1,1,490,0,0.351758," ","integrate((d*x+c)^4*sin(b*x+a),x, algorithm=""maxima"")","-\frac{c^{4} \cos\left(b x + a\right) - \frac{4 \, a c^{3} d \cos\left(b x + a\right)}{b} + \frac{6 \, a^{2} c^{2} d^{2} \cos\left(b x + a\right)}{b^{2}} - \frac{4 \, a^{3} c d^{3} \cos\left(b x + a\right)}{b^{3}} + \frac{a^{4} d^{4} \cos\left(b x + a\right)}{b^{4}} + \frac{4 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} c^{3} d}{b} - \frac{12 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{12 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{4 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{6 \, {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{12 \, {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a c d^{3}}{b^{3}} + \frac{6 \, {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{4 \, {\left({\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c d^{3}}{b^{3}} - \frac{4 \, {\left({\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left({\left({\left(b x + a\right)}^{4} - 12 \, {\left(b x + a\right)}^{2} + 24\right)} \cos\left(b x + a\right) - 4 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} d^{4}}{b^{4}}}{b}"," ",0,"-(c^4*cos(b*x + a) - 4*a*c^3*d*cos(b*x + a)/b + 6*a^2*c^2*d^2*cos(b*x + a)/b^2 - 4*a^3*c*d^3*cos(b*x + a)/b^3 + a^4*d^4*cos(b*x + a)/b^4 + 4*((b*x + a)*cos(b*x + a) - sin(b*x + a))*c^3*d/b - 12*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a*c^2*d^2/b^2 + 12*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a^2*c*d^3/b^3 - 4*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a^3*d^4/b^4 + 6*(((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*c^2*d^2/b^2 - 12*(((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*a*c*d^3/b^3 + 6*(((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*a^2*d^4/b^4 + 4*(((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 3*((b*x + a)^2 - 2)*sin(b*x + a))*c*d^3/b^3 - 4*(((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 3*((b*x + a)^2 - 2)*sin(b*x + a))*a*d^4/b^4 + (((b*x + a)^4 - 12*(b*x + a)^2 + 24)*cos(b*x + a) - 4*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^4/b^4)/b","B",0
2,1,285,0,0.430942," ","integrate((d*x+c)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{c^{3} \cos\left(b x + a\right) - \frac{3 \, a c^{2} d \cos\left(b x + a\right)}{b} + \frac{3 \, a^{2} c d^{2} \cos\left(b x + a\right)}{b^{2}} - \frac{a^{3} d^{3} \cos\left(b x + a\right)}{b^{3}} + \frac{3 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} c^{2} d}{b} - \frac{6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a c d^{2}}{b^{2}} + \frac{3 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{3 \, {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c d^{2}}{b^{2}} - \frac{3 \, {\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left({\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} d^{3}}{b^{3}}}{b}"," ",0,"-(c^3*cos(b*x + a) - 3*a*c^2*d*cos(b*x + a)/b + 3*a^2*c*d^2*cos(b*x + a)/b^2 - a^3*d^3*cos(b*x + a)/b^3 + 3*((b*x + a)*cos(b*x + a) - sin(b*x + a))*c^2*d/b - 6*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a*c*d^2/b^2 + 3*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a^2*d^3/b^3 + 3*(((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*c*d^2/b^2 - 3*(((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*a*d^3/b^3 + (((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 3*((b*x + a)^2 - 2)*sin(b*x + a))*d^3/b^3)/b","B",0
3,1,141,0,0.659311," ","integrate((d*x+c)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{c^{2} \cos\left(b x + a\right) - \frac{2 \, a c d \cos\left(b x + a\right)}{b} + \frac{a^{2} d^{2} \cos\left(b x + a\right)}{b^{2}} + \frac{2 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} c d}{b} - \frac{2 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left({\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 2 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{b}"," ",0,"-(c^2*cos(b*x + a) - 2*a*c*d*cos(b*x + a)/b + a^2*d^2*cos(b*x + a)/b^2 + 2*((b*x + a)*cos(b*x + a) - sin(b*x + a))*c*d/b - 2*((b*x + a)*cos(b*x + a) - sin(b*x + a))*a*d^2/b^2 + (((b*x + a)^2 - 2)*cos(b*x + a) - 2*(b*x + a)*sin(b*x + a))*d^2/b^2)/b","B",0
4,1,53,0,0.481865," ","integrate((d*x+c)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{c \cos\left(b x + a\right) - \frac{a d \cos\left(b x + a\right)}{b} + \frac{{\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} d}{b}}{b}"," ",0,"-(c*cos(b*x + a) - a*d*cos(b*x + a)/b + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*d/b)/b","A",0
5,1,141,0,0.446976," ","integrate(sin(b*x+a)/(d*x+c),x, algorithm=""maxima"")","-\frac{b {\left(i \, E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - i \, E_{1}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b {\left(E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{1}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{2 \, b d}"," ",0,"-1/2*(b*(I*exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - I*exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b*(exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d))/(b*d)","C",0
6,1,164,0,0.520271," ","integrate(sin(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{b^{2} {\left(i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - i \, E_{2}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b^{2} {\left(E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{2}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/2*(b^2*(I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - I*exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b^2*(exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
7,1,199,0,0.623204," ","integrate(sin(b*x+a)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - i \, E_{3}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b^{3} {\left(E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{3}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + a^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} b}"," ",0,"-1/2*(b^3*(I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - I*exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b^3*(exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d))/((b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + a^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*b)","C",0
