A - (352800*I - 352800)*B)*a*cos(2*d*x + 2*c)^4 + ((352800*I + 352800)*A - (352800*I - 352800)*B)*a*sin(2*d*x + 2*c)^4 + (-(1411200*I + 1411200)*A + (1411200*I - 1411200)*B)*a*cos(2*d*x + 2*c)^3 + ((2116800*I + 2116800)*A - (2116800*I - 2116800)*B)*a*cos(2*d*x + 2*c)^2 + (-(1411200*I + 1411200)*A + (1411200*I - 1411200)*B)*a*cos(2*d*x + 2*c) + (((705600*I + 705600)*A - (705600*I - 705600)*B)*a*cos(2*d*x + 2*c)^2 + (-(1411200*I + 1411200)*A + (1411200*I - 1411200)*B)*a*cos(2*d*x + 2*c) + ((705600*I + 705600)*A - (705600*I - 705600)*B)*a)*sin(2*d*x + 2*c)^2 + ((352800*I + 352800)*A - (352800*I - 352800)*B)*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)) + ((-(176400*I - 176400)*A - (176400*I + 176400)*B)*a*cos(2*d*x + 2*c)^4 + (-(176400*I - 176400)*A - (176400*I + 176400)*B)*a*sin(2*d*x + 2*c)^4 + ((705600*I - 705600)*A + (705600*I + 705600)*B)*a*cos(2*d*x + 2*c)^3 + (-(1058400*I - 1058400)*A - (1058400*I + 1058400)*B)*a*cos(2*d*x + 2*c)^2 + ((705600*I - 705600)*A + (705600*I + 705600)*B)*a*cos(2*d*x + 2*c) + ((-(352800*I - 352800)*A - (352800*I + 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((705600*I - 705600)*A + (705600*I + 705600)*B)*a*cos(2*d*x + 2*c) + (-(352800*I - 352800)*A - (352800*I + 352800)*B)*a)*sin(2*d*x + 2*c)^2 + (-(176400*I - 176400)*A - (176400*I + 176400)*B)*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) + (((((524580*I - 524580)*A + (496860*I + 496860)*B)*a*cos(d*x + c) + (-(524580*I + 524580)*A + (496860*I - 496860)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((524580*I - 524580)*A + (496860*I + 496860)*B)*a*cos(d*x + c) + (((524580*I - 524580)*A + (496860*I + 496860)*B)*a*cos(d*x + c) + (-(524580*I + 524580)*A + (496860*I - 496860)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (-(524580*I + 524580)*A + (496860*I - 496860)*B)*a*sin(d*x + c) + (((352800*I - 352800)*A + (352800*I + 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a*sin(2*d*x + 2*c)^2 + (-(705600*I - 705600)*A - (705600*I + 705600)*B)*a*cos(2*d*x + 2*c) + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a)*cos(5*d*x + 5*c) + ((-(823200*I - 823200)*A - (823200*I + 823200)*B)*a*cos(2*d*x + 2*c)^2 + (-(823200*I - 823200)*A - (823200*I + 823200)*B)*a*sin(2*d*x + 2*c)^2 + ((1646400*I - 1646400)*A + (1646400*I + 1646400)*B)*a*cos(2*d*x + 2*c) + (-(823200*I - 823200)*A - (823200*I + 823200)*B)*a)*cos(3*d*x + 3*c) + ((-(1049160*I - 1049160)*A - (993720*I + 993720)*B)*a*cos(d*x + c) + ((1049160*I + 1049160)*A - (993720*I - 993720)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(352800*I + 352800)*A + (352800*I - 352800)*B)*a*cos(2*d*x + 2*c)^2 + (-(352800*I + 352800)*A + (352800*I - 352800)*B)*a*sin(2*d*x + 2*c)^2 + ((705600*I + 705600)*A - (705600*I - 705600)*B)*a*cos(2*d*x + 2*c) + (-(352800*I + 352800)*A + (352800*I - 352800)*B)*a)*sin(5*d*x + 5*c) + (((823200*I + 823200)*A - (823200*I - 823200)*B)*a*cos(2*d*x + 2*c)^2 + ((823200*I + 823200)*A - (823200*I - 823200)*B)*a*sin(2*d*x + 2*c)^2 + (-(1646400*I + 1646400)*A + (1646400*I - 1646400)*B)*a*cos(2*d*x + 2*c) + ((823200*I + 823200)*A - (823200*I - 823200)*B)*a)*sin(3*d*x + 3*c))*cos(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((-(349440*I - 349440)*A - (423360*I + 423360)*B)*a*cos(d*x + c) + ((349440*I + 349440)*A - (423360*I - 423360)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^4 + ((-(349440*I - 349440)*A - (423360*I + 423360)*B)*a*cos(d*x + c) + ((349440*I + 349440)*A - (423360*I - 423360)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^4 + (((1397760*I - 1397760)*A + (1693440*I + 1693440)*B)*a*cos(d*x + c) + (-(1397760*I + 1397760)*A + (1693440*I - 1693440)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^3 + ((-(2096640*I - 2096640)*A - (2540160*I + 2540160)*B)*a*cos(d*x + c) + ((2096640*I + 2096640)*A - (2540160*I - 2540160)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(349440*I - 349440)*A - (423360*I + 423360)*B)*a*cos(d*x + c) + (((-(698880*I - 698880)*A - (846720*I + 846720)*B)*a*cos(d*x + c) + ((698880*I + 698880)*A - (846720*I - 846720)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(698880*I - 698880)*A - (846720*I + 846720)*B)*a*cos(d*x + c) + ((698880*I + 698880)*A - (846720*I - 846720)*B)*a*sin(d*x + c) + (((1397760*I - 1397760)*A + (1693440*I + 1693440)*B)*a*cos(d*x + c) + (-(1397760*I + 1397760)*A + (1693440*I - 1693440)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + ((349440*I + 349440)*A - (423360*I - 423360)*B)*a*sin(d*x + c) + (((1397760*I - 1397760)*A + (1693440*I + 1693440)*B)*a*cos(d*x + c) + (-(1397760*I + 1397760)*A + (1693440*I - 1693440)*B)*a*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)) + ((((524580*I + 524580)*A - (496860*I - 496860)*B)*a*cos(d*x + c) + ((524580*I - 524580)*A + (496860*I + 496860)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((524580*I + 524580)*A - (496860*I - 496860)*B)*a*cos(d*x + c) + (((524580*I + 524580)*A - (496860*I - 496860)*B)*a*cos(d*x + c) + ((524580*I - 524580)*A + (496860*I + 496860)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((524580*I - 524580)*A + (496860*I + 496860)*B)*a*sin(d*x + c) + (((352800*I + 352800)*A - (352800*I - 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((352800*I + 352800)*A - (352800*I - 352800)*B)*a*sin(2*d*x + 2*c)^2 + (-(705600*I + 705600)*A + (705600*I - 705600)*B)*a*cos(2*d*x + 2*c) + ((352800*I + 352800)*A - (352800*I - 352800)*B)*a)*cos(5*d*x + 5*c) + ((-(823200*I + 823200)*A + (823200*I - 823200)*B)*a*cos(2*d*x + 2*c)^2 + (-(823200*I + 823200)*A + (823200*I - 823200)*B)*a*sin(2*d*x + 2*c)^2 + ((1646400*I + 1646400)*A - (1646400*I - 1646400)*B)*a*cos(2*d*x + 2*c) + (-(823200*I + 823200)*A + (823200*I - 823200)*B)*a)*cos(3*d*x + 3*c) + ((-(1049160*I + 1049160)*A + (993720*I - 993720)*B)*a*cos(d*x + c) + (-(1049160*I - 1049160)*A - (993720*I + 993720)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c) + (((352800*I - 352800)*A + (352800*I + 352800)*B)*a*cos(2*d*x + 2*c)^2 + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a*sin(2*d*x + 2*c)^2 + (-(705600*I - 705600)*A - (705600*I + 705600)*B)*a*cos(2*d*x + 2*c) + ((352800*I - 352800)*A + (352800*I + 352800)*B)*a)*sin(5*d*x + 5*c) + ((-(823200*I - 823200)*A - (823200*I + 823200)*B)*a*cos(2*d*x + 2*c)^2 + (-(823200*I - 823200)*A - (823200*I + 823200)*B)*a*sin(2*d*x + 2*c)^2 + ((1646400*I - 1646400)*A + (1646400*I + 1646400)*B)*a*cos(2*d*x + 2*c) + (-(823200*I - 823200)*A - (823200*I + 823200)*B)*a)*sin(3*d*x + 3*c))*sin(5/2*arctan2(sin(2*d*x + 2*c), cos(2*d*x + 2*c) - 1)) + (((-(349440*I + 349440)*A + (423360*I - 423360)*B)*a*cos(d*x + c) + (-(349440*I - 349440)*A - (423360*I + 423360)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^4 + ((-(349440*I + 349440)*A + (423360*I - 423360)*B)*a*cos(d*x + c) + (-(349440*I - 349440)*A - (423360*I + 423360)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^4 + (((1397760*I + 1397760)*A - (1693440*I - 1693440)*B)*a*cos(d*x + c) + ((1397760*I - 1397760)*A + (1693440*I + 1693440)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^3 + ((-(2096640*I + 2096640)*A + (2540160*I - 2540160)*B)*a*cos(d*x + c) + (-(2096640*I - 2096640)*A - (2540160*I + 2540160)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(349440*I + 349440)*A + (423360*I - 423360)*B)*a*cos(d*x + c) + (((-(698880*I + 698880)*A + (846720*I - 846720)*B)*a*cos(d*x + c) + (-(698880*I - 698880)*A - (846720*I + 846720)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(698880*I + 698880)*A + (846720*I - 846720)*B)*a*cos(d*x + c) + (-(698880*I - 698880)*A - (846720*I + 846720)*B)*a*sin(d*x + c) + (((1397760*I + 1397760)*A - (1693440*I - 1693440)*B)*a*cos(d*x + c) + ((1397760*I - 1397760)*A + (1693440*I + 1693440)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (-(349440*I - 349440)*A - (423360*I + 423360)*B)*a*sin(d*x + c) + (((1397760*I + 1397760)*A - (1693440*I - 1693440)*B)*a*cos(d*x + c) + ((1397760*I - 1397760)*A + (1693440*I + 1693440)*B)*a*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
542,1,1437,0,1.724703," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),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(-\left(450 i + 450\right) \, A + \left(450 i - 450\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(480 i + 480\right) \, A - \left(450 i - 450\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(450 i - 450\right) \, A - \left(450 i + 450\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(480 i - 480\right) \, A + \left(450 i + 450\right) \, B\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(\left(450 i - 450\right) \, A + \left(450 i + 450\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(480 i - 480\right) \, A - \left(450 i + 450\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(450 i + 450\right) \, A + \left(450 i - 450\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(480 i + 480\right) \, A - \left(450 i - 450\right) \, B\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(\left(450 i - 450\right) \, A + \left(450 i + 450\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(450 i - 450\right) \, A + \left(450 i + 450\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(900 i - 900\right) \, A - \left(900 i + 900\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(450 i - 450\right) \, A + \left(450 i + 450\right) \, B\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(\left(225 i + 225\right) \, A - \left(225 i - 225\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(225 i + 225\right) \, A - \left(225 i - 225\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(450 i + 450\right) \, A + \left(450 i - 450\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(225 i + 225\right) \, A - \left(225 i - 225\right) \, B\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(450 i + 450\right) \, A + \left(450 i - 450\right) \, B\right)} a \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(150 i + 150\right) \, A - \left(600 i - 600\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(60 i + 60\right) \, A + \left(150 i - 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(450 i - 450\right) \, A - \left(450 i + 450\right) \, B\right)} a \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(150 i - 150\right) \, A + \left(600 i + 600\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(60 i - 60\right) \, A - \left(150 i + 150\right) \, B\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(\left(90 i + 90\right) \, A - \left(150 i - 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(90 i - 90\right) \, A + \left(150 i + 150\right) \, B\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 - \left(150 i - 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left(\left(90 i + 90\right) \, A - \left(150 i - 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(90 i - 90\right) \, A + \left(150 i + 150\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(90 i - 90\right) \, A + \left(150 i + 150\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(-\left(180 i + 180\right) \, A + \left(300 i - 300\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(180 i - 180\right) \, A - \left(300 i + 300\right) \, B\right)} a \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(450 i - 450\right) \, A + \left(450 i + 450\right) \, B\right)} a \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(150 i - 150\right) \, A - \left(600 i + 600\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(60 i - 60\right) \, A + \left(150 i + 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(450 i + 450\right) \, A + \left(450 i - 450\right) \, B\right)} a \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(150 i + 150\right) \, A - \left(600 i - 600\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(60 i + 60\right) \, A + \left(150 i - 150\right) \, B\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(-\left(90 i - 90\right) \, A - \left(150 i + 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(90 i + 90\right) \, A - \left(150 i - 150\right) \, B\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 - \left(150 i + 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left({\left(-\left(90 i - 90\right) \, A - \left(150 i + 150\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(90 i + 90\right) \, A - \left(150 i - 150\right) \, B\right)} a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(90 i + 90\right) \, A - \left(150 i - 150\right) \, B\right)} a \sin\left(d x + c\right) + {\left({\left(\left(180 i - 180\right) \, A + \left(300 i + 300\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(180 i + 180\right) \, A + \left(300 i - 300\right) \, B\right)} a \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)*(((-(450*I + 450)*A + (450*I - 450)*B)*a*cos(3*d*x + 3*c) + ((480*I + 480)*A - (450*I - 450)*B)*a*cos(d*x + c) + (-(450*I - 450)*A - (450*I + 450)*B)*a*sin(3*d*x + 3*c) + ((480*I - 480)*A + (450*I + 450)*B)*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 + (450*I + 450)*B)*a*cos(3*d*x + 3*c) + (-(480*I - 480)*A - (450*I + 450)*B)*a*cos(d*x + c) + (-(450*I + 450)*A + (450*I - 450)*B)*a*sin(3*d*x + 3*c) + ((480*I + 480)*A - (450*I - 450)*B)*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 + (450*I + 450)*B)*a*cos(2*d*x + 2*c)^2 + ((450*I - 450)*A + (450*I + 450)*B)*a*sin(2*d*x + 2*c)^2 + (-(900*I - 900)*A - (900*I + 900)*B)*a*cos(2*d*x + 2*c) + ((450*I - 450)*A + (450*I + 450)*B)*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 - (225*I - 225)*B)*a*cos(2*d*x + 2*c)^2 + ((225*I + 225)*A - (225*I - 225)*B)*a*sin(2*d*x + 2*c)^2 + (-(450*I + 450)*A + (450*I - 450)*B)*a*cos(2*d*x + 2*c) + ((225*I + 225)*A - (225*I - 225)*B)*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 + (450*I - 450)*B)*a*cos(5*d*x + 5*c) + ((150*I + 150)*A - (600*I - 600)*B)*a*cos(3*d*x + 3*c) + (-(60*I + 60)*A + (150*I - 150)*B)*a*cos(d*x + c) + (-(450*I - 450)*A - (450*I + 450)*B)*a*sin(5*d*x + 5*c) + ((150*I - 150)*A + (600*I + 600)*B)*a*sin(3*d*x + 3*c) + (-(60*I - 60)*A - (150*I + 150)*B)*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 - (150*I - 150)*B)*a*cos(d*x + c) + ((90*I - 90)*A + (150*I + 150)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((90*I + 90)*A - (150*I - 150)*B)*a*cos(d*x + c) + (((90*I + 90)*A - (150*I - 150)*B)*a*cos(d*x + c) + ((90*I - 90)*A + (150*I + 150)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((90*I - 90)*A + (150*I + 150)*B)*a*sin(d*x + c) + ((-(180*I + 180)*A + (300*I - 300)*B)*a*cos(d*x + c) + (-(180*I - 180)*A - (300*I + 300)*B)*a*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)) + (((450*I - 450)*A + (450*I + 450)*B)*a*cos(5*d*x + 5*c) + (-(150*I - 150)*A - (600*I + 600)*B)*a*cos(3*d*x + 3*c) + ((60*I - 60)*A + (150*I + 150)*B)*a*cos(d*x + c) + (-(450*I + 450)*A + (450*I - 450)*B)*a*sin(5*d*x + 5*c) + ((150*I + 150)*A - (600*I - 600)*B)*a*sin(3*d*x + 3*c) + (-(60*I + 60)*A + (150*I - 150)*B)*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 - (150*I + 150)*B)*a*cos(d*x + c) + ((90*I + 90)*A - (150*I - 150)*B)*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (-(90*I - 90)*A - (150*I + 150)*B)*a*cos(d*x + c) + ((-(90*I - 90)*A - (150*I + 150)*B)*a*cos(d*x + c) + ((90*I + 90)*A - (150*I - 150)*B)*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((90*I + 90)*A - (150*I - 150)*B)*a*sin(d*x + c) + (((180*I - 180)*A + (300*I + 300)*B)*a*cos(d*x + c) + (-(180*I + 180)*A + (300*I - 300)*B)*a*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
543,1,1101,0,1.227767," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),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(\left(18 i - 18\right) \, A + \left(18 i + 18\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(6 i - 6\right) \, A - \left(18 i + 18\right) \, B\right)} a \cos\left(d x + c\right) + {\left(-\left(18 i + 18\right) \, A + \left(18 i - 18\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(6 i + 6\right) \, A - \left(18 i - 18\right) \, B\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(\left(18 i + 18\right) \, A - \left(18 i - 18\right) \, B\right)} a \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(6 i + 6\right) \, A + \left(18 i - 18\right) \, B\right)} a \cos\left(d x + c\right) + {\left(\left(18 i - 18\right) \, A + \left(18 i + 18\right) \, B\right)} a \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(6 i - 6\right) \, A - \left(18 i + 18\right) \, B\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(\left(18 i + 18\right) \, A - \left(18 i - 18\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(18 i + 18\right) \, A - \left(18 i - 18\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(36 i + 36\right) \, A + \left(36 i - 36\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(18 i + 18\right) \, A - \left(18 i - 18\right) \, B\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(-\left(9 i - 9\right) \, A - \left(9 i + 9\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(9 i - 9\right) \, A - \left(9 i + 9\right) \, B\right)} a \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(18 i - 18\right) \, A + \left(18 i + 18\right) \, B\right)} a \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(9 i - 9\right) \, A - \left(9 i + 9\right) \, B\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 a \cos\left(d x + c\right) - \left(12 i + 12\right) \, A a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i - 12\right) \, A a \cos\left(d x + c\right) + {\left(\left(12 i - 12\right) \, A a \cos\left(d x + c\right) - \left(12 i + 12\right) \, A a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} - \left(12 i + 12\right) \, A a \sin\left(d x + c\right) + {\left(-\left(24 i - 24\right) \, A a \cos\left(d x + c\right) + \left(24 i + 24\right) \, A a \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 a \cos\left(d x + c\right) + \left(12 i - 12\right) \, A a \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i + 12\right) \, A a \cos\left(d x + c\right) + {\left(\left(12 i + 12\right) \, A a \cos\left(d x + c\right) + \left(12 i - 12\right) \, A a \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + \left(12 i - 12\right) \, A a \sin\left(d x + c\right) + {\left(-\left(24 i + 24\right) \, A a \cos\left(d x + c\right) - \left(24 i - 24\right) \, A a \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)*((((18*I - 18)*A + (18*I + 18)*B)*a*cos(3*d*x + 3*c) + (-(6*I - 6)*A - (18*I + 18)*B)*a*cos(d*x + c) + (-(18*I + 18)*A + (18*I - 18)*B)*a*sin(3*d*x + 3*c) + ((6*I + 6)*A - (18*I - 18)*B)*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 - (18*I - 18)*B)*a*cos(3*d*x + 3*c) + (-(6*I + 6)*A + (18*I - 18)*B)*a*cos(d*x + c) + ((18*I - 18)*A + (18*I + 18)*B)*a*sin(3*d*x + 3*c) + (-(6*I - 6)*A - (18*I + 18)*B)*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 - (18*I - 18)*B)*a*cos(2*d*x + 2*c)^2 + ((18*I + 18)*A - (18*I - 18)*B)*a*sin(2*d*x + 2*c)^2 + (-(36*I + 36)*A + (36*I - 36)*B)*a*cos(2*d*x + 2*c) + ((18*I + 18)*A - (18*I - 18)*B)*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 - (9*I + 9)*B)*a*cos(2*d*x + 2*c)^2 + (-(9*I - 9)*A - (9*I + 9)*B)*a*sin(2*d*x + 2*c)^2 + ((18*I - 18)*A + (18*I + 18)*B)*a*cos(2*d*x + 2*c) + (-(9*I - 9)*A - (9*I + 9)*B)*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*a*cos(d*x + c) - (12*I + 12)*A*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12*I - 12)*A*a*cos(d*x + c) + ((12*I - 12)*A*a*cos(d*x + c) - (12*I + 12)*A*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 - (12*I + 12)*A*a*sin(d*x + c) + (-(24*I - 24)*A*a*cos(d*x + c) + (24*I + 24)*A*a*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*a*cos(d*x + c) + (12*I - 12)*A*a*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (12*I + 12)*A*a*cos(d*x + c) + ((12*I + 12)*A*a*cos(d*x + c) + (12*I - 12)*A*a*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (12*I - 12)*A*a*sin(d*x + c) + (-(24*I + 24)*A*a*cos(d*x + c) - (24*I - 24)*A*a*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
544,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
545,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
546,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(3/2)/sqrt(cot(d*x + c)), x)","F",0
547,1,4459,0,11.315548," ","integrate(cot(d*x+c)^(11/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),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(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(7 \, d x + 7 \, c\right) + {\left(\left(21168000 i + 21168000\right) \, A - \left(21168000 i - 21168000\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(25824960 i + 25824960\right) \, A + \left(25824960 i - 25824960\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(11429460 i + 11429460\right) \, A - \left(11139660 i - 11139660\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(7 \, d x + 7 \, c\right) + {\left(\left(21168000 i - 21168000\right) \, A + \left(21168000 i + 21168000\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(25824960 i - 25824960\right) \, A - \left(25824960 i + 25824960\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(11429460 i - 11429460\right) \, A + \left(11139660 i + 11139660\right) \, B\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 - \left(756000 i - 756000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i - 1219680\right) \, A + \left(756000 i + 756000\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(1219680 i + 1219680\right) \, A - \left(756000 i - 756000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i - 1219680\right) \, A + \left(756000 i + 756000\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(1219680 i + 1219680\right) \, A - \left(756000 i - 756000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i - 1219680\right) \, A + \left(756000 i + 756000\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12700800 i + 12700800\right) \, A - \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(-\left(2439360 i + 2439360\right) \, A + \left(1512000 i - 1512000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(2439360 i - 2439360\right) \, A - \left(1512000 i + 1512000\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12700800 i - 12700800\right) \, A + \left(12700800 i + 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\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(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(7 \, d x + 7 \, c\right) + {\left(-\left(21168000 i - 21168000\right) \, A - \left(21168000 i + 21168000\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(25824960 i - 25824960\right) \, A + \left(25824960 i + 25824960\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(11429460 i - 11429460\right) \, A - \left(11139660 i + 11139660\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \sin\left(7 \, d x + 7 \, c\right) + {\left(\left(21168000 i + 21168000\right) \, A - \left(21168000 i - 21168000\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(25824960 i + 25824960\right) \, A + \left(25824960 i - 25824960\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(11429460 i + 11429460\right) \, A - \left(11139660 i - 11139660\right) \, B\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 - \left(756000 i + 756000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i + 1219680\right) \, A - \left(756000 i - 756000\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(1219680 i - 1219680\right) \, A - \left(756000 i + 756000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i + 1219680\right) \, A - \left(756000 i - 756000\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(1219680 i - 1219680\right) \, A - \left(756000 i + 756000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(1219680 i + 1219680\right) \, A - \left(756000 i - 756000\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(12700800 i - 12700800\right) \, A - \left(12700800 i + 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(\left(2439360 i - 2439360\right) \, A + \left(1512000 i + 1512000\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(2439360 i + 2439360\right) \, A + \left(1512000 i - 1512000\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12700800 i + 12700800\right) \, A - \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\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(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(25401600 i - 25401600\right) \, A - \left(25401600 i + 25401600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(\left(38102400 i - 38102400\right) \, A + \left(38102400 i + 38102400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(25401600 i - 25401600\right) \, A - \left(25401600 i + 25401600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} + {\left({\left(\left(12700800 i - 12700800\right) \, A + \left(12700800 i + 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(25401600 i - 25401600\right) \, A - \left(25401600 i + 25401600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(12700800 i - 12700800\right) \, A + \left(12700800 i + 12700800\right) \, B\right)} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{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(\left(3175200 i + 3175200\right) \, A - \left(3175200 i - 3175200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(3175200 i + 3175200\right) \, A - \left(3175200 i - 3175200\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(12700800 i + 12700800\right) \, A + \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(\left(19051200 i + 19051200\right) \, A - \left(19051200 i - 19051200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(12700800 i + 12700800\right) \, A + \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(3175200 i + 3175200\right) \, A - \left(3175200 i - 3175200\right) \, B\right)} a^{2} + {\left({\left(\left(6350400 i + 6350400\right) \, A - \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(12700800 i + 12700800\right) \, A + \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(6350400 i + 6350400\right) \, A - \left(6350400 i - 6350400\right) \, B\right)} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{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(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(9 \, d x + 9 \, c\right) + {\left(\left(7408800 i + 7408800\right) \, A - \left(13759200 i - 13759200\right) \, B\right)} a^{2} \cos\left(7 \, d x + 7 \, c\right) + {\left(-\left(8414280 i + 8414280\right) \, A + \left(13177080 i - 13177080\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(631260 i + 631260\right) \, A - \left(6717060 i - 6717060\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(1079820 i + 1079820\right) \, A + \left(948780 i - 948780\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(9 \, d x + 9 \, c\right) + {\left(\left(7408800 i - 7408800\right) \, A + \left(13759200 i + 13759200\right) \, B\right)} a^{2} \sin\left(7 \, d x + 7 \, c\right) + {\left(-\left(8414280 i - 8414280\right) \, A - \left(13177080 i + 13177080\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(631260 i - 631260\right) \, A + \left(6717060 i + 6717060\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(1079820 i - 1079820\right) \, A - \left(948780 i + 948780\right) \, B\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 + \left(6811560 i - 6811560\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i - 7159320\right) \, A - \left(6811560 i + 6811560\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(7159320 i + 7159320\right) \, A + \left(6811560 i - 6811560\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i - 7159320\right) \, A - \left(6811560 i + 6811560\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(7159320 i + 7159320\right) \, A + \left(6811560 i - 6811560\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i - 7159320\right) \, A - \left(6811560 i + 6811560\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12700800 i + 12700800\right) \, A - \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left({\left(\left(14817600 i + 14817600\right) \, A - \left(14817600 i - 14817600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(14817600 i + 14817600\right) \, A - \left(14817600 i - 14817600\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(29635200 i + 29635200\right) \, A + \left(29635200 i - 29635200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(14817600 i + 14817600\right) \, A - \left(14817600 i - 14817600\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(\left(14318640 i + 14318640\right) \, A - \left(13623120 i - 13623120\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(14318640 i - 14318640\right) \, A + \left(13623120 i + 13623120\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12700800 i - 12700800\right) \, A + \left(12700800 i + 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i - 6350400\right) \, A - \left(6350400 i + 6350400\right) \, B\right)} a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(\left(14817600 i - 14817600\right) \, A + \left(14817600 i + 14817600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(14817600 i - 14817600\right) \, A + \left(14817600 i + 14817600\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(29635200 i - 29635200\right) \, A - \left(29635200 i + 29635200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(14817600 i - 14817600\right) \, A + \left(14817600 i + 14817600\right) \, B\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(\left(12378240 i + 12378240\right) \, A - \left(13305600 i - 13305600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(12378240 i - 12378240\right) \, A + \left(13305600 i + 13305600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(\left(12378240 i + 12378240\right) \, A - \left(13305600 i - 13305600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(12378240 i - 12378240\right) \, A + \left(13305600 i + 13305600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(-\left(49512960 i + 49512960\right) \, A + \left(53222400 i - 53222400\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(49512960 i - 49512960\right) \, A - \left(53222400 i + 53222400\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(\left(12378240 i + 12378240\right) \, A - \left(13305600 i - 13305600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(12378240 i - 12378240\right) \, A + \left(13305600 i + 13305600\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(74269440 i + 74269440\right) \, A - \left(79833600 i - 79833600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(74269440 i - 74269440\right) \, A + \left(79833600 i + 79833600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(24756480 i + 24756480\right) \, A - \left(26611200 i - 26611200\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(24756480 i - 24756480\right) \, A + \left(26611200 i + 26611200\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(24756480 i + 24756480\right) \, A - \left(26611200 i - 26611200\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(24756480 i - 24756480\right) \, A + \left(26611200 i + 26611200\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(49512960 i + 49512960\right) \, A + \left(53222400 i - 53222400\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(49512960 i - 49512960\right) \, A - \left(53222400 i + 53222400\right) \, B\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({\left(-\left(49512960 i + 49512960\right) \, A + \left(53222400 i - 53222400\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(49512960 i - 49512960\right) \, A - \left(53222400 i + 53222400\right) \, B\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(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(9 \, d x + 9 \, c\right) + {\left(-\left(7408800 i - 7408800\right) \, A - \left(13759200 i + 13759200\right) \, B\right)} a^{2} \cos\left(7 \, d x + 7 \, c\right) + {\left(\left(8414280 i - 8414280\right) \, A + \left(13177080 i + 13177080\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(631260 i - 631260\right) \, A - \left(6717060 i + 6717060\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(1079820 i - 1079820\right) \, A + \left(948780 i + 948780\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \sin\left(9 \, d x + 9 \, c\right) + {\left(\left(7408800 i + 7408800\right) \, A - \left(13759200 i - 13759200\right) \, B\right)} a^{2} \sin\left(7 \, d x + 7 \, c\right) + {\left(-\left(8414280 i + 8414280\right) \, A + \left(13177080 i - 13177080\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(631260 i + 631260\right) \, A - \left(6717060 i - 6717060\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(1079820 i + 1079820\right) \, A + \left(948780 i - 948780\right) \, B\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 + \left(6811560 i + 6811560\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i + 7159320\right) \, A + \left(6811560 i - 6811560\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(7159320 i - 7159320\right) \, A + \left(6811560 i + 6811560\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i + 7159320\right) \, A + \left(6811560 i - 6811560\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(7159320 i - 7159320\right) \, A + \left(6811560 i + 6811560\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(7159320 i + 7159320\right) \, A + \left(6811560 i - 6811560\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(12700800 i - 12700800\right) \, A - \left(12700800 i + 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(6350400 i - 6350400\right) \, A + \left(6350400 i + 6350400\right) \, B\right)} a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(14817600 i - 14817600\right) \, A - \left(14817600 i + 14817600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(14817600 i - 14817600\right) \, A - \left(14817600 i + 14817600\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(29635200 i - 29635200\right) \, A + \left(29635200 i + 29635200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(14817600 i - 14817600\right) \, A - \left(14817600 i + 14817600\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(-\left(14318640 i - 14318640\right) \, A - \left(13623120 i + 13623120\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(14318640 i + 14318640\right) \, A - \left(13623120 i - 13623120\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(12700800 i + 12700800\right) \, A - \left(12700800 i - 12700800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(6350400 i + 6350400\right) \, A + \left(6350400 i - 6350400\right) \, B\right)} a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(\left(14817600 i + 14817600\right) \, A - \left(14817600 i - 14817600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(14817600 i + 14817600\right) \, A - \left(14817600 i - 14817600\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(29635200 i + 29635200\right) \, A + \left(29635200 i - 29635200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(14817600 i + 14817600\right) \, A - \left(14817600 i - 14817600\right) \, B\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(-\left(12378240 i - 12378240\right) \, A - \left(13305600 i + 13305600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(12378240 i + 12378240\right) \, A - \left(13305600 i - 13305600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(-\left(12378240 i - 12378240\right) \, A - \left(13305600 i + 13305600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(12378240 i + 12378240\right) \, A - \left(13305600 i - 13305600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(\left(49512960 i - 49512960\right) \, A + \left(53222400 i + 53222400\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(49512960 i + 49512960\right) \, A + \left(53222400 i - 53222400\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(12378240 i - 12378240\right) \, A - \left(13305600 i + 13305600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(12378240 i + 12378240\right) \, A - \left(13305600 i - 13305600\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(74269440 i - 74269440\right) \, A - \left(79833600 i + 79833600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(74269440 i + 74269440\right) \, A - \left(79833600 i - 79833600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(24756480 i - 24756480\right) \, A - \left(26611200 i + 26611200\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(24756480 i + 24756480\right) \, A - \left(26611200 i - 26611200\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(24756480 i - 24756480\right) \, A - \left(26611200 i + 26611200\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(24756480 i + 24756480\right) \, A - \left(26611200 i - 26611200\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(49512960 i - 49512960\right) \, A + \left(53222400 i + 53222400\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(49512960 i + 49512960\right) \, A + \left(53222400 i - 53222400\right) \, B\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({\left(\left(49512960 i - 49512960\right) \, A + \left(53222400 i + 53222400\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(49512960 i + 49512960\right) \, A + \left(53222400 i - 53222400\right) \, B\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 + (6350400*I - 6350400)*B)*a^2*cos(7*d*x + 7*c) + ((21168000*I + 21168000)*A - (21168000*I - 21168000)*B)*a^2*cos(5*d*x + 5*c) + (-(25824960*I + 25824960)*A + (25824960*I - 25824960)*B)*a^2*cos(3*d*x + 3*c) + ((11429460*I + 11429460)*A - (11139660*I - 11139660)*B)*a^2*cos(d*x + c) + (-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2*sin(7*d*x + 7*c) + ((21168000*I - 21168000)*A + (21168000*I + 21168000)*B)*a^2*sin(5*d*x + 5*c) + (-(25824960*I - 25824960)*A - (25824960*I + 25824960)*B)*a^2*sin(3*d*x + 3*c) + ((11429460*I - 11429460)*A + (11139660*I + 11139660)*B)*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 - (756000*I - 756000)*B)*a^2*cos(d*x + c) + ((1219680*I - 1219680)*A + (756000*I + 756000)*B)*a^2*sin(d*x + c) + (((1219680*I + 1219680)*A - (756000*I - 756000)*B)*a^2*cos(d*x + c) + ((1219680*I - 1219680)*A + (756000*I + 756000)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((1219680*I + 1219680)*A - (756000*I - 756000)*B)*a^2*cos(d*x + c) + ((1219680*I - 1219680)*A + (756000*I + 756000)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + ((12700800*I + 12700800)*A - (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c) + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2)*cos(3*d*x + 3*c) + ((-(2439360*I + 2439360)*A + (1512000*I - 1512000)*B)*a^2*cos(d*x + c) + (-(2439360*I - 2439360)*A - (1512000*I + 1512000)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + ((12700800*I - 12700800)*A + (12700800*I + 12700800)*B)*a^2*cos(2*d*x + 2*c) + (-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*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 + (6350400*I + 6350400)*B)*a^2*cos(7*d*x + 7*c) + (-(21168000*I - 21168000)*A - (21168000*I + 21168000)*B)*a^2*cos(5*d*x + 5*c) + ((25824960*I - 25824960)*A + (25824960*I + 25824960)*B)*a^2*cos(3*d*x + 3*c) + (-(11429460*I - 11429460)*A - (11139660*I + 11139660)*B)*a^2*cos(d*x + c) + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*sin(7*d*x + 7*c) + ((21168000*I + 21168000)*A - (21168000*I - 21168000)*B)*a^2*sin(5*d*x + 5*c) + (-(25824960*I + 25824960)*A + (25824960*I - 25824960)*B)*a^2*sin(3*d*x + 3*c) + ((11429460*I + 11429460)*A - (11139660*I - 11139660)*B)*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 - (756000*I + 756000)*B)*a^2*cos(d*x + c) + ((1219680*I + 1219680)*A - (756000*I - 756000)*B)*a^2*sin(d*x + c) + ((-(1219680*I - 1219680)*A - (756000*I + 756000)*B)*a^2*cos(d*x + c) + ((1219680*I + 1219680)*A - (756000*I - 756000)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(1219680*I - 1219680)*A - (756000*I + 756000)*B)*a^2*cos(d*x + c) + ((1219680*I + 1219680)*A - (756000*I - 756000)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + ((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(12700800*I - 12700800)*A - (12700800*I + 12700800)*B)*a^2*cos(2*d*x + 2*c) + ((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2)*cos(3*d*x + 3*c) + (((2439360*I - 2439360)*A + (1512000*I + 1512000)*B)*a^2*cos(d*x + c) + (-(2439360*I + 2439360)*A + (1512000*I - 1512000)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + ((12700800*I + 12700800)*A - (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c) + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*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 + (6350400*I + 6350400)*B)*a^2*cos(2*d*x + 2*c)^4 + ((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2*sin(2*d*x + 2*c)^4 + (-(25401600*I - 25401600)*A - (25401600*I + 25401600)*B)*a^2*cos(2*d*x + 2*c)^3 + ((38102400*I - 38102400)*A + (38102400*I + 38102400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(25401600*I - 25401600)*A - (25401600*I + 25401600)*B)*a^2*cos(2*d*x + 2*c) + ((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2 + (((12700800*I - 12700800)*A + (12700800*I + 12700800)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(25401600*I - 25401600)*A - (25401600*I + 25401600)*B)*a^2*cos(2*d*x + 2*c) + ((12700800*I - 12700800)*A + (12700800*I + 12700800)*B)*a^2)*sin(2*d*x + 2*c)^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)) + (((3175200*I + 3175200)*A - (3175200*I - 3175200)*B)*a^2*cos(2*d*x + 2*c)^4 + ((3175200*I + 3175200)*A - (3175200*I - 3175200)*B)*a^2*sin(2*d*x + 2*c)^4 + (-(12700800*I + 12700800)*A + (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c)^3 + ((19051200*I + 19051200)*A - (19051200*I - 19051200)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(12700800*I + 12700800)*A + (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c) + ((3175200*I + 3175200)*A - (3175200*I - 3175200)*B)*a^2 + (((6350400*I + 6350400)*A - (6350400*I - 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(12700800*I + 12700800)*A + (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c) + ((6350400*I + 6350400)*A - (6350400*I - 6350400)*B)*a^2)*sin(2*d*x + 2*c)^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) + (((-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*cos(9*d*x + 9*c) + ((7408800*I + 7408800)*A - (13759200*I - 13759200)*B)*a^2*cos(7*d*x + 7*c) + (-(8414280*I + 8414280)*A + (13177080*I - 13177080)*B)*a^2*cos(5*d*x + 5*c) + ((631260*I + 631260)*A - (6717060*I - 6717060)*B)*a^2*cos(3*d*x + 3*c) + ((1079820*I + 1079820)*A + (948780*I - 948780)*B)*a^2*cos(d*x + c) + (-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2*sin(9*d*x + 9*c) + ((7408800*I - 7408800)*A + (13759200*I + 13759200)*B)*a^2*sin(7*d*x + 7*c) + (-(8414280*I - 8414280)*A - (13177080*I + 13177080)*B)*a^2*sin(5*d*x + 5*c) + ((631260*I - 631260)*A + (6717060*I + 6717060)*B)*a^2*sin(3*d*x + 3*c) + ((1079820*I - 1079820)*A - (948780*I + 948780)*B)*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 + (6811560*I - 6811560)*B)*a^2*cos(d*x + c) + (-(7159320*I - 7159320)*A - (6811560*I + 6811560)*B)*a^2*sin(d*x + c) + ((-(7159320*I + 7159320)*A + (6811560*I - 6811560)*B)*a^2*cos(d*x + c) + (-(7159320*I - 7159320)*A - (6811560*I + 6811560)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(7159320*I + 7159320)*A + (6811560*I - 6811560)*B)*a^2*cos(d*x + c) + (-(7159320*I - 7159320)*A - (6811560*I + 6811560)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + ((12700800*I + 12700800)*A - (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c) + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2)*cos(5*d*x + 5*c) + (((14817600*I + 14817600)*A - (14817600*I - 14817600)*B)*a^2*cos(2*d*x + 2*c)^2 + ((14817600*I + 14817600)*A - (14817600*I - 14817600)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(29635200*I + 29635200)*A + (29635200*I - 29635200)*B)*a^2*cos(2*d*x + 2*c) + ((14817600*I + 14817600)*A - (14817600*I - 14817600)*B)*a^2)*cos(3*d*x + 3*c) + (((14318640*I + 14318640)*A - (13623120*I - 13623120)*B)*a^2*cos(d*x + c) + ((14318640*I - 14318640)*A + (13623120*I + 13623120)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + ((12700800*I - 12700800)*A + (12700800*I + 12700800)*B)*a^2*cos(2*d*x + 2*c) + (-(6350400*I - 6350400)*A - (6350400*I + 6350400)*B)*a^2)*sin(5*d*x + 5*c) + (((14817600*I - 14817600)*A + (14817600*I + 14817600)*B)*a^2*cos(2*d*x + 2*c)^2 + ((14817600*I - 14817600)*A + (14817600*I + 14817600)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(29635200*I - 29635200)*A - (29635200*I + 29635200)*B)*a^2*cos(2*d*x + 2*c) + ((14817600*I - 14817600)*A + (14817600*I + 14817600)*B)*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 - (13305600*I - 13305600)*B)*a^2*cos(d*x + c) + ((12378240*I - 12378240)*A + (13305600*I + 13305600)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + (((12378240*I + 12378240)*A - (13305600*I - 13305600)*B)*a^2*cos(d*x + c) + ((12378240*I - 12378240)*A + (13305600*I + 13305600)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + ((-(49512960*I + 49512960)*A + (53222400*I - 53222400)*B)*a^2*cos(d*x + c) + (-(49512960*I - 49512960)*A - (53222400*I + 53222400)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + ((12378240*I + 12378240)*A - (13305600*I - 13305600)*B)*a^2*cos(d*x + c) + ((12378240*I - 12378240)*A + (13305600*I + 13305600)*B)*a^2*sin(d*x + c) + (((74269440*I + 74269440)*A - (79833600*I - 79833600)*B)*a^2*cos(d*x + c) + ((74269440*I - 74269440)*A + (79833600*I + 79833600)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((24756480*I + 24756480)*A - (26611200*I - 26611200)*B)*a^2*cos(d*x + c) + ((24756480*I - 24756480)*A + (26611200*I + 26611200)*B)*a^2*sin(d*x + c) + (((24756480*I + 24756480)*A - (26611200*I - 26611200)*B)*a^2*cos(d*x + c) + ((24756480*I - 24756480)*A + (26611200*I + 26611200)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(49512960*I + 49512960)*A + (53222400*I - 53222400)*B)*a^2*cos(d*x + c) + (-(49512960*I - 49512960)*A - (53222400*I + 53222400)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + ((-(49512960*I + 49512960)*A + (53222400*I - 53222400)*B)*a^2*cos(d*x + c) + (-(49512960*I - 49512960)*A - (53222400*I + 53222400)*B)*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 + (6350400*I + 6350400)*B)*a^2*cos(9*d*x + 9*c) + (-(7408800*I - 7408800)*A - (13759200*I + 13759200)*B)*a^2*cos(7*d*x + 7*c) + ((8414280*I - 8414280)*A + (13177080*I + 13177080)*B)*a^2*cos(5*d*x + 5*c) + (-(631260*I - 631260)*A - (6717060*I + 6717060)*B)*a^2*cos(3*d*x + 3*c) + (-(1079820*I - 1079820)*A + (948780*I + 948780)*B)*a^2*cos(d*x + c) + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*sin(9*d*x + 9*c) + ((7408800*I + 7408800)*A - (13759200*I - 13759200)*B)*a^2*sin(7*d*x + 7*c) + (-(8414280*I + 8414280)*A + (13177080*I - 13177080)*B)*a^2*sin(5*d*x + 5*c) + ((631260*I + 631260)*A - (6717060*I - 6717060)*B)*a^2*sin(3*d*x + 3*c) + ((1079820*I + 1079820)*A + (948780*I - 948780)*B)*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 + (6811560*I + 6811560)*B)*a^2*cos(d*x + c) + (-(7159320*I + 7159320)*A + (6811560*I - 6811560)*B)*a^2*sin(d*x + c) + (((7159320*I - 7159320)*A + (6811560*I + 6811560)*B)*a^2*cos(d*x + c) + (-(7159320*I + 7159320)*A + (6811560*I - 6811560)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((7159320*I - 7159320)*A + (6811560*I + 6811560)*B)*a^2*cos(d*x + c) + (-(7159320*I + 7159320)*A + (6811560*I - 6811560)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + ((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(12700800*I - 12700800)*A - (12700800*I + 12700800)*B)*a^2*cos(2*d*x + 2*c) + ((6350400*I - 6350400)*A + (6350400*I + 6350400)*B)*a^2)*cos(5*d*x + 5*c) + ((-(14817600*I - 14817600)*A - (14817600*I + 14817600)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(14817600*I - 14817600)*A - (14817600*I + 14817600)*B)*a^2*sin(2*d*x + 2*c)^2 + ((29635200*I - 29635200)*A + (29635200*I + 29635200)*B)*a^2*cos(2*d*x + 2*c) + (-(14817600*I - 14817600)*A - (14817600*I + 14817600)*B)*a^2)*cos(3*d*x + 3*c) + ((-(14318640*I - 14318640)*A - (13623120*I + 13623120)*B)*a^2*cos(d*x + c) + ((14318640*I + 14318640)*A - (13623120*I - 13623120)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2*sin(2*d*x + 2*c)^2 + ((12700800*I + 12700800)*A - (12700800*I - 12700800)*B)*a^2*cos(2*d*x + 2*c) + (-(6350400*I + 6350400)*A + (6350400*I - 6350400)*B)*a^2)*sin(5*d*x + 5*c) + (((14817600*I + 14817600)*A - (14817600*I - 14817600)*B)*a^2*cos(2*d*x + 2*c)^2 + ((14817600*I + 14817600)*A - (14817600*I - 14817600)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(29635200*I + 29635200)*A + (29635200*I - 29635200)*B)*a^2*cos(2*d*x + 2*c) + ((14817600*I + 14817600)*A - (14817600*I - 14817600)*B)*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 - (13305600*I + 13305600)*B)*a^2*cos(d*x + c) + ((12378240*I + 12378240)*A - (13305600*I - 13305600)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + ((-(12378240*I - 12378240)*A - (13305600*I + 13305600)*B)*a^2*cos(d*x + c) + ((12378240*I + 12378240)*A - (13305600*I - 13305600)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + (((49512960*I - 49512960)*A + (53222400*I + 53222400)*B)*a^2*cos(d*x + c) + (-(49512960*I + 49512960)*A + (53222400*I - 53222400)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(12378240*I - 12378240)*A - (13305600*I + 13305600)*B)*a^2*cos(d*x + c) + ((12378240*I + 12378240)*A - (13305600*I - 13305600)*B)*a^2*sin(d*x + c) + ((-(74269440*I - 74269440)*A - (79833600*I + 79833600)*B)*a^2*cos(d*x + c) + ((74269440*I + 74269440)*A - (79833600*I - 79833600)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(24756480*I - 24756480)*A - (26611200*I + 26611200)*B)*a^2*cos(d*x + c) + ((24756480*I + 24756480)*A - (26611200*I - 26611200)*B)*a^2*sin(d*x + c) + ((-(24756480*I - 24756480)*A - (26611200*I + 26611200)*B)*a^2*cos(d*x + c) + ((24756480*I + 24756480)*A - (26611200*I - 26611200)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((49512960*I - 49512960)*A + (53222400*I + 53222400)*B)*a^2*cos(d*x + c) + (-(49512960*I + 49512960)*A + (53222400*I - 53222400)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (((49512960*I - 49512960)*A + (53222400*I + 53222400)*B)*a^2*cos(d*x + c) + (-(49512960*I + 49512960)*A + (53222400*I - 53222400)*B)*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
548,1,4019,0,3.699751," ","integrate(cot(d*x+c)^(9/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),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(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \cos\left(7 \, d x + 7 \, c\right) + {\left(-\left(44100 i - 44100\right) \, A - \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(26460 i - 26460\right) \, A + \left(59535 i + 59535\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(1260 i - 1260\right) \, A - \left(15435 i + 15435\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\right)} a^{2} \sin\left(7 \, d x + 7 \, c\right) + {\left(\left(44100 i + 44100\right) \, A - \left(88200 i - 88200\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(-\left(26460 i + 26460\right) \, A + \left(59535 i - 59535\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(1260 i + 1260\right) \, A - \left(15435 i - 15435\right) \, B\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 - \left(23520 i + 23520\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(27300 i + 27300\right) \, A - \left(23520 i - 23520\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(27300 i - 27300\right) \, A - \left(23520 i + 23520\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(27300 i + 27300\right) \, A - \left(23520 i - 23520\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(27300 i - 27300\right) \, A - \left(23520 i + 23520\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(27300 i + 27300\right) \, A - \left(23520 i - 23520\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(88200 i - 88200\right) \, A - \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(\left(54600 i - 54600\right) \, A + \left(47040 i + 47040\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(54600 i + 54600\right) \, A + \left(47040 i - 47040\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(88200 i + 88200\right) \, A - \left(88200 i - 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\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(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \cos\left(7 \, d x + 7 \, c\right) + {\left(-\left(44100 i + 44100\right) \, A + \left(88200 i - 88200\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(26460 i + 26460\right) \, A - \left(59535 i - 59535\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(1260 i + 1260\right) \, A + \left(15435 i - 15435\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \sin\left(7 \, d x + 7 \, c\right) + {\left(-\left(44100 i - 44100\right) \, A - \left(88200 i + 88200\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(26460 i - 26460\right) \, A + \left(59535 i + 59535\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(1260 i - 1260\right) \, A - \left(15435 i + 15435\right) \, B\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 + \left(23520 i - 23520\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(27300 i - 27300\right) \, A - \left(23520 i + 23520\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(27300 i + 27300\right) \, A + \left(23520 i - 23520\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(27300 i - 27300\right) \, A - \left(23520 i + 23520\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(27300 i + 27300\right) \, A + \left(23520 i - 23520\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(27300 i - 27300\right) \, A - \left(23520 i + 23520\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(88200 i + 88200\right) \, A + \left(88200 i - 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(\left(54600 i + 54600\right) \, A - \left(47040 i - 47040\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(54600 i - 54600\right) \, A + \left(47040 i + 47040\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(88200 i - 88200\right) \, A - \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\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(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(176400 i + 176400\right) \, A + \left(176400 i - 176400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(\left(264600 i + 264600\right) \, A - \left(264600 i - 264600\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(176400 i + 176400\right) \, A + \left(176400 i - 176400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} + {\left({\left(\left(88200 i + 88200\right) \, A - \left(88200 i - 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(176400 i + 176400\right) \, A + \left(176400 i - 176400\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(88200 i + 88200\right) \, A - \left(88200 i - 88200\right) \, B\right)} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{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(-\left(22050 i - 22050\right) \, A - \left(22050 i + 22050\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left(-\left(22050 i - 22050\right) \, A - \left(22050 i + 22050\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left(\left(88200 i - 88200\right) \, A + \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(132300 i - 132300\right) \, A - \left(132300 i + 132300\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(88200 i - 88200\right) \, A + \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(22050 i - 22050\right) \, A - \left(22050 i + 22050\right) \, B\right)} a^{2} + {\left({\left(-\left(44100 i - 44100\right) \, A - \left(44100 i + 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(88200 i - 88200\right) \, A + \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i - 44100\right) \, A - \left(44100 i + 44100\right) \, B\right)} a^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{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 + \left(61005 i + 61005\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(63840 i + 63840\right) \, A + \left(61005 i - 61005\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(63840 i - 63840\right) \, A + \left(61005 i + 61005\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(63840 i + 63840\right) \, A + \left(61005 i - 61005\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(63840 i - 63840\right) \, A + \left(61005 i + 61005\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(63840 i + 63840\right) \, A + \left(61005 i - 61005\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(88200 i - 88200\right) \, A - \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(102900 i - 102900\right) \, A - \left(102900 i + 102900\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(102900 i - 102900\right) \, A - \left(102900 i + 102900\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(205800 i - 205800\right) \, A + \left(205800 i + 205800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(102900 i - 102900\right) \, A - \left(102900 i + 102900\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(-\left(127680 i - 127680\right) \, A - \left(122010 i + 122010\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(127680 i + 127680\right) \, A - \left(122010 i - 122010\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(88200 i + 88200\right) \, A - \left(88200 i - 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(44100 i + 44100\right) \, A + \left(44100 i - 44100\right) \, B\right)} a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(\left(102900 i + 102900\right) \, A - \left(102900 i - 102900\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(102900 i + 102900\right) \, A - \left(102900 i - 102900\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(205800 i + 205800\right) \, A + \left(205800 i - 205800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(102900 i + 102900\right) \, A - \left(102900 i - 102900\right) \, B\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(-\left(48300 i - 48300\right) \, A - \left(55860 i + 55860\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(48300 i + 48300\right) \, A - \left(55860 i - 55860\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(-\left(48300 i - 48300\right) \, A - \left(55860 i + 55860\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(48300 i + 48300\right) \, A - \left(55860 i - 55860\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(\left(193200 i - 193200\right) \, A + \left(223440 i + 223440\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(193200 i + 193200\right) \, A + \left(223440 i - 223440\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(48300 i - 48300\right) \, A - \left(55860 i + 55860\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(48300 i + 48300\right) \, A - \left(55860 i - 55860\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(289800 i - 289800\right) \, A - \left(335160 i + 335160\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(289800 i + 289800\right) \, A - \left(335160 i - 335160\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(96600 i - 96600\right) \, A - \left(111720 i + 111720\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(96600 i + 96600\right) \, A - \left(111720 i - 111720\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(96600 i - 96600\right) \, A - \left(111720 i + 111720\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(96600 i + 96600\right) \, A - \left(111720 i - 111720\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(193200 i - 193200\right) \, A + \left(223440 i + 223440\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(193200 i + 193200\right) \, A + \left(223440 i - 223440\right) \, B\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({\left(\left(193200 i - 193200\right) \, A + \left(223440 i + 223440\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(193200 i + 193200\right) \, A + \left(223440 i - 223440\right) \, B\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 - \left(61005 i - 61005\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i - 63840\right) \, A + \left(61005 i + 61005\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(63840 i + 63840\right) \, A - \left(61005 i - 61005\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i - 63840\right) \, A + \left(61005 i + 61005\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(63840 i + 63840\right) \, A - \left(61005 i - 61005\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(63840 i - 63840\right) \, A + \left(61005 i + 61005\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(88200 i + 88200\right) \, A + \left(88200 i - 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i + 44100\right) \, A - \left(44100 i - 44100\right) \, B\right)} a^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(102900 i + 102900\right) \, A + \left(102900 i - 102900\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(102900 i + 102900\right) \, A + \left(102900 i - 102900\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(205800 i + 205800\right) \, A - \left(205800 i - 205800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(102900 i + 102900\right) \, A + \left(102900 i - 102900\right) \, B\right)} a^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left({\left(-\left(127680 i + 127680\right) \, A + \left(122010 i - 122010\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(127680 i - 127680\right) \, A - \left(122010 i + 122010\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(88200 i - 88200\right) \, A - \left(88200 i + 88200\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(44100 i - 44100\right) \, A + \left(44100 i + 44100\right) \, B\right)} a^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(-\left(102900 i - 102900\right) \, A - \left(102900 i + 102900\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(102900 i - 102900\right) \, A - \left(102900 i + 102900\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(205800 i - 205800\right) \, A + \left(205800 i + 205800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(-\left(102900 i - 102900\right) \, A - \left(102900 i + 102900\right) \, B\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(-\left(48300 i + 48300\right) \, A + \left(55860 i - 55860\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(48300 i - 48300\right) \, A - \left(55860 i + 55860\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(-\left(48300 i + 48300\right) \, A + \left(55860 i - 55860\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(48300 i - 48300\right) \, A - \left(55860 i + 55860\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{4} + {\left({\left(\left(193200 i + 193200\right) \, A - \left(223440 i - 223440\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, A + \left(223440 i + 223440\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + {\left(-\left(48300 i + 48300\right) \, A + \left(55860 i - 55860\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(48300 i - 48300\right) \, A - \left(55860 i + 55860\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(289800 i + 289800\right) \, A + \left(335160 i - 335160\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(289800 i - 289800\right) \, A - \left(335160 i + 335160\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(96600 i + 96600\right) \, A + \left(111720 i - 111720\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(96600 i - 96600\right) \, A - \left(111720 i + 111720\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(96600 i + 96600\right) \, A + \left(111720 i - 111720\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(96600 i - 96600\right) \, A - \left(111720 i + 111720\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(193200 i + 193200\right) \, A - \left(223440 i - 223440\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, A + \left(223440 i + 223440\right) \, B\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({\left(\left(193200 i + 193200\right) \, A - \left(223440 i - 223440\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(193200 i - 193200\right) \, A + \left(223440 i + 223440\right) \, B\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 + (44100*I + 44100)*B)*a^2*cos(7*d*x + 7*c) + (-(44100*I - 44100)*A - (88200*I + 88200)*B)*a^2*cos(5*d*x + 5*c) + ((26460*I - 26460)*A + (59535*I + 59535)*B)*a^2*cos(3*d*x + 3*c) + (-(1260*I - 1260)*A - (15435*I + 15435)*B)*a^2*cos(d*x + c) + (-(44100*I + 44100)*A + (44100*I - 44100)*B)*a^2*sin(7*d*x + 7*c) + ((44100*I + 44100)*A - (88200*I - 88200)*B)*a^2*sin(5*d*x + 5*c) + (-(26460*I + 26460)*A + (59535*I - 59535)*B)*a^2*sin(3*d*x + 3*c) + ((1260*I + 1260)*A - (15435*I - 15435)*B)*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 - (23520*I + 23520)*B)*a^2*cos(d*x + c) + ((27300*I + 27300)*A - (23520*I - 23520)*B)*a^2*sin(d*x + c) + ((-(27300*I - 27300)*A - (23520*I + 23520)*B)*a^2*cos(d*x + c) + ((27300*I + 27300)*A - (23520*I - 23520)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(27300*I - 27300)*A - (23520*I + 23520)*B)*a^2*cos(d*x + c) + ((27300*I + 27300)*A - (23520*I - 23520)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(88200*I - 88200)*A - (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2)*cos(3*d*x + 3*c) + (((54600*I - 54600)*A + (47040*I + 47040)*B)*a^2*cos(d*x + c) + (-(54600*I + 54600)*A + (47040*I - 47040)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(44100*I + 44100)*A + (44100*I - 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(44100*I + 44100)*A + (44100*I - 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + ((88200*I + 88200)*A - (88200*I - 88200)*B)*a^2*cos(2*d*x + 2*c) + (-(44100*I + 44100)*A + (44100*I - 44100)*B)*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 - (44100*I - 44100)*B)*a^2*cos(7*d*x + 7*c) + (-(44100*I + 44100)*A + (88200*I - 88200)*B)*a^2*cos(5*d*x + 5*c) + ((26460*I + 26460)*A - (59535*I - 59535)*B)*a^2*cos(3*d*x + 3*c) + (-(1260*I + 1260)*A + (15435*I - 15435)*B)*a^2*cos(d*x + c) + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*sin(7*d*x + 7*c) + (-(44100*I - 44100)*A - (88200*I + 88200)*B)*a^2*sin(5*d*x + 5*c) + ((26460*I - 26460)*A + (59535*I + 59535)*B)*a^2*sin(3*d*x + 3*c) + (-(1260*I - 1260)*A - (15435*I + 15435)*B)*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 + (23520*I - 23520)*B)*a^2*cos(d*x + c) + (-(27300*I - 27300)*A - (23520*I + 23520)*B)*a^2*sin(d*x + c) + ((-(27300*I + 27300)*A + (23520*I - 23520)*B)*a^2*cos(d*x + c) + (-(27300*I - 27300)*A - (23520*I + 23520)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(27300*I + 27300)*A + (23520*I - 23520)*B)*a^2*cos(d*x + c) + (-(27300*I - 27300)*A - (23520*I + 23520)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(88200*I + 88200)*A + (88200*I - 88200)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2)*cos(3*d*x + 3*c) + (((54600*I + 54600)*A - (47040*I - 47040)*B)*a^2*cos(d*x + c) + ((54600*I - 54600)*A + (47040*I + 47040)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(88200*I - 88200)*A - (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I - 44100)*A + (44100*I + 44100)*B)*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 - (44100*I - 44100)*B)*a^2*cos(2*d*x + 2*c)^4 + ((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2*sin(2*d*x + 2*c)^4 + (-(176400*I + 176400)*A + (176400*I - 176400)*B)*a^2*cos(2*d*x + 2*c)^3 + ((264600*I + 264600)*A - (264600*I - 264600)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(176400*I + 176400)*A + (176400*I - 176400)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2 + (((88200*I + 88200)*A - (88200*I - 88200)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(176400*I + 176400)*A + (176400*I - 176400)*B)*a^2*cos(2*d*x + 2*c) + ((88200*I + 88200)*A - (88200*I - 88200)*B)*a^2)*sin(2*d*x + 2*c)^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 - (22050*I + 22050)*B)*a^2*cos(2*d*x + 2*c)^4 + (-(22050*I - 22050)*A - (22050*I + 22050)*B)*a^2*sin(2*d*x + 2*c)^4 + ((88200*I - 88200)*A + (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c)^3 + (-(132300*I - 132300)*A - (132300*I + 132300)*B)*a^2*cos(2*d*x + 2*c)^2 + ((88200*I - 88200)*A + (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c) + (-(22050*I - 22050)*A - (22050*I + 22050)*B)*a^2 + ((-(44100*I - 44100)*A - (44100*I + 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((88200*I - 88200)*A + (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c) + (-(44100*I - 44100)*A - (44100*I + 44100)*B)*a^2)*sin(2*d*x + 2*c)^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 + (61005*I + 61005)*B)*a^2*cos(d*x + c) + (-(63840*I + 63840)*A + (61005*I - 61005)*B)*a^2*sin(d*x + c) + (((63840*I - 63840)*A + (61005*I + 61005)*B)*a^2*cos(d*x + c) + (-(63840*I + 63840)*A + (61005*I - 61005)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((63840*I - 63840)*A + (61005*I + 61005)*B)*a^2*cos(d*x + c) + (-(63840*I + 63840)*A + (61005*I - 61005)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(88200*I - 88200)*A - (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2)*cos(5*d*x + 5*c) + ((-(102900*I - 102900)*A - (102900*I + 102900)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(102900*I - 102900)*A - (102900*I + 102900)*B)*a^2*sin(2*d*x + 2*c)^2 + ((205800*I - 205800)*A + (205800*I + 205800)*B)*a^2*cos(2*d*x + 2*c) + (-(102900*I - 102900)*A - (102900*I + 102900)*B)*a^2)*cos(3*d*x + 3*c) + ((-(127680*I - 127680)*A - (122010*I + 122010)*B)*a^2*cos(d*x + c) + ((127680*I + 127680)*A - (122010*I - 122010)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + ((-(44100*I + 44100)*A + (44100*I - 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(44100*I + 44100)*A + (44100*I - 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + ((88200*I + 88200)*A - (88200*I - 88200)*B)*a^2*cos(2*d*x + 2*c) + (-(44100*I + 44100)*A + (44100*I - 44100)*B)*a^2)*sin(5*d*x + 5*c) + (((102900*I + 102900)*A - (102900*I - 102900)*B)*a^2*cos(2*d*x + 2*c)^2 + ((102900*I + 102900)*A - (102900*I - 102900)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(205800*I + 205800)*A + (205800*I - 205800)*B)*a^2*cos(2*d*x + 2*c) + ((102900*I + 102900)*A - (102900*I - 102900)*B)*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 - (55860*I + 55860)*B)*a^2*cos(d*x + c) + ((48300*I + 48300)*A - (55860*I - 55860)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + ((-(48300*I - 48300)*A - (55860*I + 55860)*B)*a^2*cos(d*x + c) + ((48300*I + 48300)*A - (55860*I - 55860)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + (((193200*I - 193200)*A + (223440*I + 223440)*B)*a^2*cos(d*x + c) + (-(193200*I + 193200)*A + (223440*I - 223440)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(48300*I - 48300)*A - (55860*I + 55860)*B)*a^2*cos(d*x + c) + ((48300*I + 48300)*A - (55860*I - 55860)*B)*a^2*sin(d*x + c) + ((-(289800*I - 289800)*A - (335160*I + 335160)*B)*a^2*cos(d*x + c) + ((289800*I + 289800)*A - (335160*I - 335160)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(96600*I - 96600)*A - (111720*I + 111720)*B)*a^2*cos(d*x + c) + ((96600*I + 96600)*A - (111720*I - 111720)*B)*a^2*sin(d*x + c) + ((-(96600*I - 96600)*A - (111720*I + 111720)*B)*a^2*cos(d*x + c) + ((96600*I + 96600)*A - (111720*I - 111720)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((193200*I - 193200)*A + (223440*I + 223440)*B)*a^2*cos(d*x + c) + (-(193200*I + 193200)*A + (223440*I - 223440)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (((193200*I - 193200)*A + (223440*I + 223440)*B)*a^2*cos(d*x + c) + (-(193200*I + 193200)*A + (223440*I - 223440)*B)*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 - (61005*I - 61005)*B)*a^2*cos(d*x + c) + ((63840*I - 63840)*A + (61005*I + 61005)*B)*a^2*sin(d*x + c) + (((63840*I + 63840)*A - (61005*I - 61005)*B)*a^2*cos(d*x + c) + ((63840*I - 63840)*A + (61005*I + 61005)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((63840*I + 63840)*A - (61005*I - 61005)*B)*a^2*cos(d*x + c) + ((63840*I - 63840)*A + (61005*I + 61005)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(88200*I + 88200)*A + (88200*I - 88200)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I + 44100)*A - (44100*I - 44100)*B)*a^2)*cos(5*d*x + 5*c) + ((-(102900*I + 102900)*A + (102900*I - 102900)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(102900*I + 102900)*A + (102900*I - 102900)*B)*a^2*sin(2*d*x + 2*c)^2 + ((205800*I + 205800)*A - (205800*I - 205800)*B)*a^2*cos(2*d*x + 2*c) + (-(102900*I + 102900)*A + (102900*I - 102900)*B)*a^2)*cos(3*d*x + 3*c) + ((-(127680*I + 127680)*A + (122010*I - 122010)*B)*a^2*cos(d*x + c) + (-(127680*I - 127680)*A - (122010*I + 122010)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c) + (((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*cos(2*d*x + 2*c)^2 + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(88200*I - 88200)*A - (88200*I + 88200)*B)*a^2*cos(2*d*x + 2*c) + ((44100*I - 44100)*A + (44100*I + 44100)*B)*a^2)*sin(5*d*x + 5*c) + ((-(102900*I - 102900)*A - (102900*I + 102900)*B)*a^2*cos(2*d*x + 2*c)^2 + (-(102900*I - 102900)*A - (102900*I + 102900)*B)*a^2*sin(2*d*x + 2*c)^2 + ((205800*I - 205800)*A + (205800*I + 205800)*B)*a^2*cos(2*d*x + 2*c) + (-(102900*I - 102900)*A - (102900*I + 102900)*B)*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 + (55860*I - 55860)*B)*a^2*cos(d*x + c) + (-(48300*I - 48300)*A - (55860*I + 55860)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^4 + ((-(48300*I + 48300)*A + (55860*I - 55860)*B)*a^2*cos(d*x + c) + (-(48300*I - 48300)*A - (55860*I + 55860)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^4 + (((193200*I + 193200)*A - (223440*I - 223440)*B)*a^2*cos(d*x + c) + ((193200*I - 193200)*A + (223440*I + 223440)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^3 + (-(48300*I + 48300)*A + (55860*I - 55860)*B)*a^2*cos(d*x + c) + (-(48300*I - 48300)*A - (55860*I + 55860)*B)*a^2*sin(d*x + c) + ((-(289800*I + 289800)*A + (335160*I - 335160)*B)*a^2*cos(d*x + c) + (-(289800*I - 289800)*A - (335160*I + 335160)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(96600*I + 96600)*A + (111720*I - 111720)*B)*a^2*cos(d*x + c) + (-(96600*I - 96600)*A - (111720*I + 111720)*B)*a^2*sin(d*x + c) + ((-(96600*I + 96600)*A + (111720*I - 111720)*B)*a^2*cos(d*x + c) + (-(96600*I - 96600)*A - (111720*I + 111720)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((193200*I + 193200)*A - (223440*I - 223440)*B)*a^2*cos(d*x + c) + ((193200*I - 193200)*A + (223440*I + 223440)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c))*sin(2*d*x + 2*c)^2 + (((193200*I + 193200)*A - (223440*I - 223440)*B)*a^2*cos(d*x + c) + ((193200*I - 193200)*A + (223440*I + 223440)*B)*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
549,1,1525,0,1.943016," ","integrate(cot(d*x+c)^(7/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),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(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(930 i + 930\right) \, A - \left(750 i - 750\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(900 i - 900\right) \, A - \left(900 i + 900\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(930 i - 930\right) \, A + \left(750 i + 750\right) \, B\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(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(930 i - 930\right) \, A - \left(750 i + 750\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(\left(930 i + 930\right) \, A - \left(750 i - 750\right) \, B\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(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(1800 i - 1800\right) \, A - \left(1800 i + 1800\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\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(\left(450 i + 450\right) \, A - \left(450 i - 450\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\left(450 i + 450\right) \, A - \left(450 i - 450\right) \, B\right)} a^{2} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} a^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(\left(450 i + 450\right) \, A - \left(450 i - 450\right) \, B\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(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(\left(750 i + 750\right) \, A - \left(1650 i - 1650\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(-\left(210 i + 210\right) \, A + \left(750 i - 750\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(900 i - 900\right) \, A - \left(900 i + 900\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(750 i - 750\right) \, A + \left(1650 i + 1650\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(210 i - 210\right) \, A - \left(750 i + 750\right) \, B\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 - \left(600 i - 600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(240 i - 240\right) \, A + \left(600 i + 600\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(240 i - 240\right) \, A + \left(600 i + 600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(240 i - 240\right) \, A + \left(600 i + 600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(480 i + 480\right) \, A + \left(1200 i - 1200\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(480 i - 480\right) \, A - \left(1200 i + 1200\right) \, B\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(900 i - 900\right) \, A + \left(900 i + 900\right) \, B\right)} a^{2} \cos\left(5 \, d x + 5 \, c\right) + {\left(-\left(750 i - 750\right) \, A - \left(1650 i + 1650\right) \, B\right)} a^{2} \cos\left(3 \, d x + 3 \, c\right) + {\left(\left(210 i - 210\right) \, A + \left(750 i + 750\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(900 i + 900\right) \, A + \left(900 i - 900\right) \, B\right)} a^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(\left(750 i + 750\right) \, A - \left(1650 i - 1650\right) \, B\right)} a^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(-\left(210 i + 210\right) \, A + \left(750 i - 750\right) \, B\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 - \left(600 i + 600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} a^{2} \sin\left(d x + c\right) + {\left({\left(-\left(240 i - 240\right) \, A - \left(600 i + 600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(-\left(240 i - 240\right) \, A - \left(600 i + 600\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(\left(240 i + 240\right) \, A - \left(600 i - 600\right) \, B\right)} a^{2} \sin\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(\left(480 i - 480\right) \, A + \left(1200 i + 1200\right) \, B\right)} a^{2} \cos\left(d x + c\right) + {\left(-\left(480 i + 480\right) \, A + \left(1200 i - 1200\right) \, B\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 + (900*I - 900)*B)*a^2*cos(3*d*x + 3*c) + ((930*I + 930)*A - (750*I - 750)*B)*a^2*cos(d*x + c) + (-(900*I - 900)*A - (900*I + 900)*B)*a^2*sin(3*d*x + 3*c) + ((930*I - 930)*A + (750*I + 750)*B)*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 + (900*I + 900)*B)*a^2*cos(3*d*x + 3*c) + (-(930*I - 930)*A - (750*I + 750)*B)*a^2*cos(d*x + c) + (-(900*I + 900)*A + (900*I - 900)*B)*a^2*sin(3*d*x + 3*c) + ((930*I + 930)*A - (750*I - 750)*B)*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 + (900*I + 900)*B)*a^2*cos(2*d*x + 2*c)^2 + ((900*I - 900)*A + (900*I + 900)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(1800*I - 1800)*A - (1800*I + 1800)*B)*a^2*cos(2*d*x + 2*c) + ((900*I - 900)*A + (900*I + 900)*B)*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 - (450*I - 450)*B)*a^2*cos(2*d*x + 2*c)^2 + ((450*I + 450)*A - (450*I - 450)*B)*a^2*sin(2*d*x + 2*c)^2 + (-(900*I + 900)*A + (900*I - 900)*B)*a^2*cos(2*d*x + 2*c) + ((450*I + 450)*A - (450*I - 450)*B)*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 + (900*I - 900)*B)*a^2*cos(5*d*x + 5*c) + ((750*I + 750)*A - (1650*I - 1650)*B)*a^2*cos(3*d*x + 3*c) + (-(210*I + 210)*A + (750*I - 750)*B)*a^2*cos(d*x + c) + (-(900*I - 900)*A - (900*I + 900)*B)*a^2*sin(5*d*x + 5*c) + ((750*I - 750)*A + (1650*I + 1650)*B)*a^2*sin(3*d*x + 3*c) + (-(210*I - 210)*A - (750*I + 750)*B)*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 - (600*I - 600)*B)*a^2*cos(d*x + c) + ((240*I - 240)*A + (600*I + 600)*B)*a^2*sin(d*x + c) + (((240*I + 240)*A - (600*I - 600)*B)*a^2*cos(d*x + c) + ((240*I - 240)*A + (600*I + 600)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + (((240*I + 240)*A - (600*I - 600)*B)*a^2*cos(d*x + c) + ((240*I - 240)*A + (600*I + 600)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + ((-(480*I + 480)*A + (1200*I - 1200)*B)*a^2*cos(d*x + c) + (-(480*I - 480)*A - (1200*I + 1200)*B)*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 + (900*I + 900)*B)*a^2*cos(5*d*x + 5*c) + (-(750*I - 750)*A - (1650*I + 1650)*B)*a^2*cos(3*d*x + 3*c) + ((210*I - 210)*A + (750*I + 750)*B)*a^2*cos(d*x + c) + (-(900*I + 900)*A + (900*I - 900)*B)*a^2*sin(5*d*x + 5*c) + ((750*I + 750)*A - (1650*I - 1650)*B)*a^2*sin(3*d*x + 3*c) + (-(210*I + 210)*A + (750*I - 750)*B)*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 - (600*I + 600)*B)*a^2*cos(d*x + c) + ((240*I + 240)*A - (600*I - 600)*B)*a^2*sin(d*x + c) + ((-(240*I - 240)*A - (600*I + 600)*B)*a^2*cos(d*x + c) + ((240*I + 240)*A - (600*I - 600)*B)*a^2*sin(d*x + c))*cos(2*d*x + 2*c)^2 + ((-(240*I - 240)*A - (600*I + 600)*B)*a^2*cos(d*x + c) + ((240*I + 240)*A - (600*I - 600)*B)*a^2*sin(d*x + c))*sin(2*d*x + 2*c)^2 + (((480*I - 480)*A + (1200*I + 1200)*B)*a^2*cos(d*x + c) + (-(480*I + 480)*A + (1200*I - 1200)*B)*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
550,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^(5/2)/sqrt(cot(d*x + c)), x)","F",0
554,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
555,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
556,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
557,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+I*a*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
558,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(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
559,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(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
560,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
561,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
562,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(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
563,-2,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(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
564,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
565,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
566,-2,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/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
567,0,0,0,0.000000," ","integrate(cot(d*x+c)^m*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n*cot(d*x + c)^m, x)","F",0
568,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n*cot(d*x + c)^(5/2), x)","F",0
569,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n*cot(d*x + c)^(3/2), x)","F",0
570,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
571,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \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)*(I*a*tan(d*x + c) + a)^n/sqrt(cot(d*x + c)), x)","F",0
572,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n/cot(d*x + c)^(3/2), x)","F",0
573,0,0,0,0.000000," ","integrate((a+I*a*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\left(i \, a \tan\left(d x + c\right) + a\right)}^{n}}{\cot\left(d x + c\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(I*a*tan(d*x + c) + a)^n/cot(d*x + c)^(5/2), x)","F",0
574,1,196,0,1.773035," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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 a}{\tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{24 \, {\left(B a + A b\right)}}{\sqrt{\tan\left(d x + c\right)}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A - B)*a - (A + B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*((A - B)*a - (A + B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*A*a/tan(d*x + c)^(3/2) - 24*(B*a + A*b)/sqrt(tan(d*x + c)))/d","A",0
575,1,178,0,0.875955," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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 a}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a + (A - B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a + (A - B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*A*a/sqrt(tan(d*x + c)))/d","A",0
576,1,178,0,1.123633," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} {\left({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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 b \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a + (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a - (A + B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a - (A + B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*B*b*sqrt(tan(d*x + c)))/d","A",0
577,1,198,0,0.741558," ","integrate((a+b*tan(d*x+c))*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A - B\right)} a - {\left(A + B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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({\left(A + B\right)} a + {\left(A - B\right)} 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 b + \frac{3 \, {\left(B a + A b\right)}}{\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)*a - (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A - B)*a - (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 3*sqrt(2)*((A + B)*a + (A - B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 3*sqrt(2)*((A + B)*a + (A - B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*(B*b + 3*(B*a + A*b)/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
578,1,279,0,1.970208," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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{24 \, A a^{2}}{\tan\left(d x + c\right)^{\frac{5}{2}}} - \frac{120 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)}}{\sqrt{\tan\left(d x + c\right)}} + \frac{40 \, {\left(B a^{2} + 2 \, A a b\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{60 \, d}"," ",0,"-1/60*(30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 24*A*a^2/tan(d*x + c)^(5/2) - 120*(A*a^2 - 2*B*a*b - A*b^2)/sqrt(tan(d*x + c)) + 40*(B*a^2 + 2*A*a*b)/tan(d*x + c)^(3/2))/d","A",0
579,1,252,0,1.718939," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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 a^{2}}{\tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{24 \, {\left(B a^{2} + 2 \, A a b\right)}}{\sqrt{\tan\left(d x + c\right)}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*A*a^2/tan(d*x + c)^(3/2) - 24*(B*a^2 + 2*A*a*b)/sqrt(tan(d*x + c)))/d","A",0
580,1,244,0,1.155619," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, B b^{2} \sqrt{\tan\left(d x + c\right)} + 2 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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 a^{2}}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(8*B*b^2*sqrt(tan(d*x + c)) + 2*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*A*a^2/sqrt(tan(d*x + c)))/d","A",0
581,1,254,0,2.759359," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^2*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{6 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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 b^{2} + \frac{3 \, {\left(2 \, B a b + A b^{2}\right)}}{\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)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*(B*b^2 + 3*(2*B*a*b + A*b^2)/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
582,1,282,0,0.860635," ","integrate((a+b*tan(d*x+c))^2*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, B b^{2} + \frac{5 \, {\left(2 \, B a b + A b^{2}\right)}}{\tan\left(d x + c\right)} + \frac{15 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 30 \, \sqrt{2} {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} - 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} + 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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*b^2 + 5*(2*B*a*b + A*b^2)/tan(d*x + c) + 15*(B*a^2 + 2*A*a*b - B*b^2)/tan(d*x + c)^2)*tan(d*x + c)^(5/2) - 30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - 30*sqrt(2)*((A - B)*a^2 - 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 15*sqrt(2)*((A + B)*a^2 + 2*(A - B)*a*b - (A + B)*b^2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
583,1,366,0,1.895557," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{210 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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{120 \, A a^{3}}{\tan\left(d x + c\right)^{\frac{7}{2}}} - \frac{840 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)}}{\sqrt{\tan\left(d x + c\right)}} - \frac{280 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{168 \, {\left(B a^{3} + 3 \, A a^{2} b\right)}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}{420 \, d}"," ",0,"-1/420*(210*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 210*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 105*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 105*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 120*A*a^3/tan(d*x + c)^(7/2) - 840*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)/sqrt(tan(d*x + c)) - 280*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)/tan(d*x + c)^(3/2) + 168*(B*a^3 + 3*A*a^2*b)/tan(d*x + c)^(5/2))/d","A",0
584,1,330,0,2.234347," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} b^{3}\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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} b^{3}\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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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) - 15 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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{24 \, A a^{3}}{\tan\left(d x + c\right)^{\frac{5}{2}}} - \frac{120 \, {\left(A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2}\right)}}{\sqrt{\tan\left(d x + c\right)}} + \frac{40 \, {\left(B a^{3} + 3 \, A a^{2} b\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{60 \, d}"," ",0,"-1/60*(30*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 30*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 15*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 15*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 24*A*a^3/tan(d*x + c)^(5/2) - 120*(A*a^3 - 3*B*a^2*b - 3*A*a*b^2)/sqrt(tan(d*x + c)) + 40*(B*a^3 + 3*A*a^2*b)/tan(d*x + c)^(3/2))/d","A",0
585,1,314,0,0.592227," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{24 \, B b^{3} \sqrt{\tan\left(d x + c\right)} + 6 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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 a^{3}}{\tan\left(d x + c\right)^{\frac{3}{2}}} - \frac{24 \, {\left(B a^{3} + 3 \, A a^{2} b\right)}}{\sqrt{\tan\left(d x + c\right)}}}{12 \, d}"," ",0,"1/12*(24*B*b^3*sqrt(tan(d*x + c)) + 6*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*A*a^3/tan(d*x + c)^(3/2) - 24*(B*a^3 + 3*A*a^2*b)/sqrt(tan(d*x + c)))/d","A",0
586,1,316,0,1.213725," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{24 \, A a^{3}}{\sqrt{\tan\left(d x + c\right)}} - 6 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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 b^{3} + \frac{3 \, {\left(3 \, B a b^{2} + A b^{3}\right)}}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{12 \, d}"," ",0,"-1/12*(24*A*a^3/sqrt(tan(d*x + c)) - 6*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - 6*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 3*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 3*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 8*(B*b^3 + 3*(3*B*a*b^2 + A*b^3)/tan(d*x + c))*tan(d*x + c)^(3/2))/d","A",0
587,1,334,0,0.772035," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^3*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, {\left(3 \, B b^{3} + \frac{5 \, {\left(3 \, B a b^{2} + A b^{3}\right)}}{\tan\left(d x + c\right)} + \frac{15 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)}}{\tan\left(d x + c\right)^{2}}\right)} \tan\left(d x + c\right)^{\frac{5}{2}} - 30 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} b^{3}\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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} b^{3}\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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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) - 15 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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)}{60 \, d}"," ",0,"1/60*(8*(3*B*b^3 + 5*(3*B*a*b^2 + A*b^3)/tan(d*x + c) + 15*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)/tan(d*x + c)^2)*tan(d*x + c)^(5/2) - 30*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - 30*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 15*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 15*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