8,1,735,0,0.461828," ","integrate((d*x+c)^4*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{10 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} c^{4} - \frac{40 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{3} d}{b} + \frac{60 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{40 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} c d^{3}}{b^{3}} + \frac{10 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{4} d^{4}}{b^{4}} + \frac{20 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b} - \frac{60 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{60 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{20 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{10 \, {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{20 \, {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{b^{3}} + \frac{10 \, {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{10 \, {\left(2 \, {\left(b x + a\right)}^{4} - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{3}}{b^{3}} - \frac{10 \, {\left(2 \, {\left(b x + a\right)}^{4} - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left(4 \, {\left(b x + a\right)}^{5} - 10 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 5 \, {\left(2 \, {\left(b x + a\right)}^{4} - 6 \, {\left(b x + a\right)}^{2} + 3\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{4}}{b^{4}}}{40 \, b}"," ",0,"1/40*(10*(2*b*x + 2*a - sin(2*b*x + 2*a))*c^4 - 40*(2*b*x + 2*a - sin(2*b*x + 2*a))*a*c^3*d/b + 60*(2*b*x + 2*a - sin(2*b*x + 2*a))*a^2*c^2*d^2/b^2 - 40*(2*b*x + 2*a - sin(2*b*x + 2*a))*a^3*c*d^3/b^3 + 10*(2*b*x + 2*a - sin(2*b*x + 2*a))*a^4*d^4/b^4 + 20*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*c^3*d/b - 60*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a*c^2*d^2/b^2 + 60*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a^2*c*d^3/b^3 - 20*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a^3*d^4/b^4 + 10*(4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c^2*d^2/b^2 - 20*(4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*c*d^3/b^3 + 10*(4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a^2*d^4/b^4 + 10*(2*(b*x + a)^4 - 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*c*d^3/b^3 - 10*(2*(b*x + a)^4 - 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*a*d^4/b^4 + (4*(b*x + a)^5 - 10*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 5*(2*(b*x + a)^4 - 6*(b*x + a)^2 + 3)*sin(2*b*x + 2*a))*d^4/b^4)/b","B",0
9,1,442,0,0.370878," ","integrate((d*x+c)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} - \frac{12 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d}{b} + \frac{12 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{4 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{3}}{b^{3}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{b} - \frac{12 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{b^{2}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{b^{2}} - \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(2 \, {\left(b x + a\right)}^{4} - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{3}}{b^{3}}}{16 \, b}"," ",0,"1/16*(4*(2*b*x + 2*a - sin(2*b*x + 2*a))*c^3 - 12*(2*b*x + 2*a - sin(2*b*x + 2*a))*a*c^2*d/b + 12*(2*b*x + 2*a - sin(2*b*x + 2*a))*a^2*c*d^2/b^2 - 4*(2*b*x + 2*a - sin(2*b*x + 2*a))*a^3*d^3/b^3 + 6*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*c^2*d/b - 12*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a*c*d^2/b^2 + 6*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a^2*d^3/b^3 + 2*(4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c*d^2/b^2 - 2*(4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*d^3/b^3 + (2*(b*x + a)^4 - 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*d^3/b^3)/b","B",0
10,1,232,0,0.398009," ","integrate((d*x+c)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{6 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} - \frac{12 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a c d}{b} + \frac{6 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{2}}{b^{2}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} c d}{b} - \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left(4 \, {\left(b x + a\right)}^{3} - 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{b^{2}}}{24 \, b}"," ",0,"1/24*(6*(2*b*x + 2*a - sin(2*b*x + 2*a))*c^2 - 12*(2*b*x + 2*a - sin(2*b*x + 2*a))*a*c*d/b + 6*(2*b*x + 2*a - sin(2*b*x + 2*a))*a^2*d^2/b^2 + 6*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*c*d/b - 6*(2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*a*d^2/b^2 + (4*(b*x + a)^3 - 6*(b*x + a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*d^2/b^2)/b","B",0
11,1,96,0,0.302700," ","integrate((d*x+c)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} c - \frac{2 \, {\left(2 \, b x + 2 \, a - \sin\left(2 \, b x + 2 \, a\right)\right)} a d}{b} + \frac{{\left(2 \, {\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)\right)} d}{b}}{8 \, b}"," ",0,"1/8*(2*(2*b*x + 2*a - sin(2*b*x + 2*a))*c - 2*(2*b*x + 2*a - sin(2*b*x + 2*a))*a*d/b + (2*(b*x + a)^2 - 2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a))*d/b)/b","B",0
12,1,160,0,0.423095," ","integrate(sin(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{b {\left(E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{1}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b {\left(-i \, E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + i \, E_{1}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, b \log\left(b c + {\left(b x + a\right)} d - a d\right)}{4 \, b d}"," ",0,"1/4*(b*(exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(1, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) + b*(-I*exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + I*exp_integral_e(1, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) + 2*b*log(b*c + (b*x + a)*d - a*d))/(b*d)","C",0
13,1,171,0,0.613764," ","integrate(sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\frac{16 \, b^{2} {\left(E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{2}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - b^{2} {\left(16 i \, E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 16 i \, E_{2}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 32 \, b^{2}}{64 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"1/64*(16*b^2*(exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(2, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) - b^2*(16*I*exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 16*I*exp_integral_e(2, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) - 32*b^2)/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
14,1,206,0,0.771460," ","integrate(sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""maxima"")","\frac{16 \, b^{3} {\left(E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{3}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - b^{3} {\left(16 i \, E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 16 i \, E_{3}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 16 \, b^{3}}{64 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + a^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} b}"," ",0,"1/64*(16*b^3*(exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(3, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) - b^3*(16*I*exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 16*I*exp_integral_e(3, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) - 16*b^3)/((b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + a^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*b)","C",0