588,1,370,0,1.951013," ","integrate((a+b*tan(d*x+c))^3*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{8 \, {\left(15 \, B b^{3} + \frac{21 \, {\left(3 \, B a b^{2} + A b^{3}\right)}}{\tan\left(d x + c\right)} + \frac{35 \, {\left(3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right)}}{\tan\left(d x + c\right)^{2}} + \frac{105 \, {\left(B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right)}}{\tan\left(d x + c\right)^{3}}\right)} \tan\left(d x + c\right)^{\frac{7}{2}} - 210 \, \sqrt{2} {\left({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A - B\right)} a^{3} - 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} + {\left(A + B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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({\left(A + B\right)} a^{3} + 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} - {\left(A - B\right)} 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*b^3 + 21*(3*B*a*b^2 + A*b^3)/tan(d*x + c) + 35*(3*B*a^2*b + 3*A*a*b^2 - B*b^3)/tan(d*x + c)^2 + 105*(B*a^3 + 3*A*a^2*b - 3*B*a*b^2 - A*b^3)/tan(d*x + c)^3)*tan(d*x + c)^(7/2) - 210*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) - 210*sqrt(2)*((A - B)*a^3 - 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 + (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - 105*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 105*sqrt(2)*((A + B)*a^3 + 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 - (A - B)*b^3)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
589,1,262,0,0.822172," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{24 \, {\left(B a b^{3} - A b^{4}\right)} \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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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{A a}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{3 \, {\left(B a - A b\right)}}{\sqrt{\tan\left(d x + c\right)}}\right)}}{a^{2}}}{12 \, d}"," ",0,"1/12*(24*(B*a*b^3 - A*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)*a - (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a + (A + B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a + (A + B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2) - 8*(A*a/tan(d*x + c)^(3/2) + 3*(B*a - A*b)/sqrt(tan(d*x + c)))/a^2)/d","A",0
590,1,239,0,0.942179," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(B a b^{2} - A b^{3}\right)} \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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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}{a \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(8*(B*a*b^2 - A*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)*a + (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a - (A - B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a - (A - B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2) + 8*A/(a*sqrt(tan(d*x + c))))/d","A",0
591,1,221,0,1.063450," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(B a b - A b^{2}\right)} \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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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*a*b - A*b^2)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2 + b^2)*sqrt(a*b)) - (2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a + (A + B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a + (A + B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
592,1,220,0,0.625821," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(B a^{2} - A a b\right)} \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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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*a^2 - A*a*b)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2 + b^2)*sqrt(a*b)) + (2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a - (A - B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a - (A - B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
593,1,238,0,0.715870," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(B a^{3} - A a^{2} b\right)} \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{8 \, B \sqrt{\tan\left(d x + c\right)}}{b} + \frac{2 \, \sqrt{2} {\left({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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*a^3 - A*a^2*b)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2*b + b^3)*sqrt(a*b)) + 8*B*sqrt(tan(d*x + c))/b + (2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a - (A - B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a + (A + B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a + (A + B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
594,1,262,0,0.636397," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{24 \, {\left(B a^{4} - A a^{3} b\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\right)}{{\left(a^{2} b^{2} + b^{4}\right)} \sqrt{a b}} - \frac{8 \, {\left(B b - \frac{3 \, {\left(B a - A b\right)}}{\tan\left(d x + c\right)}\right)} \tan\left(d x + c\right)^{\frac{3}{2}}}{b^{2}} - \frac{3 \, {\left(2 \, \sqrt{2} {\left({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A - B\right)} a + {\left(A + B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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({\left(A + B\right)} a - {\left(A - B\right)} 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}}}{12 \, d}"," ",0,"-1/12*(24*(B*a^4 - A*a^3*b)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^2*b^2 + b^4)*sqrt(a*b)) - 8*(B*b - 3*(B*a - A*b)/tan(d*x + c))*tan(d*x + c)^(3/2)/b^2 - 3*(2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a + (A + B)*b)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a - (A - B)*b)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a - (A - B)*b)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/(a^2 + b^2))/d","A",0
595,1,383,0,0.868789," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(5 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3} + B a b^{4} - 3 \, A 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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(B a b^{2} - A b^{3}\right)}}{{\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{8 \, A}{a^{2} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*(4*(5*B*a^3*b^2 - 7*A*a^2*b^3 + B*a*b^4 - 3*A*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 - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (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*b^2 - A*b^3)/((a^4*b + a^2*b^3 + (a^5 + a^3*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))) + 8*A/(a^2*sqrt(tan(d*x + c))))/d","A",0
596,1,362,0,1.062837," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(3 \, B a^{3} b - 5 \, A a^{2} b^{2} - B a b^{3} - A 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{2 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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(B a b - A b^{2}\right)}}{{\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)}}}{4 \, d}"," ",0,"1/4*(4*(3*B*a^3*b - 5*A*a^2*b^2 - B*a*b^3 - A*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)) - (2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (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*b - A*b^2)/((a^3*b + a*b^3 + (a^4 + a^2*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))))/d","A",0
597,1,347,0,0.836324," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(B a^{3} - 3 \, A a^{2} b - 3 \, B a b^{2} + A 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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(B a - A b\right)}}{{\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*(B*a^3 - 3*A*a^2*b - 3*B*a*b^2 + A*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 - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (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 - A*b)/((a^2*b + b^3 + (a^3 + a*b^2)/tan(d*x + c))*sqrt(tan(d*x + c))))/d","A",0
598,1,360,0,0.696393," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(B a^{4} + A a^{3} b + 5 \, B a^{2} b^{2} - 3 \, A a b^{3}\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{2 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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(B a^{2} - A a b\right)}}{{\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)}}}{4 \, d}"," ",0,"-1/4*(4*(B*a^4 + A*a^3*b + 5*B*a^2*b^2 - 3*A*a*b^3)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^4*b + 2*a^2*b^3 + b^5)*sqrt(a*b)) - (2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (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 - A*a*b)/((a^2*b^2 + b^4 + (a^3*b + a*b^3)/tan(d*x + c))*sqrt(tan(d*x + c))))/d","A",0
599,1,402,0,0.965760," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(3 \, B a^{5} - A a^{4} b + 7 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A - B\right)} a^{2} + 2 \, {\left(A + B\right)} a b - {\left(A - B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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({\left(A + B\right)} a^{2} - 2 \, {\left(A - B\right)} a b - {\left(A + B\right)} 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 \, B a^{2} b + 2 \, B b^{3} + \frac{3 \, B a^{3} - A a^{2} b + 2 \, B 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*B*a^5 - A*a^4*b + 7*B*a^3*b^2 - 5*A*a^2*b^3)*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 - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^2 + 2*(A + B)*a*b - (A - B)*b^2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (A + B)*b^2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^2 - 2*(A - B)*a*b - (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*B*a^2*b + 2*B*b^3 + (3*B*a^3 - A*a^2*b + 2*B*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
600,1,577,0,0.900221," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(35 \, B a^{5} b^{2} - 63 \, A a^{4} b^{3} + 6 \, B a^{3} b^{4} - 46 \, A a^{2} b^{5} + 3 \, B a b^{6} - 15 \, A 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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 \, B a^{3} b^{3} - 15 \, A a^{2} b^{4} + 3 \, B a b^{5} - 7 \, A b^{6}}{\sqrt{\tan\left(d x + c\right)}} + \frac{13 \, B a^{4} b^{2} - 17 \, A a^{3} b^{3} + 5 \, B a^{2} b^{4} - 9 \, A 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}{a^{3} \sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"-1/4*((35*B*a^5*b^2 - 63*A*a^4*b^3 + 6*B*a^3*b^4 - 46*A*a^2*b^5 + 3*B*a*b^6 - 15*A*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 - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*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*B*a^3*b^3 - 15*A*a^2*b^4 + 3*B*a*b^5 - 7*A*b^6)/sqrt(tan(d*x + c)) + (13*B*a^4*b^2 - 17*A*a^3*b^3 + 5*B*a^2*b^4 - 9*A*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/(a^3*sqrt(tan(d*x + c))))/d","A",0
601,1,558,0,0.609382," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(15 \, B a^{5} b - 35 \, A a^{4} b^{2} - 18 \, B a^{3} b^{3} - 6 \, A a^{2} b^{4} - B a b^{5} - 3 \, A 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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 \, B a^{3} b^{2} - 11 \, A a^{2} b^{3} - B a b^{4} - 3 \, A b^{5}}{\sqrt{\tan\left(d x + c\right)}} + \frac{9 \, B a^{4} b - 13 \, A a^{3} b^{2} + B a^{2} b^{3} - 5 \, A 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*((15*B*a^5*b - 35*A*a^4*b^2 - 18*B*a^3*b^3 - 6*A*a^2*b^4 - B*a*b^5 - 3*A*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 + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*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*B*a^3*b^2 - 11*A*a^2*b^3 - B*a*b^4 - 3*A*b^5)/sqrt(tan(d*x + c)) + (9*B*a^4*b - 13*A*a^3*b^2 + B*a^2*b^3 - 5*A*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
602,1,544,0,0.870800," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, B a^{5} - 15 \, A a^{4} b - 26 \, B a^{3} b^{2} + 18 \, A a^{2} b^{3} + 3 \, B a b^{4} + A 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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 \, B a^{3} b - 7 \, A a^{2} b^{2} - 5 \, B a b^{3} + A b^{4}}{\sqrt{\tan\left(d x + c\right)}} + \frac{5 \, B a^{4} - 9 \, A a^{3} b - 3 \, B a^{2} b^{2} - A 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*((3*B*a^5 - 15*A*a^4*b - 26*B*a^3*b^2 + 18*A*a^2*b^3 + 3*B*a*b^4 + A*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 - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*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*B*a^3*b - 7*A*a^2*b^2 - 5*B*a*b^3 + A*b^4)/sqrt(tan(d*x + c)) + (5*B*a^4 - 9*A*a^3*b - 3*B*a^2*b^2 - A*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
603,1,545,0,0.619725," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(B a^{5} + 3 \, A a^{4} b + 18 \, B a^{3} b^{2} - 26 \, A a^{2} b^{3} - 15 \, B a b^{4} + 3 \, A b^{5}\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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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{B a^{3} b + 3 \, A a^{2} b^{2} + 9 \, B a b^{3} - 5 \, A b^{4}}{\sqrt{\tan\left(d x + c\right)}} - \frac{B a^{4} - 5 \, A a^{3} b - 7 \, B a^{2} b^{2} + 3 \, A a b^{3}}{\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*((B*a^5 + 3*A*a^4*b + 18*B*a^3*b^2 - 26*A*a^2*b^3 - 15*B*a*b^4 + 3*A*b^5)*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 + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*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) - ((B*a^3*b + 3*A*a^2*b^2 + 9*B*a*b^3 - 5*A*b^4)/sqrt(tan(d*x + c)) - (B*a^4 - 5*A*a^3*b - 7*B*a^2*b^2 + 3*A*a*b^3)/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
604,1,556,0,0.791022," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{{\left(3 \, B a^{6} + A a^{5} b + 6 \, B a^{4} b^{2} + 18 \, A a^{3} b^{3} + 35 \, B a^{2} b^{4} - 15 \, A a b^{5}\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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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 \, B a^{4} b - A a^{3} b^{2} + 13 \, B a^{2} b^{3} - 9 \, A a b^{4}}{\sqrt{\tan\left(d x + c\right)}} + \frac{3 \, B a^{5} + A a^{4} b + 11 \, B a^{3} b^{2} - 7 \, A a^{2} b^{3}}{\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*B*a^6 + A*a^5*b + 6*B*a^4*b^2 + 18*A*a^3*b^3 + 35*B*a^2*b^4 - 15*A*a*b^5)*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 - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*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*B*a^4*b - A*a^3*b^2 + 13*B*a^2*b^3 - 9*A*a*b^4)/sqrt(tan(d*x + c)) + (3*B*a^5 + A*a^4*b + 11*B*a^3*b^2 - 7*A*a^2*b^3)/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
605,1,612,0,0.800116," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(7/2)/(a+b*tan(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{{\left(15 \, B a^{7} - 3 \, A a^{6} b + 46 \, B a^{5} b^{2} - 6 \, A a^{4} b^{3} + 63 \, B a^{3} b^{4} - 35 \, A a^{2} b^{5}\right)} \arctan\left(\frac{a}{\sqrt{a b} \sqrt{\tan\left(d x + c\right)}}\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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A + B\right)} a^{3} - 3 \, {\left(A - B\right)} a^{2} b - 3 \, {\left(A + B\right)} a b^{2} + {\left(A - B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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({\left(A - B\right)} a^{3} + 3 \, {\left(A + B\right)} a^{2} b - 3 \, {\left(A - B\right)} a b^{2} - {\left(A + B\right)} 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{8 \, B a^{4} b^{2} + 16 \, B a^{2} b^{4} + 8 \, B b^{6} + \frac{25 \, B a^{5} b - 5 \, A a^{4} b^{2} + 49 \, B a^{3} b^{3} - 13 \, A a^{2} b^{4} + 16 \, B a b^{5}}{\tan\left(d x + c\right)} + \frac{15 \, B a^{6} - 3 \, A a^{5} b + 31 \, B a^{4} b^{2} - 11 \, A a^{3} b^{3} + 8 \, B a^{2} b^{4}}{\tan\left(d x + c\right)^{2}}}{\frac{a^{4} b^{5} + 2 \, a^{2} b^{7} + b^{9}}{\sqrt{\tan\left(d x + c\right)}} + \frac{2 \, {\left(a^{5} b^{4} + 2 \, a^{3} b^{6} + a b^{8}\right)}}{\tan\left(d x + c\right)^{\frac{3}{2}}} + \frac{a^{6} b^{3} + 2 \, a^{4} b^{5} + a^{2} b^{7}}{\tan\left(d x + c\right)^{\frac{5}{2}}}}}{4 \, d}"," ",0,"1/4*((15*B*a^7 - 3*A*a^6*b + 46*B*a^5*b^2 - 6*A*a^4*b^3 + 63*B*a^3*b^4 - 35*A*a^2*b^5)*arctan(a/(sqrt(a*b)*sqrt(tan(d*x + c))))/((a^6*b^3 + 3*a^4*b^5 + 3*a^2*b^7 + b^9)*sqrt(a*b)) - (2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*((A + B)*a^3 - 3*(A - B)*a^2*b - 3*(A + B)*a*b^2 + (A - B)*b^3)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*b^3)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*((A - B)*a^3 + 3*(A + B)*a^2*b - 3*(A - B)*a*b^2 - (A + B)*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) + (8*B*a^4*b^2 + 16*B*a^2*b^4 + 8*B*b^6 + (25*B*a^5*b - 5*A*a^4*b^2 + 49*B*a^3*b^3 - 13*A*a^2*b^4 + 16*B*a*b^5)/tan(d*x + c) + (15*B*a^6 - 3*A*a^5*b + 31*B*a^4*b^2 - 11*A*a^3*b^3 + 8*B*a^2*b^4)/tan(d*x + c)^2)/((a^4*b^5 + 2*a^2*b^7 + b^9)/sqrt(tan(d*x + c)) + 2*(a^5*b^4 + 2*a^3*b^6 + a*b^8)/tan(d*x + c)^(3/2) + (a^6*b^3 + 2*a^4*b^5 + a^2*b^7)/tan(d*x + c)^(5/2)))/d","A",0
606,1,127,0,0.521878," ","integrate(cot(d*x+c)^(5/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\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) + \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)} B - \frac{8 \, B}{\tan\left(d x + c\right)^{\frac{3}{2}}}}{12 \, d}"," ",0,"1/12*(3*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*B - 8*B/tan(d*x + c)^(3/2))/d","A",0
607,1,127,0,0.835240," ","integrate(cot(d*x+c)^(3/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} B \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} B \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} B \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} B \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \frac{8 \, B}{\sqrt{\tan\left(d x + c\right)}}}{4 \, d}"," ",0,"1/4*(2*sqrt(2)*B*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*B*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*B*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*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
608,1,113,0,0.664399," ","integrate(cot(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\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) + \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)} B}{4 \, d}"," ",0,"-1/4*(2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*B/d","A",0
609,1,116,0,0.701621," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} B \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} B \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + \sqrt{2} B \log\left(\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) - \sqrt{2} B \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)*B*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*B*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + sqrt(2)*B*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - sqrt(2)*B*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))/d","A",0
610,1,126,0,0.743614," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 2 \, \sqrt{2} \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\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) + \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)} B + 8 \, B \sqrt{\tan\left(d x + c\right)}}{4 \, d}"," ",0,"1/4*((2*sqrt(2)*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 2*sqrt(2)*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) - sqrt(2)*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + sqrt(2)*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1))*B + 8*B*sqrt(tan(d*x + c)))/d","A",0
611,1,128,0,0.933134," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, \sqrt{2} B \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} + \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 6 \, \sqrt{2} B \arctan\left(-\frac{1}{2} \, \sqrt{2} {\left(\sqrt{2} - \frac{2}{\sqrt{\tan\left(d x + c\right)}}\right)}\right) + 3 \, \sqrt{2} B \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} B \log\left(-\frac{\sqrt{2}}{\sqrt{\tan\left(d x + c\right)}} + \frac{1}{\tan\left(d x + c\right)} + 1\right) + 8 \, B \tan\left(d x + c\right)^{\frac{3}{2}}}{12 \, d}"," ",0,"1/12*(6*sqrt(2)*B*arctan(1/2*sqrt(2)*(sqrt(2) + 2/sqrt(tan(d*x + c)))) + 6*sqrt(2)*B*arctan(-1/2*sqrt(2)*(sqrt(2) - 2/sqrt(tan(d*x + c)))) + 3*sqrt(2)*B*log(sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) - 3*sqrt(2)*B*log(-sqrt(2)/sqrt(tan(d*x + c)) + 1/tan(d*x + c) + 1) + 8*B*tan(d*x + c)^(3/2))/d","A",0
612,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(9/2), x)","F",0
613,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(7/2), x)","F",0
614,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(5/2), x)","F",0
615,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(3/2), x)","F",0
616,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)*sqrt(cot(d*x + c)), x)","F",0
617,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a}}{\sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)/sqrt(cot(d*x + c)), x)","F",0
618,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(1/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{b \tan\left(d x + c\right) + a}}{\cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(b*tan(d*x + c) + a)/cot(d*x + c)^(3/2), x)","F",0
619,0,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{\frac{11}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(11/2), x)","F",0
620,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(9/2), x)","F",0
621,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(7/2), x)","F",0
622,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(5/2), x)","F",0
623,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c)), x)","F",0
625,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)/sqrt(cot(d*x + c)), x)","F",0
626,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(3/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(3/2)/cot(d*x + c)^(3/2), x)","F",0
627,0,0,0,0.000000," ","integrate(cot(d*x+c)^(13/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{\frac{13}{2}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(13/2), x)","F",0
628,0,0,0,0.000000," ","integrate(cot(d*x+c)^(11/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(11/2), x)","F",0
629,0,0,0,0.000000," ","integrate(cot(d*x+c)^(9/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(9/2), x)","F",0
630,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(7/2), x)","F",0
631,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(5/2), x)","F",0
632,-1,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)*sqrt(cot(d*x + c)), x)","F",0
634,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)/sqrt(cot(d*x + c)), x)","F",0
635,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^(5/2)*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^(5/2)/cot(d*x + c)^(3/2), x)","F",0
636,0,0,0,0.000000," ","integrate(cot(d*x+c)^(7/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)^{\frac{7}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)^(7/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
637,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)^{\frac{5}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)^(5/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
638,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \cot\left(d x + c\right)^{\frac{3}{2}}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*cot(d*x + c)^(3/2)/sqrt(b*tan(d*x + c) + a), x)","F",0
639,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{\cot\left(d x + c\right)}}{\sqrt{b \tan\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(cot(d*x + c))/sqrt(b*tan(d*x + c) + a), x)","F",0
640,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{\sqrt{b \tan\left(d x + c\right) + a} \sqrt{\cot\left(d x + c\right)}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(sqrt(b*tan(d*x + c) + a)*sqrt(cot(d*x + c))), x)","F",0
641,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{\sqrt{b \tan\left(d x + c\right) + a} \cot\left(d x + c\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)/(sqrt(b*tan(d*x + c) + a)*cot(d*x + c)^(3/2)), x)","F",0
642,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
643,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(3/2), x)","F",0
644,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^(3/2), x)","F",0
645,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c))), x)","F",0
646,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(3/2)*cot(d*x + c)^(3/2)), x)","F",0
647,0,0,0,0.000000," ","integrate(cot(d*x+c)^(5/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*cot(d*x + c)^(5/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
648,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \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((B*tan(d*x + c) + A)*cot(d*x + c)^(3/2)/(b*tan(d*x + c) + a)^(5/2), x)","F",0
649,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(A+B*tan(d*x+c))/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} \sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^(5/2), x)","F",0
650,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(5/2)*sqrt(cot(d*x + c))), x)","F",0
651,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(3/2)), x)","F",0
652,0,0,0,0.000000," ","integrate((A+B*tan(d*x+c))/cot(d*x+c)^(5/2)/(a+b*tan(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{B \tan\left(d x + c\right) + A}{{\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)/((b*tan(d*x + c) + a)^(5/2)*cot(d*x + c)^(5/2)), x)","F",0
653,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a*B+b*B*tan(d*x+c))/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B b \tan\left(d x + c\right) + B a\right)} \sqrt{\cot\left(d x + c\right)}}{{\left(b \tan\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((B*b*tan(d*x + c) + B*a)*sqrt(cot(d*x + c))/(b*tan(d*x + c) + a)^(3/2), x)","F",0
654,0,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(1/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{B b \tan\left(d x + c\right) + B a}{{\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*b*tan(d*x + c) + B*a)/((b*tan(d*x + c) + a)^(3/2)*sqrt(cot(d*x + c))), x)","F",0
655,-1,0,0,0.000000," ","integrate((a*B+b*B*tan(d*x+c))/cot(d*x+c)^(3/2)/(a+b*tan(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,0,0,0,0.000000," ","integrate(cot(d*x+c)^m*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\left(b \tan\left(d x + c\right) + a\right)}^{n} \cot\left(d x + c\right)^{m}\,{d x}"," ",0,"integrate((B*tan(d*x + c) + A)*(b*tan(d*x + c) + a)^n*cot(d*x + c)^m, x)","F",0
657,0,0,0,0.000000," ","integrate(cot(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*cot(d*x + c)^(3/2), x)","F",0
658,0,0,0,0.000000," ","integrate(cot(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*sqrt(cot(d*x + c)), x)","F",0
659,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n/sqrt(cot(d*x + c)), x)","F",0
660,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/cot(d*x+c)^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n/cot(d*x + c)^(3/2), x)","F",0
661,0,0,0,0.000000," ","integrate(tan(d*x+c)^(3/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*tan(d*x + c)^(3/2), x)","F",0
662,0,0,0,0.000000," ","integrate(tan(d*x+c)^(1/2)*(a+b*tan(d*x+c))^n*(A+B*tan(d*x+c)),x, algorithm=""maxima"")","\int {\left(B \tan\left(d x + c\right) + A\right)} {\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)*(b*tan(d*x + c) + a)^n*sqrt(tan(d*x + c)), x)","F",0
663,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,-1,0,0,0.000000," ","integrate((a+b*tan(d*x+c))^n*(A+B*tan(d*x+c))/tan(d*x+c)^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
665,1,311,0,2.290260," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{{\left({\left(A - i \, B\right)} a c^{n} n + {\left(A - i \, B\right)} a 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({\left(A + i \, B\right)} a c^{n} n + {\left(A - i \, B\right)} a c^{n}\right)} 2^{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) - {\left({\left(i \, A + B\right)} a c^{n} n + {\left(i \, A + B\right)} a 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({\left(i \, A - B\right)} a c^{n} n + {\left(i \, A + B\right)} a c^{n}\right)} 2^{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)}{{\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,"(((A - I*B)*a*c^n*n + (A - I*B)*a*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) + ((A + I*B)*a*c^n*n + (A - I*B)*a*c^n)*2^n*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) - ((I*A + B)*a*c^n*n + (I*A + B)*a*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*A - B)*a*c^n*n + (I*A + B)*a*c^n)*2^n*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))/((-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
666,1,93,0,1.223385," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\frac{12 i \, B a c^{4} \tan\left(f x + e\right)^{5} + {\left(15 i \, A - 45 \, B\right)} a c^{4} \tan\left(f x + e\right)^{4} - 60 \, {\left(A + i \, B\right)} a c^{4} \tan\left(f x + e\right)^{3} + {\left(-90 i \, A + 30 \, B\right)} a c^{4} \tan\left(f x + e\right)^{2} + 60 \, A a c^{4} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*I*B*a*c^4*tan(f*x + e)^5 + (15*I*A - 45*B)*a*c^4*tan(f*x + e)^4 - 60*(A + I*B)*a*c^4*tan(f*x + e)^3 + (-90*I*A + 30*B)*a*c^4*tan(f*x + e)^2 + 60*A*a*c^4*tan(f*x + e))/f","A",0
667,1,73,0,0.903339," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{3 \, B a c^{3} \tan\left(f x + e\right)^{4} + 4 \, {\left(A + 2 i \, B\right)} a c^{3} \tan\left(f x + e\right)^{3} + {\left(12 i \, A - 6 \, B\right)} a c^{3} \tan\left(f x + e\right)^{2} - 12 \, A a c^{3} \tan\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(3*B*a*c^3*tan(f*x + e)^4 + 4*(A + 2*I*B)*a*c^3*tan(f*x + e)^3 + (12*I*A - 6*B)*a*c^3*tan(f*x + e)^2 - 12*A*a*c^3*tan(f*x + e))/f","A",0
668,1,54,0,0.892266," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{-2 i \, B a c^{2} \tan\left(f x + e\right)^{3} + {\left(-3 i \, A + 3 \, B\right)} a c^{2} \tan\left(f x + e\right)^{2} + 6 \, A a c^{2} \tan\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(-2*I*B*a*c^2*tan(f*x + e)^3 + (-3*I*A + 3*B)*a*c^2*tan(f*x + e)^2 + 6*A*a*c^2*tan(f*x + e))/f","A",0
669,1,29,0,0.871435," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","\frac{B a c \tan\left(f x + e\right)^{2} + 2 \, A a c \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(B*a*c*tan(f*x + e)^2 + 2*A*a*c*tan(f*x + e))/f","A",0
670,1,50,0,0.837748," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} {\left(A - i \, B\right)} a - {\left(-i \, A - B\right)} a \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 2 i \, B a \tan\left(f x + e\right)}{2 \, f}"," ",0,"1/2*(2*(f*x + e)*(A - I*B)*a - (-I*A - B)*a*log(tan(f*x + e)^2 + 1) + 2*I*B*a*tan(f*x + e))/f","A",0
671,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*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
672,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*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
673,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*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
674,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*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
675,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*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
676,1,664,0,1.119999," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{2 \, {\left({\left(A + i \, B\right)} a^{2} c^{n} n^{2} + 4 \, A a^{2} c^{n} n + 4 \, {\left(A - i \, B\right)} 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) + 2 \, {\left({\left(A - i \, B\right)} a^{2} c^{n} n^{2} + 3 \, {\left(A - i \, B\right)} a^{2} c^{n} n + 2 \, {\left(A - i \, B\right)} a^{2} 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) + 2 \, {\left({\left(A + i \, B\right)} a^{2} c^{n} n + 2 \, {\left(A - i \, B\right)} a^{2} c^{n}\right)} 2^{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) + {\left({\left(-2 i \, A + 2 \, B\right)} a^{2} c^{n} n^{2} - 8 i \, A a^{2} c^{n} n + {\left(-8 i \, A - 8 \, B\right)} 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({\left(-2 i \, A - 2 \, B\right)} a^{2} c^{n} n^{2} + {\left(-6 i \, A - 6 \, B\right)} a^{2} c^{n} n + {\left(-4 i \, A - 4 \, B\right)} a^{2} 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(-2 i \, A + 2 \, B\right)} a^{2} c^{n} n + {\left(-4 i \, A - 4 \, B\right)} a^{2} c^{n}\right)} 2^{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)}{{\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*((A + I*B)*a^2*c^n*n^2 + 4*A*a^2*c^n*n + 4*(A - I*B)*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*((A - I*B)*a^2*c^n*n^2 + 3*(A - I*B)*a^2*c^n*n + 2*(A - I*B)*a^2*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) + 2*((A + I*B)*a^2*c^n*n + 2*(A - I*B)*a^2*c^n)*2^n*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + ((-2*I*A + 2*B)*a^2*c^n*n^2 - 8*I*A*a^2*c^n*n + (-8*I*A - 8*B)*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) + ((-2*I*A - 2*B)*a^2*c^n*n^2 + (-6*I*A - 6*B)*a^2*c^n*n + (-4*I*A - 4*B)*a^2*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) + ((-2*I*A + 2*B)*a^2*c^n*n + (-4*I*A - 4*B)*a^2*c^n)*2^n*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))/(((-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
677,1,150,0,0.902244," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5,x, algorithm=""maxima"")","-\frac{-60 i \, B a^{2} c^{5} \tan\left(f x + e\right)^{7} + {\left(-70 i \, A + 210 \, B\right)} a^{2} c^{5} \tan\left(f x + e\right)^{6} + 84 \, {\left(3 \, A + 2 i \, B\right)} a^{2} c^{5} \tan\left(f x + e\right)^{5} + {\left(210 i \, A + 210 \, B\right)} a^{2} c^{5} \tan\left(f x + e\right)^{4} + 140 \, {\left(2 \, A + 3 i \, B\right)} a^{2} c^{5} \tan\left(f x + e\right)^{3} + {\left(630 i \, A - 210 \, B\right)} a^{2} c^{5} \tan\left(f x + e\right)^{2} - 420 \, A a^{2} c^{5} \tan\left(f x + e\right)}{420 \, f}"," ",0,"-1/420*(-60*I*B*a^2*c^5*tan(f*x + e)^7 + (-70*I*A + 210*B)*a^2*c^5*tan(f*x + e)^6 + 84*(3*A + 2*I*B)*a^2*c^5*tan(f*x + e)^5 + (210*I*A + 210*B)*a^2*c^5*tan(f*x + e)^4 + 140*(2*A + 3*I*B)*a^2*c^5*tan(f*x + e)^3 + (630*I*A - 210*B)*a^2*c^5*tan(f*x + e)^2 - 420*A*a^2*c^5*tan(f*x + e))/f","A",0
678,1,116,0,0.889575," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","-\frac{10 \, B a^{2} c^{4} \tan\left(f x + e\right)^{6} + 12 \, {\left(A + 2 i \, B\right)} a^{2} c^{4} \tan\left(f x + e\right)^{5} + 30 i \, A a^{2} c^{4} \tan\left(f x + e\right)^{4} + 40 i \, B a^{2} c^{4} \tan\left(f x + e\right)^{3} - {\left(-60 i \, A + 30 \, B\right)} a^{2} c^{4} \tan\left(f x + e\right)^{2} - 60 \, A a^{2} c^{4} \tan\left(f x + e\right)}{60 \, f}"," ",0,"-1/60*(10*B*a^2*c^4*tan(f*x + e)^6 + 12*(A + 2*I*B)*a^2*c^4*tan(f*x + e)^5 + 30*I*A*a^2*c^4*tan(f*x + e)^4 + 40*I*B*a^2*c^4*tan(f*x + e)^3 - (-60*I*A + 30*B)*a^2*c^4*tan(f*x + e)^2 - 60*A*a^2*c^4*tan(f*x + e))/f","A",0
679,1,103,0,1.622802," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{12 i \, B a^{2} c^{3} \tan\left(f x + e\right)^{5} + {\left(15 i \, A - 15 \, B\right)} a^{2} c^{3} \tan\left(f x + e\right)^{4} - 20 \, {\left(A - i \, B\right)} a^{2} c^{3} \tan\left(f x + e\right)^{3} + {\left(30 i \, A - 30 \, B\right)} a^{2} c^{3} \tan\left(f x + e\right)^{2} - 60 \, A a^{2} c^{3} \tan\left(f x + e\right)}{60 \, f}"," ",0,"-1/60*(12*I*B*a^2*c^3*tan(f*x + e)^5 + (15*I*A - 15*B)*a^2*c^3*tan(f*x + e)^4 - 20*(A - I*B)*a^2*c^3*tan(f*x + e)^3 + (30*I*A - 30*B)*a^2*c^3*tan(f*x + e)^2 - 60*A*a^2*c^3*tan(f*x + e))/f","A",0
680,1,72,0,0.461522," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{3 \, B a^{2} c^{2} \tan\left(f x + e\right)^{4} + 4 \, A a^{2} c^{2} \tan\left(f x + e\right)^{3} + 6 \, B a^{2} c^{2} \tan\left(f x + e\right)^{2} + 12 \, A a^{2} c^{2} \tan\left(f x + e\right)}{12 \, f}"," ",0,"1/12*(3*B*a^2*c^2*tan(f*x + e)^4 + 4*A*a^2*c^2*tan(f*x + e)^3 + 6*B*a^2*c^2*tan(f*x + e)^2 + 12*A*a^2*c^2*tan(f*x + e))/f","A",0
681,1,54,0,0.681301," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{-2 i \, B a^{2} c \tan\left(f x + e\right)^{3} + {\left(-3 i \, A - 3 \, B\right)} a^{2} c \tan\left(f x + e\right)^{2} - 6 \, A a^{2} c \tan\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(-2*I*B*a^2*c*tan(f*x + e)^3 + (-3*I*A - 3*B)*a^2*c*tan(f*x + e)^2 - 6*A*a^2*c*tan(f*x + e))/f","A",0
682,1,71,0,0.732594," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{B a^{2} \tan\left(f x + e\right)^{2} - 4 \, {\left(f x + e\right)} {\left(A - i \, B\right)} a^{2} - 2 \, {\left(i \, A + B\right)} a^{2} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 2 \, {\left(A - 2 i \, B\right)} a^{2} \tan\left(f x + e\right)}{2 \, f}"," ",0,"-1/2*(B*a^2*tan(f*x + e)^2 - 4*(f*x + e)*(A - I*B)*a^2 - 2*(I*A + B)*a^2*log(tan(f*x + e)^2 + 1) + 2*(A - 2*I*B)*a^2*tan(f*x + e))/f","A",0
683,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*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
684,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*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
685,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*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
686,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*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
687,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*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
688,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^6,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
689,1,1057,0,1.214159," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\frac{8 \, {\left({\left(A + i \, B\right)} a^{3} c^{n} n^{2} + 6 \, A a^{3} c^{n} n + 9 \, {\left(A - i \, B\right)} 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({\left(A + i \, B\right)} a^{3} c^{n} n^{3} + 2 \, {\left(4 \, A + i \, B\right)} a^{3} c^{n} n^{2} + 3 \, {\left(7 \, A - 3 i \, B\right)} a^{3} c^{n} n + 18 \, {\left(A - i \, B\right)} 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) + 4 \, {\left({\left(A - i \, B\right)} a^{3} c^{n} n^{3} + 6 \, {\left(A - i \, B\right)} a^{3} c^{n} n^{2} + 11 \, {\left(A - i \, B\right)} a^{3} c^{n} n + 6 \, {\left(A - i \, B\right)} a^{3} 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) + 8 \, {\left({\left(A + i \, B\right)} a^{3} c^{n} n + 3 \, {\left(A - i \, B\right)} a^{3} c^{n}\right)} 2^{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) + {\left({\left(-8 i \, A + 8 \, B\right)} a^{3} c^{n} n^{2} - 48 i \, A a^{3} c^{n} n + {\left(-72 i \, A - 72 \, B\right)} 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({\left(-4 i \, A + 4 \, B\right)} a^{3} c^{n} n^{3} + {\left(-32 i \, A + 8 \, B\right)} a^{3} c^{n} n^{2} + {\left(-84 i \, A - 36 \, B\right)} a^{3} c^{n} n + {\left(-72 i \, A - 72 \, B\right)} 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(-4 i \, A - 4 \, B\right)} a^{3} c^{n} n^{3} + {\left(-24 i \, A - 24 \, B\right)} a^{3} c^{n} n^{2} + {\left(-44 i \, A - 44 \, B\right)} a^{3} c^{n} n + {\left(-24 i \, A - 24 \, B\right)} a^{3} 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(-8 i \, A + 8 \, B\right)} a^{3} c^{n} n + {\left(-24 i \, A - 24 \, B\right)} a^{3} c^{n}\right)} 2^{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)}{{\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,"(8*((A + I*B)*a^3*c^n*n^2 + 6*A*a^3*c^n*n + 9*(A - I*B)*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 + I*B)*a^3*c^n*n^3 + 2*(4*A + I*B)*a^3*c^n*n^2 + 3*(7*A - 3*I*B)*a^3*c^n*n + 18*(A - I*B)*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) + 4*((A - I*B)*a^3*c^n*n^3 + 6*(A - I*B)*a^3*c^n*n^2 + 11*(A - I*B)*a^3*c^n*n + 6*(A - I*B)*a^3*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) + 8*((A + I*B)*a^3*c^n*n + 3*(A - I*B)*a^3*c^n)*2^n*cos(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)) + ((-8*I*A + 8*B)*a^3*c^n*n^2 - 48*I*A*a^3*c^n*n + (-72*I*A - 72*B)*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 + 4*B)*a^3*c^n*n^3 + (-32*I*A + 8*B)*a^3*c^n*n^2 + (-84*I*A - 36*B)*a^3*c^n*n + (-72*I*A - 72*B)*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) + ((-4*I*A - 4*B)*a^3*c^n*n^3 + (-24*I*A - 24*B)*a^3*c^n*n^2 + (-44*I*A - 44*B)*a^3*c^n*n + (-24*I*A - 24*B)*a^3*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) + ((-8*I*A + 8*B)*a^3*c^n*n + (-24*I*A - 24*B)*a^3*c^n)*2^n*sin(n*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e) + 1)))/(((-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
690,1,191,0,0.778337," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^6,x, algorithm=""maxima"")","\frac{280 i \, B a^{3} c^{6} \tan\left(f x + e\right)^{9} + {\left(315 i \, A - 945 \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{8} - 360 \, {\left(3 \, A + i \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{7} + {\left(-420 i \, A - 2100 \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{6} - 2520 \, {\left(A + i \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{5} + {\left(-3150 i \, A - 630 \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{4} - 840 \, {\left(A + 3 i \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{3} + {\left(-3780 i \, A + 1260 \, B\right)} a^{3} c^{6} \tan\left(f x + e\right)^{2} + 2520 \, A a^{3} c^{6} \tan\left(f x + e\right)}{2520 \, f}"," ",0,"1/2520*(280*I*B*a^3*c^6*tan(f*x + e)^9 + (315*I*A - 945*B)*a^3*c^6*tan(f*x + e)^8 - 360*(3*A + I*B)*a^3*c^6*tan(f*x + e)^7 + (-420*I*A - 2100*B)*a^3*c^6*tan(f*x + e)^6 - 2520*(A + I*B)*a^3*c^6*tan(f*x + e)^5 + (-3150*I*A - 630*B)*a^3*c^6*tan(f*x + e)^4 - 840*(A + 3*I*B)*a^3*c^6*tan(f*x + e)^3 + (-3780*I*A + 1260*B)*a^3*c^6*tan(f*x + e)^2 + 2520*A*a^3*c^6*tan(f*x + e))/f","A",0
691,1,167,0,0.896814," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5,x, algorithm=""maxima"")","-\frac{105 \, B a^{3} c^{5} \tan\left(f x + e\right)^{8} + 120 \, {\left(A + 2 i \, B\right)} a^{3} c^{5} \tan\left(f x + e\right)^{7} + {\left(280 i \, A + 140 \, B\right)} a^{3} c^{5} \tan\left(f x + e\right)^{6} + 168 \, {\left(A + 4 i \, B\right)} a^{3} c^{5} \tan\left(f x + e\right)^{5} + {\left(840 i \, A - 210 \, B\right)} a^{3} c^{5} \tan\left(f x + e\right)^{4} - 280 \, {\left(A - 2 i \, B\right)} a^{3} c^{5} \tan\left(f x + e\right)^{3} + {\left(840 i \, A - 420 \, B\right)} a^{3} c^{5} \tan\left(f x + e\right)^{2} - 840 \, A a^{3} c^{5} \tan\left(f x + e\right)}{840 \, f}"," ",0,"-1/840*(105*B*a^3*c^5*tan(f*x + e)^8 + 120*(A + 2*I*B)*a^3*c^5*tan(f*x + e)^7 + (280*I*A + 140*B)*a^3*c^5*tan(f*x + e)^6 + 168*(A + 4*I*B)*a^3*c^5*tan(f*x + e)^5 + (840*I*A - 210*B)*a^3*c^5*tan(f*x + e)^4 - 280*(A - 2*I*B)*a^3*c^5*tan(f*x + e)^3 + (840*I*A - 420*B)*a^3*c^5*tan(f*x + e)^2 - 840*A*a^3*c^5*tan(f*x + e))/f","A",0
692,1,148,0,0.866288," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^4,x, algorithm=""maxima"")","\frac{-60 i \, B a^{3} c^{4} \tan\left(f x + e\right)^{7} + {\left(-70 i \, A + 70 \, B\right)} a^{3} c^{4} \tan\left(f x + e\right)^{6} + 84 \, {\left(A - 2 i \, B\right)} a^{3} c^{4} \tan\left(f x + e\right)^{5} + {\left(-210 i \, A + 210 \, B\right)} a^{3} c^{4} \tan\left(f x + e\right)^{4} + 140 \, {\left(2 \, A - i \, B\right)} a^{3} c^{4} \tan\left(f x + e\right)^{3} + {\left(-210 i \, A + 210 \, B\right)} a^{3} c^{4} \tan\left(f x + e\right)^{2} + 420 \, A a^{3} c^{4} \tan\left(f x + e\right)}{420 \, f}"," ",0,"1/420*(-60*I*B*a^3*c^4*tan(f*x + e)^7 + (-70*I*A + 70*B)*a^3*c^4*tan(f*x + e)^6 + 84*(A - 2*I*B)*a^3*c^4*tan(f*x + e)^5 + (-210*I*A + 210*B)*a^3*c^4*tan(f*x + e)^4 + 140*(2*A - I*B)*a^3*c^4*tan(f*x + e)^3 + (-210*I*A + 210*B)*a^3*c^4*tan(f*x + e)^2 + 420*A*a^3*c^4*tan(f*x + e))/f","A",0
693,1,106,0,0.834162," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{5 \, B a^{3} c^{3} \tan\left(f x + e\right)^{6} + 6 \, A a^{3} c^{3} \tan\left(f x + e\right)^{5} + 15 \, B a^{3} c^{3} \tan\left(f x + e\right)^{4} + 20 \, A a^{3} c^{3} \tan\left(f x + e\right)^{3} + 15 \, B a^{3} c^{3} \tan\left(f x + e\right)^{2} + 30 \, A a^{3} c^{3} \tan\left(f x + e\right)}{30 \, f}"," ",0,"1/30*(5*B*a^3*c^3*tan(f*x + e)^6 + 6*A*a^3*c^3*tan(f*x + e)^5 + 15*B*a^3*c^3*tan(f*x + e)^4 + 20*A*a^3*c^3*tan(f*x + e)^3 + 15*B*a^3*c^3*tan(f*x + e)^2 + 30*A*a^3*c^3*tan(f*x + e))/f","A",0
694,1,103,0,2.711596," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^2,x, algorithm=""maxima"")","\frac{12 i \, B a^{3} c^{2} \tan\left(f x + e\right)^{5} + {\left(15 i \, A + 15 \, B\right)} a^{3} c^{2} \tan\left(f x + e\right)^{4} + 20 \, {\left(A + i \, B\right)} a^{3} c^{2} \tan\left(f x + e\right)^{3} + {\left(30 i \, A + 30 \, B\right)} a^{3} c^{2} \tan\left(f x + e\right)^{2} + 60 \, A a^{3} c^{2} \tan\left(f x + e\right)}{60 \, f}"," ",0,"1/60*(12*I*B*a^3*c^2*tan(f*x + e)^5 + (15*I*A + 15*B)*a^3*c^2*tan(f*x + e)^4 + 20*(A + I*B)*a^3*c^2*tan(f*x + e)^3 + (30*I*A + 30*B)*a^3*c^2*tan(f*x + e)^2 + 60*A*a^3*c^2*tan(f*x + e))/f","A",0
695,1,73,0,0.526694," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{3 \, B a^{3} c \tan\left(f x + e\right)^{4} + 4 \, {\left(A - 2 i \, B\right)} a^{3} c \tan\left(f x + e\right)^{3} + {\left(-12 i \, A - 6 \, B\right)} a^{3} c \tan\left(f x + e\right)^{2} - 12 \, A a^{3} c \tan\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(3*B*a^3*c*tan(f*x + e)^4 + 4*(A - 2*I*B)*a^3*c*tan(f*x + e)^3 + (-12*I*A - 6*B)*a^3*c*tan(f*x + e)^2 - 12*A*a^3*c*tan(f*x + e))/f","A",0
696,1,96,0,0.658473," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{2 i \, B a^{3} \tan\left(f x + e\right)^{3} - {\left(-3 i \, A - 9 \, B\right)} a^{3} \tan\left(f x + e\right)^{2} - 24 \, {\left(f x + e\right)} {\left(A - i \, B\right)} a^{3} - 6 \, {\left(2 i \, A + 2 \, B\right)} a^{3} \log\left(\tan\left(f x + e\right)^{2} + 1\right) + 6 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \tan\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(2*I*B*a^3*tan(f*x + e)^3 - (-3*I*A - 9*B)*a^3*tan(f*x + e)^2 - 24*(f*x + e)*(A - I*B)*a^3 - 6*(2*I*A + 2*B)*a^3*log(tan(f*x + e)^2 + 1) + 6*(3*A - 4*I*B)*a^3*tan(f*x + e))/f","A",0
697,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*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
698,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*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