15,1,256,0,0.860483," ","integrate(sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""maxima"")","\frac{3 \, b^{4} {\left(E_{4}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{4}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - b^{4} {\left(3 i \, E_{4}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 3 i \, E_{4}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, b^{4}}{12 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} + {\left(b x + a\right)}^{3} d^{4} - a^{3} d^{4} + 3 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} b}"," ",0,"1/12*(3*b^4*(exp_integral_e(4, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(4, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) - b^4*(3*I*exp_integral_e(4, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 3*I*exp_integral_e(4, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) - 2*b^4)/((b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 + (b*x + a)^3*d^4 - a^3*d^4 + 3*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 3*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a))*b)","C",0
16,1,934,0,0.406926," ","integrate((d*x+c)^4*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{108 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} c^{4} - \frac{432 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a c^{3} d}{b} + \frac{648 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{432 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a^{3} c d^{3}}{b^{3}} + \frac{108 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a^{4} d^{4}}{b^{4}} + \frac{36 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} c^{3} d}{b} - \frac{108 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{108 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{36 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{18 \, {\left({\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 6 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{36 \, {\left({\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 6 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a c d^{3}}{b^{3}} + \frac{18 \, {\left({\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 6 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{12 \, {\left(3 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) + 243 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c d^{3}}{b^{3}} - \frac{12 \, {\left(3 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) + 243 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left({\left(27 \, {\left(b x + a\right)}^{4} - 36 \, {\left(b x + a\right)}^{2} + 8\right)} \cos\left(3 \, b x + 3 \, a\right) - 243 \, {\left({\left(b x + a\right)}^{4} - 12 \, {\left(b x + a\right)}^{2} + 24\right)} \cos\left(b x + a\right) - 12 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) + 972 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} d^{4}}{b^{4}}}{324 \, b}"," ",0,"1/324*(108*(cos(b*x + a)^3 - 3*cos(b*x + a))*c^4 - 432*(cos(b*x + a)^3 - 3*cos(b*x + a))*a*c^3*d/b + 648*(cos(b*x + a)^3 - 3*cos(b*x + a))*a^2*c^2*d^2/b^2 - 432*(cos(b*x + a)^3 - 3*cos(b*x + a))*a^3*c*d^3/b^3 + 108*(cos(b*x + a)^3 - 3*cos(b*x + a))*a^4*d^4/b^4 + 36*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*c^3*d/b - 108*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*a*c^2*d^2/b^2 + 108*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*a^2*c*d^3/b^3 - 36*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*a^3*d^4/b^4 + 18*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) + 162*(b*x + a)*sin(b*x + a))*c^2*d^2/b^2 - 36*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) + 162*(b*x + a)*sin(b*x + a))*a*c*d^3/b^3 + 18*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) + 162*(b*x + a)*sin(b*x + a))*a^2*d^4/b^4 + 12*(3*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 81*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) + 243*((b*x + a)^2 - 2)*sin(b*x + a))*c*d^3/b^3 - 12*(3*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 81*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) + 243*((b*x + a)^2 - 2)*sin(b*x + a))*a*d^4/b^4 + ((27*(b*x + a)^4 - 36*(b*x + a)^2 + 8)*cos(3*b*x + 3*a) - 243*((b*x + a)^4 - 12*(b*x + a)^2 + 24)*cos(b*x + a) - 12*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) + 972*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^4/b^4)/b","B",0
17,1,541,0,0.376763," ","integrate((d*x+c)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{36 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} c^{3} - \frac{108 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a c^{2} d}{b} + \frac{108 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{36 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a^{3} d^{3}}{b^{3}} + \frac{9 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} c^{2} d}{b} - \frac{18 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} a c d^{2}}{b^{2}} + \frac{9 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{3 \, {\left({\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 6 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c d^{2}}{b^{2}} - \frac{3 \, {\left({\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 6 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(3 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) + 243 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} d^{3}}{b^{3}}}{108 \, b}"," ",0,"1/108*(36*(cos(b*x + a)^3 - 3*cos(b*x + a))*c^3 - 108*(cos(b*x + a)^3 - 3*cos(b*x + a))*a*c^2*d/b + 108*(cos(b*x + a)^3 - 3*cos(b*x + a))*a^2*c*d^2/b^2 - 36*(cos(b*x + a)^3 - 3*cos(b*x + a))*a^3*d^3/b^3 + 9*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*c^2*d/b - 18*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*a*c*d^2/b^2 + 9*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*a^2*d^3/b^3 + 3*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) + 162*(b*x + a)*sin(b*x + a))*c*d^2/b^2 - 3*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) + 162*(b*x + a)*sin(b*x + a))*a*d^3/b^3 + (3*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 81*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) + 243*((b*x + a)^2 - 2)*sin(b*x + a))*d^3/b^3)/b","B",0
18,1,270,0,0.456376," ","integrate((d*x+c)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{36 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} c^{2} - \frac{72 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a c d}{b} + \frac{36 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a^{2} d^{2}}{b^{2}} + \frac{6 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} c d}{b} - \frac{6 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left({\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 6 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{108 \, b}"," ",0,"1/108*(36*(cos(b*x + a)^3 - 3*cos(b*x + a))*c^2 - 72*(cos(b*x + a)^3 - 3*cos(b*x + a))*a*c*d/b + 36*(cos(b*x + a)^3 - 3*cos(b*x + a))*a^2*d^2/b^2 + 6*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*c*d/b - 6*(3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*a*d^2/b^2 + ((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) + 162*(b*x + a)*sin(b*x + a))*d^2/b^2)/b","B",0
19,1,104,0,0.305032," ","integrate((d*x+c)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{12 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} c - \frac{12 \, {\left(\cos\left(b x + a\right)^{3} - 3 \, \cos\left(b x + a\right)\right)} a d}{b} + \frac{{\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 27 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) + 27 \, \sin\left(b x + a\right)\right)} d}{b}}{36 \, b}"," ",0,"1/36*(12*(cos(b*x + a)^3 - 3*cos(b*x + a))*c - 12*(cos(b*x + a)^3 - 3*cos(b*x + a))*a*d/b + (3*(b*x + a)*cos(3*b*x + 3*a) - 27*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) + 27*sin(b*x + a))*d/b)/b","A",0
20,1,274,0,0.510128," ","integrate(sin(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{b {\left(-3 i \, E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 3 i \, E_{1}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b {\left(i \, E_{1}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 3 \, b {\left(E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{1}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + b {\left(E_{1}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{1}\left(-\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, b d}"," ",0,"1/8*(b*(-3*I*exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 3*I*exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b*(I*exp_integral_e(1, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - I*exp_integral_e(1, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) - 3*b*(exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b*(exp_integral_e(1, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(1, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d))/(b*d)","C",0
21,1,301,0,0.576025," ","integrate(sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(-3 i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 3 i \, E_{2}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b^{2} {\left(i \, E_{2}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - i \, E_{2}\left(-\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 3 \, b^{2} {\left(E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{2}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + b^{2} {\left(E_{2}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{2}\left(-\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"1/8*(b^2*(-3*I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 3*I*exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b^2*(I*exp_integral_e(2, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - I*exp_integral_e(2, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) - 3*b^2*(exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^2*(exp_integral_e(2, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(2, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
22,1,336,0,0.712739," ","integrate(sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""maxima"")","\frac{b^{3} {\left(-3 i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 3 i \, E_{3}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b^{3} {\left(i \, E_{3}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - i \, E_{3}\left(-\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 3 \, b^{3} {\left(E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{3}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + b^{3} {\left(E_{3}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{3}\left(-\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + a^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} b}"," ",0,"1/8*(b^3*(-3*I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 3*I*exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b^3*(I*exp_integral_e(3, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - I*exp_integral_e(3, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) - 3*b^3*(exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^3*(exp_integral_e(3, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(3, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d))/((b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + a^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*b)","C",0
23,1,706,0,0.677396," ","integrate((d*x+c)^3*csc(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, c^{3} \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right) - \frac{6 \, a c^{2} d \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right)}{b} + \frac{6 \, a^{2} c d^{2} \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right)}{b^{2}} - \frac{2 \, a^{3} d^{3} \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right)}{b^{3}} + \frac{12 i \, d^{3} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - 12 i \, d^{3} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(2 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + 6 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(2 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + 6 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(-6 i \, b^{2} c^{2} d + 12 i \, a b c d^{2} - 6 i \, {\left(b x + a\right)}^{2} d^{3} - 6 i \, a^{2} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + 6 i \, {\left(b x + a\right)}^{2} d^{3} + 6 i \, a^{2} d^{3} + {\left(12 i \, b c d^{2} - 12 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) + 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)})}{b^{3}}}{2 \, b}"," ",0,"-1/2*(2*c^3*log(cot(b*x + a) + csc(b*x + a)) - 6*a*c^2*d*log(cot(b*x + a) + csc(b*x + a))/b + 6*a^2*c*d^2*log(cot(b*x + a) + csc(b*x + a))/b^2 - 2*a^3*d^3*log(cot(b*x + a) + csc(b*x + a))/b^3 + (12*I*d^3*polylog(4, -e^(I*b*x + I*a)) - 12*I*d^3*polylog(4, e^(I*b*x + I*a)) + (2*I*(b*x + a)^3*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a)^2 + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + 6*I*a^2*d^3)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (2*I*(b*x + a)^3*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a)^2 + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + 6*I*a^2*d^3)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-6*I*b^2*c^2*d + 12*I*a*b*c*d^2 - 6*I*(b*x + a)^2*d^3 - 6*I*a^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*dilog(-e^(I*b*x + I*a)) + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + 6*I*(b*x + a)^2*d^3 + 6*I*a^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*dilog(e^(I*b*x + I*a)) + ((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - ((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, -e^(I*b*x + I*a)) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, e^(I*b*x + I*a)))/b^3)/b","B",0
24,1,392,0,0.683443," ","integrate((d*x+c)^2*csc(b*x+a),x, algorithm=""maxima"")","-\frac{2 \, c^{2} \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right) - \frac{4 \, a c d \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right)}{b} + \frac{2 \, a^{2} d^{2} \log\left(\cot\left(b x + a\right) + \csc\left(b x + a\right)\right)}{b^{2}} + \frac{4 \, d^{2} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - 4 \, d^{2} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(2 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(4 i \, b c d - 4 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(2 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(4 i \, b c d - 4 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right)}{b^{2}}}{2 \, b}"," ",0,"-1/2*(2*c^2*log(cot(b*x + a) + csc(b*x + a)) - 4*a*c*d*log(cot(b*x + a) + csc(b*x + a))/b + 2*a^2*d^2*log(cot(b*x + a) + csc(b*x + a))/b^2 + (4*d^2*polylog(3, -e^(I*b*x + I*a)) - 4*d^2*polylog(3, e^(I*b*x + I*a)) + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*dilog(-e^(I*b*x + I*a)) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*dilog(e^(I*b*x + I*a)) + ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1))/b^2)/b","B",0