699,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*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
700,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*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
701,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*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
702,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^6,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
703,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^7,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
704,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^8,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
705,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
706,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
707,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
708,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
709,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
710,-2,0,0,0.000000," ","integrate((A+B*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
711,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
712,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
713,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
714,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
715,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
716,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5/(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
717,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
718,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
719,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
720,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
721,-2,0,0,0.000000," ","integrate((A+B*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
722,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
723,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
724,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
725,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
726,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2/(c-I*c*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
727,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
728,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^5/(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
729,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
730,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
731,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
732,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
733,-2,0,0,0.000000," ","integrate((A+B*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
734,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
735,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
736,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
737,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
738,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*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
739,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3/(c-I*c*tan(f*x+e))^6,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
740,1,48,0,0.467399," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(7 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} B a + 9 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} {\left(A - i \, B\right)} a c\right)}}{63 \, c f}"," ",0,"2/63*I*(7*I*(-I*c*tan(f*x + e) + c)^(9/2)*B*a + 9*(-I*c*tan(f*x + e) + c)^(7/2)*(A - I*B)*a*c)/(c*f)","A",0
741,1,48,0,0.687655," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(5 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} B a + 7 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(A - i \, B\right)} a c\right)}}{35 \, c f}"," ",0,"2/35*I*(5*I*(-I*c*tan(f*x + e) + c)^(7/2)*B*a + 7*(-I*c*tan(f*x + e) + c)^(5/2)*(A - I*B)*a*c)/(c*f)","A",0
742,1,48,0,0.445653," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(3 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} B a + 5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - i \, B\right)} a c\right)}}{15 \, c f}"," ",0,"2/15*I*(3*I*(-I*c*tan(f*x + e) + c)^(5/2)*B*a + 5*(-I*c*tan(f*x + e) + c)^(3/2)*(A - I*B)*a*c)/(c*f)","A",0
743,1,48,0,0.409427," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","\frac{2 i \, {\left(i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} B a + 3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - i \, B\right)} a c\right)}}{3 \, c f}"," ",0,"2/3*I*(I*(-I*c*tan(f*x + e) + c)^(3/2)*B*a + 3*sqrt(-I*c*tan(f*x + e) + c)*(A - I*B)*a*c)/(c*f)","A",0
744,1,48,0,0.454119," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} B a - \frac{{\left(A - i \, B\right)} a c}{\sqrt{-i \, c \tan\left(f x + e\right) + c}}\right)}}{c f}"," ",0,"2*I*(I*sqrt(-I*c*tan(f*x + e) + c)*B*a - (A - I*B)*a*c/sqrt(-I*c*tan(f*x + e) + c))/(c*f)","A",0
745,1,45,0,0.669168," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(3 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} B a + {\left(A - i \, B\right)} a 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*(-I*c*tan(f*x + e) + c)*B*a + (A - I*B)*a*c)/((-I*c*tan(f*x + e) + c)^(3/2)*c*f)","A",0
746,1,46,0,0.595567," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(5 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} B a + 3 \, {\left(A - i \, B\right)} a 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*(-I*c*tan(f*x + e) + c)*B*a + 3*(A - I*B)*a*c)/((-I*c*tan(f*x + e) + c)^(5/2)*c*f)","A",0
747,1,46,0,0.475969," ","integrate((a+I*a*tan(f*x+e))*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(7 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} B a + 5 \, {\left(A - i \, B\right)} a c\right)}}{35 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} c f}"," ",0,"-2/35*I*(7*I*(-I*c*tan(f*x + e) + c)*B*a + 5*(A - I*B)*a*c)/((-I*c*tan(f*x + e) + c)^(7/2)*c*f)","A",0
748,1,78,0,0.513916," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(63 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{11}{2}} B a^{2} + 77 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} {\left(A - 3 i \, B\right)} a^{2} c - 198 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} {\left(A - i \, B\right)} a^{2} c^{2}\right)}}{693 \, c^{2} f}"," ",0,"-2/693*I*(63*I*(-I*c*tan(f*x + e) + c)^(11/2)*B*a^2 + 77*(-I*c*tan(f*x + e) + c)^(9/2)*(A - 3*I*B)*a^2*c - 198*(-I*c*tan(f*x + e) + c)^(7/2)*(A - I*B)*a^2*c^2)/(c^2*f)","A",0
749,1,78,0,0.448966," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(35 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} B a^{2} + 45 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} {\left(A - 3 i \, B\right)} a^{2} c - 126 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(A - i \, B\right)} a^{2} c^{2}\right)}}{315 \, c^{2} f}"," ",0,"-2/315*I*(35*I*(-I*c*tan(f*x + e) + c)^(9/2)*B*a^2 + 45*(-I*c*tan(f*x + e) + c)^(7/2)*(A - 3*I*B)*a^2*c - 126*(-I*c*tan(f*x + e) + c)^(5/2)*(A - I*B)*a^2*c^2)/(c^2*f)","A",0
750,1,78,0,0.535402," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(15 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} B a^{2} + 21 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(A - 3 i \, B\right)} a^{2} c - 70 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - i \, B\right)} a^{2} c^{2}\right)}}{105 \, c^{2} f}"," ",0,"-2/105*I*(15*I*(-I*c*tan(f*x + e) + c)^(7/2)*B*a^2 + 21*(-I*c*tan(f*x + e) + c)^(5/2)*(A - 3*I*B)*a^2*c - 70*(-I*c*tan(f*x + e) + c)^(3/2)*(A - I*B)*a^2*c^2)/(c^2*f)","A",0
751,1,78,0,0.397442," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{2 i \, {\left(3 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} B a^{2} + 5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - 3 i \, B\right)} a^{2} c - 30 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - i \, B\right)} a^{2} c^{2}\right)}}{15 \, c^{2} f}"," ",0,"-2/15*I*(3*I*(-I*c*tan(f*x + e) + c)^(5/2)*B*a^2 + 5*(-I*c*tan(f*x + e) + c)^(3/2)*(A - 3*I*B)*a^2*c - 30*sqrt(-I*c*tan(f*x + e) + c)*(A - I*B)*a^2*c^2)/(c^2*f)","A",0
752,1,81,0,0.809319," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(\frac{6 \, {\left(A - i \, B\right)} a^{2} c}{\sqrt{-i \, c \tan\left(f x + e\right) + c}} + \frac{i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} B a^{2} + 3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - 3 i \, B\right)} a^{2} c}{c}\right)}}{3 \, c f}"," ",0,"-2/3*I*(6*(A - I*B)*a^2*c/sqrt(-I*c*tan(f*x + e) + c) + (I*(-I*c*tan(f*x + e) + c)^(3/2)*B*a^2 + 3*sqrt(-I*c*tan(f*x + e) + c)*(A - 3*I*B)*a^2*c)/c)/(c*f)","A",0
753,1,79,0,0.528800," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(\frac{3 i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} B a^{2}}{c} - \frac{3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(A - 3 i \, B\right)} a^{2} - 2 \, {\left(A - i \, B\right)} a^{2} c}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\right)}}{3 \, c f}"," ",0,"-2/3*I*(3*I*sqrt(-I*c*tan(f*x + e) + c)*B*a^2/c - (3*(-I*c*tan(f*x + e) + c)*(A - 3*I*B)*a^2 - 2*(A - I*B)*a^2*c)/(-I*c*tan(f*x + e) + c)^(3/2))/(c*f)","A",0
754,1,76,0,0.721164," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(15 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} B a^{2} + 5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(A - 3 i \, B\right)} a^{2} c - 6 \, {\left(A - i \, B\right)} a^{2} 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*(-I*c*tan(f*x + e) + c)^2*B*a^2 + 5*(-I*c*tan(f*x + e) + c)*(A - 3*I*B)*a^2*c - 6*(A - I*B)*a^2*c^2)/((-I*c*tan(f*x + e) + c)^(5/2)*c^2*f)","A",0
755,1,76,0,0.568257," ","integrate((a+I*a*tan(f*x+e))^2*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(35 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} B a^{2} + 21 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(A - 3 i \, B\right)} a^{2} c - 30 \, {\left(A - i \, B\right)} a^{2} c^{2}\right)}}{105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} c^{2} f}"," ",0,"2/105*I*(35*I*(-I*c*tan(f*x + e) + c)^2*B*a^2 + 21*(-I*c*tan(f*x + e) + c)*(A - 3*I*B)*a^2*c - 30*(A - I*B)*a^2*c^2)/((-I*c*tan(f*x + e) + c)^(7/2)*c^2*f)","A",0
756,1,104,0,0.557723," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(693 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{13}{2}} B a^{3} + 819 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{11}{2}} {\left(A - 5 i \, B\right)} a^{3} c - 4004 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} {\left(A - 2 i \, B\right)} a^{3} c^{2} + 5148 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} {\left(A - i \, B\right)} a^{3} c^{3}\right)}}{9009 \, c^{3} f}"," ",0,"2/9009*I*(693*I*(-I*c*tan(f*x + e) + c)^(13/2)*B*a^3 + 819*(-I*c*tan(f*x + e) + c)^(11/2)*(A - 5*I*B)*a^3*c - 4004*(-I*c*tan(f*x + e) + c)^(9/2)*(A - 2*I*B)*a^3*c^2 + 5148*(-I*c*tan(f*x + e) + c)^(7/2)*(A - I*B)*a^3*c^3)/(c^3*f)","A",0
757,1,104,0,0.667544," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(315 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{11}{2}} B a^{3} + 385 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} {\left(A - 5 i \, B\right)} a^{3} c - 1980 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} {\left(A - 2 i \, B\right)} a^{3} c^{2} + 2772 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(A - i \, B\right)} a^{3} c^{3}\right)}}{3465 \, c^{3} f}"," ",0,"2/3465*I*(315*I*(-I*c*tan(f*x + e) + c)^(11/2)*B*a^3 + 385*(-I*c*tan(f*x + e) + c)^(9/2)*(A - 5*I*B)*a^3*c - 1980*(-I*c*tan(f*x + e) + c)^(7/2)*(A - 2*I*B)*a^3*c^2 + 2772*(-I*c*tan(f*x + e) + c)^(5/2)*(A - I*B)*a^3*c^3)/(c^3*f)","A",0
758,1,104,0,0.350878," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(35 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{9}{2}} B a^{3} + 45 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} {\left(A - 5 i \, B\right)} a^{3} c - 252 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(A - 2 i \, B\right)} a^{3} c^{2} + 420 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - i \, B\right)} a^{3} c^{3}\right)}}{315 \, c^{3} f}"," ",0,"2/315*I*(35*I*(-I*c*tan(f*x + e) + c)^(9/2)*B*a^3 + 45*(-I*c*tan(f*x + e) + c)^(7/2)*(A - 5*I*B)*a^3*c - 252*(-I*c*tan(f*x + e) + c)^(5/2)*(A - 2*I*B)*a^3*c^2 + 420*(-I*c*tan(f*x + e) + c)^(3/2)*(A - I*B)*a^3*c^3)/(c^3*f)","A",0
759,1,104,0,0.762118," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","\frac{2 i \, {\left(15 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} B a^{3} + 21 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(A - 5 i \, B\right)} a^{3} c - 140 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - 2 i \, B\right)} a^{3} c^{2} + 420 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - i \, B\right)} a^{3} c^{3}\right)}}{105 \, c^{3} f}"," ",0,"2/105*I*(15*I*(-I*c*tan(f*x + e) + c)^(7/2)*B*a^3 + 21*(-I*c*tan(f*x + e) + c)^(5/2)*(A - 5*I*B)*a^3*c - 140*(-I*c*tan(f*x + e) + c)^(3/2)*(A - 2*I*B)*a^3*c^2 + 420*sqrt(-I*c*tan(f*x + e) + c)*(A - I*B)*a^3*c^3)/(c^3*f)","A",0
760,1,108,0,0.616791," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(\frac{60 \, {\left(A - i \, B\right)} a^{3} c}{\sqrt{-i \, c \tan\left(f x + e\right) + c}} - \frac{3 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} B a^{3} + 5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - 5 i \, B\right)} a^{3} c - 60 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - 2 i \, B\right)} a^{3} c^{2}}{c^{2}}\right)}}{15 \, c f}"," ",0,"-2/15*I*(60*(A - I*B)*a^3*c/sqrt(-I*c*tan(f*x + e) + c) - (3*I*(-I*c*tan(f*x + e) + c)^(5/2)*B*a^3 + 5*(-I*c*tan(f*x + e) + c)^(3/2)*(A - 5*I*B)*a^3*c - 60*sqrt(-I*c*tan(f*x + e) + c)*(A - 2*I*B)*a^3*c^2)/c^2)/(c*f)","A",0
761,1,105,0,0.604018," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{2 i \, {\left(\frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(A - 2 i \, B\right)} a^{3} - {\left(A - i \, B\right)} a^{3} c\right)}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}}} + \frac{i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} B a^{3} + 3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - 5 i \, B\right)} a^{3} c}{c^{2}}\right)}}{3 \, c f}"," ",0,"2/3*I*(4*(3*(-I*c*tan(f*x + e) + c)*(A - 2*I*B)*a^3 - (A - I*B)*a^3*c)/(-I*c*tan(f*x + e) + c)^(3/2) + (I*(-I*c*tan(f*x + e) + c)^(3/2)*B*a^3 + 3*sqrt(-I*c*tan(f*x + e) + c)*(A - 5*I*B)*a^3*c)/c^2)/(c*f)","A",0
762,1,107,0,0.724889," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(-\frac{15 i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} B a^{3}}{c^{2}} + \frac{15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(A - 5 i \, B\right)} a^{3} - 20 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(A - 2 i \, B\right)} a^{3} c + 12 \, {\left(A - i \, B\right)} a^{3} c^{2}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} c}\right)}}{15 \, c f}"," ",0,"-2/15*I*(-15*I*sqrt(-I*c*tan(f*x + e) + c)*B*a^3/c^2 + (15*(-I*c*tan(f*x + e) + c)^2*(A - 5*I*B)*a^3 - 20*(-I*c*tan(f*x + e) + c)*(A - 2*I*B)*a^3*c + 12*(A - I*B)*a^3*c^2)/((-I*c*tan(f*x + e) + c)^(5/2)*c))/(c*f)","A",0
763,1,102,0,0.426837," ","integrate((a+I*a*tan(f*x+e))^3*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{2 i \, {\left(105 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} B a^{3} + 35 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(A - 5 i \, B\right)} a^{3} c - 84 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(A - 2 i \, B\right)} a^{3} c^{2} + 60 \, {\left(A - i \, B\right)} a^{3} c^{3}\right)}}{105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{7}{2}} c^{3} f}"," ",0,"-2/105*I*(105*I*(-I*c*tan(f*x + e) + c)^3*B*a^3 + 35*(-I*c*tan(f*x + e) + c)^2*(A - 5*I*B)*a^3*c - 84*(-I*c*tan(f*x + e) + c)*(A - 2*I*B)*a^3*c^2 + 60*(A - I*B)*a^3*c^3)/((-I*c*tan(f*x + e) + c)^(7/2)*c^3*f)","A",0
764,1,190,0,0.661054," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{15 \, \sqrt{2} {\left(5 \, A + 9 i \, B\right)} c^{\frac{9}{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{60 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + i \, B\right)} c^{5}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)} a - 2 \, a c} + \frac{2 \, {\left(3 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} B c^{2} + 5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A + 3 i \, B\right)} c^{3} + 60 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + 2 i \, B\right)} c^{4}\right)}}{a}\right)}}{15 \, c f}"," ",0,"1/15*I*(15*sqrt(2)*(5*A + 9*I*B)*c^(9/2)*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 - 60*sqrt(-I*c*tan(f*x + e) + c)*(A + I*B)*c^5/((-I*c*tan(f*x + e) + c)*a - 2*a*c) + 2*(3*I*(-I*c*tan(f*x + e) + c)^(5/2)*B*c^2 + 5*(-I*c*tan(f*x + e) + c)^(3/2)*(A + 3*I*B)*c^3 + 60*sqrt(-I*c*tan(f*x + e) + c)*(A + 2*I*B)*c^4)/a)/(c*f)","A",0
765,1,167,0,0.615109," ","integrate((A+B*tan(f*x+e))*(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} {\left(3 \, A + 7 i \, B\right)} 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{12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + i \, B\right)} c^{4}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)} a - 2 \, a c} + \frac{4 \, {\left(i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} B c^{2} + 3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + 3 i \, B\right)} c^{3}\right)}}{a}\right)}}{6 \, c f}"," ",0,"1/6*I*(3*sqrt(2)*(3*A + 7*I*B)*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 - 12*sqrt(-I*c*tan(f*x + e) + c)*(A + I*B)*c^4/((-I*c*tan(f*x + e) + c)*a - 2*a*c) + 4*(I*(-I*c*tan(f*x + e) + c)^(3/2)*B*c^2 + 3*sqrt(-I*c*tan(f*x + e) + c)*(A + 3*I*B)*c^3)/a)/(c*f)","A",0
766,1,138,0,0.759636," ","integrate((A+B*tan(f*x+e))*(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} {\left(A + 5 i \, B\right)} 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} {\left(A + i \, B\right)} c^{3}}{{\left(-i \, c \tan\left(f x + e\right) + c\right)} a - 2 \, a c} + \frac{8 i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} B c^{2}}{a}\right)}}{4 \, c f}"," ",0,"1/4*I*(sqrt(2)*(A + 5*I*B)*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)*(A + I*B)*c^3/((-I*c*tan(f*x + e) + c)*a - 2*a*c) + 8*I*sqrt(-I*c*tan(f*x + e) + c)*B*c^2/a)/(c*f)","A",0
767,1,116,0,0.730101," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e)),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{\sqrt{2} {\left(A - 3 i \, B\right)} 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} {\left(A + i \, B\right)} 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)*(A - 3*I*B)*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)*(A + I*B)*c^2/((-I*c*tan(f*x + e) + c)*a - 2*a*c))/(c*f)","A",0
768,1,143,0,0.638947," ","integrate((A+B*tan(f*x+e))/(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} {\left(3 \, A - i \, B\right)} \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({\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(3 \, A - i \, B\right)} c - 4 \, {\left(A - i \, B\right)} 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*(sqrt(2)*(3*A - I*B)*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*((-I*c*tan(f*x + e) + c)*(3*A - I*B)*c - 4*(A - I*B)*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
769,1,167,0,0.711076," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{3 \, \sqrt{2} {\left(5 \, A + i \, B\right)} \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}} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(5 \, A + i \, B\right)} - 4 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(5 \, A + i \, B\right)} c - 8 \, {\left(A - i \, B\right)} 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}\right)}}{96 \, c f}"," ",0,"-1/96*I*(3*sqrt(2)*(5*A + I*B)*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)) + 4*(3*(-I*c*tan(f*x + e) + c)^2*(5*A + I*B) - 4*(-I*c*tan(f*x + e) + c)*(5*A + I*B)*c - 8*(A - I*B)*c^2)/((-I*c*tan(f*x + e) + c)^(5/2)*a - 2*(-I*c*tan(f*x + e) + c)^(3/2)*a*c))/(c*f)","A",0
770,1,195,0,0.720548," ","integrate((A+B*tan(f*x+e))/(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(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} {\left(7 \, A + 3 i \, B\right)} - 20 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(7 \, A + 3 i \, B\right)} c - 8 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(7 \, A + 3 i \, B\right)} c^{2} - 48 \, {\left(A - i \, B\right)} 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{15 \, \sqrt{2} {\left(7 \, A + 3 i \, B\right)} \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*(15*(-I*c*tan(f*x + e) + c)^3*(7*A + 3*I*B) - 20*(-I*c*tan(f*x + e) + c)^2*(7*A + 3*I*B)*c - 8*(-I*c*tan(f*x + e) + c)*(7*A + 3*I*B)*c^2 - 48*(A - I*B)*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) + 15*sqrt(2)*(7*A + 3*I*B)*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
771,1,244,0,0.670910," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{105 \, \sqrt{2} {\left(5 \, A + 13 i \, B\right)} c^{\frac{11}{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{60 \, {\left({\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(13 \, A + 21 i \, B\right)} c^{6} - 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(11 \, A + 19 i \, B\right)} c^{7}\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}} + \frac{8 \, {\left(3 i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} B c^{3} + 5 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A + 5 i \, B\right)} c^{4} + 90 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + 3 i \, B\right)} c^{5}\right)}}{a^{2}}\right)}}{60 \, c f}"," ",0,"-1/60*I*(105*sqrt(2)*(5*A + 13*I*B)*c^(11/2)*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 - 60*((-I*c*tan(f*x + e) + c)^(3/2)*(13*A + 21*I*B)*c^6 - 2*sqrt(-I*c*tan(f*x + e) + c)*(11*A + 19*I*B)*c^7)/((-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) + 8*(3*I*(-I*c*tan(f*x + e) + c)^(5/2)*B*c^3 + 5*(-I*c*tan(f*x + e) + c)^(3/2)*(A + 5*I*B)*c^4 + 90*sqrt(-I*c*tan(f*x + e) + c)*(A + 3*I*B)*c^5)/a^2)/(c*f)","A",0
772,1,221,0,0.938922," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{15 \, \sqrt{2} {\left(3 \, A + 11 i \, B\right)} c^{\frac{9}{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{12 \, {\left({\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(9 \, A + 17 i \, B\right)} c^{5} - 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(7 \, A + 15 i \, B\right)} c^{6}\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}} + \frac{16 \, {\left(i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} B c^{3} + 3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + 5 i \, B\right)} c^{4}\right)}}{a^{2}}\right)}}{24 \, c f}"," ",0,"-1/24*I*(15*sqrt(2)*(3*A + 11*I*B)*c^(9/2)*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 - 12*((-I*c*tan(f*x + e) + c)^(3/2)*(9*A + 17*I*B)*c^5 - 2*sqrt(-I*c*tan(f*x + e) + c)*(7*A + 15*I*B)*c^6)/((-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) + 16*(I*(-I*c*tan(f*x + e) + c)^(3/2)*B*c^3 + 3*sqrt(-I*c*tan(f*x + e) + c)*(A + 5*I*B)*c^4)/a^2)/(c*f)","A",0
773,1,193,0,0.547989," ","integrate((A+B*tan(f*x+e))*(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} {\left(A + 9 i \, B\right)} 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{32 i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} B c^{3}}{a^{2}} - \frac{4 \, {\left({\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(5 \, A + 13 i \, B\right)} c^{4} - 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(3 \, A + 11 i \, B\right)} 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)*(A + 9*I*B)*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 + 32*I*sqrt(-I*c*tan(f*x + e) + c)*B*c^3/a^2 - 4*((-I*c*tan(f*x + e) + c)^(3/2)*(5*A + 13*I*B)*c^4 - 2*sqrt(-I*c*tan(f*x + e) + c)*(3*A + 11*I*B)*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
774,1,166,0,1.012259," ","integrate((A+B*tan(f*x+e))*(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} {\left(A - 7 i \, B\right)} 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}} {\left(A + 9 i \, B\right)} c^{3} + 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - 7 i \, B\right)} 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)*(A - 7*I*B)*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)*(A + 9*I*B)*c^3 + 2*sqrt(-I*c*tan(f*x + e) + c)*(A - 7*I*B)*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
775,1,172,0,0.663991," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^2,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{\sqrt{2} {\left(3 \, A - 5 i \, B\right)} 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({\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(3 \, A - 5 i \, B\right)} c^{2} - 2 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(5 \, A - 3 i \, B\right)} 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*(sqrt(2)*(3*A - 5*I*B)*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*((-I*c*tan(f*x + e) + c)^(3/2)*(3*A - 5*I*B)*c^2 - 2*sqrt(-I*c*tan(f*x + e) + c)*(5*A - 3*I*B)*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
776,1,195,0,0.956254," ","integrate((A+B*tan(f*x+e))/(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} {\left(5 \, A - 3 i \, B\right)} \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}} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(5 \, A - 3 i \, B\right)} c - 10 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(5 \, A - 3 i \, B\right)} c^{2} + 32 \, {\left(A - i \, B\right)} 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}}\right)}}{128 \, c f}"," ",0,"-1/128*I*(3*sqrt(2)*(5*A - 3*I*B)*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 + 4*(3*(-I*c*tan(f*x + e) + c)^2*(5*A - 3*I*B)*c - 10*(-I*c*tan(f*x + e) + c)*(5*A - 3*I*B)*c^2 + 32*(A - I*B)*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))/(c*f)","A",0
777,1,217,0,0.882903," ","integrate((A+B*tan(f*x+e))/(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(15 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} {\left(7 \, A - i \, B\right)} - 50 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(7 \, A - i \, B\right)} c + 32 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(7 \, A - i \, B\right)} c^{2} + 64 \, {\left(A - i \, B\right)} 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{15 \, \sqrt{2} {\left(7 \, A - i \, B\right)} \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*(15*(-I*c*tan(f*x + e) + c)^3*(7*A - I*B) - 50*(-I*c*tan(f*x + e) + c)^2*(7*A - I*B)*c + 32*(-I*c*tan(f*x + e) + c)*(7*A - I*B)*c^2 + 64*(A - I*B)*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) + 15*sqrt(2)*(7*A - I*B)*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
778,1,245,0,0.966783," ","integrate((A+B*tan(f*x+e))/(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(105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} {\left(9 \, A + i \, B\right)} - 350 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} {\left(9 \, A + i \, B\right)} c + 224 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(9 \, A + i \, B\right)} c^{2} + 64 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(9 \, A + i \, B\right)} c^{3} + 384 \, {\left(A - i \, B\right)} 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{105 \, \sqrt{2} {\left(9 \, A + i \, B\right)} \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)}}{7680 \, c f}"," ",0,"-1/7680*I*(4*(105*(-I*c*tan(f*x + e) + c)^4*(9*A + I*B) - 350*(-I*c*tan(f*x + e) + c)^3*(9*A + I*B)*c + 224*(-I*c*tan(f*x + e) + c)^2*(9*A + I*B)*c^2 + 64*(-I*c*tan(f*x + e) + c)*(9*A + I*B)*c^3 + 384*(A - I*B)*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) + 105*sqrt(2)*(9*A + I*B)*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
779,1,266,0,0.558453," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{i \, {\left(\frac{105 \, \sqrt{2} {\left(A + 5 i \, B\right)} c^{\frac{11}{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}} {\left(29 \, A + 81 i \, B\right)} c^{6} - 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(17 \, A + 53 i \, B\right)} c^{7} + 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(19 \, A + 63 i \, B\right)} c^{8}\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{32 \, {\left(i \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} B c^{4} + 3 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A + 7 i \, B\right)} c^{5}\right)}}{a^{3}}\right)}}{48 \, c f}"," ",0,"1/48*I*(105*sqrt(2)*(A + 5*I*B)*c^(11/2)*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)*(29*A + 81*I*B)*c^6 - 16*(-I*c*tan(f*x + e) + c)^(3/2)*(17*A + 53*I*B)*c^7 + 12*sqrt(-I*c*tan(f*x + e) + c)*(19*A + 63*I*B)*c^8)/((-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) + 32*(I*(-I*c*tan(f*x + e) + c)^(3/2)*B*c^4 + 3*sqrt(-I*c*tan(f*x + e) + c)*(A + 7*I*B)*c^5)/a^3)/(c*f)","A",0
780,1,240,0,0.951003," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","\frac{i \, {\left(\frac{15 \, \sqrt{2} {\left(A + 13 i \, B\right)} c^{\frac{9}{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{192 i \, \sqrt{-i \, c \tan\left(f x + e\right) + c} B c^{4}}{a^{3}} - \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(11 \, A + 47 i \, B\right)} c^{5} - 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(5 \, A + 29 i \, B\right)} c^{6} + 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(5 \, A + 33 i \, B\right)} c^{7}\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)}}{96 \, c f}"," ",0,"1/96*I*(15*sqrt(2)*(A + 13*I*B)*c^(9/2)*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 + 192*I*sqrt(-I*c*tan(f*x + e) + c)*B*c^4/a^3 - 4*(3*(-I*c*tan(f*x + e) + c)^(5/2)*(11*A + 47*I*B)*c^5 - 16*(-I*c*tan(f*x + e) + c)^(3/2)*(5*A + 29*I*B)*c^6 + 12*sqrt(-I*c*tan(f*x + e) + c)*(5*A + 33*I*B)*c^7)/((-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
781,1,212,0,0.943894," ","integrate((A+B*tan(f*x+e))*(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} {\left(A - 11 i \, B\right)} 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}} {\left(A + 21 i \, B\right)} c^{4} + 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A - 11 i \, B\right)} c^{5} - 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - 11 i \, B\right)} 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)*(A - 11*I*B)*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)*(A + 21*I*B)*c^4 + 16*(-I*c*tan(f*x + e) + c)^(3/2)*(A - 11*I*B)*c^5 - 12*sqrt(-I*c*tan(f*x + e) + c)*(A - 11*I*B)*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
782,1,212,0,1.115092," ","integrate((A+B*tan(f*x+e))*(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} {\left(A - 3 i \, B\right)} 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}} {\left(A - 3 i \, B\right)} c^{3} - 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(A + i \, B\right)} c^{4} - 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(A - 3 i \, B\right)} 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)*(A - 3*I*B)*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)*(A - 3*I*B)*c^3 - 16*(-I*c*tan(f*x + e) + c)^(3/2)*(A + I*B)*c^4 - 12*sqrt(-I*c*tan(f*x + e) + c)*(A - 3*I*B)*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
783,1,220,0,0.622768," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^3,x, algorithm=""maxima"")","-\frac{i \, {\left(\frac{3 \, \sqrt{2} {\left(5 \, A - 7 i \, B\right)} 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}} + \frac{4 \, {\left(3 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(5 \, A - 7 i \, B\right)} c^{2} - 16 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(5 \, A - 7 i \, B\right)} c^{3} + 12 \, \sqrt{-i \, c \tan\left(f x + e\right) + c} {\left(11 \, A - 9 i \, B\right)} 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}}\right)}}{768 \, c f}"," ",0,"-1/768*I*(3*sqrt(2)*(5*A - 7*I*B)*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 + 4*(3*(-I*c*tan(f*x + e) + c)^(5/2)*(5*A - 7*I*B)*c^2 - 16*(-I*c*tan(f*x + e) + c)^(3/2)*(5*A - 7*I*B)*c^3 + 12*sqrt(-I*c*tan(f*x + e) + c)*(11*A - 9*I*B)*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))/(c*f)","A",0
784,1,241,0,0.644656," ","integrate((A+B*tan(f*x+e))/(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)}^{3} {\left(7 \, A - 5 i \, B\right)} c - 80 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(7 \, A - 5 i \, B\right)} c^{2} + 132 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(7 \, A - 5 i \, B\right)} c^{3} - 384 \, {\left(A - i \, B\right)} 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{15 \, \sqrt{2} {\left(7 \, A - 5 i \, B\right)} \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*(15*(-I*c*tan(f*x + e) + c)^3*(7*A - 5*I*B)*c - 80*(-I*c*tan(f*x + e) + c)^2*(7*A - 5*I*B)*c^2 + 132*(-I*c*tan(f*x + e) + c)*(7*A - 5*I*B)*c^3 - 384*(A - I*B)*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) + 15*sqrt(2)*(7*A - 5*I*B)*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
785,1,263,0,0.679101," ","integrate((A+B*tan(f*x+e))/(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(105 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} {\left(3 \, A - i \, B\right)} - 560 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} {\left(3 \, A - i \, B\right)} c + 924 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(3 \, A - i \, B\right)} c^{2} - 384 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(3 \, A - i \, B\right)} c^{3} - 256 \, {\left(A - i \, B\right)} 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{105 \, \sqrt{2} {\left(3 \, A - i \, B\right)} \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*(105*(-I*c*tan(f*x + e) + c)^4*(3*A - I*B) - 560*(-I*c*tan(f*x + e) + c)^3*(3*A - I*B)*c + 924*(-I*c*tan(f*x + e) + c)^2*(3*A - I*B)*c^2 - 384*(-I*c*tan(f*x + e) + c)*(3*A - I*B)*c^3 - 256*(A - I*B)*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) + 105*sqrt(2)*(3*A - I*B)*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
786,1,291,0,0.620627," ","integrate((A+B*tan(f*x+e))/(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(315 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{5} {\left(11 \, A - i \, B\right)} - 1680 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{4} {\left(11 \, A - i \, B\right)} c + 2772 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{3} {\left(11 \, A - i \, B\right)} c^{2} - 1152 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)}^{2} {\left(11 \, A - i \, B\right)} c^{3} - 256 \, {\left(-i \, c \tan\left(f x + e\right) + c\right)} {\left(11 \, A - i \, B\right)} c^{4} - 1536 \, {\left(A - i \, B\right)} 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{315 \, \sqrt{2} {\left(11 \, A - i \, B\right)} \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*(315*(-I*c*tan(f*x + e) + c)^5*(11*A - I*B) - 1680*(-I*c*tan(f*x + e) + c)^4*(11*A - I*B)*c + 2772*(-I*c*tan(f*x + e) + c)^3*(11*A - I*B)*c^2 - 1152*(-I*c*tan(f*x + e) + c)^2*(11*A - I*B)*c^3 - 256*(-I*c*tan(f*x + e) + c)*(11*A - I*B)*c^4 - 1536*(A - I*B)*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) + 315*sqrt(2)*(11*A - I*B)*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
787,1,1342,0,2.889905," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(5760 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \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) + 21120 \, {\left(4 \, A + 3 i \, B\right)} c^{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) + 28032 \, {\left(4 \, A + 3 i \, B\right)} c^{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) + 1152 \, {\left(44 \, A + 49 i \, B\right)} c^{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) - {\left(-23040 i \, A + 17280 \, B\right)} c^{3} \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) - {\left(-84480 i \, A + 63360 \, B\right)} c^{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) - {\left(-112128 i \, A + 84096 \, B\right)} c^{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(-50688 i \, A + 56448 \, B\right)} c^{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) + {\left(2880 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 11520 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 17280 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 11520 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-11520 i \, A + 8640 \, B\right)} c^{3} \sin\left(8 \, f x + 8 \, e\right) - {\left(-46080 i \, A + 34560 \, B\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-69120 i \, A + 51840 \, B\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-46080 i \, A + 34560 \, B\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 2880 \, {\left(4 \, A + 3 i \, B\right)} c^{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(2880 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 11520 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 17280 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 11520 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-11520 i \, A + 8640 \, B\right)} c^{3} \sin\left(8 \, f x + 8 \, e\right) - {\left(-46080 i \, A + 34560 \, B\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-69120 i \, A + 51840 \, B\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-46080 i \, A + 34560 \, B\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 2880 \, {\left(4 \, A + 3 i \, B\right)} c^{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({\left(-5760 i \, A + 4320 \, B\right)} c^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(-23040 i \, A + 17280 \, B\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(-34560 i \, A + 25920 \, B\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-23040 i \, A + 17280 \, B\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 1440 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 5760 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 8640 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 5760 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-5760 i \, A + 4320 \, B\right)} c^{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({\left(5760 i \, A - 4320 \, B\right)} c^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(23040 i \, A - 17280 \, B\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(34560 i \, A - 25920 \, B\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(23040 i \, A - 17280 \, B\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) - 1440 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(8 \, f x + 8 \, e\right) - 5760 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right) - 8640 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) - 5760 \, {\left(4 \, A + 3 i \, B\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(5760 i \, A - 4320 \, B\right)} c^{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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-4608 i \, \cos\left(8 \, f x + 8 \, e\right) - 18432 i \, \cos\left(6 \, f x + 6 \, e\right) - 27648 i \, \cos\left(4 \, f x + 4 \, e\right) - 18432 i \, \cos\left(2 \, f x + 2 \, e\right) + 4608 \, \sin\left(8 \, f x + 8 \, e\right) + 18432 \, \sin\left(6 \, f x + 6 \, e\right) + 27648 \, \sin\left(4 \, f x + 4 \, e\right) + 18432 \, \sin\left(2 \, f x + 2 \, e\right) - 4608 i\right)}}"," ",0,"-(5760*(4*A + 3*I*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 21120*(4*A + 3*I*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 28032*(4*A + 3*I*B)*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1152*(44*A + 49*I*B)*c^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-23040*I*A + 17280*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-84480*I*A + 63360*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-112128*I*A + 84096*B)*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-50688*I*A + 56448*B)*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (2880*(4*A + 3*I*B)*c^3*cos(8*f*x + 8*e) + 11520*(4*A + 3*I*B)*c^3*cos(6*f*x + 6*e) + 17280*(4*A + 3*I*B)*c^3*cos(4*f*x + 4*e) + 11520*(4*A + 3*I*B)*c^3*cos(2*f*x + 2*e) - (-11520*I*A + 8640*B)*c^3*sin(8*f*x + 8*e) - (-46080*I*A + 34560*B)*c^3*sin(6*f*x + 6*e) - (-69120*I*A + 51840*B)*c^3*sin(4*f*x + 4*e) - (-46080*I*A + 34560*B)*c^3*sin(2*f*x + 2*e) + 2880*(4*A + 3*I*B)*c^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) + (2880*(4*A + 3*I*B)*c^3*cos(8*f*x + 8*e) + 11520*(4*A + 3*I*B)*c^3*cos(6*f*x + 6*e) + 17280*(4*A + 3*I*B)*c^3*cos(4*f*x + 4*e) + 11520*(4*A + 3*I*B)*c^3*cos(2*f*x + 2*e) - (-11520*I*A + 8640*B)*c^3*sin(8*f*x + 8*e) - (-46080*I*A + 34560*B)*c^3*sin(6*f*x + 6*e) - (-69120*I*A + 51840*B)*c^3*sin(4*f*x + 4*e) - (-46080*I*A + 34560*B)*c^3*sin(2*f*x + 2*e) + 2880*(4*A + 3*I*B)*c^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) - ((-5760*I*A + 4320*B)*c^3*cos(8*f*x + 8*e) + (-23040*I*A + 17280*B)*c^3*cos(6*f*x + 6*e) + (-34560*I*A + 25920*B)*c^3*cos(4*f*x + 4*e) + (-23040*I*A + 17280*B)*c^3*cos(2*f*x + 2*e) + 1440*(4*A + 3*I*B)*c^3*sin(8*f*x + 8*e) + 5760*(4*A + 3*I*B)*c^3*sin(6*f*x + 6*e) + 8640*(4*A + 3*I*B)*c^3*sin(4*f*x + 4*e) + 5760*(4*A + 3*I*B)*c^3*sin(2*f*x + 2*e) + (-5760*I*A + 4320*B)*c^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) - ((5760*I*A - 4320*B)*c^3*cos(8*f*x + 8*e) + (23040*I*A - 17280*B)*c^3*cos(6*f*x + 6*e) + (34560*I*A - 25920*B)*c^3*cos(4*f*x + 4*e) + (23040*I*A - 17280*B)*c^3*cos(2*f*x + 2*e) - 1440*(4*A + 3*I*B)*c^3*sin(8*f*x + 8*e) - 5760*(4*A + 3*I*B)*c^3*sin(6*f*x + 6*e) - 8640*(4*A + 3*I*B)*c^3*sin(4*f*x + 4*e) - 5760*(4*A + 3*I*B)*c^3*sin(2*f*x + 2*e) + (5760*I*A - 4320*B)*c^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))*sqrt(a)*sqrt(c)/(f*(-4608*I*cos(8*f*x + 8*e) - 18432*I*cos(6*f*x + 6*e) - 27648*I*cos(4*f*x + 4*e) - 18432*I*cos(2*f*x + 2*e) + 4608*sin(8*f*x + 8*e) + 18432*sin(6*f*x + 6*e) + 27648*sin(4*f*x + 4*e) + 18432*sin(2*f*x + 2*e) - 4608*I))","B",0
788,1,1086,0,1.382725," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(72 \, {\left(3 \, A + 2 i \, B\right)} 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) + 192 \, {\left(3 \, A + 2 i \, B\right)} 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) + 72 \, {\left(5 \, A + 6 i \, B\right)} 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) - {\left(-216 i \, A + 144 \, B\right)} 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) - {\left(-576 i \, A + 384 \, B\right)} 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) - {\left(-360 i \, A + 432 \, B\right)} 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(36 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 108 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 108 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-108 i \, A + 72 \, B\right)} c^{2} \sin\left(6 \, f x + 6 \, e\right) - {\left(-324 i \, A + 216 \, B\right)} c^{2} \sin\left(4 \, f x + 4 \, e\right) - {\left(-324 i \, A + 216 \, B\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 36 \, {\left(3 \, A + 2 i \, B\right)} 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(36 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 108 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 108 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-108 i \, A + 72 \, B\right)} c^{2} \sin\left(6 \, f x + 6 \, e\right) - {\left(-324 i \, A + 216 \, B\right)} c^{2} \sin\left(4 \, f x + 4 \, e\right) - {\left(-324 i \, A + 216 \, B\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 36 \, {\left(3 \, A + 2 i \, B\right)} 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({\left(-54 i \, A + 36 \, B\right)} c^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(-162 i \, A + 108 \, B\right)} c^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-162 i \, A + 108 \, B\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 54 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 54 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-54 i \, A + 36 \, B\right)} 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({\left(54 i \, A - 36 \, B\right)} c^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(162 i \, A - 108 \, B\right)} c^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(162 i \, A - 108 \, B\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) - 18 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \sin\left(6 \, f x + 6 \, e\right) - 54 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \sin\left(4 \, f x + 4 \, e\right) - 54 \, {\left(3 \, A + 2 i \, B\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(54 i \, A - 36 \, B\right)} 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(-72 i \, \cos\left(6 \, f x + 6 \, e\right) - 216 i \, \cos\left(4 \, f x + 4 \, e\right) - 216 i \, \cos\left(2 \, f x + 2 \, e\right) + 72 \, \sin\left(6 \, f x + 6 \, e\right) + 216 \, \sin\left(4 \, f x + 4 \, e\right) + 216 \, \sin\left(2 \, f x + 2 \, e\right) - 72 i\right)}}"," ",0,"-(72*(3*A + 2*I*B)*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 192*(3*A + 2*I*B)*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 72*(5*A + 6*I*B)*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-216*I*A + 144*B)*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-576*I*A + 384*B)*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-360*I*A + 432*B)*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (36*(3*A + 2*I*B)*c^2*cos(6*f*x + 6*e) + 108*(3*A + 2*I*B)*c^2*cos(4*f*x + 4*e) + 108*(3*A + 2*I*B)*c^2*cos(2*f*x + 2*e) - (-108*I*A + 72*B)*c^2*sin(6*f*x + 6*e) - (-324*I*A + 216*B)*c^2*sin(4*f*x + 4*e) - (-324*I*A + 216*B)*c^2*sin(2*f*x + 2*e) + 36*(3*A + 2*I*B)*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) + (36*(3*A + 2*I*B)*c^2*cos(6*f*x + 6*e) + 108*(3*A + 2*I*B)*c^2*cos(4*f*x + 4*e) + 108*(3*A + 2*I*B)*c^2*cos(2*f*x + 2*e) - (-108*I*A + 72*B)*c^2*sin(6*f*x + 6*e) - (-324*I*A + 216*B)*c^2*sin(4*f*x + 4*e) - (-324*I*A + 216*B)*c^2*sin(2*f*x + 2*e) + 36*(3*A + 2*I*B)*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) - ((-54*I*A + 36*B)*c^2*cos(6*f*x + 6*e) + (-162*I*A + 108*B)*c^2*cos(4*f*x + 4*e) + (-162*I*A + 108*B)*c^2*cos(2*f*x + 2*e) + 18*(3*A + 2*I*B)*c^2*sin(6*f*x + 6*e) + 54*(3*A + 2*I*B)*c^2*sin(4*f*x + 4*e) + 54*(3*A + 2*I*B)*c^2*sin(2*f*x + 2*e) + (-54*I*A + 36*B)*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) - ((54*I*A - 36*B)*c^2*cos(6*f*x + 6*e) + (162*I*A - 108*B)*c^2*cos(4*f*x + 4*e) + (162*I*A - 108*B)*c^2*cos(2*f*x + 2*e) - 18*(3*A + 2*I*B)*c^2*sin(6*f*x + 6*e) - 54*(3*A + 2*I*B)*c^2*sin(4*f*x + 4*e) - 54*(3*A + 2*I*B)*c^2*sin(2*f*x + 2*e) + (54*I*A - 36*B)*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*(-72*I*cos(6*f*x + 6*e) - 216*I*cos(4*f*x + 4*e) - 216*I*cos(2*f*x + 2*e) + 72*sin(6*f*x + 6*e) + 216*sin(4*f*x + 4*e) + 216*sin(2*f*x + 2*e) - 72*I))","B",0
789,1,782,0,1.027157," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(16 \, {\left(2 \, A + i \, B\right)} 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) + 16 \, {\left(2 \, A + 3 i \, B\right)} 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) - {\left(-32 i \, A + 16 \, B\right)} 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) - {\left(-32 i \, A + 48 \, B\right)} 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(8 \, {\left(2 \, A + i \, B\right)} c \cos\left(4 \, f x + 4 \, e\right) + 16 \, {\left(2 \, A + i \, B\right)} c \cos\left(2 \, f x + 2 \, e\right) - {\left(-16 i \, A + 8 \, B\right)} c \sin\left(4 \, f x + 4 \, e\right) - {\left(-32 i \, A + 16 \, B\right)} c \sin\left(2 \, f x + 2 \, e\right) + 8 \, {\left(2 \, A + i \, B\right)} 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(8 \, {\left(2 \, A + i \, B\right)} c \cos\left(4 \, f x + 4 \, e\right) + 16 \, {\left(2 \, A + i \, B\right)} c \cos\left(2 \, f x + 2 \, e\right) - {\left(-16 i \, A + 8 \, B\right)} c \sin\left(4 \, f x + 4 \, e\right) - {\left(-32 i \, A + 16 \, B\right)} c \sin\left(2 \, f x + 2 \, e\right) + 8 \, {\left(2 \, A + i \, B\right)} 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({\left(-8 i \, A + 4 \, B\right)} c \cos\left(4 \, f x + 4 \, e\right) + {\left(-16 i \, A + 8 \, B\right)} c \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(2 \, A + i \, B\right)} c \sin\left(4 \, f x + 4 \, e\right) + 8 \, {\left(2 \, A + i \, B\right)} c \sin\left(2 \, f x + 2 \, e\right) + {\left(-8 i \, A + 4 \, B\right)} 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({\left(8 i \, A - 4 \, B\right)} c \cos\left(4 \, f x + 4 \, e\right) + {\left(16 i \, A - 8 \, B\right)} c \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(2 \, A + i \, B\right)} c \sin\left(4 \, f x + 4 \, e\right) - 8 \, {\left(2 \, A + i \, B\right)} c \sin\left(2 \, f x + 2 \, e\right) + {\left(8 i \, A - 4 \, B\right)} 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(-16 i \, \cos\left(4 \, f x + 4 \, e\right) - 32 i \, \cos\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(4 \, f x + 4 \, e\right) + 32 \, \sin\left(2 \, f x + 2 \, e\right) - 16 i\right)}}"," ",0,"-(16*(2*A + I*B)*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*(2*A + 3*I*B)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-32*I*A + 16*B)*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-32*I*A + 48*B)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (8*(2*A + I*B)*c*cos(4*f*x + 4*e) + 16*(2*A + I*B)*c*cos(2*f*x + 2*e) - (-16*I*A + 8*B)*c*sin(4*f*x + 4*e) - (-32*I*A + 16*B)*c*sin(2*f*x + 2*e) + 8*(2*A + I*B)*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) + (8*(2*A + I*B)*c*cos(4*f*x + 4*e) + 16*(2*A + I*B)*c*cos(2*f*x + 2*e) - (-16*I*A + 8*B)*c*sin(4*f*x + 4*e) - (-32*I*A + 16*B)*c*sin(2*f*x + 2*e) + 8*(2*A + I*B)*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) - ((-8*I*A + 4*B)*c*cos(4*f*x + 4*e) + (-16*I*A + 8*B)*c*cos(2*f*x + 2*e) + 4*(2*A + I*B)*c*sin(4*f*x + 4*e) + 8*(2*A + I*B)*c*sin(2*f*x + 2*e) + (-8*I*A + 4*B)*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) - ((8*I*A - 4*B)*c*cos(4*f*x + 4*e) + (16*I*A - 8*B)*c*cos(2*f*x + 2*e) - 4*(2*A + I*B)*c*sin(4*f*x + 4*e) - 8*(2*A + I*B)*c*sin(2*f*x + 2*e) + (8*I*A - 4*B)*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*(-16*I*cos(4*f*x + 4*e) - 32*I*cos(2*f*x + 2*e) + 16*sin(4*f*x + 4*e) + 32*sin(2*f*x + 2*e) - 16*I))","B",0
790,1,447,0,1.169944," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e)),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 i \, B \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 \, B \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*I*B*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*B*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
791,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),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((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(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
793,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(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
794,-2,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(c-I*c*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
795,1,1652,0,5.936386," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(28800 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 134400 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \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) + 245760 \, {\left(5 \, A + 2 i \, B\right)} a c^{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) + 19200 \, {\left(29 \, A + 50 i \, B\right)} a c^{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) - 28800 \, {\left(5 \, A + 2 i \, B\right)} a c^{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) - {\left(-144000 i \, A + 57600 \, B\right)} a c^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-672000 i \, A + 268800 \, B\right)} a c^{3} \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) - {\left(-1228800 i \, A + 491520 \, B\right)} a c^{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) - {\left(-556800 i \, A + 960000 \, B\right)} a c^{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(144000 i \, A - 57600 \, B\right)} a c^{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) + {\left(14400 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(10 \, f x + 10 \, e\right) + 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(8 \, f x + 8 \, e\right) + 144000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(6 \, f x + 6 \, e\right) + 144000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-72000 i \, A + 28800 \, B\right)} a c^{3} \sin\left(10 \, f x + 10 \, e\right) - {\left(-360000 i \, A + 144000 \, B\right)} a c^{3} \sin\left(8 \, f x + 8 \, e\right) - {\left(-720000 i \, A + 288000 \, B\right)} a c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-720000 i \, A + 288000 \, B\right)} a c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-360000 i \, A + 144000 \, B\right)} a c^{3} \sin\left(2 \, f x + 2 \, e\right) + 14400 \, {\left(5 \, A + 2 i \, B\right)} a c^{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(14400 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(10 \, f x + 10 \, e\right) + 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(8 \, f x + 8 \, e\right) + 144000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(6 \, f x + 6 \, e\right) + 144000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(4 \, f x + 4 \, e\right) + 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-72000 i \, A + 28800 \, B\right)} a c^{3} \sin\left(10 \, f x + 10 \, e\right) - {\left(-360000 i \, A + 144000 \, B\right)} a c^{3} \sin\left(8 \, f x + 8 \, e\right) - {\left(-720000 i \, A + 288000 \, B\right)} a c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-720000 i \, A + 288000 \, B\right)} a c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-360000 i \, A + 144000 \, B\right)} a c^{3} \sin\left(2 \, f x + 2 \, e\right) + 14400 \, {\left(5 \, A + 2 i \, B\right)} a c^{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({\left(-36000 i \, A + 14400 \, B\right)} a c^{3} \cos\left(10 \, f x + 10 \, e\right) + {\left(-180000 i \, A + 72000 \, B\right)} a c^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(-360000 i \, A + 144000 \, B\right)} a c^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(-360000 i \, A + 144000 \, B\right)} a c^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-180000 i \, A + 72000 \, B\right)} a c^{3} \cos\left(2 \, f x + 2 \, e\right) + 7200 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(10 \, f x + 10 \, e\right) + 36000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(8 \, f x + 8 \, e\right) + 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(6 \, f x + 6 \, e\right) + 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(4 \, f x + 4 \, e\right) + 36000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-36000 i \, A + 14400 \, B\right)} a c^{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({\left(36000 i \, A - 14400 \, B\right)} a c^{3} \cos\left(10 \, f x + 10 \, e\right) + {\left(180000 i \, A - 72000 \, B\right)} a c^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(360000 i \, A - 144000 \, B\right)} a c^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(360000 i \, A - 144000 \, B\right)} a c^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(180000 i \, A - 72000 \, B\right)} a c^{3} \cos\left(2 \, f x + 2 \, e\right) - 7200 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(10 \, f x + 10 \, e\right) - 36000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(8 \, f x + 8 \, e\right) - 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(6 \, f x + 6 \, e\right) - 72000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(4 \, f x + 4 \, e\right) - 36000 \, {\left(5 \, A + 2 i \, B\right)} a c^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(36000 i \, A - 14400 \, B\right)} a c^{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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-115200 i \, \cos\left(10 \, f x + 10 \, e\right) - 576000 i \, \cos\left(8 \, f x + 8 \, e\right) - 1152000 i \, \cos\left(6 \, f x + 6 \, e\right) - 1152000 i \, \cos\left(4 \, f x + 4 \, e\right) - 576000 i \, \cos\left(2 \, f x + 2 \, e\right) + 115200 \, \sin\left(10 \, f x + 10 \, e\right) + 576000 \, \sin\left(8 \, f x + 8 \, e\right) + 1152000 \, \sin\left(6 \, f x + 6 \, e\right) + 1152000 \, \sin\left(4 \, f x + 4 \, e\right) + 576000 \, \sin\left(2 \, f x + 2 \, e\right) - 115200 i\right)}}"," ",0,"-(28800*(5*A + 2*I*B)*a*c^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 134400*(5*A + 2*I*B)*a*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 245760*(5*A + 2*I*B)*a*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 19200*(29*A + 50*I*B)*a*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 28800*(5*A + 2*I*B)*a*c^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-144000*I*A + 57600*B)*a*c^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-672000*I*A + 268800*B)*a*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1228800*I*A + 491520*B)*a*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-556800*I*A + 960000*B)*a*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (144000*I*A - 57600*B)*a*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (14400*(5*A + 2*I*B)*a*c^3*cos(10*f*x + 10*e) + 72000*(5*A + 2*I*B)*a*c^3*cos(8*f*x + 8*e) + 144000*(5*A + 2*I*B)*a*c^3*cos(6*f*x + 6*e) + 144000*(5*A + 2*I*B)*a*c^3*cos(4*f*x + 4*e) + 72000*(5*A + 2*I*B)*a*c^3*cos(2*f*x + 2*e) - (-72000*I*A + 28800*B)*a*c^3*sin(10*f*x + 10*e) - (-360000*I*A + 144000*B)*a*c^3*sin(8*f*x + 8*e) - (-720000*I*A + 288000*B)*a*c^3*sin(6*f*x + 6*e) - (-720000*I*A + 288000*B)*a*c^3*sin(4*f*x + 4*e) - (-360000*I*A + 144000*B)*a*c^3*sin(2*f*x + 2*e) + 14400*(5*A + 2*I*B)*a*c^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) + (14400*(5*A + 2*I*B)*a*c^3*cos(10*f*x + 10*e) + 72000*(5*A + 2*I*B)*a*c^3*cos(8*f*x + 8*e) + 144000*(5*A + 2*I*B)*a*c^3*cos(6*f*x + 6*e) + 144000*(5*A + 2*I*B)*a*c^3*cos(4*f*x + 4*e) + 72000*(5*A + 2*I*B)*a*c^3*cos(2*f*x + 2*e) - (-72000*I*A + 28800*B)*a*c^3*sin(10*f*x + 10*e) - (-360000*I*A + 144000*B)*a*c^3*sin(8*f*x + 8*e) - (-720000*I*A + 288000*B)*a*c^3*sin(6*f*x + 6*e) - (-720000*I*A + 288000*B)*a*c^3*sin(4*f*x + 4*e) - (-360000*I*A + 144000*B)*a*c^3*sin(2*f*x + 2*e) + 14400*(5*A + 2*I*B)*a*c^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) - ((-36000*I*A + 14400*B)*a*c^3*cos(10*f*x + 10*e) + (-180000*I*A + 72000*B)*a*c^3*cos(8*f*x + 8*e) + (-360000*I*A + 144000*B)*a*c^3*cos(6*f*x + 6*e) + (-360000*I*A + 144000*B)*a*c^3*cos(4*f*x + 4*e) + (-180000*I*A + 72000*B)*a*c^3*cos(2*f*x + 2*e) + 7200*(5*A + 2*I*B)*a*c^3*sin(10*f*x + 10*e) + 36000*(5*A + 2*I*B)*a*c^3*sin(8*f*x + 8*e) + 72000*(5*A + 2*I*B)*a*c^3*sin(6*f*x + 6*e) + 72000*(5*A + 2*I*B)*a*c^3*sin(4*f*x + 4*e) + 36000*(5*A + 2*I*B)*a*c^3*sin(2*f*x + 2*e) + (-36000*I*A + 14400*B)*a*c^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) - ((36000*I*A - 14400*B)*a*c^3*cos(10*f*x + 10*e) + (180000*I*A - 72000*B)*a*c^3*cos(8*f*x + 8*e) + (360000*I*A - 144000*B)*a*c^3*cos(6*f*x + 6*e) + (360000*I*A - 144000*B)*a*c^3*cos(4*f*x + 4*e) + (180000*I*A - 72000*B)*a*c^3*cos(2*f*x + 2*e) - 7200*(5*A + 2*I*B)*a*c^3*sin(10*f*x + 10*e) - 36000*(5*A + 2*I*B)*a*c^3*sin(8*f*x + 8*e) - 72000*(5*A + 2*I*B)*a*c^3*sin(6*f*x + 6*e) - 72000*(5*A + 2*I*B)*a*c^3*sin(4*f*x + 4*e) - 36000*(5*A + 2*I*B)*a*c^3*sin(2*f*x + 2*e) + (36000*I*A - 14400*B)*a*c^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))*sqrt(a)*sqrt(c)/(f*(-115200*I*cos(10*f*x + 10*e) - 576000*I*cos(8*f*x + 8*e) - 1152000*I*cos(6*f*x + 6*e) - 1152000*I*cos(4*f*x + 4*e) - 576000*I*cos(2*f*x + 2*e) + 115200*sin(10*f*x + 10*e) + 576000*sin(8*f*x + 8*e) + 1152000*sin(6*f*x + 6*e) + 1152000*sin(4*f*x + 4*e) + 576000*sin(2*f*x + 2*e) - 115200*I))","B",0
796,1,1386,0,2.550950," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(1152 \, {\left(4 \, A + i \, B\right)} a 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) + 4224 \, {\left(4 \, A + i \, B\right)} 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) + 384 \, {\left(20 \, A + 53 i \, B\right)} 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) - 1152 \, {\left(4 \, A + i \, B\right)} 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) - {\left(-4608 i \, A + 1152 \, B\right)} a 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) - {\left(-16896 i \, A + 4224 \, B\right)} 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) - {\left(-7680 i \, A + 20352 \, B\right)} 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) - {\left(4608 i \, A - 1152 \, B\right)} 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(576 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(8 \, f x + 8 \, e\right) + 2304 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 3456 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2304 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2304 i \, A + 576 \, B\right)} a c^{2} \sin\left(8 \, f x + 8 \, e\right) - {\left(-9216 i \, A + 2304 \, B\right)} a c^{2} \sin\left(6 \, f x + 6 \, e\right) - {\left(-13824 i \, A + 3456 \, B\right)} a c^{2} \sin\left(4 \, f x + 4 \, e\right) - {\left(-9216 i \, A + 2304 \, B\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 576 \, {\left(4 \, A + i \, B\right)} 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(576 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(8 \, f x + 8 \, e\right) + 2304 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(6 \, f x + 6 \, e\right) + 3456 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(4 \, f x + 4 \, e\right) + 2304 \, {\left(4 \, A + i \, B\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-2304 i \, A + 576 \, B\right)} a c^{2} \sin\left(8 \, f x + 8 \, e\right) - {\left(-9216 i \, A + 2304 \, B\right)} a c^{2} \sin\left(6 \, f x + 6 \, e\right) - {\left(-13824 i \, A + 3456 \, B\right)} a c^{2} \sin\left(4 \, f x + 4 \, e\right) - {\left(-9216 i \, A + 2304 \, B\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right) + 576 \, {\left(4 \, A + i \, B\right)} 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({\left(-1152 i \, A + 288 \, B\right)} a c^{2} \cos\left(8 \, f x + 8 \, e\right) + {\left(-4608 i \, A + 1152 \, B\right)} a c^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(-6912 i \, A + 1728 \, B\right)} a c^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-4608 i \, A + 1152 \, B\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) + 288 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(8 \, f x + 8 \, e\right) + 1152 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(6 \, f x + 6 \, e\right) + 1728 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(4 \, f x + 4 \, e\right) + 1152 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-1152 i \, A + 288 \, B\right)} 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({\left(1152 i \, A - 288 \, B\right)} a c^{2} \cos\left(8 \, f x + 8 \, e\right) + {\left(4608 i \, A - 1152 \, B\right)} a c^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(6912 i \, A - 1728 \, B\right)} a c^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(4608 i \, A - 1152 \, B\right)} a c^{2} \cos\left(2 \, f x + 2 \, e\right) - 288 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(8 \, f x + 8 \, e\right) - 1152 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(6 \, f x + 6 \, e\right) - 1728 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(4 \, f x + 4 \, e\right) - 1152 \, {\left(4 \, A + i \, B\right)} a c^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(1152 i \, A - 288 \, B\right)} 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(-4608 i \, \cos\left(8 \, f x + 8 \, e\right) - 18432 i \, \cos\left(6 \, f x + 6 \, e\right) - 27648 i \, \cos\left(4 \, f x + 4 \, e\right) - 18432 i \, \cos\left(2 \, f x + 2 \, e\right) + 4608 \, \sin\left(8 \, f x + 8 \, e\right) + 18432 \, \sin\left(6 \, f x + 6 \, e\right) + 27648 \, \sin\left(4 \, f x + 4 \, e\right) + 18432 \, \sin\left(2 \, f x + 2 \, e\right) - 4608 i\right)}}"," ",0,"-(1152*(4*A + I*B)*a*c^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 4224*(4*A + I*B)*a*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 384*(20*A + 53*I*B)*a*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1152*(4*A + I*B)*a*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-4608*I*A + 1152*B)*a*c^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-16896*I*A + 4224*B)*a*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-7680*I*A + 20352*B)*a*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (4608*I*A - 1152*B)*a*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (576*(4*A + I*B)*a*c^2*cos(8*f*x + 8*e) + 2304*(4*A + I*B)*a*c^2*cos(6*f*x + 6*e) + 3456*(4*A + I*B)*a*c^2*cos(4*f*x + 4*e) + 2304*(4*A + I*B)*a*c^2*cos(2*f*x + 2*e) - (-2304*I*A + 576*B)*a*c^2*sin(8*f*x + 8*e) - (-9216*I*A + 2304*B)*a*c^2*sin(6*f*x + 6*e) - (-13824*I*A + 3456*B)*a*c^2*sin(4*f*x + 4*e) - (-9216*I*A + 2304*B)*a*c^2*sin(2*f*x + 2*e) + 576*(4*A + I*B)*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) + (576*(4*A + I*B)*a*c^2*cos(8*f*x + 8*e) + 2304*(4*A + I*B)*a*c^2*cos(6*f*x + 6*e) + 3456*(4*A + I*B)*a*c^2*cos(4*f*x + 4*e) + 2304*(4*A + I*B)*a*c^2*cos(2*f*x + 2*e) - (-2304*I*A + 576*B)*a*c^2*sin(8*f*x + 8*e) - (-9216*I*A + 2304*B)*a*c^2*sin(6*f*x + 6*e) - (-13824*I*A + 3456*B)*a*c^2*sin(4*f*x + 4*e) - (-9216*I*A + 2304*B)*a*c^2*sin(2*f*x + 2*e) + 576*(4*A + I*B)*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) - ((-1152*I*A + 288*B)*a*c^2*cos(8*f*x + 8*e) + (-4608*I*A + 1152*B)*a*c^2*cos(6*f*x + 6*e) + (-6912*I*A + 1728*B)*a*c^2*cos(4*f*x + 4*e) + (-4608*I*A + 1152*B)*a*c^2*cos(2*f*x + 2*e) + 288*(4*A + I*B)*a*c^2*sin(8*f*x + 8*e) + 1152*(4*A + I*B)*a*c^2*sin(6*f*x + 6*e) + 1728*(4*A + I*B)*a*c^2*sin(4*f*x + 4*e) + 1152*(4*A + I*B)*a*c^2*sin(2*f*x + 2*e) + (-1152*I*A + 288*B)*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) - ((1152*I*A - 288*B)*a*c^2*cos(8*f*x + 8*e) + (4608*I*A - 1152*B)*a*c^2*cos(6*f*x + 6*e) + (6912*I*A - 1728*B)*a*c^2*cos(4*f*x + 4*e) + (4608*I*A - 1152*B)*a*c^2*cos(2*f*x + 2*e) - 288*(4*A + I*B)*a*c^2*sin(8*f*x + 8*e) - 1152*(4*A + I*B)*a*c^2*sin(6*f*x + 6*e) - 1728*(4*A + I*B)*a*c^2*sin(4*f*x + 4*e) - 1152*(4*A + I*B)*a*c^2*sin(2*f*x + 2*e) + (1152*I*A - 288*B)*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*(-4608*I*cos(8*f*x + 8*e) - 18432*I*cos(6*f*x + 6*e) - 27648*I*cos(4*f*x + 4*e) - 18432*I*cos(2*f*x + 2*e) + 4608*sin(8*f*x + 8*e) + 18432*sin(6*f*x + 6*e) + 27648*sin(4*f*x + 4*e) + 18432*sin(2*f*x + 2*e) - 4608*I))","B",0
797,1,856,0,1.055924," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(12 \, A a 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 i \, B 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) - 12 \, A 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) + 12 i \, A a 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 \, B 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) - 12 i \, A 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(6 \, A a c \cos\left(6 \, f x + 6 \, e\right) + 18 \, A a c \cos\left(4 \, f x + 4 \, e\right) + 18 \, A a c \cos\left(2 \, f x + 2 \, e\right) + 6 i \, A a c \sin\left(6 \, f x + 6 \, e\right) + 18 i \, A a c \sin\left(4 \, f x + 4 \, e\right) + 18 i \, A a c \sin\left(2 \, f x + 2 \, e\right) + 6 \, A 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(6 \, A a c \cos\left(6 \, f x + 6 \, e\right) + 18 \, A a c \cos\left(4 \, f x + 4 \, e\right) + 18 \, A a c \cos\left(2 \, f x + 2 \, e\right) + 6 i \, A a c \sin\left(6 \, f x + 6 \, e\right) + 18 i \, A a c \sin\left(4 \, f x + 4 \, e\right) + 18 i \, A a c \sin\left(2 \, f x + 2 \, e\right) + 6 \, A 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(-3 i \, A a c \cos\left(6 \, f x + 6 \, e\right) - 9 i \, A a c \cos\left(4 \, f x + 4 \, e\right) - 9 i \, A a c \cos\left(2 \, f x + 2 \, e\right) + 3 \, A a c \sin\left(6 \, f x + 6 \, e\right) + 9 \, A a c \sin\left(4 \, f x + 4 \, e\right) + 9 \, A a c \sin\left(2 \, f x + 2 \, e\right) - 3 i \, A 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(3 i \, A a c \cos\left(6 \, f x + 6 \, e\right) + 9 i \, A a c \cos\left(4 \, f x + 4 \, e\right) + 9 i \, A a c \cos\left(2 \, f x + 2 \, e\right) - 3 \, A a c \sin\left(6 \, f x + 6 \, e\right) - 9 \, A a c \sin\left(4 \, f x + 4 \, e\right) - 9 \, A a c \sin\left(2 \, f x + 2 \, e\right) + 3 i \, A 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(-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*a*c*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 32*I*B*a*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*A*a*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*I*A*a*c*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*B*a*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*I*A*a*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (6*A*a*c*cos(6*f*x + 6*e) + 18*A*a*c*cos(4*f*x + 4*e) + 18*A*a*c*cos(2*f*x + 2*e) + 6*I*A*a*c*sin(6*f*x + 6*e) + 18*I*A*a*c*sin(4*f*x + 4*e) + 18*I*A*a*c*sin(2*f*x + 2*e) + 6*A*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) + (6*A*a*c*cos(6*f*x + 6*e) + 18*A*a*c*cos(4*f*x + 4*e) + 18*A*a*c*cos(2*f*x + 2*e) + 6*I*A*a*c*sin(6*f*x + 6*e) + 18*I*A*a*c*sin(4*f*x + 4*e) + 18*I*A*a*c*sin(2*f*x + 2*e) + 6*A*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) - (-3*I*A*a*c*cos(6*f*x + 6*e) - 9*I*A*a*c*cos(4*f*x + 4*e) - 9*I*A*a*c*cos(2*f*x + 2*e) + 3*A*a*c*sin(6*f*x + 6*e) + 9*A*a*c*sin(4*f*x + 4*e) + 9*A*a*c*sin(2*f*x + 2*e) - 3*I*A*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) - (3*I*A*a*c*cos(6*f*x + 6*e) + 9*I*A*a*c*cos(4*f*x + 4*e) + 9*I*A*a*c*cos(2*f*x + 2*e) - 3*A*a*c*sin(6*f*x + 6*e) - 9*A*a*c*sin(4*f*x + 4*e) - 9*A*a*c*sin(2*f*x + 2*e) + 3*I*A*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*(-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
798,1,779,0,0.958096," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(16 \, {\left(2 \, A - 3 i \, B\right)} 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) + 16 \, {\left(2 \, A - i \, B\right)} 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(-32 i \, A - 48 \, B\right)} 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) - {\left(-32 i \, A - 16 \, B\right)} 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) - {\left(8 \, {\left(2 \, A - i \, B\right)} a \cos\left(4 \, f x + 4 \, e\right) + 16 \, {\left(2 \, A - i \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(16 i \, A + 8 \, B\right)} a \sin\left(4 \, f x + 4 \, e\right) + {\left(32 i \, A + 16 \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + 8 \, {\left(2 \, A - i \, B\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) - {\left(8 \, {\left(2 \, A - i \, B\right)} a \cos\left(4 \, f x + 4 \, e\right) + 16 \, {\left(2 \, A - i \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(16 i \, A + 8 \, B\right)} a \sin\left(4 \, f x + 4 \, e\right) + {\left(32 i \, A + 16 \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + 8 \, {\left(2 \, A - i \, B\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) - {\left({\left(8 i \, A + 4 \, B\right)} a \cos\left(4 \, f x + 4 \, e\right) + {\left(16 i \, A + 8 \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(2 \, A - i \, B\right)} a \sin\left(4 \, f x + 4 \, e\right) - 8 \, {\left(2 \, A - i \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + {\left(8 i \, A + 4 \, B\right)} 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({\left(-8 i \, A - 4 \, B\right)} a \cos\left(4 \, f x + 4 \, e\right) + {\left(-16 i \, A - 8 \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(2 \, A - i \, B\right)} a \sin\left(4 \, f x + 4 \, e\right) + 8 \, {\left(2 \, A - i \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + {\left(-8 i \, A - 4 \, B\right)} 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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-16 i \, \cos\left(4 \, f x + 4 \, e\right) - 32 i \, \cos\left(2 \, f x + 2 \, e\right) + 16 \, \sin\left(4 \, f x + 4 \, e\right) + 32 \, \sin\left(2 \, f x + 2 \, e\right) - 16 i\right)}}"," ",0,"(16*(2*A - 3*I*B)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*(2*A - I*B)*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-32*I*A - 48*B)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-32*I*A - 16*B)*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (8*(2*A - I*B)*a*cos(4*f*x + 4*e) + 16*(2*A - I*B)*a*cos(2*f*x + 2*e) + (16*I*A + 8*B)*a*sin(4*f*x + 4*e) + (32*I*A + 16*B)*a*sin(2*f*x + 2*e) + 8*(2*A - I*B)*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) - (8*(2*A - I*B)*a*cos(4*f*x + 4*e) + 16*(2*A - I*B)*a*cos(2*f*x + 2*e) + (16*I*A + 8*B)*a*sin(4*f*x + 4*e) + (32*I*A + 16*B)*a*sin(2*f*x + 2*e) + 8*(2*A - I*B)*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) - ((8*I*A + 4*B)*a*cos(4*f*x + 4*e) + (16*I*A + 8*B)*a*cos(2*f*x + 2*e) - 4*(2*A - I*B)*a*sin(4*f*x + 4*e) - 8*(2*A - I*B)*a*sin(2*f*x + 2*e) + (8*I*A + 4*B)*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) - ((-8*I*A - 4*B)*a*cos(4*f*x + 4*e) + (-16*I*A - 8*B)*a*cos(2*f*x + 2*e) + 4*(2*A - I*B)*a*sin(4*f*x + 4*e) + 8*(2*A - I*B)*a*sin(2*f*x + 2*e) + (-8*I*A - 4*B)*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))*sqrt(a)*sqrt(c)/(f*(-16*I*cos(4*f*x + 4*e) - 32*I*cos(2*f*x + 2*e) + 16*sin(4*f*x + 4*e) + 32*sin(2*f*x + 2*e) - 16*I))","B",0
799,1,605,0,1.064375," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(2 \, {\left(A - 2 i \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(2 i \, A + 4 \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(A - 2 i \, B\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) + {\left(2 \, {\left(A - 2 i \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(2 i \, A + 4 \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(A - 2 i \, B\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) - {\left(4 \, {\left(A - i \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, A - 4 \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(A - 2 i \, B\right)} a\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({\left(i \, A + 2 \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) - {\left(A - 2 i \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + {\left(i \, A + 2 \, B\right)} 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({\left(-i \, A - 2 \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + {\left(A - 2 i \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + {\left(-i \, A - 2 \, B\right)} 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({\left(-4 i \, A - 4 \, B\right)} a \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(A - i \, B\right)} a \sin\left(2 \, f x + 2 \, e\right) + {\left(-4 i \, A - 8 \, B\right)} a\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,"((2*(A - 2*I*B)*a*cos(2*f*x + 2*e) + (2*I*A + 4*B)*a*sin(2*f*x + 2*e) + 2*(A - 2*I*B)*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 - 2*I*B)*a*cos(2*f*x + 2*e) + (2*I*A + 4*B)*a*sin(2*f*x + 2*e) + 2*(A - 2*I*B)*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 - I*B)*a*cos(2*f*x + 2*e) - (-4*I*A - 4*B)*a*sin(2*f*x + 2*e) + 4*(A - 2*I*B)*a)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((I*A + 2*B)*a*cos(2*f*x + 2*e) - (A - 2*I*B)*a*sin(2*f*x + 2*e) + (I*A + 2*B)*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 - 2*B)*a*cos(2*f*x + 2*e) + (A - 2*I*B)*a*sin(2*f*x + 2*e) + (-I*A - 2*B)*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 - 4*B)*a*cos(2*f*x + 2*e) + 4*(A - I*B)*a*sin(2*f*x + 2*e) + (-4*I*A - 8*B)*a)*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
800,1,169,0,0.847083," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(6 \, B a \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 6 \, B a \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(2 i \, A + 2 \, B\right)} a \cos\left(3 \, f x + 3 \, e\right) - 12 \, B a \cos\left(f x + e\right) + 3 i \, B a \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 i \, B a \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) - 2 \, {\left(A - i \, B\right)} a \sin\left(3 \, f x + 3 \, e\right) - 12 i \, B a \sin\left(f x + e\right)\right)} \sqrt{a}}{6 \, c^{\frac{3}{2}} f}"," ",0,"-1/6*(6*B*a*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 6*B*a*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (2*I*A + 2*B)*a*cos(3*f*x + 3*e) - 12*B*a*cos(f*x + e) + 3*I*B*a*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 3*I*B*a*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 2*(A - I*B)*a*sin(3*f*x + 3*e) - 12*I*B*a*sin(f*x + e))*sqrt(a)/(c^(3/2)*f)","A",0
801,1,155,0,1.256504," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(90 \, {\left(A - i \, B\right)} a \cos\left(7 \, f x + 7 \, e\right) + 60 \, {\left(4 \, A + i \, B\right)} a \cos\left(5 \, f x + 5 \, e\right) + 150 \, {\left(A + i \, B\right)} a \cos\left(3 \, f x + 3 \, e\right) + {\left(90 i \, A + 90 \, B\right)} a \sin\left(7 \, f x + 7 \, e\right) + {\left(240 i \, A - 60 \, B\right)} a \sin\left(5 \, f x + 5 \, e\right) + {\left(150 i \, A - 150 \, B\right)} a \sin\left(3 \, f x + 3 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-900 i \, c^{3} \cos\left(2 \, f x + 2 \, e\right) + 900 \, c^{3} \sin\left(2 \, f x + 2 \, e\right) - 900 i \, c^{3}\right)} f}"," ",0,"-(90*(A - I*B)*a*cos(7*f*x + 7*e) + 60*(4*A + I*B)*a*cos(5*f*x + 5*e) + 150*(A + I*B)*a*cos(3*f*x + 3*e) + (90*I*A + 90*B)*a*sin(7*f*x + 7*e) + (240*I*A - 60*B)*a*sin(5*f*x + 5*e) + (150*I*A - 150*B)*a*sin(3*f*x + 3*e))*sqrt(a)*sqrt(c)/((-900*I*c^3*cos(2*f*x + 2*e) + 900*c^3*sin(2*f*x + 2*e) - 900*I*c^3)*f)","A",0
802,1,186,0,0.745704," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left({\left(15 i \, A + 15 \, B\right)} a \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) + 42 i \, A 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) + {\left(35 i \, A - 35 \, B\right)} 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) - 15 \, {\left(A - i \, B\right)} a \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) - 42 \, A 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) - 35 \, {\left(A + i \, B\right)} 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}}{420 \, c^{\frac{7}{2}} f}"," ",0,"-1/420*((15*I*A + 15*B)*a*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 42*I*A*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (35*I*A - 35*B)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 15*(A - I*B)*a*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 42*A*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 35*(A + I*B)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(7/2)*f)","A",0
803,1,260,0,0.813974," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{{\left({\left(35 i \, A + 35 \, B\right)} a \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(135 i \, A + 45 \, B\right)} a \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) + {\left(189 i \, A - 63 \, B\right)} 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) + {\left(105 i \, A - 105 \, B\right)} 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) - 35 \, {\left(A - i \, B\right)} a \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 45 \, {\left(3 \, A - i \, B\right)} a \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) - 63 \, {\left(3 \, A + i \, B\right)} 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) - 105 \, {\left(A + i \, B\right)} 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}}{2520 \, c^{\frac{9}{2}} f}"," ",0,"-1/2520*((35*I*A + 35*B)*a*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (135*I*A + 45*B)*a*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (189*I*A - 63*B)*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (105*I*A - 105*B)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 35*(A - I*B)*a*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 45*(3*A - I*B)*a*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 63*(3*A + I*B)*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 105*(A + I*B)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(9/2)*f)","A",0
804,1,312,0,0.883559," ","integrate((a+I*a*tan(f*x+e))^(3/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{{\left({\left(315 i \, A + 315 \, B\right)} a \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(1540 i \, A + 770 \, B\right)} a \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2970 i \, A a \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) + {\left(2772 i \, A - 1386 \, B\right)} 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) + {\left(1155 i \, A - 1155 \, B\right)} 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) - 315 \, {\left(A - i \, B\right)} a \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 770 \, {\left(2 \, A - i \, B\right)} a \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2970 \, A a \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) - 1386 \, {\left(2 \, A + i \, B\right)} 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) - 1155 \, {\left(A + i \, B\right)} 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}}{55440 \, c^{\frac{11}{2}} f}"," ",0,"-1/55440*((315*I*A + 315*B)*a*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1540*I*A + 770*B)*a*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2970*I*A*a*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (2772*I*A - 1386*B)*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1155*I*A - 1155*B)*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 315*(A - I*B)*a*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 770*(2*A - I*B)*a*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2970*A*a*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1386*(2*A + I*B)*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1155*(A + I*B)*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(11/2)*f)","A",0
805,1,2046,0,8.534065," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(230400 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1305600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 3041280 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \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) + 92160 \, {\left(58 \, A + 223 i \, B\right)} a^{2} c^{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) - 1305600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{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) - 230400 \, {\left(6 \, A + i \, B\right)} a^{2} c^{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) - {\left(-1382400 i \, A + 230400 \, B\right)} a^{2} c^{3} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-7833600 i \, A + 1305600 \, B\right)} a^{2} c^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-18247680 i \, A + 3041280 \, B\right)} a^{2} c^{3} \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) - {\left(-5345280 i \, A + 20551680 \, B\right)} a^{2} c^{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) - {\left(7833600 i \, A - 1305600 \, B\right)} a^{2} c^{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(1382400 i \, A - 230400 \, B\right)} a^{2} c^{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) + {\left(115200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(12 \, f x + 12 \, e\right) + 691200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 1728000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 2304000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 1728000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 691200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-691200 i \, A + 115200 \, B\right)} a^{2} c^{3} \sin\left(12 \, f x + 12 \, e\right) - {\left(-4147200 i \, A + 691200 \, B\right)} a^{2} c^{3} \sin\left(10 \, f x + 10 \, e\right) - {\left(-10368000 i \, A + 1728000 \, B\right)} a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) - {\left(-13824000 i \, A + 2304000 \, B\right)} a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-10368000 i \, A + 1728000 \, B\right)} a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-4147200 i \, A + 691200 \, B\right)} a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 115200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{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(115200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(12 \, f x + 12 \, e\right) + 691200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 1728000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 2304000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 1728000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 691200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-691200 i \, A + 115200 \, B\right)} a^{2} c^{3} \sin\left(12 \, f x + 12 \, e\right) - {\left(-4147200 i \, A + 691200 \, B\right)} a^{2} c^{3} \sin\left(10 \, f x + 10 \, e\right) - {\left(-10368000 i \, A + 1728000 \, B\right)} a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) - {\left(-13824000 i \, A + 2304000 \, B\right)} a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-10368000 i \, A + 1728000 \, B\right)} a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-4147200 i \, A + 691200 \, B\right)} a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 115200 \, {\left(6 \, A + i \, B\right)} a^{2} c^{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({\left(-345600 i \, A + 57600 \, B\right)} a^{2} c^{3} \cos\left(12 \, f x + 12 \, e\right) + {\left(-2073600 i \, A + 345600 \, B\right)} a^{2} c^{3} \cos\left(10 \, f x + 10 \, e\right) + {\left(-5184000 i \, A + 864000 \, B\right)} a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(-6912000 i \, A + 1152000 \, B\right)} a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(-5184000 i \, A + 864000 \, B\right)} a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-2073600 i \, A + 345600 \, B\right)} a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 57600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(12 \, f x + 12 \, e\right) + 345600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(10 \, f x + 10 \, e\right) + 864000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 1152000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 864000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 345600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-345600 i \, A + 57600 \, B\right)} a^{2} c^{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({\left(345600 i \, A - 57600 \, B\right)} a^{2} c^{3} \cos\left(12 \, f x + 12 \, e\right) + {\left(2073600 i \, A - 345600 \, B\right)} a^{2} c^{3} \cos\left(10 \, f x + 10 \, e\right) + {\left(5184000 i \, A - 864000 \, B\right)} a^{2} c^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(6912000 i \, A - 1152000 \, B\right)} a^{2} c^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(5184000 i \, A - 864000 \, B\right)} a^{2} c^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(2073600 i \, A - 345600 \, B\right)} a^{2} c^{3} \cos\left(2 \, f x + 2 \, e\right) - 57600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(12 \, f x + 12 \, e\right) - 345600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(10 \, f x + 10 \, e\right) - 864000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(8 \, f x + 8 \, e\right) - 1152000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(6 \, f x + 6 \, e\right) - 864000 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(4 \, f x + 4 \, e\right) - 345600 \, {\left(6 \, A + i \, B\right)} a^{2} c^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(345600 i \, A - 57600 \, B\right)} a^{2} c^{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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-1843200 i \, \cos\left(12 \, f x + 12 \, e\right) - 11059200 i \, \cos\left(10 \, f x + 10 \, e\right) - 27648000 i \, \cos\left(8 \, f x + 8 \, e\right) - 36864000 i \, \cos\left(6 \, f x + 6 \, e\right) - 27648000 i \, \cos\left(4 \, f x + 4 \, e\right) - 11059200 i \, \cos\left(2 \, f x + 2 \, e\right) + 1843200 \, \sin\left(12 \, f x + 12 \, e\right) + 11059200 \, \sin\left(10 \, f x + 10 \, e\right) + 27648000 \, \sin\left(8 \, f x + 8 \, e\right) + 36864000 \, \sin\left(6 \, f x + 6 \, e\right) + 27648000 \, \sin\left(4 \, f x + 4 \, e\right) + 11059200 \, \sin\left(2 \, f x + 2 \, e\right) - 1843200 i\right)}}"," ",0,"-(230400*(6*A + I*B)*a^2*c^3*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1305600*(6*A + I*B)*a^2*c^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 3041280*(6*A + I*B)*a^2*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 92160*(58*A + 223*I*B)*a^2*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1305600*(6*A + I*B)*a^2*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 230400*(6*A + I*B)*a^2*c^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1382400*I*A + 230400*B)*a^2*c^3*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-7833600*I*A + 1305600*B)*a^2*c^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-18247680*I*A + 3041280*B)*a^2*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-5345280*I*A + 20551680*B)*a^2*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (7833600*I*A - 1305600*B)*a^2*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (1382400*I*A - 230400*B)*a^2*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (115200*(6*A + I*B)*a^2*c^3*cos(12*f*x + 12*e) + 691200*(6*A + I*B)*a^2*c^3*cos(10*f*x + 10*e) + 1728000*(6*A + I*B)*a^2*c^3*cos(8*f*x + 8*e) + 2304000*(6*A + I*B)*a^2*c^3*cos(6*f*x + 6*e) + 1728000*(6*A + I*B)*a^2*c^3*cos(4*f*x + 4*e) + 691200*(6*A + I*B)*a^2*c^3*cos(2*f*x + 2*e) - (-691200*I*A + 115200*B)*a^2*c^3*sin(12*f*x + 12*e) - (-4147200*I*A + 691200*B)*a^2*c^3*sin(10*f*x + 10*e) - (-10368000*I*A + 1728000*B)*a^2*c^3*sin(8*f*x + 8*e) - (-13824000*I*A + 2304000*B)*a^2*c^3*sin(6*f*x + 6*e) - (-10368000*I*A + 1728000*B)*a^2*c^3*sin(4*f*x + 4*e) - (-4147200*I*A + 691200*B)*a^2*c^3*sin(2*f*x + 2*e) + 115200*(6*A + I*B)*a^2*c^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) + (115200*(6*A + I*B)*a^2*c^3*cos(12*f*x + 12*e) + 691200*(6*A + I*B)*a^2*c^3*cos(10*f*x + 10*e) + 1728000*(6*A + I*B)*a^2*c^3*cos(8*f*x + 8*e) + 2304000*(6*A + I*B)*a^2*c^3*cos(6*f*x + 6*e) + 1728000*(6*A + I*B)*a^2*c^3*cos(4*f*x + 4*e) + 691200*(6*A + I*B)*a^2*c^3*cos(2*f*x + 2*e) - (-691200*I*A + 115200*B)*a^2*c^3*sin(12*f*x + 12*e) - (-4147200*I*A + 691200*B)*a^2*c^3*sin(10*f*x + 10*e) - (-10368000*I*A + 1728000*B)*a^2*c^3*sin(8*f*x + 8*e) - (-13824000*I*A + 2304000*B)*a^2*c^3*sin(6*f*x + 6*e) - (-10368000*I*A + 1728000*B)*a^2*c^3*sin(4*f*x + 4*e) - (-4147200*I*A + 691200*B)*a^2*c^3*sin(2*f*x + 2*e) + 115200*(6*A + I*B)*a^2*c^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) - ((-345600*I*A + 57600*B)*a^2*c^3*cos(12*f*x + 12*e) + (-2073600*I*A + 345600*B)*a^2*c^3*cos(10*f*x + 10*e) + (-5184000*I*A + 864000*B)*a^2*c^3*cos(8*f*x + 8*e) + (-6912000*I*A + 1152000*B)*a^2*c^3*cos(6*f*x + 6*e) + (-5184000*I*A + 864000*B)*a^2*c^3*cos(4*f*x + 4*e) + (-2073600*I*A + 345600*B)*a^2*c^3*cos(2*f*x + 2*e) + 57600*(6*A + I*B)*a^2*c^3*sin(12*f*x + 12*e) + 345600*(6*A + I*B)*a^2*c^3*sin(10*f*x + 10*e) + 864000*(6*A + I*B)*a^2*c^3*sin(8*f*x + 8*e) + 1152000*(6*A + I*B)*a^2*c^3*sin(6*f*x + 6*e) + 864000*(6*A + I*B)*a^2*c^3*sin(4*f*x + 4*e) + 345600*(6*A + I*B)*a^2*c^3*sin(2*f*x + 2*e) + (-345600*I*A + 57600*B)*a^2*c^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) - ((345600*I*A - 57600*B)*a^2*c^3*cos(12*f*x + 12*e) + (2073600*I*A - 345600*B)*a^2*c^3*cos(10*f*x + 10*e) + (5184000*I*A - 864000*B)*a^2*c^3*cos(8*f*x + 8*e) + (6912000*I*A - 1152000*B)*a^2*c^3*cos(6*f*x + 6*e) + (5184000*I*A - 864000*B)*a^2*c^3*cos(4*f*x + 4*e) + (2073600*I*A - 345600*B)*a^2*c^3*cos(2*f*x + 2*e) - 57600*(6*A + I*B)*a^2*c^3*sin(12*f*x + 12*e) - 345600*(6*A + I*B)*a^2*c^3*sin(10*f*x + 10*e) - 864000*(6*A + I*B)*a^2*c^3*sin(8*f*x + 8*e) - 1152000*(6*A + I*B)*a^2*c^3*sin(6*f*x + 6*e) - 864000*(6*A + I*B)*a^2*c^3*sin(4*f*x + 4*e) - 345600*(6*A + I*B)*a^2*c^3*sin(2*f*x + 2*e) + (345600*I*A - 57600*B)*a^2*c^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))*sqrt(a)*sqrt(c)/(f*(-1843200*I*cos(12*f*x + 12*e) - 11059200*I*cos(10*f*x + 10*e) - 27648000*I*cos(8*f*x + 8*e) - 36864000*I*cos(6*f*x + 6*e) - 27648000*I*cos(4*f*x + 4*e) - 11059200*I*cos(2*f*x + 2*e) + 1843200*sin(12*f*x + 12*e) + 11059200*sin(10*f*x + 10*e) + 27648000*sin(8*f*x + 8*e) + 36864000*sin(6*f*x + 6*e) + 27648000*sin(4*f*x + 4*e) + 11059200*sin(2*f*x + 2*e) - 1843200*I))","B",0