25,1,174,0,0.698493," ","integrate((d*x+c)*csc(b*x+a),x, algorithm=""maxima"")","-\frac{2 i \, b d x \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 2 i \, b c \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(2 i \, b d x + 2 i \, b c\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - 2 i \, d {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + 2 i \, d {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right)}{2 \, b^{2}}"," ",0,"-1/2*(2*I*b*d*x*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 2*I*b*c*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*I*b*d*x + 2*I*b*c)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - 2*I*d*dilog(-e^(I*b*x + I*a)) + 2*I*d*dilog(e^(I*b*x + I*a)) + (b*d*x + b*c)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (b*d*x + b*c)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1))/b^2","B",0
26,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(csc(b*x + a)/(d*x + c), x)","F",0
27,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)/(d*x + c)^2, x)","F",0
28,1,1650,0,0.723108," ","integrate((d*x+c)^3*csc(b*x+a)^2,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b} - \frac{6 \, {\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{2}} + \frac{3 \, {\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{3}} - \frac{2 \, c^{3}}{\tan\left(b x + a\right)} + \frac{6 \, a c^{2} d}{b \tan\left(b x + a\right)} - \frac{6 \, a^{2} c d^{2}}{b^{2} \tan\left(b x + a\right)} + \frac{2 \, a^{3} d^{3}}{b^{3} \tan\left(b x + a\right)} - \frac{2 \, {\left({\left(6 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 6 \, {\left({\left(b x + a\right)}^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(6 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(12 i \, b c d^{2} - 12 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 6 \, {\left({\left(b x + a\right)}^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 \, b c d^{2} + 12 \, {\left(b x + a\right)} d^{3} - 12 \, a d^{3} - 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(12 \, b c d^{2} + 12 \, {\left(b x + a\right)} d^{3} - 12 \, a d^{3} - 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(3 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-6 i \, b c d^{2} + 6 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(3 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-6 i \, b c d^{2} + 6 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - {\left(-12 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 12 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-12 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 12 i \, d^{3}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(-4 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-2 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 i \, b^{3}}}{2 \, b}"," ",0,"1/2*(3*((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 4*(b*x + a)*sin(2*b*x + 2*a))*c^2*d/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*b) - 6*((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 4*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^2/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*b^2) + 3*((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 4*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^3/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*b^3) - 2*c^3/tan(b*x + a) + 6*a*c^2*d/(b*tan(b*x + a)) - 6*a^2*c*d^2/(b^2*tan(b*x + a)) + 2*a^3*d^3/(b^3*tan(b*x + a)) - 2*((6*(b*x + a)^2*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (6*(b*x + a)^2*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 4*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*cos(2*b*x + 2*a) - (12*b*c*d^2 + 12*(b*x + a)*d^3 - 12*a*d^3 - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) - (12*b*c*d^2 + 12*(b*x + a)*d^3 - 12*a*d^3 - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a) + (-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a) + (-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-12*I*d^3*cos(2*b*x + 2*a) + 12*d^3*sin(2*b*x + 2*a) + 12*I*d^3)*polylog(3, -e^(I*b*x + I*a)) - (-12*I*d^3*cos(2*b*x + 2*a) + 12*d^3*sin(2*b*x + 2*a) + 12*I*d^3)*polylog(3, e^(I*b*x + I*a)) - (-4*I*(b*x + a)^3*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-2*I*b^3*cos(2*b*x + 2*a) + 2*b^3*sin(2*b*x + 2*a) + 2*I*b^3))/b","B",0
29,1,555,0,0.514189," ","integrate((d*x+c)^2*csc(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, b^{2} c^{2} + {\left(2 \, b d^{2} x + 2 \, b c d - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(2 \, b c d \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b c d \sin\left(2 \, b x + 2 \, a\right) - 2 \, b c d\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(2 \, b d^{2} x \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b d^{2} x \sin\left(2 \, b x + 2 \, a\right) - 2 \, b d^{2} x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(2 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(i \, b d^{2} x + i \, b c d + {\left(-i \, b d^{2} x - i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) - {\left(i \, b d^{2} x + i \, b c d + {\left(-i \, b d^{2} x - i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - {\left(-2 i \, b^{2} d^{2} x^{2} - 4 i \, b^{2} c d x\right)} \sin\left(2 \, b x + 2 \, a\right)}{-i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + b^{3} \sin\left(2 \, b x + 2 \, a\right) + i \, b^{3}}"," ",0,"-(2*b^2*c^2 + (2*b*d^2*x + 2*b*c*d - 2*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a) - (2*I*b*d^2*x + 2*I*b*c*d)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*b*c*d*cos(2*b*x + 2*a) + 2*I*b*c*d*sin(2*b*x + 2*a) - 2*b*c*d)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*b*d^2*x*cos(2*b*x + 2*a) + 2*I*b*d^2*x*sin(2*b*x + 2*a) - 2*b*d^2*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x)*cos(2*b*x + 2*a) + (2*d^2*cos(2*b*x + 2*a) + 2*I*d^2*sin(2*b*x + 2*a) - 2*d^2)*dilog(-e^(I*b*x + I*a)) + (2*d^2*cos(2*b*x + 2*a) + 2*I*d^2*sin(2*b*x + 2*a) - 2*d^2)*dilog(e^(I*b*x + I*a)) - (I*b*d^2*x + I*b*c*d + (-I*b*d^2*x - I*b*c*d)*cos(2*b*x + 2*a) + (b*d^2*x + b*c*d)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (I*b*d^2*x + I*b*c*d + (-I*b*d^2*x - I*b*c*d)*cos(2*b*x + 2*a) + (b*d^2*x + b*c*d)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-2*I*b^2*d^2*x^2 - 4*I*b^2*c*d*x)*sin(2*b*x + 2*a))/(-I*b^3*cos(2*b*x + 2*a) + b^3*sin(2*b*x + 2*a) + I*b^3)","B",0
30,1,217,0,0.530088," ","integrate((d*x+c)*csc(b*x+a)^2,x, algorithm=""maxima"")","\frac{\frac{{\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d}{{\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b} - \frac{2 \, c}{\tan\left(b x + a\right)} + \frac{2 \, a d}{b \tan\left(b x + a\right)}}{2 \, b}"," ",0,"1/2*(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 4*(b*x + a)*sin(2*b*x + 2*a))*d/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*b) - 2*c/tan(b*x + a) + 2*a*d/(b*tan(b*x + a)))/b","B",0