806,1,1448,0,1.932123," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(60 \, A a^{2} c^{2} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 280 \, A 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) + 512 i \, B 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) - 280 \, A 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) - 60 \, A 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) + 60 i \, A a^{2} c^{2} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 280 i \, A 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) - 512 \, B 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) - 280 i \, A 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) - 60 i \, A 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(30 \, A a^{2} c^{2} \cos\left(10 \, f x + 10 \, e\right) + 150 \, A a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 300 \, A a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 300 \, A a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 150 \, A a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 30 i \, A a^{2} c^{2} \sin\left(10 \, f x + 10 \, e\right) + 150 i \, A a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 300 i \, A a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 300 i \, A a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 150 i \, A a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 30 \, A 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(30 \, A a^{2} c^{2} \cos\left(10 \, f x + 10 \, e\right) + 150 \, A a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 300 \, A a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 300 \, A a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 150 \, A a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 30 i \, A a^{2} c^{2} \sin\left(10 \, f x + 10 \, e\right) + 150 i \, A a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 300 i \, A a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 300 i \, A a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 150 i \, A a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 30 \, A 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(-15 i \, A a^{2} c^{2} \cos\left(10 \, f x + 10 \, e\right) - 75 i \, A a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) - 150 i \, A a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) - 150 i \, A a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) - 75 i \, A a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 15 \, A a^{2} c^{2} \sin\left(10 \, f x + 10 \, e\right) + 75 \, A a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 150 \, A a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 150 \, A a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 75 \, A a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) - 15 i \, A 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(15 i \, A a^{2} c^{2} \cos\left(10 \, f x + 10 \, e\right) + 75 i \, A a^{2} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 150 i \, A a^{2} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 150 i \, A a^{2} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 75 i \, A a^{2} c^{2} \cos\left(2 \, f x + 2 \, e\right) - 15 \, A a^{2} c^{2} \sin\left(10 \, f x + 10 \, e\right) - 75 \, A a^{2} c^{2} \sin\left(8 \, f x + 8 \, e\right) - 150 \, A a^{2} c^{2} \sin\left(6 \, f x + 6 \, e\right) - 150 \, A a^{2} c^{2} \sin\left(4 \, f x + 4 \, e\right) - 75 \, A a^{2} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 15 i \, A 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(-80 i \, \cos\left(10 \, f x + 10 \, e\right) - 400 i \, \cos\left(8 \, f x + 8 \, e\right) - 800 i \, \cos\left(6 \, f x + 6 \, e\right) - 800 i \, \cos\left(4 \, f x + 4 \, e\right) - 400 i \, \cos\left(2 \, f x + 2 \, e\right) + 80 \, \sin\left(10 \, f x + 10 \, e\right) + 400 \, \sin\left(8 \, f x + 8 \, e\right) + 800 \, \sin\left(6 \, f x + 6 \, e\right) + 800 \, \sin\left(4 \, f x + 4 \, e\right) + 400 \, \sin\left(2 \, f x + 2 \, e\right) - 80 i\right)}}"," ",0,"-(60*A*a^2*c^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 280*A*a^2*c^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 512*I*B*a^2*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 280*A*a^2*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 60*A*a^2*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 60*I*A*a^2*c^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 280*I*A*a^2*c^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 512*B*a^2*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 280*I*A*a^2*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 60*I*A*a^2*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (30*A*a^2*c^2*cos(10*f*x + 10*e) + 150*A*a^2*c^2*cos(8*f*x + 8*e) + 300*A*a^2*c^2*cos(6*f*x + 6*e) + 300*A*a^2*c^2*cos(4*f*x + 4*e) + 150*A*a^2*c^2*cos(2*f*x + 2*e) + 30*I*A*a^2*c^2*sin(10*f*x + 10*e) + 150*I*A*a^2*c^2*sin(8*f*x + 8*e) + 300*I*A*a^2*c^2*sin(6*f*x + 6*e) + 300*I*A*a^2*c^2*sin(4*f*x + 4*e) + 150*I*A*a^2*c^2*sin(2*f*x + 2*e) + 30*A*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) + (30*A*a^2*c^2*cos(10*f*x + 10*e) + 150*A*a^2*c^2*cos(8*f*x + 8*e) + 300*A*a^2*c^2*cos(6*f*x + 6*e) + 300*A*a^2*c^2*cos(4*f*x + 4*e) + 150*A*a^2*c^2*cos(2*f*x + 2*e) + 30*I*A*a^2*c^2*sin(10*f*x + 10*e) + 150*I*A*a^2*c^2*sin(8*f*x + 8*e) + 300*I*A*a^2*c^2*sin(6*f*x + 6*e) + 300*I*A*a^2*c^2*sin(4*f*x + 4*e) + 150*I*A*a^2*c^2*sin(2*f*x + 2*e) + 30*A*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) - (-15*I*A*a^2*c^2*cos(10*f*x + 10*e) - 75*I*A*a^2*c^2*cos(8*f*x + 8*e) - 150*I*A*a^2*c^2*cos(6*f*x + 6*e) - 150*I*A*a^2*c^2*cos(4*f*x + 4*e) - 75*I*A*a^2*c^2*cos(2*f*x + 2*e) + 15*A*a^2*c^2*sin(10*f*x + 10*e) + 75*A*a^2*c^2*sin(8*f*x + 8*e) + 150*A*a^2*c^2*sin(6*f*x + 6*e) + 150*A*a^2*c^2*sin(4*f*x + 4*e) + 75*A*a^2*c^2*sin(2*f*x + 2*e) - 15*I*A*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) - (15*I*A*a^2*c^2*cos(10*f*x + 10*e) + 75*I*A*a^2*c^2*cos(8*f*x + 8*e) + 150*I*A*a^2*c^2*cos(6*f*x + 6*e) + 150*I*A*a^2*c^2*cos(4*f*x + 4*e) + 75*I*A*a^2*c^2*cos(2*f*x + 2*e) - 15*A*a^2*c^2*sin(10*f*x + 10*e) - 75*A*a^2*c^2*sin(8*f*x + 8*e) - 150*A*a^2*c^2*sin(6*f*x + 6*e) - 150*A*a^2*c^2*sin(4*f*x + 4*e) - 75*A*a^2*c^2*sin(2*f*x + 2*e) + 15*I*A*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*(-80*I*cos(10*f*x + 10*e) - 400*I*cos(8*f*x + 8*e) - 800*I*cos(6*f*x + 6*e) - 800*I*cos(4*f*x + 4*e) - 400*I*cos(2*f*x + 2*e) + 80*sin(10*f*x + 10*e) + 400*sin(8*f*x + 8*e) + 800*sin(6*f*x + 6*e) + 800*sin(4*f*x + 4*e) + 400*sin(2*f*x + 2*e) - 80*I))","B",0
807,1,1372,0,2.306026," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(1152 \, {\left(4 \, A - i \, B\right)} a^{2} c \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) - 384 \, {\left(20 \, A - 53 i \, B\right)} 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) - 4224 \, {\left(4 \, A - i \, B\right)} 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) - 1152 \, {\left(4 \, A - i \, B\right)} 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) + {\left(4608 i \, A + 1152 \, B\right)} a^{2} c \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) + {\left(-7680 i \, A - 20352 \, B\right)} 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) + {\left(-16896 i \, A - 4224 \, B\right)} 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) + {\left(-4608 i \, A - 1152 \, B\right)} 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(576 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(8 \, f x + 8 \, e\right) + 2304 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 3456 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 2304 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) + {\left(2304 i \, A + 576 \, B\right)} a^{2} c \sin\left(8 \, f x + 8 \, e\right) + {\left(9216 i \, A + 2304 \, B\right)} a^{2} c \sin\left(6 \, f x + 6 \, e\right) + {\left(13824 i \, A + 3456 \, B\right)} a^{2} c \sin\left(4 \, f x + 4 \, e\right) + {\left(9216 i \, A + 2304 \, B\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 576 \, {\left(4 \, A - i \, B\right)} 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(576 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(8 \, f x + 8 \, e\right) + 2304 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(6 \, f x + 6 \, e\right) + 3456 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(4 \, f x + 4 \, e\right) + 2304 \, {\left(4 \, A - i \, B\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) + {\left(2304 i \, A + 576 \, B\right)} a^{2} c \sin\left(8 \, f x + 8 \, e\right) + {\left(9216 i \, A + 2304 \, B\right)} a^{2} c \sin\left(6 \, f x + 6 \, e\right) + {\left(13824 i \, A + 3456 \, B\right)} a^{2} c \sin\left(4 \, f x + 4 \, e\right) + {\left(9216 i \, A + 2304 \, B\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right) + 576 \, {\left(4 \, A - i \, B\right)} 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({\left(1152 i \, A + 288 \, B\right)} a^{2} c \cos\left(8 \, f x + 8 \, e\right) + {\left(4608 i \, A + 1152 \, B\right)} a^{2} c \cos\left(6 \, f x + 6 \, e\right) + {\left(6912 i \, A + 1728 \, B\right)} a^{2} c \cos\left(4 \, f x + 4 \, e\right) + {\left(4608 i \, A + 1152 \, B\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) - 288 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(8 \, f x + 8 \, e\right) - 1152 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(6 \, f x + 6 \, e\right) - 1728 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(4 \, f x + 4 \, e\right) - 1152 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right) + {\left(1152 i \, A + 288 \, B\right)} 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({\left(-1152 i \, A - 288 \, B\right)} a^{2} c \cos\left(8 \, f x + 8 \, e\right) + {\left(-4608 i \, A - 1152 \, B\right)} a^{2} c \cos\left(6 \, f x + 6 \, e\right) + {\left(-6912 i \, A - 1728 \, B\right)} a^{2} c \cos\left(4 \, f x + 4 \, e\right) + {\left(-4608 i \, A - 1152 \, B\right)} a^{2} c \cos\left(2 \, f x + 2 \, e\right) + 288 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(8 \, f x + 8 \, e\right) + 1152 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(6 \, f x + 6 \, e\right) + 1728 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(4 \, f x + 4 \, e\right) + 1152 \, {\left(4 \, A - i \, B\right)} a^{2} c \sin\left(2 \, f x + 2 \, e\right) + {\left(-1152 i \, A - 288 \, B\right)} 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(-4608 i \, \cos\left(8 \, f x + 8 \, e\right) - 18432 i \, \cos\left(6 \, f x + 6 \, e\right) - 27648 i \, \cos\left(4 \, f x + 4 \, e\right) - 18432 i \, \cos\left(2 \, f x + 2 \, e\right) + 4608 \, \sin\left(8 \, f x + 8 \, e\right) + 18432 \, \sin\left(6 \, f x + 6 \, e\right) + 27648 \, \sin\left(4 \, f x + 4 \, e\right) + 18432 \, \sin\left(2 \, f x + 2 \, e\right) - 4608 i\right)}}"," ",0,"-(1152*(4*A - I*B)*a^2*c*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 384*(20*A - 53*I*B)*a^2*c*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4224*(4*A - I*B)*a^2*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1152*(4*A - I*B)*a^2*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (4608*I*A + 1152*B)*a^2*c*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-7680*I*A - 20352*B)*a^2*c*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-16896*I*A - 4224*B)*a^2*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-4608*I*A - 1152*B)*a^2*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (576*(4*A - I*B)*a^2*c*cos(8*f*x + 8*e) + 2304*(4*A - I*B)*a^2*c*cos(6*f*x + 6*e) + 3456*(4*A - I*B)*a^2*c*cos(4*f*x + 4*e) + 2304*(4*A - I*B)*a^2*c*cos(2*f*x + 2*e) + (2304*I*A + 576*B)*a^2*c*sin(8*f*x + 8*e) + (9216*I*A + 2304*B)*a^2*c*sin(6*f*x + 6*e) + (13824*I*A + 3456*B)*a^2*c*sin(4*f*x + 4*e) + (9216*I*A + 2304*B)*a^2*c*sin(2*f*x + 2*e) + 576*(4*A - I*B)*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) + (576*(4*A - I*B)*a^2*c*cos(8*f*x + 8*e) + 2304*(4*A - I*B)*a^2*c*cos(6*f*x + 6*e) + 3456*(4*A - I*B)*a^2*c*cos(4*f*x + 4*e) + 2304*(4*A - I*B)*a^2*c*cos(2*f*x + 2*e) + (2304*I*A + 576*B)*a^2*c*sin(8*f*x + 8*e) + (9216*I*A + 2304*B)*a^2*c*sin(6*f*x + 6*e) + (13824*I*A + 3456*B)*a^2*c*sin(4*f*x + 4*e) + (9216*I*A + 2304*B)*a^2*c*sin(2*f*x + 2*e) + 576*(4*A - I*B)*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) + ((1152*I*A + 288*B)*a^2*c*cos(8*f*x + 8*e) + (4608*I*A + 1152*B)*a^2*c*cos(6*f*x + 6*e) + (6912*I*A + 1728*B)*a^2*c*cos(4*f*x + 4*e) + (4608*I*A + 1152*B)*a^2*c*cos(2*f*x + 2*e) - 288*(4*A - I*B)*a^2*c*sin(8*f*x + 8*e) - 1152*(4*A - I*B)*a^2*c*sin(6*f*x + 6*e) - 1728*(4*A - I*B)*a^2*c*sin(4*f*x + 4*e) - 1152*(4*A - I*B)*a^2*c*sin(2*f*x + 2*e) + (1152*I*A + 288*B)*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) + ((-1152*I*A - 288*B)*a^2*c*cos(8*f*x + 8*e) + (-4608*I*A - 1152*B)*a^2*c*cos(6*f*x + 6*e) + (-6912*I*A - 1728*B)*a^2*c*cos(4*f*x + 4*e) + (-4608*I*A - 1152*B)*a^2*c*cos(2*f*x + 2*e) + 288*(4*A - I*B)*a^2*c*sin(8*f*x + 8*e) + 1152*(4*A - I*B)*a^2*c*sin(6*f*x + 6*e) + 1728*(4*A - I*B)*a^2*c*sin(4*f*x + 4*e) + 1152*(4*A - I*B)*a^2*c*sin(2*f*x + 2*e) + (-1152*I*A - 288*B)*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*(-4608*I*cos(8*f*x + 8*e) - 18432*I*cos(6*f*x + 6*e) - 27648*I*cos(4*f*x + 4*e) - 18432*I*cos(2*f*x + 2*e) + 4608*sin(8*f*x + 8*e) + 18432*sin(6*f*x + 6*e) + 27648*sin(4*f*x + 4*e) + 18432*sin(2*f*x + 2*e) - 4608*I))","B",0
808,1,1081,0,1.075783," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(72 \, {\left(5 \, A - 6 i \, B\right)} a^{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) + 192 \, {\left(3 \, A - 2 i \, B\right)} 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) + 72 \, {\left(3 \, A - 2 i \, B\right)} 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) - {\left(-360 i \, A - 432 \, B\right)} a^{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) - {\left(-576 i \, A - 384 \, B\right)} 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) - {\left(-216 i \, A - 144 \, B\right)} 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(36 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 108 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 108 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(108 i \, A + 72 \, B\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + {\left(324 i \, A + 216 \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + {\left(324 i \, A + 216 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 36 \, {\left(3 \, A - 2 i \, B\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) - {\left(36 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + 108 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 108 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(108 i \, A + 72 \, B\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + {\left(324 i \, A + 216 \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + {\left(324 i \, A + 216 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 36 \, {\left(3 \, A - 2 i \, B\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) - {\left({\left(54 i \, A + 36 \, B\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(162 i \, A + 108 \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(162 i \, A + 108 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 18 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) - 54 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) - 54 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(54 i \, A + 36 \, B\right)} 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({\left(-54 i \, A - 36 \, B\right)} a^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(-162 i \, A - 108 \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-162 i \, A - 108 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \sin\left(6 \, f x + 6 \, e\right) + 54 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 54 \, {\left(3 \, A - 2 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-54 i \, A - 36 \, B\right)} 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(-72 i \, \cos\left(6 \, f x + 6 \, e\right) - 216 i \, \cos\left(4 \, f x + 4 \, e\right) - 216 i \, \cos\left(2 \, f x + 2 \, e\right) + 72 \, \sin\left(6 \, f x + 6 \, e\right) + 216 \, \sin\left(4 \, f x + 4 \, e\right) + 216 \, \sin\left(2 \, f x + 2 \, e\right) - 72 i\right)}}"," ",0,"(72*(5*A - 6*I*B)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 192*(3*A - 2*I*B)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 72*(3*A - 2*I*B)*a^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-360*I*A - 432*B)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-576*I*A - 384*B)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-216*I*A - 144*B)*a^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (36*(3*A - 2*I*B)*a^2*cos(6*f*x + 6*e) + 108*(3*A - 2*I*B)*a^2*cos(4*f*x + 4*e) + 108*(3*A - 2*I*B)*a^2*cos(2*f*x + 2*e) + (108*I*A + 72*B)*a^2*sin(6*f*x + 6*e) + (324*I*A + 216*B)*a^2*sin(4*f*x + 4*e) + (324*I*A + 216*B)*a^2*sin(2*f*x + 2*e) + 36*(3*A - 2*I*B)*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) - (36*(3*A - 2*I*B)*a^2*cos(6*f*x + 6*e) + 108*(3*A - 2*I*B)*a^2*cos(4*f*x + 4*e) + 108*(3*A - 2*I*B)*a^2*cos(2*f*x + 2*e) + (108*I*A + 72*B)*a^2*sin(6*f*x + 6*e) + (324*I*A + 216*B)*a^2*sin(4*f*x + 4*e) + (324*I*A + 216*B)*a^2*sin(2*f*x + 2*e) + 36*(3*A - 2*I*B)*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) - ((54*I*A + 36*B)*a^2*cos(6*f*x + 6*e) + (162*I*A + 108*B)*a^2*cos(4*f*x + 4*e) + (162*I*A + 108*B)*a^2*cos(2*f*x + 2*e) - 18*(3*A - 2*I*B)*a^2*sin(6*f*x + 6*e) - 54*(3*A - 2*I*B)*a^2*sin(4*f*x + 4*e) - 54*(3*A - 2*I*B)*a^2*sin(2*f*x + 2*e) + (54*I*A + 36*B)*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) - ((-54*I*A - 36*B)*a^2*cos(6*f*x + 6*e) + (-162*I*A - 108*B)*a^2*cos(4*f*x + 4*e) + (-162*I*A - 108*B)*a^2*cos(2*f*x + 2*e) + 18*(3*A - 2*I*B)*a^2*sin(6*f*x + 6*e) + 54*(3*A - 2*I*B)*a^2*sin(4*f*x + 4*e) + 54*(3*A - 2*I*B)*a^2*sin(2*f*x + 2*e) + (-54*I*A - 36*B)*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*(-72*I*cos(6*f*x + 6*e) - 216*I*cos(4*f*x + 4*e) - 216*I*cos(2*f*x + 2*e) + 72*sin(6*f*x + 6*e) + 216*sin(4*f*x + 4*e) + 216*sin(2*f*x + 2*e) - 72*I))","B",0
809,1,996,0,1.102947," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(16 \, {\left(2 \, A - 7 i \, B\right)} 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) - {\left(-32 i \, A - 112 \, B\right)} 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) - {\left(24 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 48 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(48 i \, A + 72 \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + {\left(96 i \, A + 144 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 24 \, {\left(2 \, A - 3 i \, B\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) - {\left(24 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 48 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(48 i \, A + 72 \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + {\left(96 i \, A + 144 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 24 \, {\left(2 \, A - 3 i \, B\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) + {\left(64 \, {\left(A - i \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + 128 \, {\left(A - i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-64 i \, A - 64 \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) - {\left(-128 i \, A - 128 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 48 \, {\left(2 \, A - 3 i \, B\right)} 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({\left(24 i \, A + 36 \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(48 i \, A + 72 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 12 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) - 24 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(24 i \, A + 36 \, B\right)} 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({\left(-24 i \, A - 36 \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-48 i \, A - 72 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 12 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 24 \, {\left(2 \, A - 3 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-24 i \, A - 36 \, B\right)} 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({\left(-64 i \, A - 64 \, B\right)} a^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-128 i \, A - 128 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 64 \, {\left(A - i \, B\right)} a^{2} \sin\left(4 \, f x + 4 \, e\right) + 128 \, {\left(A - i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-96 i \, A - 144 \, B\right)} 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(-16 i \, c \cos\left(4 \, f x + 4 \, e\right) - 32 i \, c \cos\left(2 \, f x + 2 \, e\right) + 16 \, c \sin\left(4 \, f x + 4 \, e\right) + 32 \, c \sin\left(2 \, f x + 2 \, e\right) - 16 i \, c\right)} f}"," ",0,"-(16*(2*A - 7*I*B)*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-32*I*A - 112*B)*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (24*(2*A - 3*I*B)*a^2*cos(4*f*x + 4*e) + 48*(2*A - 3*I*B)*a^2*cos(2*f*x + 2*e) + (48*I*A + 72*B)*a^2*sin(4*f*x + 4*e) + (96*I*A + 144*B)*a^2*sin(2*f*x + 2*e) + 24*(2*A - 3*I*B)*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) - (24*(2*A - 3*I*B)*a^2*cos(4*f*x + 4*e) + 48*(2*A - 3*I*B)*a^2*cos(2*f*x + 2*e) + (48*I*A + 72*B)*a^2*sin(4*f*x + 4*e) + (96*I*A + 144*B)*a^2*sin(2*f*x + 2*e) + 24*(2*A - 3*I*B)*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) + (64*(A - I*B)*a^2*cos(4*f*x + 4*e) + 128*(A - I*B)*a^2*cos(2*f*x + 2*e) - (-64*I*A - 64*B)*a^2*sin(4*f*x + 4*e) - (-128*I*A - 128*B)*a^2*sin(2*f*x + 2*e) + 48*(2*A - 3*I*B)*a^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - ((24*I*A + 36*B)*a^2*cos(4*f*x + 4*e) + (48*I*A + 72*B)*a^2*cos(2*f*x + 2*e) - 12*(2*A - 3*I*B)*a^2*sin(4*f*x + 4*e) - 24*(2*A - 3*I*B)*a^2*sin(2*f*x + 2*e) + (24*I*A + 36*B)*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) - ((-24*I*A - 36*B)*a^2*cos(4*f*x + 4*e) + (-48*I*A - 72*B)*a^2*cos(2*f*x + 2*e) + 12*(2*A - 3*I*B)*a^2*sin(4*f*x + 4*e) + 24*(2*A - 3*I*B)*a^2*sin(2*f*x + 2*e) + (-24*I*A - 36*B)*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) - ((-64*I*A - 64*B)*a^2*cos(4*f*x + 4*e) + (-128*I*A - 128*B)*a^2*cos(2*f*x + 2*e) + 64*(A - I*B)*a^2*sin(4*f*x + 4*e) + 128*(A - I*B)*a^2*sin(2*f*x + 2*e) + (-96*I*A - 144*B)*a^2)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-16*I*c*cos(4*f*x + 4*e) - 32*I*c*cos(2*f*x + 2*e) + 16*c*sin(4*f*x + 4*e) + 32*c*sin(2*f*x + 2*e) - 16*I*c)*f)","B",0
810,1,796,0,0.956672," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(18 \, {\left(A - 4 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(18 i \, A + 72 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 18 \, {\left(A - 4 i \, B\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) + {\left(18 \, {\left(A - 4 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(18 i \, A + 72 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 18 \, {\left(A - 4 i \, B\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) + {\left(12 \, {\left(A - i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(12 i \, A + 12 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 12 \, {\left(A - i \, B\right)} a^{2}\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(36 \, {\left(A - 3 i \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-36 i \, A - 108 \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + 36 \, {\left(A - 4 i \, B\right)} 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({\left(9 i \, A + 36 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 9 \, {\left(A - 4 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(9 i \, A + 36 \, B\right)} 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({\left(-9 i \, A - 36 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 9 \, {\left(A - 4 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-9 i \, A - 36 \, B\right)} 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({\left(12 i \, A + 12 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) - 12 \, {\left(A - i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(12 i \, A + 12 \, B\right)} a^{2}\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({\left(-36 i \, A - 108 \, B\right)} a^{2} \cos\left(2 \, f x + 2 \, e\right) + 36 \, {\left(A - 3 i \, B\right)} a^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-36 i \, A - 144 \, B\right)} 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(-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,"-((18*(A - 4*I*B)*a^2*cos(2*f*x + 2*e) + (18*I*A + 72*B)*a^2*sin(2*f*x + 2*e) + 18*(A - 4*I*B)*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) + (18*(A - 4*I*B)*a^2*cos(2*f*x + 2*e) + (18*I*A + 72*B)*a^2*sin(2*f*x + 2*e) + 18*(A - 4*I*B)*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) + (12*(A - I*B)*a^2*cos(2*f*x + 2*e) + (12*I*A + 12*B)*a^2*sin(2*f*x + 2*e) + 12*(A - I*B)*a^2)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (36*(A - 3*I*B)*a^2*cos(2*f*x + 2*e) - (-36*I*A - 108*B)*a^2*sin(2*f*x + 2*e) + 36*(A - 4*I*B)*a^2)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((9*I*A + 36*B)*a^2*cos(2*f*x + 2*e) - 9*(A - 4*I*B)*a^2*sin(2*f*x + 2*e) + (9*I*A + 36*B)*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) + ((-9*I*A - 36*B)*a^2*cos(2*f*x + 2*e) + 9*(A - 4*I*B)*a^2*sin(2*f*x + 2*e) + (-9*I*A - 36*B)*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) + ((12*I*A + 12*B)*a^2*cos(2*f*x + 2*e) - 12*(A - I*B)*a^2*sin(2*f*x + 2*e) + (12*I*A + 12*B)*a^2)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((-36*I*A - 108*B)*a^2*cos(2*f*x + 2*e) + 36*(A - 3*I*B)*a^2*sin(2*f*x + 2*e) + (-36*I*A - 144*B)*a^2)*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
811,1,215,0,0.919288," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(30 \, B a^{2} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 30 \, B a^{2} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-6 i \, A - 6 \, B\right)} a^{2} \cos\left(5 \, f x + 5 \, e\right) + 20 \, B a^{2} \cos\left(3 \, f x + 3 \, e\right) - 60 \, B a^{2} \cos\left(f x + e\right) + 15 i \, B a^{2} \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) - 15 i \, B a^{2} \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) + 6 \, {\left(A - i \, B\right)} a^{2} \sin\left(5 \, f x + 5 \, e\right) + 20 i \, B a^{2} \sin\left(3 \, f x + 3 \, e\right) - 60 i \, B a^{2} \sin\left(f x + e\right)\right)} \sqrt{a}}{30 \, c^{\frac{5}{2}} f}"," ",0,"1/30*(30*B*a^2*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 30*B*a^2*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-6*I*A - 6*B)*a^2*cos(5*f*x + 5*e) + 20*B*a^2*cos(3*f*x + 3*e) - 60*B*a^2*cos(f*x + e) + 15*I*B*a^2*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 15*I*B*a^2*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + 6*(A - I*B)*a^2*sin(5*f*x + 5*e) + 20*I*B*a^2*sin(3*f*x + 3*e) - 60*I*B*a^2*sin(f*x + e))*sqrt(a)/(c^(5/2)*f)","A",0
812,1,167,0,1.031098," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(350 \, {\left(A - i \, B\right)} a^{2} \cos\left(9 \, f x + 9 \, e\right) + 140 \, {\left(6 \, A + i \, B\right)} a^{2} \cos\left(7 \, f x + 7 \, e\right) + 490 \, {\left(A + i \, B\right)} a^{2} \cos\left(5 \, f x + 5 \, e\right) + {\left(350 i \, A + 350 \, B\right)} a^{2} \sin\left(9 \, f x + 9 \, e\right) + {\left(840 i \, A - 140 \, B\right)} a^{2} \sin\left(7 \, f x + 7 \, e\right) + {\left(490 i \, A - 490 \, B\right)} a^{2} \sin\left(5 \, f x + 5 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-4900 i \, c^{4} \cos\left(2 \, f x + 2 \, e\right) + 4900 \, c^{4} \sin\left(2 \, f x + 2 \, e\right) - 4900 i \, c^{4}\right)} f}"," ",0,"-(350*(A - I*B)*a^2*cos(9*f*x + 9*e) + 140*(6*A + I*B)*a^2*cos(7*f*x + 7*e) + 490*(A + I*B)*a^2*cos(5*f*x + 5*e) + (350*I*A + 350*B)*a^2*sin(9*f*x + 9*e) + (840*I*A - 140*B)*a^2*sin(7*f*x + 7*e) + (490*I*A - 490*B)*a^2*sin(5*f*x + 5*e))*sqrt(a)*sqrt(c)/((-4900*I*c^4*cos(2*f*x + 2*e) + 4900*c^4*sin(2*f*x + 2*e) - 4900*I*c^4)*f)","B",0
813,1,198,0,1.038609," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{{\left({\left(35 i \, A + 35 \, B\right)} a^{2} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 90 i \, A a^{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) + {\left(63 i \, A - 63 \, B\right)} a^{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) - 35 \, {\left(A - i \, B\right)} a^{2} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 90 \, A a^{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) - 63 \, {\left(A + i \, B\right)} a^{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)\right)} \sqrt{a}}{1260 \, c^{\frac{9}{2}} f}"," ",0,"-1/1260*((35*I*A + 35*B)*a^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 90*I*A*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (63*I*A - 63*B)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 35*(A - I*B)*a^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 90*A*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 63*(A + I*B)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(9/2)*f)","A",0
814,1,276,0,1.221062," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{{\left({\left(315 i \, A + 315 \, B\right)} a^{2} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(1155 i \, A + 385 \, B\right)} a^{2} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(1485 i \, A - 495 \, B\right)} a^{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) + {\left(693 i \, A - 693 \, B\right)} a^{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) - 315 \, {\left(A - i \, B\right)} a^{2} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 385 \, {\left(3 \, A - i \, B\right)} a^{2} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 495 \, {\left(3 \, A + i \, B\right)} a^{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) - 693 \, {\left(A + i \, B\right)} a^{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)\right)} \sqrt{a}}{27720 \, c^{\frac{11}{2}} f}"," ",0,"-1/27720*((315*I*A + 315*B)*a^2*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1155*I*A + 385*B)*a^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1485*I*A - 495*B)*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (693*I*A - 693*B)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 315*(A - I*B)*a^2*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 385*(3*A - I*B)*a^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 495*(3*A + I*B)*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 693*(A + I*B)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(11/2)*f)","A",0
815,1,332,0,1.219547," ","integrate((a+I*a*tan(f*x+e))^(5/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(13/2),x, algorithm=""maxima"")","-\frac{{\left({\left(1155 i \, A + 1155 \, B\right)} a^{2} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(5460 i \, A + 2730 \, B\right)} a^{2} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 10010 i \, A a^{2} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(8580 i \, A - 4290 \, B\right)} a^{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) + {\left(3003 i \, A - 3003 \, B\right)} a^{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) - 1155 \, {\left(A - i \, B\right)} a^{2} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 2730 \, {\left(2 \, A - i \, B\right)} a^{2} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10010 \, A a^{2} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 4290 \, {\left(2 \, A + i \, B\right)} a^{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) - 3003 \, {\left(A + i \, B\right)} a^{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)\right)} \sqrt{a}}{240240 \, c^{\frac{13}{2}} f}"," ",0,"-1/240240*((1155*I*A + 1155*B)*a^2*cos(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (5460*I*A + 2730*B)*a^2*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 10010*I*A*a^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (8580*I*A - 4290*B)*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (3003*I*A - 3003*B)*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1155*(A - I*B)*a^2*sin(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2730*(2*A - I*B)*a^2*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10010*A*a^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 4290*(2*A + I*B)*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3003*(A + I*B)*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(13/2)*f)","A",0
816,1,2618,0,38.452070," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{{\left(36126720 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 276971520 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 922435584 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1738555392 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 344064 \, {\left(8728 \, A + 44099 i \, B\right)} a^{3} c^{4} \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) - 922435584 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \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) - 276971520 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \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) - 36126720 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \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(-289013760 i \, A + 36126720 \, B\right)} a^{3} c^{4} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-2215772160 i \, A + 276971520 \, B\right)} a^{3} c^{4} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-7379484672 i \, A + 922435584 \, B\right)} a^{3} c^{4} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-13908443136 i \, A + 1738555392 \, B\right)} a^{3} c^{4} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - {\left(-3002990592 i \, A + 15172878336 \, B\right)} a^{3} c^{4} \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) - {\left(7379484672 i \, A - 922435584 \, B\right)} a^{3} c^{4} \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(2215772160 i \, A - 276971520 \, B\right)} a^{3} c^{4} \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(289013760 i \, A - 36126720 \, B\right)} a^{3} c^{4} \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(18063360 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(16 \, f x + 16 \, e\right) + 144506880 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(14 \, f x + 14 \, e\right) + 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(12 \, f x + 12 \, e\right) + 1011548160 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(10 \, f x + 10 \, e\right) + 1264435200 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(8 \, f x + 8 \, e\right) + 1011548160 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(6 \, f x + 6 \, e\right) + 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(4 \, f x + 4 \, e\right) + 144506880 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(2 \, f x + 2 \, e\right) - {\left(-144506880 i \, A + 18063360 \, B\right)} a^{3} c^{4} \sin\left(16 \, f x + 16 \, e\right) - {\left(-1156055040 i \, A + 144506880 \, B\right)} a^{3} c^{4} \sin\left(14 \, f x + 14 \, e\right) - {\left(-4046192640 i \, A + 505774080 \, B\right)} a^{3} c^{4} \sin\left(12 \, f x + 12 \, e\right) - {\left(-8092385280 i \, A + 1011548160 \, B\right)} a^{3} c^{4} \sin\left(10 \, f x + 10 \, e\right) - {\left(-10115481600 i \, A + 1264435200 \, B\right)} a^{3} c^{4} \sin\left(8 \, f x + 8 \, e\right) - {\left(-8092385280 i \, A + 1011548160 \, B\right)} a^{3} c^{4} \sin\left(6 \, f x + 6 \, e\right) - {\left(-4046192640 i \, A + 505774080 \, B\right)} a^{3} c^{4} \sin\left(4 \, f x + 4 \, e\right) - {\left(-1156055040 i \, A + 144506880 \, B\right)} a^{3} c^{4} \sin\left(2 \, f x + 2 \, e\right) + 18063360 \, {\left(8 \, A + i \, B\right)} a^{3} c^{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(18063360 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(16 \, f x + 16 \, e\right) + 144506880 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(14 \, f x + 14 \, e\right) + 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(12 \, f x + 12 \, e\right) + 1011548160 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(10 \, f x + 10 \, e\right) + 1264435200 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(8 \, f x + 8 \, e\right) + 1011548160 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(6 \, f x + 6 \, e\right) + 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(4 \, f x + 4 \, e\right) + 144506880 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \cos\left(2 \, f x + 2 \, e\right) - {\left(-144506880 i \, A + 18063360 \, B\right)} a^{3} c^{4} \sin\left(16 \, f x + 16 \, e\right) - {\left(-1156055040 i \, A + 144506880 \, B\right)} a^{3} c^{4} \sin\left(14 \, f x + 14 \, e\right) - {\left(-4046192640 i \, A + 505774080 \, B\right)} a^{3} c^{4} \sin\left(12 \, f x + 12 \, e\right) - {\left(-8092385280 i \, A + 1011548160 \, B\right)} a^{3} c^{4} \sin\left(10 \, f x + 10 \, e\right) - {\left(-10115481600 i \, A + 1264435200 \, B\right)} a^{3} c^{4} \sin\left(8 \, f x + 8 \, e\right) - {\left(-8092385280 i \, A + 1011548160 \, B\right)} a^{3} c^{4} \sin\left(6 \, f x + 6 \, e\right) - {\left(-4046192640 i \, A + 505774080 \, B\right)} a^{3} c^{4} \sin\left(4 \, f x + 4 \, e\right) - {\left(-1156055040 i \, A + 144506880 \, B\right)} a^{3} c^{4} \sin\left(2 \, f x + 2 \, e\right) + 18063360 \, {\left(8 \, A + i \, B\right)} a^{3} c^{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({\left(-72253440 i \, A + 9031680 \, B\right)} a^{3} c^{4} \cos\left(16 \, f x + 16 \, e\right) + {\left(-578027520 i \, A + 72253440 \, B\right)} a^{3} c^{4} \cos\left(14 \, f x + 14 \, e\right) + {\left(-2023096320 i \, A + 252887040 \, B\right)} a^{3} c^{4} \cos\left(12 \, f x + 12 \, e\right) + {\left(-4046192640 i \, A + 505774080 \, B\right)} a^{3} c^{4} \cos\left(10 \, f x + 10 \, e\right) + {\left(-5057740800 i \, A + 632217600 \, B\right)} a^{3} c^{4} \cos\left(8 \, f x + 8 \, e\right) + {\left(-4046192640 i \, A + 505774080 \, B\right)} a^{3} c^{4} \cos\left(6 \, f x + 6 \, e\right) + {\left(-2023096320 i \, A + 252887040 \, B\right)} a^{3} c^{4} \cos\left(4 \, f x + 4 \, e\right) + {\left(-578027520 i \, A + 72253440 \, B\right)} a^{3} c^{4} \cos\left(2 \, f x + 2 \, e\right) + 9031680 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(16 \, f x + 16 \, e\right) + 72253440 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(14 \, f x + 14 \, e\right) + 252887040 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(12 \, f x + 12 \, e\right) + 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(10 \, f x + 10 \, e\right) + 632217600 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(8 \, f x + 8 \, e\right) + 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(6 \, f x + 6 \, e\right) + 252887040 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(4 \, f x + 4 \, e\right) + 72253440 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(2 \, f x + 2 \, e\right) + {\left(-72253440 i \, A + 9031680 \, B\right)} a^{3} c^{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({\left(72253440 i \, A - 9031680 \, B\right)} a^{3} c^{4} \cos\left(16 \, f x + 16 \, e\right) + {\left(578027520 i \, A - 72253440 \, B\right)} a^{3} c^{4} \cos\left(14 \, f x + 14 \, e\right) + {\left(2023096320 i \, A - 252887040 \, B\right)} a^{3} c^{4} \cos\left(12 \, f x + 12 \, e\right) + {\left(4046192640 i \, A - 505774080 \, B\right)} a^{3} c^{4} \cos\left(10 \, f x + 10 \, e\right) + {\left(5057740800 i \, A - 632217600 \, B\right)} a^{3} c^{4} \cos\left(8 \, f x + 8 \, e\right) + {\left(4046192640 i \, A - 505774080 \, B\right)} a^{3} c^{4} \cos\left(6 \, f x + 6 \, e\right) + {\left(2023096320 i \, A - 252887040 \, B\right)} a^{3} c^{4} \cos\left(4 \, f x + 4 \, e\right) + {\left(578027520 i \, A - 72253440 \, B\right)} a^{3} c^{4} \cos\left(2 \, f x + 2 \, e\right) - 9031680 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(16 \, f x + 16 \, e\right) - 72253440 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(14 \, f x + 14 \, e\right) - 252887040 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(12 \, f x + 12 \, e\right) - 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(10 \, f x + 10 \, e\right) - 632217600 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(8 \, f x + 8 \, e\right) - 505774080 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(6 \, f x + 6 \, e\right) - 252887040 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(4 \, f x + 4 \, e\right) - 72253440 \, {\left(8 \, A + i \, B\right)} a^{3} c^{4} \sin\left(2 \, f x + 2 \, e\right) + {\left(72253440 i \, A - 9031680 \, B\right)} a^{3} c^{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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-462422016 i \, \cos\left(16 \, f x + 16 \, e\right) - 3699376128 i \, \cos\left(14 \, f x + 14 \, e\right) - 12947816448 i \, \cos\left(12 \, f x + 12 \, e\right) - 25895632896 i \, \cos\left(10 \, f x + 10 \, e\right) - 32369541120 i \, \cos\left(8 \, f x + 8 \, e\right) - 25895632896 i \, \cos\left(6 \, f x + 6 \, e\right) - 12947816448 i \, \cos\left(4 \, f x + 4 \, e\right) - 3699376128 i \, \cos\left(2 \, f x + 2 \, e\right) + 462422016 \, \sin\left(16 \, f x + 16 \, e\right) + 3699376128 \, \sin\left(14 \, f x + 14 \, e\right) + 12947816448 \, \sin\left(12 \, f x + 12 \, e\right) + 25895632896 \, \sin\left(10 \, f x + 10 \, e\right) + 32369541120 \, \sin\left(8 \, f x + 8 \, e\right) + 25895632896 \, \sin\left(6 \, f x + 6 \, e\right) + 12947816448 \, \sin\left(4 \, f x + 4 \, e\right) + 3699376128 \, \sin\left(2 \, f x + 2 \, e\right) - 462422016 i\right)}}"," ",0,"-(36126720*(8*A + I*B)*a^3*c^4*cos(15/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 276971520*(8*A + I*B)*a^3*c^4*cos(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 922435584*(8*A + I*B)*a^3*c^4*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1738555392*(8*A + I*B)*a^3*c^4*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 344064*(8728*A + 44099*I*B)*a^3*c^4*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 922435584*(8*A + I*B)*a^3*c^4*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 276971520*(8*A + I*B)*a^3*c^4*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 36126720*(8*A + I*B)*a^3*c^4*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-289013760*I*A + 36126720*B)*a^3*c^4*sin(15/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-2215772160*I*A + 276971520*B)*a^3*c^4*sin(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-7379484672*I*A + 922435584*B)*a^3*c^4*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-13908443136*I*A + 1738555392*B)*a^3*c^4*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-3002990592*I*A + 15172878336*B)*a^3*c^4*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (7379484672*I*A - 922435584*B)*a^3*c^4*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (2215772160*I*A - 276971520*B)*a^3*c^4*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (289013760*I*A - 36126720*B)*a^3*c^4*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (18063360*(8*A + I*B)*a^3*c^4*cos(16*f*x + 16*e) + 144506880*(8*A + I*B)*a^3*c^4*cos(14*f*x + 14*e) + 505774080*(8*A + I*B)*a^3*c^4*cos(12*f*x + 12*e) + 1011548160*(8*A + I*B)*a^3*c^4*cos(10*f*x + 10*e) + 1264435200*(8*A + I*B)*a^3*c^4*cos(8*f*x + 8*e) + 1011548160*(8*A + I*B)*a^3*c^4*cos(6*f*x + 6*e) + 505774080*(8*A + I*B)*a^3*c^4*cos(4*f*x + 4*e) + 144506880*(8*A + I*B)*a^3*c^4*cos(2*f*x + 2*e) - (-144506880*I*A + 18063360*B)*a^3*c^4*sin(16*f*x + 16*e) - (-1156055040*I*A + 144506880*B)*a^3*c^4*sin(14*f*x + 14*e) - (-4046192640*I*A + 505774080*B)*a^3*c^4*sin(12*f*x + 12*e) - (-8092385280*I*A + 1011548160*B)*a^3*c^4*sin(10*f*x + 10*e) - (-10115481600*I*A + 1264435200*B)*a^3*c^4*sin(8*f*x + 8*e) - (-8092385280*I*A + 1011548160*B)*a^3*c^4*sin(6*f*x + 6*e) - (-4046192640*I*A + 505774080*B)*a^3*c^4*sin(4*f*x + 4*e) - (-1156055040*I*A + 144506880*B)*a^3*c^4*sin(2*f*x + 2*e) + 18063360*(8*A + I*B)*a^3*c^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) + (18063360*(8*A + I*B)*a^3*c^4*cos(16*f*x + 16*e) + 144506880*(8*A + I*B)*a^3*c^4*cos(14*f*x + 14*e) + 505774080*(8*A + I*B)*a^3*c^4*cos(12*f*x + 12*e) + 1011548160*(8*A + I*B)*a^3*c^4*cos(10*f*x + 10*e) + 1264435200*(8*A + I*B)*a^3*c^4*cos(8*f*x + 8*e) + 1011548160*(8*A + I*B)*a^3*c^4*cos(6*f*x + 6*e) + 505774080*(8*A + I*B)*a^3*c^4*cos(4*f*x + 4*e) + 144506880*(8*A + I*B)*a^3*c^4*cos(2*f*x + 2*e) - (-144506880*I*A + 18063360*B)*a^3*c^4*sin(16*f*x + 16*e) - (-1156055040*I*A + 144506880*B)*a^3*c^4*sin(14*f*x + 14*e) - (-4046192640*I*A + 505774080*B)*a^3*c^4*sin(12*f*x + 12*e) - (-8092385280*I*A + 1011548160*B)*a^3*c^4*sin(10*f*x + 10*e) - (-10115481600*I*A + 1264435200*B)*a^3*c^4*sin(8*f*x + 8*e) - (-8092385280*I*A + 1011548160*B)*a^3*c^4*sin(6*f*x + 6*e) - (-4046192640*I*A + 505774080*B)*a^3*c^4*sin(4*f*x + 4*e) - (-1156055040*I*A + 144506880*B)*a^3*c^4*sin(2*f*x + 2*e) + 18063360*(8*A + I*B)*a^3*c^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) - ((-72253440*I*A + 9031680*B)*a^3*c^4*cos(16*f*x + 16*e) + (-578027520*I*A + 72253440*B)*a^3*c^4*cos(14*f*x + 14*e) + (-2023096320*I*A + 252887040*B)*a^3*c^4*cos(12*f*x + 12*e) + (-4046192640*I*A + 505774080*B)*a^3*c^4*cos(10*f*x + 10*e) + (-5057740800*I*A + 632217600*B)*a^3*c^4*cos(8*f*x + 8*e) + (-4046192640*I*A + 505774080*B)*a^3*c^4*cos(6*f*x + 6*e) + (-2023096320*I*A + 252887040*B)*a^3*c^4*cos(4*f*x + 4*e) + (-578027520*I*A + 72253440*B)*a^3*c^4*cos(2*f*x + 2*e) + 9031680*(8*A + I*B)*a^3*c^4*sin(16*f*x + 16*e) + 72253440*(8*A + I*B)*a^3*c^4*sin(14*f*x + 14*e) + 252887040*(8*A + I*B)*a^3*c^4*sin(12*f*x + 12*e) + 505774080*(8*A + I*B)*a^3*c^4*sin(10*f*x + 10*e) + 632217600*(8*A + I*B)*a^3*c^4*sin(8*f*x + 8*e) + 505774080*(8*A + I*B)*a^3*c^4*sin(6*f*x + 6*e) + 252887040*(8*A + I*B)*a^3*c^4*sin(4*f*x + 4*e) + 72253440*(8*A + I*B)*a^3*c^4*sin(2*f*x + 2*e) + (-72253440*I*A + 9031680*B)*a^3*c^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) - ((72253440*I*A - 9031680*B)*a^3*c^4*cos(16*f*x + 16*e) + (578027520*I*A - 72253440*B)*a^3*c^4*cos(14*f*x + 14*e) + (2023096320*I*A - 252887040*B)*a^3*c^4*cos(12*f*x + 12*e) + (4046192640*I*A - 505774080*B)*a^3*c^4*cos(10*f*x + 10*e) + (5057740800*I*A - 632217600*B)*a^3*c^4*cos(8*f*x + 8*e) + (4046192640*I*A - 505774080*B)*a^3*c^4*cos(6*f*x + 6*e) + (2023096320*I*A - 252887040*B)*a^3*c^4*cos(4*f*x + 4*e) + (578027520*I*A - 72253440*B)*a^3*c^4*cos(2*f*x + 2*e) - 9031680*(8*A + I*B)*a^3*c^4*sin(16*f*x + 16*e) - 72253440*(8*A + I*B)*a^3*c^4*sin(14*f*x + 14*e) - 252887040*(8*A + I*B)*a^3*c^4*sin(12*f*x + 12*e) - 505774080*(8*A + I*B)*a^3*c^4*sin(10*f*x + 10*e) - 632217600*(8*A + I*B)*a^3*c^4*sin(8*f*x + 8*e) - 505774080*(8*A + I*B)*a^3*c^4*sin(6*f*x + 6*e) - 252887040*(8*A + I*B)*a^3*c^4*sin(4*f*x + 4*e) - 72253440*(8*A + I*B)*a^3*c^4*sin(2*f*x + 2*e) + (72253440*I*A - 9031680*B)*a^3*c^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))*sqrt(a)*sqrt(c)/(f*(-462422016*I*cos(16*f*x + 16*e) - 3699376128*I*cos(14*f*x + 14*e) - 12947816448*I*cos(12*f*x + 12*e) - 25895632896*I*cos(10*f*x + 10*e) - 32369541120*I*cos(8*f*x + 8*e) - 25895632896*I*cos(6*f*x + 6*e) - 12947816448*I*cos(4*f*x + 4*e) - 3699376128*I*cos(2*f*x + 2*e) + 462422016*sin(16*f*x + 16*e) + 3699376128*sin(14*f*x + 14*e) + 12947816448*sin(12*f*x + 12*e) + 25895632896*sin(10*f*x + 10*e) + 32369541120*sin(8*f*x + 8*e) + 25895632896*sin(6*f*x + 6*e) + 12947816448*sin(4*f*x + 4*e) + 3699376128*sin(2*f*x + 2*e) - 462422016*I))","B",0
817,1,1904,0,5.281233," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(420 \, A a^{3} c^{3} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2800 \, A a^{3} c^{3} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 7924 \, A a^{3} c^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 12288 i \, B a^{3} c^{3} \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) - 7924 \, A a^{3} c^{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) - 2800 \, A a^{3} c^{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) - 420 \, A a^{3} c^{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) + 420 i \, A a^{3} c^{3} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 2800 i \, A a^{3} c^{3} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 7924 i \, A a^{3} c^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 12288 \, B a^{3} c^{3} \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) - 7924 i \, A a^{3} c^{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) - 2800 i \, A a^{3} c^{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) - 420 i \, A a^{3} c^{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) + {\left(210 \, A a^{3} c^{3} \cos\left(14 \, f x + 14 \, e\right) + 1470 \, A a^{3} c^{3} \cos\left(12 \, f x + 12 \, e\right) + 4410 \, A a^{3} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 7350 \, A a^{3} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 7350 \, A a^{3} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 4410 \, A a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 1470 \, A a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 210 i \, A a^{3} c^{3} \sin\left(14 \, f x + 14 \, e\right) + 1470 i \, A a^{3} c^{3} \sin\left(12 \, f x + 12 \, e\right) + 4410 i \, A a^{3} c^{3} \sin\left(10 \, f x + 10 \, e\right) + 7350 i \, A a^{3} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 7350 i \, A a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 4410 i \, A a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 1470 i \, A a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 210 \, A a^{3} c^{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(210 \, A a^{3} c^{3} \cos\left(14 \, f x + 14 \, e\right) + 1470 \, A a^{3} c^{3} \cos\left(12 \, f x + 12 \, e\right) + 4410 \, A a^{3} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 7350 \, A a^{3} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 7350 \, A a^{3} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 4410 \, A a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 1470 \, A a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 210 i \, A a^{3} c^{3} \sin\left(14 \, f x + 14 \, e\right) + 1470 i \, A a^{3} c^{3} \sin\left(12 \, f x + 12 \, e\right) + 4410 i \, A a^{3} c^{3} \sin\left(10 \, f x + 10 \, e\right) + 7350 i \, A a^{3} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 7350 i \, A a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 4410 i \, A a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 1470 i \, A a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 210 \, A a^{3} c^{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(-105 i \, A a^{3} c^{3} \cos\left(14 \, f x + 14 \, e\right) - 735 i \, A a^{3} c^{3} \cos\left(12 \, f x + 12 \, e\right) - 2205 i \, A a^{3} c^{3} \cos\left(10 \, f x + 10 \, e\right) - 3675 i \, A a^{3} c^{3} \cos\left(8 \, f x + 8 \, e\right) - 3675 i \, A a^{3} c^{3} \cos\left(6 \, f x + 6 \, e\right) - 2205 i \, A a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right) - 735 i \, A a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) + 105 \, A a^{3} c^{3} \sin\left(14 \, f x + 14 \, e\right) + 735 \, A a^{3} c^{3} \sin\left(12 \, f x + 12 \, e\right) + 2205 \, A a^{3} c^{3} \sin\left(10 \, f x + 10 \, e\right) + 3675 \, A a^{3} c^{3} \sin\left(8 \, f x + 8 \, e\right) + 3675 \, A a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right) + 2205 \, A a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) + 735 \, A a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right) - 105 i \, A a^{3} c^{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(105 i \, A a^{3} c^{3} \cos\left(14 \, f x + 14 \, e\right) + 735 i \, A a^{3} c^{3} \cos\left(12 \, f x + 12 \, e\right) + 2205 i \, A a^{3} c^{3} \cos\left(10 \, f x + 10 \, e\right) + 3675 i \, A a^{3} c^{3} \cos\left(8 \, f x + 8 \, e\right) + 3675 i \, A a^{3} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 2205 i \, A a^{3} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 735 i \, A a^{3} c^{3} \cos\left(2 \, f x + 2 \, e\right) - 105 \, A a^{3} c^{3} \sin\left(14 \, f x + 14 \, e\right) - 735 \, A a^{3} c^{3} \sin\left(12 \, f x + 12 \, e\right) - 2205 \, A a^{3} c^{3} \sin\left(10 \, f x + 10 \, e\right) - 3675 \, A a^{3} c^{3} \sin\left(8 \, f x + 8 \, e\right) - 3675 \, A a^{3} c^{3} \sin\left(6 \, f x + 6 \, e\right) - 2205 \, A a^{3} c^{3} \sin\left(4 \, f x + 4 \, e\right) - 735 \, A a^{3} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 105 i \, A a^{3} c^{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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-672 i \, \cos\left(14 \, f x + 14 \, e\right) - 4704 i \, \cos\left(12 \, f x + 12 \, e\right) - 14112 i \, \cos\left(10 \, f x + 10 \, e\right) - 23520 i \, \cos\left(8 \, f x + 8 \, e\right) - 23520 i \, \cos\left(6 \, f x + 6 \, e\right) - 14112 i \, \cos\left(4 \, f x + 4 \, e\right) - 4704 i \, \cos\left(2 \, f x + 2 \, e\right) + 672 \, \sin\left(14 \, f x + 14 \, e\right) + 4704 \, \sin\left(12 \, f x + 12 \, e\right) + 14112 \, \sin\left(10 \, f x + 10 \, e\right) + 23520 \, \sin\left(8 \, f x + 8 \, e\right) + 23520 \, \sin\left(6 \, f x + 6 \, e\right) + 14112 \, \sin\left(4 \, f x + 4 \, e\right) + 4704 \, \sin\left(2 \, f x + 2 \, e\right) - 672 i\right)}}"," ",0,"-(420*A*a^3*c^3*cos(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2800*A*a^3*c^3*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 7924*A*a^3*c^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12288*I*B*a^3*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7924*A*a^3*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2800*A*a^3*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 420*A*a^3*c^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 420*I*A*a^3*c^3*sin(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2800*I*A*a^3*c^3*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 7924*I*A*a^3*c^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12288*B*a^3*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 7924*I*A*a^3*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2800*I*A*a^3*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 420*I*A*a^3*c^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (210*A*a^3*c^3*cos(14*f*x + 14*e) + 1470*A*a^3*c^3*cos(12*f*x + 12*e) + 4410*A*a^3*c^3*cos(10*f*x + 10*e) + 7350*A*a^3*c^3*cos(8*f*x + 8*e) + 7350*A*a^3*c^3*cos(6*f*x + 6*e) + 4410*A*a^3*c^3*cos(4*f*x + 4*e) + 1470*A*a^3*c^3*cos(2*f*x + 2*e) + 210*I*A*a^3*c^3*sin(14*f*x + 14*e) + 1470*I*A*a^3*c^3*sin(12*f*x + 12*e) + 4410*I*A*a^3*c^3*sin(10*f*x + 10*e) + 7350*I*A*a^3*c^3*sin(8*f*x + 8*e) + 7350*I*A*a^3*c^3*sin(6*f*x + 6*e) + 4410*I*A*a^3*c^3*sin(4*f*x + 4*e) + 1470*I*A*a^3*c^3*sin(2*f*x + 2*e) + 210*A*a^3*c^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) + (210*A*a^3*c^3*cos(14*f*x + 14*e) + 1470*A*a^3*c^3*cos(12*f*x + 12*e) + 4410*A*a^3*c^3*cos(10*f*x + 10*e) + 7350*A*a^3*c^3*cos(8*f*x + 8*e) + 7350*A*a^3*c^3*cos(6*f*x + 6*e) + 4410*A*a^3*c^3*cos(4*f*x + 4*e) + 1470*A*a^3*c^3*cos(2*f*x + 2*e) + 210*I*A*a^3*c^3*sin(14*f*x + 14*e) + 1470*I*A*a^3*c^3*sin(12*f*x + 12*e) + 4410*I*A*a^3*c^3*sin(10*f*x + 10*e) + 7350*I*A*a^3*c^3*sin(8*f*x + 8*e) + 7350*I*A*a^3*c^3*sin(6*f*x + 6*e) + 4410*I*A*a^3*c^3*sin(4*f*x + 4*e) + 1470*I*A*a^3*c^3*sin(2*f*x + 2*e) + 210*A*a^3*c^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) - (-105*I*A*a^3*c^3*cos(14*f*x + 14*e) - 735*I*A*a^3*c^3*cos(12*f*x + 12*e) - 2205*I*A*a^3*c^3*cos(10*f*x + 10*e) - 3675*I*A*a^3*c^3*cos(8*f*x + 8*e) - 3675*I*A*a^3*c^3*cos(6*f*x + 6*e) - 2205*I*A*a^3*c^3*cos(4*f*x + 4*e) - 735*I*A*a^3*c^3*cos(2*f*x + 2*e) + 105*A*a^3*c^3*sin(14*f*x + 14*e) + 735*A*a^3*c^3*sin(12*f*x + 12*e) + 2205*A*a^3*c^3*sin(10*f*x + 10*e) + 3675*A*a^3*c^3*sin(8*f*x + 8*e) + 3675*A*a^3*c^3*sin(6*f*x + 6*e) + 2205*A*a^3*c^3*sin(4*f*x + 4*e) + 735*A*a^3*c^3*sin(2*f*x + 2*e) - 105*I*A*a^3*c^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) - (105*I*A*a^3*c^3*cos(14*f*x + 14*e) + 735*I*A*a^3*c^3*cos(12*f*x + 12*e) + 2205*I*A*a^3*c^3*cos(10*f*x + 10*e) + 3675*I*A*a^3*c^3*cos(8*f*x + 8*e) + 3675*I*A*a^3*c^3*cos(6*f*x + 6*e) + 2205*I*A*a^3*c^3*cos(4*f*x + 4*e) + 735*I*A*a^3*c^3*cos(2*f*x + 2*e) - 105*A*a^3*c^3*sin(14*f*x + 14*e) - 735*A*a^3*c^3*sin(12*f*x + 12*e) - 2205*A*a^3*c^3*sin(10*f*x + 10*e) - 3675*A*a^3*c^3*sin(8*f*x + 8*e) - 3675*A*a^3*c^3*sin(6*f*x + 6*e) - 2205*A*a^3*c^3*sin(4*f*x + 4*e) - 735*A*a^3*c^3*sin(2*f*x + 2*e) + 105*I*A*a^3*c^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))*sqrt(a)*sqrt(c)/(f*(-672*I*cos(14*f*x + 14*e) - 4704*I*cos(12*f*x + 12*e) - 14112*I*cos(10*f*x + 10*e) - 23520*I*cos(8*f*x + 8*e) - 23520*I*cos(6*f*x + 6*e) - 14112*I*cos(4*f*x + 4*e) - 4704*I*cos(2*f*x + 2*e) + 672*sin(14*f*x + 14*e) + 4704*sin(12*f*x + 12*e) + 14112*sin(10*f*x + 10*e) + 23520*sin(8*f*x + 8*e) + 23520*sin(6*f*x + 6*e) + 14112*sin(4*f*x + 4*e) + 4704*sin(2*f*x + 2*e) - 672*I))","B",0
818,1,2026,0,9.018071," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(230400 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 1305600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 92160 \, {\left(58 \, A - 223 i \, B\right)} a^{3} 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) - 3041280 \, {\left(6 \, A - i \, B\right)} a^{3} 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) - 1305600 \, {\left(6 \, A - i \, B\right)} a^{3} 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) - 230400 \, {\left(6 \, A - i \, B\right)} a^{3} 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) + {\left(1382400 i \, A + 230400 \, B\right)} a^{3} c^{2} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(7833600 i \, A + 1305600 \, B\right)} a^{3} c^{2} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(-5345280 i \, A - 20551680 \, B\right)} a^{3} 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) + {\left(-18247680 i \, A - 3041280 \, B\right)} a^{3} 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) + {\left(-7833600 i \, A - 1305600 \, B\right)} a^{3} 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) + {\left(-1382400 i \, A - 230400 \, B\right)} a^{3} 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(115200 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(12 \, f x + 12 \, e\right) + 691200 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(10 \, f x + 10 \, e\right) + 1728000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 2304000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 1728000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 691200 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(691200 i \, A + 115200 \, B\right)} a^{3} c^{2} \sin\left(12 \, f x + 12 \, e\right) + {\left(4147200 i \, A + 691200 \, B\right)} a^{3} c^{2} \sin\left(10 \, f x + 10 \, e\right) + {\left(10368000 i \, A + 1728000 \, B\right)} a^{3} c^{2} \sin\left(8 \, f x + 8 \, e\right) + {\left(13824000 i \, A + 2304000 \, B\right)} a^{3} c^{2} \sin\left(6 \, f x + 6 \, e\right) + {\left(10368000 i \, A + 1728000 \, B\right)} a^{3} c^{2} \sin\left(4 \, f x + 4 \, e\right) + {\left(4147200 i \, A + 691200 \, B\right)} a^{3} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 115200 \, {\left(6 \, A - i \, B\right)} a^{3} 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(115200 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(12 \, f x + 12 \, e\right) + 691200 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(10 \, f x + 10 \, e\right) + 1728000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(8 \, f x + 8 \, e\right) + 2304000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(6 \, f x + 6 \, e\right) + 1728000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 691200 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \cos\left(2 \, f x + 2 \, e\right) + {\left(691200 i \, A + 115200 \, B\right)} a^{3} c^{2} \sin\left(12 \, f x + 12 \, e\right) + {\left(4147200 i \, A + 691200 \, B\right)} a^{3} c^{2} \sin\left(10 \, f x + 10 \, e\right) + {\left(10368000 i \, A + 1728000 \, B\right)} a^{3} c^{2} \sin\left(8 \, f x + 8 \, e\right) + {\left(13824000 i \, A + 2304000 \, B\right)} a^{3} c^{2} \sin\left(6 \, f x + 6 \, e\right) + {\left(10368000 i \, A + 1728000 \, B\right)} a^{3} c^{2} \sin\left(4 \, f x + 4 \, e\right) + {\left(4147200 i \, A + 691200 \, B\right)} a^{3} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 115200 \, {\left(6 \, A - i \, B\right)} a^{3} 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({\left(345600 i \, A + 57600 \, B\right)} a^{3} c^{2} \cos\left(12 \, f x + 12 \, e\right) + {\left(2073600 i \, A + 345600 \, B\right)} a^{3} c^{2} \cos\left(10 \, f x + 10 \, e\right) + {\left(5184000 i \, A + 864000 \, B\right)} a^{3} c^{2} \cos\left(8 \, f x + 8 \, e\right) + {\left(6912000 i \, A + 1152000 \, B\right)} a^{3} c^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(5184000 i \, A + 864000 \, B\right)} a^{3} c^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(2073600 i \, A + 345600 \, B\right)} a^{3} c^{2} \cos\left(2 \, f x + 2 \, e\right) - 57600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(12 \, f x + 12 \, e\right) - 345600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(10 \, f x + 10 \, e\right) - 864000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(8 \, f x + 8 \, e\right) - 1152000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(6 \, f x + 6 \, e\right) - 864000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(4 \, f x + 4 \, e\right) - 345600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(345600 i \, A + 57600 \, B\right)} a^{3} 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({\left(-345600 i \, A - 57600 \, B\right)} a^{3} c^{2} \cos\left(12 \, f x + 12 \, e\right) + {\left(-2073600 i \, A - 345600 \, B\right)} a^{3} c^{2} \cos\left(10 \, f x + 10 \, e\right) + {\left(-5184000 i \, A - 864000 \, B\right)} a^{3} c^{2} \cos\left(8 \, f x + 8 \, e\right) + {\left(-6912000 i \, A - 1152000 \, B\right)} a^{3} c^{2} \cos\left(6 \, f x + 6 \, e\right) + {\left(-5184000 i \, A - 864000 \, B\right)} a^{3} c^{2} \cos\left(4 \, f x + 4 \, e\right) + {\left(-2073600 i \, A - 345600 \, B\right)} a^{3} c^{2} \cos\left(2 \, f x + 2 \, e\right) + 57600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(12 \, f x + 12 \, e\right) + 345600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(10 \, f x + 10 \, e\right) + 864000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(8 \, f x + 8 \, e\right) + 1152000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(6 \, f x + 6 \, e\right) + 864000 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(4 \, f x + 4 \, e\right) + 345600 \, {\left(6 \, A - i \, B\right)} a^{3} c^{2} \sin\left(2 \, f x + 2 \, e\right) + {\left(-345600 i \, A - 57600 \, B\right)} a^{3} 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(-1843200 i \, \cos\left(12 \, f x + 12 \, e\right) - 11059200 i \, \cos\left(10 \, f x + 10 \, e\right) - 27648000 i \, \cos\left(8 \, f x + 8 \, e\right) - 36864000 i \, \cos\left(6 \, f x + 6 \, e\right) - 27648000 i \, \cos\left(4 \, f x + 4 \, e\right) - 11059200 i \, \cos\left(2 \, f x + 2 \, e\right) + 1843200 \, \sin\left(12 \, f x + 12 \, e\right) + 11059200 \, \sin\left(10 \, f x + 10 \, e\right) + 27648000 \, \sin\left(8 \, f x + 8 \, e\right) + 36864000 \, \sin\left(6 \, f x + 6 \, e\right) + 27648000 \, \sin\left(4 \, f x + 4 \, e\right) + 11059200 \, \sin\left(2 \, f x + 2 \, e\right) - 1843200 i\right)}}"," ",0,"-(230400*(6*A - I*B)*a^3*c^2*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 1305600*(6*A - I*B)*a^3*c^2*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 92160*(58*A - 223*I*B)*a^3*c^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3041280*(6*A - I*B)*a^3*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1305600*(6*A - I*B)*a^3*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 230400*(6*A - I*B)*a^3*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1382400*I*A + 230400*B)*a^3*c^2*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (7833600*I*A + 1305600*B)*a^3*c^2*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-5345280*I*A - 20551680*B)*a^3*c^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-18247680*I*A - 3041280*B)*a^3*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-7833600*I*A - 1305600*B)*a^3*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-1382400*I*A - 230400*B)*a^3*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (115200*(6*A - I*B)*a^3*c^2*cos(12*f*x + 12*e) + 691200*(6*A - I*B)*a^3*c^2*cos(10*f*x + 10*e) + 1728000*(6*A - I*B)*a^3*c^2*cos(8*f*x + 8*e) + 2304000*(6*A - I*B)*a^3*c^2*cos(6*f*x + 6*e) + 1728000*(6*A - I*B)*a^3*c^2*cos(4*f*x + 4*e) + 691200*(6*A - I*B)*a^3*c^2*cos(2*f*x + 2*e) + (691200*I*A + 115200*B)*a^3*c^2*sin(12*f*x + 12*e) + (4147200*I*A + 691200*B)*a^3*c^2*sin(10*f*x + 10*e) + (10368000*I*A + 1728000*B)*a^3*c^2*sin(8*f*x + 8*e) + (13824000*I*A + 2304000*B)*a^3*c^2*sin(6*f*x + 6*e) + (10368000*I*A + 1728000*B)*a^3*c^2*sin(4*f*x + 4*e) + (4147200*I*A + 691200*B)*a^3*c^2*sin(2*f*x + 2*e) + 115200*(6*A - I*B)*a^3*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) + (115200*(6*A - I*B)*a^3*c^2*cos(12*f*x + 12*e) + 691200*(6*A - I*B)*a^3*c^2*cos(10*f*x + 10*e) + 1728000*(6*A - I*B)*a^3*c^2*cos(8*f*x + 8*e) + 2304000*(6*A - I*B)*a^3*c^2*cos(6*f*x + 6*e) + 1728000*(6*A - I*B)*a^3*c^2*cos(4*f*x + 4*e) + 691200*(6*A - I*B)*a^3*c^2*cos(2*f*x + 2*e) + (691200*I*A + 115200*B)*a^3*c^2*sin(12*f*x + 12*e) + (4147200*I*A + 691200*B)*a^3*c^2*sin(10*f*x + 10*e) + (10368000*I*A + 1728000*B)*a^3*c^2*sin(8*f*x + 8*e) + (13824000*I*A + 2304000*B)*a^3*c^2*sin(6*f*x + 6*e) + (10368000*I*A + 1728000*B)*a^3*c^2*sin(4*f*x + 4*e) + (4147200*I*A + 691200*B)*a^3*c^2*sin(2*f*x + 2*e) + 115200*(6*A - I*B)*a^3*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) + ((345600*I*A + 57600*B)*a^3*c^2*cos(12*f*x + 12*e) + (2073600*I*A + 345600*B)*a^3*c^2*cos(10*f*x + 10*e) + (5184000*I*A + 864000*B)*a^3*c^2*cos(8*f*x + 8*e) + (6912000*I*A + 1152000*B)*a^3*c^2*cos(6*f*x + 6*e) + (5184000*I*A + 864000*B)*a^3*c^2*cos(4*f*x + 4*e) + (2073600*I*A + 345600*B)*a^3*c^2*cos(2*f*x + 2*e) - 57600*(6*A - I*B)*a^3*c^2*sin(12*f*x + 12*e) - 345600*(6*A - I*B)*a^3*c^2*sin(10*f*x + 10*e) - 864000*(6*A - I*B)*a^3*c^2*sin(8*f*x + 8*e) - 1152000*(6*A - I*B)*a^3*c^2*sin(6*f*x + 6*e) - 864000*(6*A - I*B)*a^3*c^2*sin(4*f*x + 4*e) - 345600*(6*A - I*B)*a^3*c^2*sin(2*f*x + 2*e) + (345600*I*A + 57600*B)*a^3*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) + ((-345600*I*A - 57600*B)*a^3*c^2*cos(12*f*x + 12*e) + (-2073600*I*A - 345600*B)*a^3*c^2*cos(10*f*x + 10*e) + (-5184000*I*A - 864000*B)*a^3*c^2*cos(8*f*x + 8*e) + (-6912000*I*A - 1152000*B)*a^3*c^2*cos(6*f*x + 6*e) + (-5184000*I*A - 864000*B)*a^3*c^2*cos(4*f*x + 4*e) + (-2073600*I*A - 345600*B)*a^3*c^2*cos(2*f*x + 2*e) + 57600*(6*A - I*B)*a^3*c^2*sin(12*f*x + 12*e) + 345600*(6*A - I*B)*a^3*c^2*sin(10*f*x + 10*e) + 864000*(6*A - I*B)*a^3*c^2*sin(8*f*x + 8*e) + 1152000*(6*A - I*B)*a^3*c^2*sin(6*f*x + 6*e) + 864000*(6*A - I*B)*a^3*c^2*sin(4*f*x + 4*e) + 345600*(6*A - I*B)*a^3*c^2*sin(2*f*x + 2*e) + (-345600*I*A - 57600*B)*a^3*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*(-1843200*I*cos(12*f*x + 12*e) - 11059200*I*cos(10*f*x + 10*e) - 27648000*I*cos(8*f*x + 8*e) - 36864000*I*cos(6*f*x + 6*e) - 27648000*I*cos(4*f*x + 4*e) - 11059200*I*cos(2*f*x + 2*e) + 1843200*sin(12*f*x + 12*e) + 11059200*sin(10*f*x + 10*e) + 27648000*sin(8*f*x + 8*e) + 36864000*sin(6*f*x + 6*e) + 27648000*sin(4*f*x + 4*e) + 11059200*sin(2*f*x + 2*e) - 1843200*I))","B",0
819,1,1635,0,5.425299," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(28800 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 19200 \, {\left(29 \, A - 50 i \, B\right)} a^{3} c \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) - 245760 \, {\left(5 \, A - 2 i \, B\right)} a^{3} 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) - 134400 \, {\left(5 \, A - 2 i \, B\right)} a^{3} 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) - 28800 \, {\left(5 \, A - 2 i \, B\right)} a^{3} 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) + {\left(144000 i \, A + 57600 \, B\right)} a^{3} c \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(-556800 i \, A - 960000 \, B\right)} a^{3} c \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) + {\left(-1228800 i \, A - 491520 \, B\right)} a^{3} 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) + {\left(-672000 i \, A - 268800 \, B\right)} a^{3} 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) + {\left(-144000 i \, A - 57600 \, B\right)} a^{3} 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(14400 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(10 \, f x + 10 \, e\right) + 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(8 \, f x + 8 \, e\right) + 144000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(6 \, f x + 6 \, e\right) + 144000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(4 \, f x + 4 \, e\right) + 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(2 \, f x + 2 \, e\right) + {\left(72000 i \, A + 28800 \, B\right)} a^{3} c \sin\left(10 \, f x + 10 \, e\right) + {\left(360000 i \, A + 144000 \, B\right)} a^{3} c \sin\left(8 \, f x + 8 \, e\right) + {\left(720000 i \, A + 288000 \, B\right)} a^{3} c \sin\left(6 \, f x + 6 \, e\right) + {\left(720000 i \, A + 288000 \, B\right)} a^{3} c \sin\left(4 \, f x + 4 \, e\right) + {\left(360000 i \, A + 144000 \, B\right)} a^{3} c \sin\left(2 \, f x + 2 \, e\right) + 14400 \, {\left(5 \, A - 2 i \, B\right)} a^{3} 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(14400 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(10 \, f x + 10 \, e\right) + 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(8 \, f x + 8 \, e\right) + 144000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(6 \, f x + 6 \, e\right) + 144000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(4 \, f x + 4 \, e\right) + 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \cos\left(2 \, f x + 2 \, e\right) + {\left(72000 i \, A + 28800 \, B\right)} a^{3} c \sin\left(10 \, f x + 10 \, e\right) + {\left(360000 i \, A + 144000 \, B\right)} a^{3} c \sin\left(8 \, f x + 8 \, e\right) + {\left(720000 i \, A + 288000 \, B\right)} a^{3} c \sin\left(6 \, f x + 6 \, e\right) + {\left(720000 i \, A + 288000 \, B\right)} a^{3} c \sin\left(4 \, f x + 4 \, e\right) + {\left(360000 i \, A + 144000 \, B\right)} a^{3} c \sin\left(2 \, f x + 2 \, e\right) + 14400 \, {\left(5 \, A - 2 i \, B\right)} a^{3} 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({\left(36000 i \, A + 14400 \, B\right)} a^{3} c \cos\left(10 \, f x + 10 \, e\right) + {\left(180000 i \, A + 72000 \, B\right)} a^{3} c \cos\left(8 \, f x + 8 \, e\right) + {\left(360000 i \, A + 144000 \, B\right)} a^{3} c \cos\left(6 \, f x + 6 \, e\right) + {\left(360000 i \, A + 144000 \, B\right)} a^{3} c \cos\left(4 \, f x + 4 \, e\right) + {\left(180000 i \, A + 72000 \, B\right)} a^{3} c \cos\left(2 \, f x + 2 \, e\right) - 7200 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(10 \, f x + 10 \, e\right) - 36000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(8 \, f x + 8 \, e\right) - 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(6 \, f x + 6 \, e\right) - 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(4 \, f x + 4 \, e\right) - 36000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(2 \, f x + 2 \, e\right) + {\left(36000 i \, A + 14400 \, B\right)} a^{3} 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({\left(-36000 i \, A - 14400 \, B\right)} a^{3} c \cos\left(10 \, f x + 10 \, e\right) + {\left(-180000 i \, A - 72000 \, B\right)} a^{3} c \cos\left(8 \, f x + 8 \, e\right) + {\left(-360000 i \, A - 144000 \, B\right)} a^{3} c \cos\left(6 \, f x + 6 \, e\right) + {\left(-360000 i \, A - 144000 \, B\right)} a^{3} c \cos\left(4 \, f x + 4 \, e\right) + {\left(-180000 i \, A - 72000 \, B\right)} a^{3} c \cos\left(2 \, f x + 2 \, e\right) + 7200 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(10 \, f x + 10 \, e\right) + 36000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(8 \, f x + 8 \, e\right) + 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(6 \, f x + 6 \, e\right) + 72000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(4 \, f x + 4 \, e\right) + 36000 \, {\left(5 \, A - 2 i \, B\right)} a^{3} c \sin\left(2 \, f x + 2 \, e\right) + {\left(-36000 i \, A - 14400 \, B\right)} a^{3} 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(-115200 i \, \cos\left(10 \, f x + 10 \, e\right) - 576000 i \, \cos\left(8 \, f x + 8 \, e\right) - 1152000 i \, \cos\left(6 \, f x + 6 \, e\right) - 1152000 i \, \cos\left(4 \, f x + 4 \, e\right) - 576000 i \, \cos\left(2 \, f x + 2 \, e\right) + 115200 \, \sin\left(10 \, f x + 10 \, e\right) + 576000 \, \sin\left(8 \, f x + 8 \, e\right) + 1152000 \, \sin\left(6 \, f x + 6 \, e\right) + 1152000 \, \sin\left(4 \, f x + 4 \, e\right) + 576000 \, \sin\left(2 \, f x + 2 \, e\right) - 115200 i\right)}}"," ",0,"-(28800*(5*A - 2*I*B)*a^3*c*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 19200*(29*A - 50*I*B)*a^3*c*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 245760*(5*A - 2*I*B)*a^3*c*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 134400*(5*A - 2*I*B)*a^3*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 28800*(5*A - 2*I*B)*a^3*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (144000*I*A + 57600*B)*a^3*c*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-556800*I*A - 960000*B)*a^3*c*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-1228800*I*A - 491520*B)*a^3*c*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-672000*I*A - 268800*B)*a^3*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-144000*I*A - 57600*B)*a^3*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (14400*(5*A - 2*I*B)*a^3*c*cos(10*f*x + 10*e) + 72000*(5*A - 2*I*B)*a^3*c*cos(8*f*x + 8*e) + 144000*(5*A - 2*I*B)*a^3*c*cos(6*f*x + 6*e) + 144000*(5*A - 2*I*B)*a^3*c*cos(4*f*x + 4*e) + 72000*(5*A - 2*I*B)*a^3*c*cos(2*f*x + 2*e) + (72000*I*A + 28800*B)*a^3*c*sin(10*f*x + 10*e) + (360000*I*A + 144000*B)*a^3*c*sin(8*f*x + 8*e) + (720000*I*A + 288000*B)*a^3*c*sin(6*f*x + 6*e) + (720000*I*A + 288000*B)*a^3*c*sin(4*f*x + 4*e) + (360000*I*A + 144000*B)*a^3*c*sin(2*f*x + 2*e) + 14400*(5*A - 2*I*B)*a^3*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) + (14400*(5*A - 2*I*B)*a^3*c*cos(10*f*x + 10*e) + 72000*(5*A - 2*I*B)*a^3*c*cos(8*f*x + 8*e) + 144000*(5*A - 2*I*B)*a^3*c*cos(6*f*x + 6*e) + 144000*(5*A - 2*I*B)*a^3*c*cos(4*f*x + 4*e) + 72000*(5*A - 2*I*B)*a^3*c*cos(2*f*x + 2*e) + (72000*I*A + 28800*B)*a^3*c*sin(10*f*x + 10*e) + (360000*I*A + 144000*B)*a^3*c*sin(8*f*x + 8*e) + (720000*I*A + 288000*B)*a^3*c*sin(6*f*x + 6*e) + (720000*I*A + 288000*B)*a^3*c*sin(4*f*x + 4*e) + (360000*I*A + 144000*B)*a^3*c*sin(2*f*x + 2*e) + 14400*(5*A - 2*I*B)*a^3*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) + ((36000*I*A + 14400*B)*a^3*c*cos(10*f*x + 10*e) + (180000*I*A + 72000*B)*a^3*c*cos(8*f*x + 8*e) + (360000*I*A + 144000*B)*a^3*c*cos(6*f*x + 6*e) + (360000*I*A + 144000*B)*a^3*c*cos(4*f*x + 4*e) + (180000*I*A + 72000*B)*a^3*c*cos(2*f*x + 2*e) - 7200*(5*A - 2*I*B)*a^3*c*sin(10*f*x + 10*e) - 36000*(5*A - 2*I*B)*a^3*c*sin(8*f*x + 8*e) - 72000*(5*A - 2*I*B)*a^3*c*sin(6*f*x + 6*e) - 72000*(5*A - 2*I*B)*a^3*c*sin(4*f*x + 4*e) - 36000*(5*A - 2*I*B)*a^3*c*sin(2*f*x + 2*e) + (36000*I*A + 14400*B)*a^3*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) + ((-36000*I*A - 14400*B)*a^3*c*cos(10*f*x + 10*e) + (-180000*I*A - 72000*B)*a^3*c*cos(8*f*x + 8*e) + (-360000*I*A - 144000*B)*a^3*c*cos(6*f*x + 6*e) + (-360000*I*A - 144000*B)*a^3*c*cos(4*f*x + 4*e) + (-180000*I*A - 72000*B)*a^3*c*cos(2*f*x + 2*e) + 7200*(5*A - 2*I*B)*a^3*c*sin(10*f*x + 10*e) + 36000*(5*A - 2*I*B)*a^3*c*sin(8*f*x + 8*e) + 72000*(5*A - 2*I*B)*a^3*c*sin(6*f*x + 6*e) + 72000*(5*A - 2*I*B)*a^3*c*sin(4*f*x + 4*e) + 36000*(5*A - 2*I*B)*a^3*c*sin(2*f*x + 2*e) + (-36000*I*A - 14400*B)*a^3*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*(-115200*I*cos(10*f*x + 10*e) - 576000*I*cos(8*f*x + 8*e) - 1152000*I*cos(6*f*x + 6*e) - 1152000*I*cos(4*f*x + 4*e) - 576000*I*cos(2*f*x + 2*e) + 115200*sin(10*f*x + 10*e) + 576000*sin(8*f*x + 8*e) + 1152000*sin(6*f*x + 6*e) + 1152000*sin(4*f*x + 4*e) + 576000*sin(2*f*x + 2*e) - 115200*I))","B",0
820,1,1335,0,2.954730," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e)),x, algorithm=""maxima"")","\frac{{\left(1152 \, {\left(44 \, A - 49 i \, B\right)} a^{3} \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) + 28032 \, {\left(4 \, A - 3 i \, B\right)} 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) + 21120 \, {\left(4 \, A - 3 i \, B\right)} 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) + 5760 \, {\left(4 \, A - 3 i \, B\right)} 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) - {\left(-50688 i \, A - 56448 \, B\right)} a^{3} \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) - {\left(-112128 i \, A - 84096 \, B\right)} 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) - {\left(-84480 i \, A - 63360 \, B\right)} 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(-23040 i \, A - 17280 \, B\right)} 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) - {\left(2880 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(8 \, f x + 8 \, e\right) + 11520 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + 17280 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 11520 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(11520 i \, A + 8640 \, B\right)} a^{3} \sin\left(8 \, f x + 8 \, e\right) + {\left(46080 i \, A + 34560 \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + {\left(69120 i \, A + 51840 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(46080 i \, A + 34560 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 2880 \, {\left(4 \, A - 3 i \, B\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) - {\left(2880 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(8 \, f x + 8 \, e\right) + 11520 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + 17280 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 11520 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(11520 i \, A + 8640 \, B\right)} a^{3} \sin\left(8 \, f x + 8 \, e\right) + {\left(46080 i \, A + 34560 \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + {\left(69120 i \, A + 51840 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(46080 i \, A + 34560 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 2880 \, {\left(4 \, A - 3 i \, B\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) - {\left({\left(5760 i \, A + 4320 \, B\right)} a^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(23040 i \, A + 17280 \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(34560 i \, A + 25920 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(23040 i \, A + 17280 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 1440 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(8 \, f x + 8 \, e\right) - 5760 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) - 8640 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) - 5760 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(5760 i \, A + 4320 \, B\right)} 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({\left(-5760 i \, A - 4320 \, B\right)} a^{3} \cos\left(8 \, f x + 8 \, e\right) + {\left(-23040 i \, A - 17280 \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(-34560 i \, A - 25920 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-23040 i \, A - 17280 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 1440 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(8 \, f x + 8 \, e\right) + 5760 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + 8640 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + 5760 \, {\left(4 \, A - 3 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-5760 i \, A - 4320 \, B\right)} 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)\right)} \sqrt{a} \sqrt{c}}{f {\left(-4608 i \, \cos\left(8 \, f x + 8 \, e\right) - 18432 i \, \cos\left(6 \, f x + 6 \, e\right) - 27648 i \, \cos\left(4 \, f x + 4 \, e\right) - 18432 i \, \cos\left(2 \, f x + 2 \, e\right) + 4608 \, \sin\left(8 \, f x + 8 \, e\right) + 18432 \, \sin\left(6 \, f x + 6 \, e\right) + 27648 \, \sin\left(4 \, f x + 4 \, e\right) + 18432 \, \sin\left(2 \, f x + 2 \, e\right) - 4608 i\right)}}"," ",0,"(1152*(44*A - 49*I*B)*a^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 28032*(4*A - 3*I*B)*a^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 21120*(4*A - 3*I*B)*a^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 5760*(4*A - 3*I*B)*a^3*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-50688*I*A - 56448*B)*a^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-112128*I*A - 84096*B)*a^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-84480*I*A - 63360*B)*a^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-23040*I*A - 17280*B)*a^3*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (2880*(4*A - 3*I*B)*a^3*cos(8*f*x + 8*e) + 11520*(4*A - 3*I*B)*a^3*cos(6*f*x + 6*e) + 17280*(4*A - 3*I*B)*a^3*cos(4*f*x + 4*e) + 11520*(4*A - 3*I*B)*a^3*cos(2*f*x + 2*e) + (11520*I*A + 8640*B)*a^3*sin(8*f*x + 8*e) + (46080*I*A + 34560*B)*a^3*sin(6*f*x + 6*e) + (69120*I*A + 51840*B)*a^3*sin(4*f*x + 4*e) + (46080*I*A + 34560*B)*a^3*sin(2*f*x + 2*e) + 2880*(4*A - 3*I*B)*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) - (2880*(4*A - 3*I*B)*a^3*cos(8*f*x + 8*e) + 11520*(4*A - 3*I*B)*a^3*cos(6*f*x + 6*e) + 17280*(4*A - 3*I*B)*a^3*cos(4*f*x + 4*e) + 11520*(4*A - 3*I*B)*a^3*cos(2*f*x + 2*e) + (11520*I*A + 8640*B)*a^3*sin(8*f*x + 8*e) + (46080*I*A + 34560*B)*a^3*sin(6*f*x + 6*e) + (69120*I*A + 51840*B)*a^3*sin(4*f*x + 4*e) + (46080*I*A + 34560*B)*a^3*sin(2*f*x + 2*e) + 2880*(4*A - 3*I*B)*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) - ((5760*I*A + 4320*B)*a^3*cos(8*f*x + 8*e) + (23040*I*A + 17280*B)*a^3*cos(6*f*x + 6*e) + (34560*I*A + 25920*B)*a^3*cos(4*f*x + 4*e) + (23040*I*A + 17280*B)*a^3*cos(2*f*x + 2*e) - 1440*(4*A - 3*I*B)*a^3*sin(8*f*x + 8*e) - 5760*(4*A - 3*I*B)*a^3*sin(6*f*x + 6*e) - 8640*(4*A - 3*I*B)*a^3*sin(4*f*x + 4*e) - 5760*(4*A - 3*I*B)*a^3*sin(2*f*x + 2*e) + (5760*I*A + 4320*B)*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) - ((-5760*I*A - 4320*B)*a^3*cos(8*f*x + 8*e) + (-23040*I*A - 17280*B)*a^3*cos(6*f*x + 6*e) + (-34560*I*A - 25920*B)*a^3*cos(4*f*x + 4*e) + (-23040*I*A - 17280*B)*a^3*cos(2*f*x + 2*e) + 1440*(4*A - 3*I*B)*a^3*sin(8*f*x + 8*e) + 5760*(4*A - 3*I*B)*a^3*sin(6*f*x + 6*e) + 8640*(4*A - 3*I*B)*a^3*sin(4*f*x + 4*e) + 5760*(4*A - 3*I*B)*a^3*sin(2*f*x + 2*e) + (-5760*I*A - 4320*B)*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))*sqrt(a)*sqrt(c)/(f*(-4608*I*cos(8*f*x + 8*e) - 18432*I*cos(6*f*x + 6*e) - 27648*I*cos(4*f*x + 4*e) - 18432*I*cos(2*f*x + 2*e) + 4608*sin(8*f*x + 8*e) + 18432*sin(6*f*x + 6*e) + 27648*sin(4*f*x + 4*e) + 18432*sin(2*f*x + 2*e) - 4608*I))","B",0
821,1,1331,0,2.388197," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(72 \, {\left(9 \, A - 20 i \, B\right)} 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) + 192 \, {\left(6 \, A - 11 i \, B\right)} 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) - {\left(-648 i \, A - 1440 \, B\right)} 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) - {\left(-1152 i \, A - 2112 \, B\right)} 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(180 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + 540 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 540 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(540 i \, A + 720 \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + {\left(1620 i \, A + 2160 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(1620 i \, A + 2160 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 180 \, {\left(3 \, A - 4 i \, B\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) - {\left(180 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + 540 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 540 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(540 i \, A + 720 \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + {\left(1620 i \, A + 2160 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(1620 i \, A + 2160 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 180 \, {\left(3 \, A - 4 i \, B\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) + {\left(576 \, {\left(A - i \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + 1728 \, {\left(A - i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 1728 \, {\left(A - i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-576 i \, A - 576 \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-1728 i \, A - 1728 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-1728 i \, A - 1728 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 360 \, {\left(3 \, A - 4 i \, B\right)} 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({\left(270 i \, A + 360 \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(810 i \, A + 1080 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(810 i \, A + 1080 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 90 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) - 270 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) - 270 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(270 i \, A + 360 \, B\right)} 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({\left(-270 i \, A - 360 \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(-810 i \, A - 1080 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-810 i \, A - 1080 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 90 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + 270 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + 270 \, {\left(3 \, A - 4 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-270 i \, A - 360 \, B\right)} 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({\left(-576 i \, A - 576 \, B\right)} a^{3} \cos\left(6 \, f x + 6 \, e\right) + {\left(-1728 i \, A - 1728 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-1728 i \, A - 1728 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 576 \, {\left(A - i \, B\right)} a^{3} \sin\left(6 \, f x + 6 \, e\right) + 1728 \, {\left(A - i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + 1728 \, {\left(A - i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-1080 i \, A - 1440 \, B\right)} 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(-72 i \, c \cos\left(6 \, f x + 6 \, e\right) - 216 i \, c \cos\left(4 \, f x + 4 \, e\right) - 216 i \, c \cos\left(2 \, f x + 2 \, e\right) + 72 \, c \sin\left(6 \, f x + 6 \, e\right) + 216 \, c \sin\left(4 \, f x + 4 \, e\right) + 216 \, c \sin\left(2 \, f x + 2 \, e\right) - 72 i \, c\right)} f}"," ",0,"-(72*(9*A - 20*I*B)*a^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 192*(6*A - 11*I*B)*a^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-648*I*A - 1440*B)*a^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1152*I*A - 2112*B)*a^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (180*(3*A - 4*I*B)*a^3*cos(6*f*x + 6*e) + 540*(3*A - 4*I*B)*a^3*cos(4*f*x + 4*e) + 540*(3*A - 4*I*B)*a^3*cos(2*f*x + 2*e) + (540*I*A + 720*B)*a^3*sin(6*f*x + 6*e) + (1620*I*A + 2160*B)*a^3*sin(4*f*x + 4*e) + (1620*I*A + 2160*B)*a^3*sin(2*f*x + 2*e) + 180*(3*A - 4*I*B)*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) - (180*(3*A - 4*I*B)*a^3*cos(6*f*x + 6*e) + 540*(3*A - 4*I*B)*a^3*cos(4*f*x + 4*e) + 540*(3*A - 4*I*B)*a^3*cos(2*f*x + 2*e) + (540*I*A + 720*B)*a^3*sin(6*f*x + 6*e) + (1620*I*A + 2160*B)*a^3*sin(4*f*x + 4*e) + (1620*I*A + 2160*B)*a^3*sin(2*f*x + 2*e) + 180*(3*A - 4*I*B)*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) + (576*(A - I*B)*a^3*cos(6*f*x + 6*e) + 1728*(A - I*B)*a^3*cos(4*f*x + 4*e) + 1728*(A - I*B)*a^3*cos(2*f*x + 2*e) - (-576*I*A - 576*B)*a^3*sin(6*f*x + 6*e) - (-1728*I*A - 1728*B)*a^3*sin(4*f*x + 4*e) - (-1728*I*A - 1728*B)*a^3*sin(2*f*x + 2*e) + 360*(3*A - 4*I*B)*a^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - ((270*I*A + 360*B)*a^3*cos(6*f*x + 6*e) + (810*I*A + 1080*B)*a^3*cos(4*f*x + 4*e) + (810*I*A + 1080*B)*a^3*cos(2*f*x + 2*e) - 90*(3*A - 4*I*B)*a^3*sin(6*f*x + 6*e) - 270*(3*A - 4*I*B)*a^3*sin(4*f*x + 4*e) - 270*(3*A - 4*I*B)*a^3*sin(2*f*x + 2*e) + (270*I*A + 360*B)*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) - ((-270*I*A - 360*B)*a^3*cos(6*f*x + 6*e) + (-810*I*A - 1080*B)*a^3*cos(4*f*x + 4*e) + (-810*I*A - 1080*B)*a^3*cos(2*f*x + 2*e) + 90*(3*A - 4*I*B)*a^3*sin(6*f*x + 6*e) + 270*(3*A - 4*I*B)*a^3*sin(4*f*x + 4*e) + 270*(3*A - 4*I*B)*a^3*sin(2*f*x + 2*e) + (-270*I*A - 360*B)*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) - ((-576*I*A - 576*B)*a^3*cos(6*f*x + 6*e) + (-1728*I*A - 1728*B)*a^3*cos(4*f*x + 4*e) + (-1728*I*A - 1728*B)*a^3*cos(2*f*x + 2*e) + 576*(A - I*B)*a^3*sin(6*f*x + 6*e) + 1728*(A - I*B)*a^3*sin(4*f*x + 4*e) + 1728*(A - I*B)*a^3*sin(2*f*x + 2*e) + (-1080*I*A - 1440*B)*a^3)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-72*I*c*cos(6*f*x + 6*e) - 216*I*c*cos(4*f*x + 4*e) - 216*I*c*cos(2*f*x + 2*e) + 72*c*sin(6*f*x + 6*e) + 216*c*sin(4*f*x + 4*e) + 216*c*sin(2*f*x + 2*e) - 72*I*c)*f)","B",0
822,1,1161,0,1.338077," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(60 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 120 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(120 i \, A + 300 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(240 i \, A + 600 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 60 \, {\left(2 \, A - 5 i \, B\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) + {\left(60 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 120 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(120 i \, A + 300 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(240 i \, A + 600 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 60 \, {\left(2 \, A - 5 i \, B\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) + {\left(32 \, {\left(A - i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 64 \, {\left(A - i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(32 i \, A + 32 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + {\left(64 i \, A + 64 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) - 8 \, {\left(2 \, A - 29 i \, B\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) - {\left(192 \, {\left(A - 2 i \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + 384 \, {\left(A - 2 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-192 i \, A - 384 \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-384 i \, A - 768 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 120 \, {\left(2 \, A - 5 i \, B\right)} 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({\left(60 i \, A + 150 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(120 i \, A + 300 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 30 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) - 60 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(60 i \, A + 150 \, B\right)} 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({\left(-60 i \, A - 150 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-120 i \, A - 300 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 30 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + 60 \, {\left(2 \, A - 5 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-60 i \, A - 150 \, B\right)} 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({\left(32 i \, A + 32 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(64 i \, A + 64 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 32 \, {\left(A - i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) - 64 \, {\left(A - i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-16 i \, A - 232 \, B\right)} 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({\left(-192 i \, A - 384 \, B\right)} a^{3} \cos\left(4 \, f x + 4 \, e\right) + {\left(-384 i \, A - 768 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 192 \, {\left(A - 2 i \, B\right)} a^{3} \sin\left(4 \, f x + 4 \, e\right) + 384 \, {\left(A - 2 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-240 i \, A - 600 \, B\right)} 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(-24 i \, c^{2} \cos\left(4 \, f x + 4 \, e\right) - 48 i \, c^{2} \cos\left(2 \, f x + 2 \, e\right) + 24 \, c^{2} \sin\left(4 \, f x + 4 \, e\right) + 48 \, c^{2} \sin\left(2 \, f x + 2 \, e\right) - 24 i \, c^{2}\right)} f}"," ",0,"-((60*(2*A - 5*I*B)*a^3*cos(4*f*x + 4*e) + 120*(2*A - 5*I*B)*a^3*cos(2*f*x + 2*e) + (120*I*A + 300*B)*a^3*sin(4*f*x + 4*e) + (240*I*A + 600*B)*a^3*sin(2*f*x + 2*e) + 60*(2*A - 5*I*B)*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*(2*A - 5*I*B)*a^3*cos(4*f*x + 4*e) + 120*(2*A - 5*I*B)*a^3*cos(2*f*x + 2*e) + (120*I*A + 300*B)*a^3*sin(4*f*x + 4*e) + (240*I*A + 600*B)*a^3*sin(2*f*x + 2*e) + 60*(2*A - 5*I*B)*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) + (32*(A - I*B)*a^3*cos(4*f*x + 4*e) + 64*(A - I*B)*a^3*cos(2*f*x + 2*e) + (32*I*A + 32*B)*a^3*sin(4*f*x + 4*e) + (64*I*A + 64*B)*a^3*sin(2*f*x + 2*e) - 8*(2*A - 29*I*B)*a^3)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (192*(A - 2*I*B)*a^3*cos(4*f*x + 4*e) + 384*(A - 2*I*B)*a^3*cos(2*f*x + 2*e) - (-192*I*A - 384*B)*a^3*sin(4*f*x + 4*e) - (-384*I*A - 768*B)*a^3*sin(2*f*x + 2*e) + 120*(2*A - 5*I*B)*a^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((60*I*A + 150*B)*a^3*cos(4*f*x + 4*e) + (120*I*A + 300*B)*a^3*cos(2*f*x + 2*e) - 30*(2*A - 5*I*B)*a^3*sin(4*f*x + 4*e) - 60*(2*A - 5*I*B)*a^3*sin(2*f*x + 2*e) + (60*I*A + 150*B)*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) + ((-60*I*A - 150*B)*a^3*cos(4*f*x + 4*e) + (-120*I*A - 300*B)*a^3*cos(2*f*x + 2*e) + 30*(2*A - 5*I*B)*a^3*sin(4*f*x + 4*e) + 60*(2*A - 5*I*B)*a^3*sin(2*f*x + 2*e) + (-60*I*A - 150*B)*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) + ((32*I*A + 32*B)*a^3*cos(4*f*x + 4*e) + (64*I*A + 64*B)*a^3*cos(2*f*x + 2*e) - 32*(A - I*B)*a^3*sin(4*f*x + 4*e) - 64*(A - I*B)*a^3*sin(2*f*x + 2*e) + (-16*I*A - 232*B)*a^3)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((-192*I*A - 384*B)*a^3*cos(4*f*x + 4*e) + (-384*I*A - 768*B)*a^3*cos(2*f*x + 2*e) + 192*(A - 2*I*B)*a^3*sin(4*f*x + 4*e) + 384*(A - 2*I*B)*a^3*sin(2*f*x + 2*e) + (-240*I*A - 600*B)*a^3)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)*sqrt(c)/((-24*I*c^2*cos(4*f*x + 4*e) - 48*I*c^2*cos(2*f*x + 2*e) + 24*c^2*sin(4*f*x + 4*e) + 48*c^2*sin(2*f*x + 2*e) - 24*I*c^2)*f)","B",0