31,0,0,0,0.000000," ","integrate(csc(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{{\left(b d^{2} x + b c d + {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)}^{2} {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right)}}\,{d x}}{b} - \frac{{\left(b d^{2} x + b c d + {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)}^{2} {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right)}}\,{d x}}{b} - 2 \, \sin\left(2 \, b x + 2 \, a\right)}{b d x + {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + b c - 2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right)}"," ",0,"((b*d^2*x + b*c*d + (b*d^2*x + b*c*d)*cos(2*b*x + 2*a)^2 + (b*d^2*x + b*c*d)*sin(2*b*x + 2*a)^2 - 2*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a))*integrate(sin(b*x + a)/(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cos(b*x + a)^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sin(b*x + a)^2 + 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cos(b*x + a)), x) - (b*d^2*x + b*c*d + (b*d^2*x + b*c*d)*cos(2*b*x + 2*a)^2 + (b*d^2*x + b*c*d)*sin(2*b*x + 2*a)^2 - 2*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a))*integrate(sin(b*x + a)/(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cos(b*x + a)^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sin(b*x + a)^2 - 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cos(b*x + a)), x) - 2*sin(2*b*x + 2*a))/(b*d*x + (b*d*x + b*c)*cos(2*b*x + 2*a)^2 + (b*d*x + b*c)*sin(2*b*x + 2*a)^2 + b*c - 2*(b*d*x + b*c)*cos(2*b*x + 2*a))","F",0
32,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,1,3877,0,3.889788," ","integrate((d*x+c)^3*csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{c^{3} {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{3}} - \frac{4 \, {\left({\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 12 \, b c d^{2} - 12 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{3} d^{3} + 6 \, b c d^{2} - 6 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{3} d^{3} + 6 \, b c d^{2} - 6 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{3} d^{3} + 12 i \, b c d^{2} - 12 i \, a d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + {\left(6 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{3} - 24 i \, b c d^{2} + 24 i \, a d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} + {\left(-12 i \, a^{2} - 24 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(12 \, b c d^{2} - 12 \, a d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, b c d^{2} - 24 i \, a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + {\left(6 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} + {\left(-12 i \, a^{2} - 24 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(4 i \, {\left(b x + a\right)}^{3} d^{3} + 12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, a^{2} d^{3} + {\left(12 i \, b c d^{2} - 12 \, {\left(i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d - 24 \, {\left(i \, a - 1\right)} b c d^{2} + {\left(12 i \, a^{2} - 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} d^{3} - 12 \, b^{2} c^{2} d + 24 \, a b c d^{2} - 12 \, a^{2} d^{3} - 12 \, {\left(-i \, b c d^{2} + {\left(i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d - 24 \, {\left(i \, a + 1\right)} b c d^{2} + {\left(12 i \, a^{2} + 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) - {\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 6 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(a^{2} + 2\right)} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 2\right)} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 2\right)} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, b^{2} c^{2} d + 12 i \, a b c d^{2} - 6 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-6 i \, a^{2} - 12 i\right)} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, b^{2} c^{2} d - 24 i \, a b c d^{2} + 12 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(12 i \, a^{2} + 24 i\right)} d^{3} + {\left(24 i \, b c d^{2} - 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 6 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(a^{2} + 2\right)} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 2\right)} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 2\right)} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + 6 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(6 i \, a^{2} + 12 i\right)} d^{3} + {\left(12 i \, b c d^{2} - 12 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-12 i \, a^{2} - 24 i\right)} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-3 i \, b c d^{2} + 3 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-3 i \, b^{2} c^{2} d + 6 i \, a b c d^{2} + {\left(-3 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-3 i \, b c d^{2} + 3 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-3 i \, b^{2} c^{2} d + 6 i \, a b c d^{2} + {\left(-3 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{3} d^{3} + 12 i \, b c d^{2} - 12 i \, a d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d - 12 i \, a b c d^{2} + {\left(6 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)}^{3} d^{3} + 6 \, b c d^{2} - 6 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 2 \, {\left({\left(b x + a\right)}^{3} d^{3} + 6 \, b c d^{2} - 6 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(3 i \, b c d^{2} - 3 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 i \, b^{2} c^{2} d - 6 i \, a b c d^{2} + {\left(3 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(3 i \, b c d^{2} - 3 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 i \, b^{2} c^{2} d - 6 i \, a b c d^{2} + {\left(3 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-2 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-6 i \, b c d^{2} + 6 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-6 i \, b^{2} c^{2} d + 12 i \, a b c d^{2} + {\left(-6 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left({\left(b x + a\right)}^{3} d^{3} + 6 \, b c d^{2} - 6 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{3} d^{3} + 6 \, b c d^{2} - 6 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) + {\left(12 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 24 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 12 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 24 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 12 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(12 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 24 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 12 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 24 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 12 \, d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(-12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3} + {\left(-12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(24 i \, b c d^{2} + 24 i \, {\left(b x + a\right)} d^{3} - 24 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(12 i \, b c d^{2} + 12 i \, {\left(b x + a\right)} d^{3} - 12 i \, a d^{3} + {\left(12 i \, b c d^{2} + 12 i \, {\left(b x + a\right)} d^{3} - 12 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(4 \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, a^{2} d^{3} + {\left(12 \, b c d^{2} - {\left(12 \, a + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(12 \, b^{2} c^{2} d - {\left(24 \, a + 24 i\right)} b c d^{2} + 12 \, {\left(a^{2} + 2 i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 12 i \, b^{2} c^{2} d - 24 i \, a b c d^{2} + 12 i \, a^{2} d^{3} + {\left(12 \, b c d^{2} - {\left(12 \, a - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(12 \, b^{2} c^{2} d - {\left(24 \, a - 24 i\right)} b c d^{2} + 12 \, {\left(a^{2} - 2 i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)}}{-4 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + 8 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) - 8 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{3}}}{4 \, b}"," ",0,"1/4*(c^3*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 3*a*c^2*d*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + 3*a^2*c*d^2*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 - a^3*d^3*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^3 - 4*((2*(b*x + a)^3*d^3 + 12*b*c*d^2 - 12*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a) + 2*((b*x + a)^3*d^3 + 6*b*c*d^2 - 6*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 4*((b*x + a)^3*d^3 + 6*b*c*d^2 - 6*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^3*d^3 + 12*I*b*c*d^2 - 12*I*a*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a)^2 + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + (6*I*a^2 + 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-4*I*(b*x + a)^3*d^3 - 24*I*b*c*d^2 + 24*I*a*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a)^2 + (-12*I*b^2*c^2*d + 24*I*a*b*c*d^2 + (-12*I*a^2 - 24*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (12*b*c*d^2 - 12*a*d^3 + 12*(b*c*d^2 - a*d^3)*cos(4*b*x + 4*a) - 24*(b*c*d^2 - a*d^3)*cos(2*b*x + 2*a) - (-12*I*b*c*d^2 + 12*I*a*d^3)*sin(4*b*x + 4*a) - (24*I*b*c*d^2 - 24*I*a*d^3)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*(b*x + a)^3*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a) + 2*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 4*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^3*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a)^2 + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + (6*I*a^2 + 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-4*I*(b*x + a)^3*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a)^2 + (-12*I*b^2*c^2*d + 24*I*a*b*c*d^2 + (-12*I*a^2 - 24*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (4*I*(b*x + a)^3*d^3 + 12*b^2*c^2*d - 24*a*b*c*d^2 + 12*a^2*d^3 + (12*I*b*c*d^2 - 12*(I*a - 1)*d^3)*(b*x + a)^2 + (12*I*b^2*c^2*d - 24*(I*a - 1)*b*c*d^2 + (12*I*a^2 - 24*a)*d^3)*(b*x + a))*cos(3*b*x + 3*a) + (4*I*(b*x + a)^3*d^3 - 12*b^2*c^2*d + 24*a*b*c*d^2 - 12*a^2*d^3 - 12*(-I*b*c*d^2 + (I*a + 1)*d^3)*(b*x + a)^2 + (12*I*b^2*c^2*d - 24*(I*a + 1)*b*c*d^2 + (12*I*a^2 + 24*a)*d^3)*(b*x + a))*cos(b*x + a) - (6*b^2*c^2*d - 12*a*b*c*d^2 + 6*(b*x + a)^2*d^3 + 6*(a^2 + 2)*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 2)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 12*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 2)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-6*I*b^2*c^2*d + 12*I*a*b*c*d^2 - 6*I*(b*x + a)^2*d^3 + (-6*I*a^2 - 12*I)*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (12*I*b^2*c^2*d - 24*I*a*b*c*d^2 + 12*I*(b*x + a)^2*d^3 + (12*I*a^2 + 24*I)*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (6*b^2*c^2*d - 12*a*b*c*d^2 + 6*(b*x + a)^2*d^3 + 6*(a^2 + 2)*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 2)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 12*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 2)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + 6*I*(b*x + a)^2*d^3 + (6*I*a^2 + 12*I)*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-12*I*b^2*c^2*d + 24*I*a*b*c*d^2 - 12*I*(b*x + a)^2*d^3 + (-12*I*a^2 - 24*I)*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (-I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-3*I*b*c*d^2 + 3*I*a*d^3)*(b*x + a)^2 + (-3*I*b^2*c^2*d + 6*I*a*b*c*d^2 + (-3*I*a^2 - 6*I)*d^3)*(b*x + a) + (-I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-3*I*b*c*d^2 + 3*I*a*d^3)*(b*x + a)^2 + (-3*I*b^2*c^2*d + 6*I*a*b*c*d^2 + (-3*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (2*I*(b*x + a)^3*d^3 + 12*I*b*c*d^2 - 12*I*a*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a)^2 + (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + (6*I*a^2 + 12*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)^3*d^3 + 6*b*c*d^2 - 6*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - 2*((b*x + a)^3*d^3 + 6*b*c*d^2 - 6*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (3*I*b*c*d^2 - 3*I*a*d^3)*(b*x + a)^2 + (3*I*b^2*c^2*d - 6*I*a*b*c*d^2 + (3*I*a^2 + 6*I)*d^3)*(b*x + a) + (I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (3*I*b*c*d^2 - 3*I*a*d^3)*(b*x + a)^2 + (3*I*b^2*c^2*d - 6*I*a*b*c*d^2 + (3*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-2*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a)^2 + (-6*I*b^2*c^2*d + 12*I*a*b*c*d^2 + (-6*I*a^2 - 12*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - ((b*x + a)^3*d^3 + 6*b*c*d^2 - 6*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 2*((b*x + a)^3*d^3 + 6*b*c*d^2 - 6*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 2)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (12*d^3*cos(4*b*x + 4*a) - 24*d^3*cos(2*b*x + 2*a) + 12*I*d^3*sin(4*b*x + 4*a) - 24*I*d^3*sin(2*b*x + 2*a) + 12*d^3)*polylog(4, -e^(I*b*x + I*a)) - (12*d^3*cos(4*b*x + 4*a) - 24*d^3*cos(2*b*x + 2*a) + 12*I*d^3*sin(4*b*x + 4*a) - 24*I*d^3*sin(2*b*x + 2*a) + 12*d^3)*polylog(4, e^(I*b*x + I*a)) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3 + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*cos(4*b*x + 4*a) + (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*cos(2*b*x + 2*a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) + (12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3 + (12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*cos(4*b*x + 4*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*cos(2*b*x + 2*a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) - (4*(b*x + a)^3*d^3 - 12*I*b^2*c^2*d + 24*I*a*b*c*d^2 - 12*I*a^2*d^3 + (12*b*c*d^2 - (12*a + 12*I)*d^3)*(b*x + a)^2 + (12*b^2*c^2*d - (24*a + 24*I)*b*c*d^2 + 12*(a^2 + 2*I*a)*d^3)*(b*x + a))*sin(3*b*x + 3*a) - (4*(b*x + a)^3*d^3 + 12*I*b^2*c^2*d - 24*I*a*b*c*d^2 + 12*I*a^2*d^3 + (12*b*c*d^2 - (12*a - 12*I)*d^3)*(b*x + a)^2 + (12*b^2*c^2*d - (24*a - 24*I)*b*c*d^2 + 12*(a^2 - 2*I*a)*d^3)*(b*x + a))*sin(b*x + a))/(-4*I*b^3*cos(4*b*x + 4*a) + 8*I*b^3*cos(2*b*x + 2*a) + 4*b^3*sin(4*b*x + 4*a) - 8*b^3*sin(2*b*x + 2*a) - 4*I*b^3))/b","B",0