823,1,944,0,1.274309," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left({\left(450 \, {\left(A - 6 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(450 i \, A + 2700 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 450 \, {\left(A - 6 i \, B\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) + {\left(450 \, {\left(A - 6 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(450 i \, A + 2700 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 450 \, {\left(A - 6 i \, B\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) - {\left(180 \, {\left(A - i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-180 i \, A - 180 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 180 \, {\left(A - i \, B\right)} a^{3}\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(300 \, {\left(A - 3 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + {\left(300 i \, A + 900 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 300 \, {\left(A - 3 i \, B\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) - {\left(900 \, {\left(A - 5 i \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-900 i \, A - 4500 \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + 900 \, {\left(A - 6 i \, B\right)} 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({\left(225 i \, A + 1350 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 225 \, {\left(A - 6 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(225 i \, A + 1350 \, B\right)} 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({\left(-225 i \, A - 1350 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 225 \, {\left(A - 6 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-225 i \, A - 1350 \, B\right)} 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({\left(-180 i \, A - 180 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 180 \, {\left(A - i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-180 i \, A - 180 \, B\right)} a^{3}\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({\left(300 i \, A + 900 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) - 300 \, {\left(A - 3 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(300 i \, A + 900 \, B\right)} 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({\left(-900 i \, A - 4500 \, B\right)} a^{3} \cos\left(2 \, f x + 2 \, e\right) + 900 \, {\left(A - 5 i \, B\right)} a^{3} \sin\left(2 \, f x + 2 \, e\right) + {\left(-900 i \, A - 5400 \, B\right)} 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(-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,"((450*(A - 6*I*B)*a^3*cos(2*f*x + 2*e) + (450*I*A + 2700*B)*a^3*sin(2*f*x + 2*e) + 450*(A - 6*I*B)*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) + (450*(A - 6*I*B)*a^3*cos(2*f*x + 2*e) + (450*I*A + 2700*B)*a^3*sin(2*f*x + 2*e) + 450*(A - 6*I*B)*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) - (180*(A - I*B)*a^3*cos(2*f*x + 2*e) - (-180*I*A - 180*B)*a^3*sin(2*f*x + 2*e) + 180*(A - I*B)*a^3)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (300*(A - 3*I*B)*a^3*cos(2*f*x + 2*e) + (300*I*A + 900*B)*a^3*sin(2*f*x + 2*e) + 300*(A - 3*I*B)*a^3)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (900*(A - 5*I*B)*a^3*cos(2*f*x + 2*e) - (-900*I*A - 4500*B)*a^3*sin(2*f*x + 2*e) + 900*(A - 6*I*B)*a^3)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((225*I*A + 1350*B)*a^3*cos(2*f*x + 2*e) - 225*(A - 6*I*B)*a^3*sin(2*f*x + 2*e) + (225*I*A + 1350*B)*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) + ((-225*I*A - 1350*B)*a^3*cos(2*f*x + 2*e) + 225*(A - 6*I*B)*a^3*sin(2*f*x + 2*e) + (-225*I*A - 1350*B)*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) + ((-180*I*A - 180*B)*a^3*cos(2*f*x + 2*e) + 180*(A - I*B)*a^3*sin(2*f*x + 2*e) + (-180*I*A - 180*B)*a^3)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((300*I*A + 900*B)*a^3*cos(2*f*x + 2*e) - 300*(A - 3*I*B)*a^3*sin(2*f*x + 2*e) + (300*I*A + 900*B)*a^3)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + ((-900*I*A - 4500*B)*a^3*cos(2*f*x + 2*e) + 900*(A - 5*I*B)*a^3*sin(2*f*x + 2*e) + (-900*I*A - 5400*B)*a^3)*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
824,1,245,0,1.017377," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(7/2),x, algorithm=""maxima"")","-\frac{{\left(210 \, B a^{3} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 210 \, B a^{3} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(30 i \, A + 30 \, B\right)} a^{3} \cos\left(7 \, f x + 7 \, e\right) - 84 \, B a^{3} \cos\left(5 \, f x + 5 \, e\right) + 140 \, B a^{3} \cos\left(3 \, f x + 3 \, e\right) - 420 \, B a^{3} \cos\left(f x + e\right) + 105 i \, B a^{3} \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) - 105 i \, B a^{3} \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) - 30 \, {\left(A - i \, B\right)} a^{3} \sin\left(7 \, f x + 7 \, e\right) - 84 i \, B a^{3} \sin\left(5 \, f x + 5 \, e\right) + 140 i \, B a^{3} \sin\left(3 \, f x + 3 \, e\right) - 420 i \, B a^{3} \sin\left(f x + e\right)\right)} \sqrt{a}}{210 \, c^{\frac{7}{2}} f}"," ",0,"-1/210*(210*B*a^3*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 210*B*a^3*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (30*I*A + 30*B)*a^3*cos(7*f*x + 7*e) - 84*B*a^3*cos(5*f*x + 5*e) + 140*B*a^3*cos(3*f*x + 3*e) - 420*B*a^3*cos(f*x + e) + 105*I*B*a^3*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 105*I*B*a^3*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 30*(A - I*B)*a^3*sin(7*f*x + 7*e) - 84*I*B*a^3*sin(5*f*x + 5*e) + 140*I*B*a^3*sin(3*f*x + 3*e) - 420*I*B*a^3*sin(f*x + e))*sqrt(a)/(c^(7/2)*f)","A",0
825,1,167,0,1.218848," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(9/2),x, algorithm=""maxima"")","-\frac{{\left(882 \, {\left(A - i \, B\right)} a^{3} \cos\left(11 \, f x + 11 \, e\right) + 252 \, {\left(8 \, A + i \, B\right)} a^{3} \cos\left(9 \, f x + 9 \, e\right) + 1134 \, {\left(A + i \, B\right)} a^{3} \cos\left(7 \, f x + 7 \, e\right) + {\left(882 i \, A + 882 \, B\right)} a^{3} \sin\left(11 \, f x + 11 \, e\right) + {\left(2016 i \, A - 252 \, B\right)} a^{3} \sin\left(9 \, f x + 9 \, e\right) + {\left(1134 i \, A - 1134 \, B\right)} a^{3} \sin\left(7 \, f x + 7 \, e\right)\right)} \sqrt{a} \sqrt{c}}{{\left(-15876 i \, c^{5} \cos\left(2 \, f x + 2 \, e\right) + 15876 \, c^{5} \sin\left(2 \, f x + 2 \, e\right) - 15876 i \, c^{5}\right)} f}"," ",0,"-(882*(A - I*B)*a^3*cos(11*f*x + 11*e) + 252*(8*A + I*B)*a^3*cos(9*f*x + 9*e) + 1134*(A + I*B)*a^3*cos(7*f*x + 7*e) + (882*I*A + 882*B)*a^3*sin(11*f*x + 11*e) + (2016*I*A - 252*B)*a^3*sin(9*f*x + 9*e) + (1134*I*A - 1134*B)*a^3*sin(7*f*x + 7*e))*sqrt(a)*sqrt(c)/((-15876*I*c^5*cos(2*f*x + 2*e) + 15876*c^5*sin(2*f*x + 2*e) - 15876*I*c^5)*f)","B",0
826,1,198,0,0.718352," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(11/2),x, algorithm=""maxima"")","-\frac{{\left({\left(63 i \, A + 63 \, B\right)} a^{3} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 154 i \, A a^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(99 i \, A - 99 \, B\right)} a^{3} \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) - 63 \, {\left(A - i \, B\right)} a^{3} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 154 \, A a^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 99 \, {\left(A + i \, B\right)} a^{3} \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)\right)} \sqrt{a}}{2772 \, c^{\frac{11}{2}} f}"," ",0,"-1/2772*((63*I*A + 63*B)*a^3*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 154*I*A*a^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (99*I*A - 99*B)*a^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 63*(A - I*B)*a^3*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 154*A*a^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 99*(A + I*B)*a^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(11/2)*f)","A",0
827,1,276,0,0.967149," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(13/2),x, algorithm=""maxima"")","-\frac{{\left({\left(693 i \, A + 693 \, B\right)} a^{3} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(2457 i \, A + 819 \, B\right)} a^{3} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(3003 i \, A - 1001 \, B\right)} a^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(1287 i \, A - 1287 \, B\right)} a^{3} \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) - 693 \, {\left(A - i \, B\right)} a^{3} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 819 \, {\left(3 \, A - i \, B\right)} a^{3} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 1001 \, {\left(3 \, A + i \, B\right)} a^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 1287 \, {\left(A + i \, B\right)} a^{3} \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)\right)} \sqrt{a}}{72072 \, c^{\frac{13}{2}} f}"," ",0,"-1/72072*((693*I*A + 693*B)*a^3*cos(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (2457*I*A + 819*B)*a^3*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (3003*I*A - 1001*B)*a^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (1287*I*A - 1287*B)*a^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 693*(A - I*B)*a^3*sin(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 819*(3*A - I*B)*a^3*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1001*(3*A + I*B)*a^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 1287*(A + I*B)*a^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(13/2)*f)","A",0
828,1,332,0,0.885775," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(15/2),x, algorithm=""maxima"")","-\frac{{\left({\left(3003 i \, A + 3003 \, B\right)} a^{3} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(13860 i \, A + 6930 \, B\right)} a^{3} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + 24570 i \, A a^{3} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(20020 i \, A - 10010 \, B\right)} a^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(6435 i \, A - 6435 \, B\right)} a^{3} \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) - 3003 \, {\left(A - i \, B\right)} a^{3} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 6930 \, {\left(2 \, A - i \, B\right)} a^{3} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 24570 \, A a^{3} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 10010 \, {\left(2 \, A + i \, B\right)} a^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 6435 \, {\left(A + i \, B\right)} a^{3} \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)\right)} \sqrt{a}}{720720 \, c^{\frac{15}{2}} f}"," ",0,"-1/720720*((3003*I*A + 3003*B)*a^3*cos(15/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (13860*I*A + 6930*B)*a^3*cos(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 24570*I*A*a^3*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (20020*I*A - 10010*B)*a^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (6435*I*A - 6435*B)*a^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3003*(A - I*B)*a^3*sin(15/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6930*(2*A - I*B)*a^3*sin(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 24570*A*a^3*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 10010*(2*A + I*B)*a^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 6435*(A + I*B)*a^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(15/2)*f)","A",0
829,1,410,0,1.295912," ","integrate((a+I*a*tan(f*x+e))^(7/2)*(A+B*tan(f*x+e))/(c-I*c*tan(f*x+e))^(17/2),x, algorithm=""maxima"")","-\frac{{\left({\left(45045 i \, A + 45045 \, B\right)} a^{3} \cos\left(\frac{17}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(255255 i \, A + 153153 \, B\right)} a^{3} \cos\left(\frac{15}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(589050 i \, A + 117810 \, B\right)} a^{3} \cos\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(696150 i \, A - 139230 \, B\right)} a^{3} \cos\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(425425 i \, A - 255255 \, B\right)} a^{3} \cos\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) + {\left(109395 i \, A - 109395 \, B\right)} a^{3} \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) - 45045 \, {\left(A - i \, B\right)} a^{3} \sin\left(\frac{17}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 51051 \, {\left(5 \, A - 3 i \, B\right)} a^{3} \sin\left(\frac{15}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 117810 \, {\left(5 \, A - i \, B\right)} a^{3} \sin\left(\frac{13}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 139230 \, {\left(5 \, A + i \, B\right)} a^{3} \sin\left(\frac{11}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 85085 \, {\left(5 \, A + 3 i \, B\right)} a^{3} \sin\left(\frac{9}{2} \, \arctan\left(\sin\left(2 \, f x + 2 \, e\right), \cos\left(2 \, f x + 2 \, e\right)\right)\right) - 109395 \, {\left(A + i \, B\right)} a^{3} \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)\right)} \sqrt{a}}{24504480 \, c^{\frac{17}{2}} f}"," ",0,"-1/24504480*((45045*I*A + 45045*B)*a^3*cos(17/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (255255*I*A + 153153*B)*a^3*cos(15/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (589050*I*A + 117810*B)*a^3*cos(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (696150*I*A - 139230*B)*a^3*cos(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (425425*I*A - 255255*B)*a^3*cos(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (109395*I*A - 109395*B)*a^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 45045*(A - I*B)*a^3*sin(17/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 51051*(5*A - 3*I*B)*a^3*sin(15/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 117810*(5*A - I*B)*a^3*sin(13/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 139230*(5*A + I*B)*a^3*sin(11/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 85085*(5*A + 3*I*B)*a^3*sin(9/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 109395*(A + I*B)*a^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*sqrt(a)/(c^(17/2)*f)","A",0
830,1,1324,0,1.814869," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left(48 \, {\left(2 \, A + 3 i \, B\right)} c^{2} \cos\left(4 \, f x + 4 \, e\right) + 80 \, {\left(2 \, A + 3 i \, B\right)} c^{2} \cos\left(2 \, f x + 2 \, e\right) - {\left(-96 i \, A + 144 \, B\right)} c^{2} \sin\left(4 \, f x + 4 \, e\right) - {\left(-160 i \, A + 240 \, B\right)} c^{2} \sin\left(2 \, f x + 2 \, e\right) + 64 \, {\left(A + i \, B\right)} c^{2} + {\left(24 \, {\left(2 \, A + 3 i \, B\right)} 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) + 48 \, {\left(2 \, A + 3 i \, B\right)} 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) + 24 \, {\left(2 \, A + 3 i \, B\right)} 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) - {\left(-48 i \, A + 72 \, B\right)} 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) - {\left(-96 i \, A + 144 \, B\right)} 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) - {\left(-48 i \, A + 72 \, B\right)} 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)\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(24 \, {\left(2 \, A + 3 i \, B\right)} 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) + 48 \, {\left(2 \, A + 3 i \, B\right)} 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) + 24 \, {\left(2 \, A + 3 i \, B\right)} 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) - {\left(-48 i \, A + 72 \, B\right)} 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) - {\left(-96 i \, A + 144 \, B\right)} 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) - {\left(-48 i \, A + 72 \, B\right)} 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)\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({\left(-24 i \, A + 36 \, B\right)} 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) + {\left(-48 i \, A + 72 \, B\right)} 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) + {\left(-24 i \, A + 36 \, B\right)} 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 \, {\left(2 \, A + 3 i \, B\right)} 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) + 24 \, {\left(2 \, A + 3 i \, B\right)} 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 \, {\left(2 \, A + 3 i \, B\right)} 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)\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({\left(24 i \, A - 36 \, B\right)} 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) + {\left(48 i \, A - 72 \, B\right)} 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) + {\left(24 i \, A - 36 \, B\right)} 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 \, {\left(2 \, A + 3 i \, B\right)} 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) - 24 \, {\left(2 \, A + 3 i \, B\right)} 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 \, {\left(2 \, A + 3 i \, B\right)} 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)\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}}{{\left(-16 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) - 32 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) - 16 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) + 16 \, 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) + 32 \, 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) + 16 \, 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)} f}"," ",0,"(48*(2*A + 3*I*B)*c^2*cos(4*f*x + 4*e) + 80*(2*A + 3*I*B)*c^2*cos(2*f*x + 2*e) - (-96*I*A + 144*B)*c^2*sin(4*f*x + 4*e) - (-160*I*A + 240*B)*c^2*sin(2*f*x + 2*e) + 64*(A + I*B)*c^2 + (24*(2*A + 3*I*B)*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 48*(2*A + 3*I*B)*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 24*(2*A + 3*I*B)*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-48*I*A + 72*B)*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-96*I*A + 144*B)*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-48*I*A + 72*B)*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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*(2*A + 3*I*B)*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 48*(2*A + 3*I*B)*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 24*(2*A + 3*I*B)*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-48*I*A + 72*B)*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-96*I*A + 144*B)*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-48*I*A + 72*B)*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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*I*A + 36*B)*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-48*I*A + 72*B)*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-24*I*A + 36*B)*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*(2*A + 3*I*B)*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 24*(2*A + 3*I*B)*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 12*(2*A + 3*I*B)*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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 - 36*B)*c^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (48*I*A - 72*B)*c^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (24*I*A - 36*B)*c^2*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(2*A + 3*I*B)*c^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 24*(2*A + 3*I*B)*c^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 12*(2*A + 3*I*B)*c^2*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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)/((-16*I*a*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 32*I*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 16*I*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*a*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 32*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 16*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
831,1,904,0,0.919191," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{{\left(4 \, {\left(A + 2 i \, B\right)} c \cos\left(2 \, f x + 2 \, e\right) - {\left(-4 i \, A + 8 \, B\right)} c \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(A + i \, B\right)} c + {\left(2 \, {\left(A + 2 i \, B\right)} 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) + 2 \, {\left(A + 2 i \, B\right)} 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) - {\left(-2 i \, A + 4 \, B\right)} 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) - {\left(-2 i \, A + 4 \, B\right)} 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)\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 \, {\left(A + 2 i \, B\right)} 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) + 2 \, {\left(A + 2 i \, B\right)} 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) - {\left(-2 i \, A + 4 \, B\right)} 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) - {\left(-2 i \, A + 4 \, B\right)} 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)\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({\left(-i \, A + 2 \, B\right)} 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) + {\left(-i \, A + 2 \, B\right)} 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) + {\left(A + 2 i \, B\right)} 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) + {\left(A + 2 i \, B\right)} 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)\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({\left(i \, A - 2 \, B\right)} 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) + {\left(i \, A - 2 \, B\right)} 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) - {\left(A + 2 i \, B\right)} 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) - {\left(A + 2 i \, B\right)} 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)\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}}{{\left(-2 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) - 2 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) + 2 \, 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) + 2 \, 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)} f}"," ",0,"(4*(A + 2*I*B)*c*cos(2*f*x + 2*e) - (-4*I*A + 8*B)*c*sin(2*f*x + 2*e) + 4*(A + I*B)*c + (2*(A + 2*I*B)*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(A + 2*I*B)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-2*I*A + 4*B)*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-2*I*A + 4*B)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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 + 2*I*B)*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*(A + 2*I*B)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-2*I*A + 4*B)*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-2*I*A + 4*B)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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 + 2*B)*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-I*A + 2*B)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (A + 2*I*B)*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (A + 2*I*B)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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 - 2*B)*c*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (I*A - 2*B)*c*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (A + 2*I*B)*c*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (A + 2*I*B)*c*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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)/((-2*I*a*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 2*I*a*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*a*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 2*a*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
832,1,137,0,0.828749," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(2 \, B \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 2 \, B \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-2 i \, A + 2 \, B\right)} \cos\left(f x + e\right) + i \, B \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) - i \, B \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) - 2 \, {\left(A + i \, B\right)} \sin\left(f x + e\right)\right)} \sqrt{c}}{2 \, \sqrt{a} f}"," ",0,"-1/2*(2*B*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 2*B*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-2*I*A + 2*B)*cos(f*x + e) + I*B*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - I*B*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 2*(A + I*B)*sin(f*x + e))*sqrt(c)/(sqrt(a)*f)","A",0
833,1,124,0,0.802192," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(1/2)/(c-I*c*tan(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{{\left(2 \, {\left(A - i \, B\right)} \cos\left(4 \, f x + 4 \, e\right) - 4 i \, B \cos\left(2 \, f x + 2 \, e\right) + {\left(2 i \, A + 2 \, B\right)} \sin\left(4 \, f x + 4 \, e\right) + 4 \, B \sin\left(2 \, f x + 2 \, e\right) - 2 \, A - 2 i \, B\right)} \sqrt{a} \sqrt{c}}{{\left(-4 i \, a c \cos\left(3 \, f x + 3 \, e\right) - 4 i \, a c \cos\left(f x + e\right) + 4 \, a c \sin\left(3 \, f x + 3 \, e\right) + 4 \, a c \sin\left(f x + e\right)\right)} f}"," ",0,"-(2*(A - I*B)*cos(4*f*x + 4*e) - 4*I*B*cos(2*f*x + 2*e) + (2*I*A + 2*B)*sin(4*f*x + 4*e) + 4*B*sin(2*f*x + 2*e) - 2*A - 2*I*B)*sqrt(a)*sqrt(c)/((-4*I*a*c*cos(3*f*x + 3*e) - 4*I*a*c*cos(f*x + e) + 4*a*c*sin(3*f*x + 3*e) + 4*a*c*sin(f*x + e))*f)","A",0
834,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
835,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
836,1,1379,0,2.883023," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left(720 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 1200 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) + 384 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-1440 i \, A + 3600 \, B\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-2400 i \, A + 6000 \, B\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(-768 i \, A + 1920 \, B\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) - 192 \, {\left(A + i \, B\right)} c^{3} + {\left(360 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \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) + 720 \, {\left(2 \, A + 5 i \, B\right)} c^{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) + 360 \, {\left(2 \, A + 5 i \, B\right)} c^{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) - {\left(-720 i \, A + 1800 \, B\right)} c^{3} \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) - {\left(-1440 i \, A + 3600 \, B\right)} c^{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) - {\left(-720 i \, A + 1800 \, B\right)} c^{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)\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(360 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \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) + 720 \, {\left(2 \, A + 5 i \, B\right)} c^{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) + 360 \, {\left(2 \, A + 5 i \, B\right)} c^{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) - {\left(-720 i \, A + 1800 \, B\right)} c^{3} \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) - {\left(-1440 i \, A + 3600 \, B\right)} c^{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) - {\left(-720 i \, A + 1800 \, B\right)} c^{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)\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({\left(-360 i \, A + 900 \, B\right)} c^{3} \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) + {\left(-720 i \, A + 1800 \, B\right)} c^{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) + {\left(-360 i \, A + 900 \, B\right)} c^{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) + 180 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \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) + 360 \, {\left(2 \, A + 5 i \, B\right)} c^{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) + 180 \, {\left(2 \, A + 5 i \, B\right)} c^{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)\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({\left(360 i \, A - 900 \, B\right)} c^{3} \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) + {\left(720 i \, A - 1800 \, B\right)} c^{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) + {\left(360 i \, A - 900 \, B\right)} c^{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) - 180 \, {\left(2 \, A + 5 i \, B\right)} c^{3} \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) - 360 \, {\left(2 \, A + 5 i \, B\right)} c^{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) - 180 \, {\left(2 \, A + 5 i \, B\right)} c^{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)\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}}{{\left(-144 i \, a^{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) - 288 i \, a^{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) - 144 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) + 144 \, a^{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) + 288 \, a^{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) + 144 \, 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)\right)} f}"," ",0,"-(720*(2*A + 5*I*B)*c^3*cos(6*f*x + 6*e) + 1200*(2*A + 5*I*B)*c^3*cos(4*f*x + 4*e) + 384*(2*A + 5*I*B)*c^3*cos(2*f*x + 2*e) - (-1440*I*A + 3600*B)*c^3*sin(6*f*x + 6*e) - (-2400*I*A + 6000*B)*c^3*sin(4*f*x + 4*e) - (-768*I*A + 1920*B)*c^3*sin(2*f*x + 2*e) - 192*(A + I*B)*c^3 + (360*(2*A + 5*I*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 720*(2*A + 5*I*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 360*(2*A + 5*I*B)*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-720*I*A + 1800*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1440*I*A + 3600*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-720*I*A + 1800*B)*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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*(2*A + 5*I*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 720*(2*A + 5*I*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 360*(2*A + 5*I*B)*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-720*I*A + 1800*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-1440*I*A + 3600*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-720*I*A + 1800*B)*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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*I*A + 900*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-720*I*A + 1800*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-360*I*A + 900*B)*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 180*(2*A + 5*I*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 360*(2*A + 5*I*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 180*(2*A + 5*I*B)*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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 - 900*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (720*I*A - 1800*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (360*I*A - 900*B)*c^3*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 180*(2*A + 5*I*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 360*(2*A + 5*I*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 180*(2*A + 5*I*B)*c^3*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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)/((-144*I*a^2*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 288*I*a^2*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 144*I*a^2*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 144*a^2*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 288*a^2*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 144*a^2*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
837,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*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
838,1,169,0,0.672493," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{{\left(6 \, B c \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 6 \, B c \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(2 i \, A - 2 \, B\right)} c \cos\left(3 \, f x + 3 \, e\right) + 12 \, B c \cos\left(f x + e\right) + 3 i \, B 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) - 3 i \, B 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) + 2 \, {\left(A + i \, B\right)} c \sin\left(3 \, f x + 3 \, e\right) - 12 i \, B c \sin\left(f x + e\right)\right)} \sqrt{c}}{6 \, a^{\frac{3}{2}} f}"," ",0,"1/6*(6*B*c*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 6*B*c*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (2*I*A - 2*B)*c*cos(3*f*x + 3*e) + 12*B*c*cos(f*x + e) + 3*I*B*c*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 3*I*B*c*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + 2*(A + I*B)*c*sin(3*f*x + 3*e) - 12*I*B*c*sin(f*x + e))*sqrt(c)/(a^(3/2)*f)","A",0
839,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(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
840,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
841,1,199,0,1.105460," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2)/(c-I*c*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(-9 i \, A + 3 \, B\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(3 \, A + i \, B\right)} \sin\left(2 \, f x + 2 \, e\right) + 2 \, B\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(9 i \, A + 3 \, B\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 \, {\left(3 \, A + i \, B\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-9 i \, A + 3 \, B\right)} \sin\left(2 \, f x + 2 \, e\right) + 2 \, A\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) - 3 \, {\left(3 \, A - i \, B\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)}{24 \, a^{\frac{3}{2}} c^{\frac{3}{2}} f}"," ",0,"-1/24*(((-9*I*A + 3*B)*cos(2*f*x + 2*e) + 3*(3*A + I*B)*sin(2*f*x + 2*e) + 2*B)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (9*I*A + 3*B)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (3*(3*A + I*B)*cos(2*f*x + 2*e) - (-9*I*A + 3*B)*sin(2*f*x + 2*e) + 2*A)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 3*(3*A - I*B)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))/(a^(3/2)*c^(3/2)*f)","A",0
842,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
843,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(9/2)/(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
844,1,1032,0,1.303613," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(7/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(900 \, {\left(A + 6 i \, B\right)} c^{3} \cos\left(6 \, f x + 6 \, e\right) + 600 \, {\left(A + 6 i \, B\right)} c^{3} \cos\left(4 \, f x + 4 \, e\right) - 120 \, {\left(A + 6 i \, B\right)} c^{3} \cos\left(2 \, f x + 2 \, e\right) - {\left(-900 i \, A + 5400 \, B\right)} c^{3} \sin\left(6 \, f x + 6 \, e\right) - {\left(-600 i \, A + 3600 \, B\right)} c^{3} \sin\left(4 \, f x + 4 \, e\right) - {\left(120 i \, A - 720 \, B\right)} c^{3} \sin\left(2 \, f x + 2 \, e\right) + 180 \, {\left(A + i \, B\right)} c^{3} + {\left(450 \, {\left(A + 6 i \, B\right)} c^{3} \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) + 450 \, {\left(A + 6 i \, B\right)} c^{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) - {\left(-450 i \, A + 2700 \, B\right)} c^{3} \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) - {\left(-450 i \, A + 2700 \, B\right)} c^{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)\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(450 \, {\left(A + 6 i \, B\right)} c^{3} \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) + 450 \, {\left(A + 6 i \, B\right)} c^{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) - {\left(-450 i \, A + 2700 \, B\right)} c^{3} \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) - {\left(-450 i \, A + 2700 \, B\right)} c^{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)\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({\left(-225 i \, A + 1350 \, B\right)} c^{3} \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) + {\left(-225 i \, A + 1350 \, B\right)} c^{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) + 225 \, {\left(A + 6 i \, B\right)} c^{3} \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) + 225 \, {\left(A + 6 i \, B\right)} c^{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)\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({\left(225 i \, A - 1350 \, B\right)} c^{3} \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) + {\left(225 i \, A - 1350 \, B\right)} c^{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) - 225 \, {\left(A + 6 i \, B\right)} c^{3} \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) - 225 \, {\left(A + 6 i \, B\right)} c^{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)\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}}{{\left(-450 i \, a^{3} \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) - 450 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) + 450 \, a^{3} \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) + 450 \, 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)\right)} f}"," ",0,"(900*(A + 6*I*B)*c^3*cos(6*f*x + 6*e) + 600*(A + 6*I*B)*c^3*cos(4*f*x + 4*e) - 120*(A + 6*I*B)*c^3*cos(2*f*x + 2*e) - (-900*I*A + 5400*B)*c^3*sin(6*f*x + 6*e) - (-600*I*A + 3600*B)*c^3*sin(4*f*x + 4*e) - (120*I*A - 720*B)*c^3*sin(2*f*x + 2*e) + 180*(A + I*B)*c^3 + (450*(A + 6*I*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 450*(A + 6*I*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-450*I*A + 2700*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-450*I*A + 2700*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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) + (450*(A + 6*I*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 450*(A + 6*I*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-450*I*A + 2700*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (-450*I*A + 2700*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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) - ((-225*I*A + 1350*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (-225*I*A + 1350*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 225*(A + 6*I*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 225*(A + 6*I*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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) - ((225*I*A - 1350*B)*c^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (225*I*A - 1350*B)*c^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 225*(A + 6*I*B)*c^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 225*(A + 6*I*B)*c^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*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)/((-450*I*a^3*cos(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 450*I*a^3*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 450*a^3*sin(7/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + 450*a^3*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))*f)","B",0
845,1,215,0,1.131112," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(5/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left(30 \, B c^{2} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) + 30 \, B c^{2} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) + {\left(-6 i \, A + 6 \, B\right)} c^{2} \cos\left(5 \, f x + 5 \, e\right) - 20 \, B c^{2} \cos\left(3 \, f x + 3 \, e\right) + 60 \, B c^{2} \cos\left(f x + e\right) + 15 i \, B c^{2} \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) - 15 i \, B c^{2} \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) - 6 \, {\left(A + i \, B\right)} c^{2} \sin\left(5 \, f x + 5 \, e\right) + 20 i \, B c^{2} \sin\left(3 \, f x + 3 \, e\right) - 60 i \, B c^{2} \sin\left(f x + e\right)\right)} \sqrt{c}}{30 \, a^{\frac{5}{2}} f}"," ",0,"-1/30*(30*B*c^2*arctan2(cos(f*x + e), sin(f*x + e) + 1) + 30*B*c^2*arctan2(cos(f*x + e), -sin(f*x + e) + 1) + (-6*I*A + 6*B)*c^2*cos(5*f*x + 5*e) - 20*B*c^2*cos(3*f*x + 3*e) + 60*B*c^2*cos(f*x + e) + 15*I*B*c^2*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 15*I*B*c^2*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) - 6*(A + I*B)*c^2*sin(5*f*x + 5*e) + 20*I*B*c^2*sin(3*f*x + 3*e) - 60*I*B*c^2*sin(f*x + e))*sqrt(c)/(a^(5/2)*f)","A",0
846,1,150,0,1.258171," ","integrate((A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(3/2)/(a+I*a*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{{\left(150 \, {\left(A - i \, B\right)} c \cos\left(4 \, f x + 4 \, e\right) + 60 \, {\left(4 \, A - i \, B\right)} c \cos\left(2 \, f x + 2 \, e\right) + {\left(150 i \, A + 150 \, B\right)} c \sin\left(4 \, f x + 4 \, e\right) + {\left(240 i \, A + 60 \, B\right)} c \sin\left(2 \, f x + 2 \, e\right) + 90 \, {\left(A + i \, B\right)} c\right)} \sqrt{a} \sqrt{c}}{{\left(-900 i \, a^{3} \cos\left(7 \, f x + 7 \, e\right) - 900 i \, a^{3} \cos\left(5 \, f x + 5 \, e\right) + 900 \, a^{3} \sin\left(7 \, f x + 7 \, e\right) + 900 \, a^{3} \sin\left(5 \, f x + 5 \, e\right)\right)} f}"," ",0,"(150*(A - I*B)*c*cos(4*f*x + 4*e) + 60*(4*A - I*B)*c*cos(2*f*x + 2*e) + (150*I*A + 150*B)*c*sin(4*f*x + 4*e) + (240*I*A + 60*B)*c*sin(2*f*x + 2*e) + 90*(A + I*B)*c)*sqrt(a)*sqrt(c)/((-900*I*a^3*cos(7*f*x + 7*e) - 900*I*a^3*cos(5*f*x + 5*e) + 900*a^3*sin(7*f*x + 7*e) + 900*a^3*sin(5*f*x + 5*e))*f)","A",0
847,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^(1/2)*(A+B*tan(f*x+e))/(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
848,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
849,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))/(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
850,1,331,0,0.786243," ","integrate((A+B*tan(f*x+e))/(a+I*a*tan(f*x+e))^(5/2)/(c-I*c*tan(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(-150 i \, A + 30 \, B\right)} \cos\left(4 \, f x + 4 \, e\right) + {\left(-25 i \, A + 15 \, B\right)} \cos\left(2 \, f x + 2 \, e\right) + 30 \, {\left(5 \, A + i \, B\right)} \sin\left(4 \, f x + 4 \, e\right) + 5 \, {\left(5 \, A + 3 i \, B\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, B\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(25 i \, A + 15 \, B\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(150 i \, A + 30 \, B\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 \, {\left(5 \, A + i \, B\right)} \cos\left(4 \, f x + 4 \, e\right) + 5 \, {\left(5 \, A + 3 i \, B\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(-150 i \, A + 30 \, B\right)} \sin\left(4 \, f x + 4 \, e\right) - {\left(-25 i \, A + 15 \, B\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, A\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) - 5 \, {\left(5 \, A - 3 i \, B\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) - 30 \, {\left(5 \, A - i \, B\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)}{480 \, a^{\frac{5}{2}} c^{\frac{5}{2}} f}"," ",0,"-1/480*(((-150*I*A + 30*B)*cos(4*f*x + 4*e) + (-25*I*A + 15*B)*cos(2*f*x + 2*e) + 30*(5*A + I*B)*sin(4*f*x + 4*e) + 5*(5*A + 3*I*B)*sin(2*f*x + 2*e) + 6*B)*cos(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (25*I*A + 15*B)*cos(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) + (150*I*A + 30*B)*cos(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - (30*(5*A + I*B)*cos(4*f*x + 4*e) + 5*(5*A + 3*I*B)*cos(2*f*x + 2*e) - (-150*I*A + 30*B)*sin(4*f*x + 4*e) - (-25*I*A + 15*B)*sin(2*f*x + 2*e) + 6*A)*sin(5/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 5*(5*A - 3*I*B)*sin(3/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))) - 30*(5*A - I*B)*sin(1/2*arctan2(sin(2*f*x + 2*e), cos(2*f*x + 2*e))))/(a^(5/2)*c^(5/2)*f)","B",0
851,0,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^m*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \tan\left(f x + e\right) + A\right)} {\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((B*tan(f*x + e) + A)*(I*a*tan(f*x + e) + a)^m*(-I*c*tan(f*x + e) + c)^n, x)","F",0
852,-1,0,0,0.000000," ","integrate((a+I*a*tan(f*x+e))^(1+m)*(A+B*tan(f*x+e))*(c-I*c*tan(f*x+e))^(-1-m),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-2,0,0,0.000000," ","integrate((c-I*c*tan(f*x+e))^n*(-I*(2+n)+(-2+n)*tan(f*x+e))/(-I+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
854,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e))*(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
855,1,143,0,0.640702," ","integrate((A+B*tan(f*x+e))*(c+d*tan(f*x+e))/(a+I*a*tan(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{i \, {\left(\frac{3 \, \sqrt{2} {\left(A - i \, B\right)} {\left(c - i \, d\right)} \log\left(-\frac{\sqrt{2} \sqrt{a} - \sqrt{i \, a \tan\left(f x + e\right) + a}}{\sqrt{2} \sqrt{a} + \sqrt{i \, a \tan\left(f x + e\right) + a}}\right)}{\sqrt{a}} + \frac{4 \, {\left(2 \, {\left(A + i \, B\right)} a c - {\left(-2 i \, A + 2 \, B\right)} a d + {\left(3 \, {\left(A - i \, B\right)} c - {\left(3 i \, A - 9 \, B\right)} d\right)} {\left(i \, a \tan\left(f x + e\right) + a\right)}\right)}}{{\left(i \, a \tan\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\right)}}{24 \, a f}"," ",0,"1/24*I*(3*sqrt(2)*(A - I*B)*(c - I*d)*log(-(sqrt(2)*sqrt(a) - sqrt(I*a*tan(f*x + e) + a))/(sqrt(2)*sqrt(a) + sqrt(I*a*tan(f*x + e) + a)))/sqrt(a) + 4*(2*(A + I*B)*a*c - (-2*I*A + 2*B)*a*d + (3*(A - I*B)*c - (3*I*A - 9*B)*d)*(I*a*tan(f*x + e) + a))/(I*a*tan(f*x + e) + a)^(3/2))/(a*f)","A",0