34,1,1934,0,1.876055," ","integrate((d*x+c)^2*csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{c^{2} {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{2 \, a c d {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{2 \, \cos\left(b x + a\right)}{\cos\left(b x + a\right)^{2} - 1} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{4 \, {\left({\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 4 \, d^{2} + 2 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(4 i \, b c d - 4 i \, a d^{2}\right)} {\left(b x + a\right)} + 4 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-8 i \, b c d + 8 i \, a d^{2}\right)} {\left(b x + a\right)} - 8 i \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(4 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 4 \, d^{2}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(4 i \, b c d - 4 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-8 i \, b c d + 8 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(4 i \, {\left(b x + a\right)}^{2} d^{2} + 8 \, b c d - 8 \, a d^{2} + {\left(8 i \, b c d - 8 \, {\left(i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{2} d^{2} - 8 \, b c d + 8 \, a d^{2} - 8 \, {\left(-i \, b c d + {\left(i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) - {\left(4 \, b c d + 4 \, {\left(b x + a\right)} d^{2} - 4 \, a d^{2} + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(8 i \, b c d + 8 i \, {\left(b x + a\right)} d^{2} - 8 i \, a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(4 \, b c d + 4 \, {\left(b x + a\right)} d^{2} - 4 \, a d^{2} + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-8 i \, b c d - 8 i \, {\left(b x + a\right)} d^{2} + 8 i \, a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-2 i \, b c d + 2 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2} + {\left(-i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-2 i \, b c d + 2 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(4 i \, b c d - 4 i \, a d^{2}\right)} {\left(b x + a\right)} + 4 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 2 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(i \, {\left(b x + a\right)}^{2} d^{2} + {\left(2 i \, b c d - 2 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2} + {\left(i \, {\left(b x + a\right)}^{2} d^{2} + {\left(2 i \, b c d - 2 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-2 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-4 i \, b c d + 4 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) + {\left(-4 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 8 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(4 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) - 4 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 8 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 4 i \, d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(4 \, {\left(b x + a\right)}^{2} d^{2} - 8 i \, b c d + 8 i \, a d^{2} + {\left(8 \, b c d - {\left(8 \, a + 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(4 \, {\left(b x + a\right)}^{2} d^{2} + 8 i \, b c d - 8 i \, a d^{2} + {\left(8 \, b c d - {\left(8 \, a - 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)}}{-4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 8 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{2}}}{4 \, b}"," ",0,"1/4*(c^2*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 2*a*c*d*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + a^2*d^2*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 - 4*((2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + 4*d^2 + 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(4*b*x + 4*a) - 4*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(2*b*x + 2*a) + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a) + 4*I*d^2)*sin(4*b*x + 4*a) + (-4*I*(b*x + a)^2*d^2 + (-8*I*b*c*d + 8*I*a*d^2)*(b*x + a) - 8*I*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (4*d^2*cos(4*b*x + 4*a) - 8*d^2*cos(2*b*x + 2*a) + 4*I*d^2*sin(4*b*x + 4*a) - 8*I*d^2*sin(2*b*x + 2*a) + 4*d^2)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(4*b*x + 4*a) - 4*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a))*sin(4*b*x + 4*a) + (-4*I*(b*x + a)^2*d^2 + (-8*I*b*c*d + 8*I*a*d^2)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (4*I*(b*x + a)^2*d^2 + 8*b*c*d - 8*a*d^2 + (8*I*b*c*d - 8*(I*a - 1)*d^2)*(b*x + a))*cos(3*b*x + 3*a) + (4*I*(b*x + a)^2*d^2 - 8*b*c*d + 8*a*d^2 - 8*(-I*b*c*d + (I*a + 1)*d^2)*(b*x + a))*cos(b*x + a) - (4*b*c*d + 4*(b*x + a)*d^2 - 4*a*d^2 + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(4*b*x + 4*a) - (8*I*b*c*d + 8*I*(b*x + a)*d^2 - 8*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (4*b*c*d + 4*(b*x + a)*d^2 - 4*a*d^2 + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*sin(4*b*x + 4*a) + (-8*I*b*c*d - 8*I*(b*x + a)*d^2 + 8*I*a*d^2)*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a) - 2*I*d^2 + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(4*b*x + 4*a) + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a) + 4*I*d^2)*cos(2*b*x + 2*a) + ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(4*b*x + 4*a) - 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + 2*I*d^2 + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(4*b*x + 4*a) + (-2*I*(b*x + a)^2*d^2 + (-4*I*b*c*d + 4*I*a*d^2)*(b*x + a) - 4*I*d^2)*cos(2*b*x + 2*a) - ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(4*b*x + 4*a) + 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (-4*I*d^2*cos(4*b*x + 4*a) + 8*I*d^2*cos(2*b*x + 2*a) + 4*d^2*sin(4*b*x + 4*a) - 8*d^2*sin(2*b*x + 2*a) - 4*I*d^2)*polylog(3, -e^(I*b*x + I*a)) + (4*I*d^2*cos(4*b*x + 4*a) - 8*I*d^2*cos(2*b*x + 2*a) - 4*d^2*sin(4*b*x + 4*a) + 8*d^2*sin(2*b*x + 2*a) + 4*I*d^2)*polylog(3, e^(I*b*x + I*a)) - (4*(b*x + a)^2*d^2 - 8*I*b*c*d + 8*I*a*d^2 + (8*b*c*d - (8*a + 8*I)*d^2)*(b*x + a))*sin(3*b*x + 3*a) - (4*(b*x + a)^2*d^2 + 8*I*b*c*d - 8*I*a*d^2 + (8*b*c*d - (8*a - 8*I)*d^2)*(b*x + a))*sin(b*x + a))/(-4*I*b^2*cos(4*b*x + 4*a) + 8*I*b^2*cos(2*b*x + 2*a) + 4*b^2*sin(4*b*x + 4*a) - 8*b^2*sin(2*b*x + 2*a) - 4*I*b^2))/b","B",0
35,1,769,0,0.542217," ","integrate((d*x+c)*csc(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, b d x + 2 \, b c + 2 \, {\left(b d x + b c\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, b d x + 2 i \, b c\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, b d x - 4 i \, b c\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(2 \, b c \cos\left(4 \, b x + 4 \, a\right) - 4 \, b c \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b c \sin\left(4 \, b x + 4 \, a\right) - 4 i \, b c \sin\left(2 \, b x + 2 \, a\right) + 2 \, b c\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(2 \, b d x \cos\left(4 \, b x + 4 \, a\right) - 4 \, b d x \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b d x \sin\left(4 \, b x + 4 \, a\right) - 4 i \, b d x \sin\left(2 \, b x + 2 \, a\right) + 2 \, b d x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(4 i \, b d x + 4 i \, b c + 4 \, d\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(4 i \, b d x + 4 i \, b c - 4 \, d\right)} \cos\left(b x + a\right) - {\left(2 \, d \cos\left(4 \, b x + 4 \, a\right) - 4 \, d \cos\left(2 \, b x + 2 \, a\right) + 2 i \, d \sin\left(4 \, b x + 4 \, a\right) - 4 i \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, d\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(2 \, d \cos\left(4 \, b x + 4 \, a\right) - 4 \, d \cos\left(2 \, b x + 2 \, a\right) + 2 i \, d \sin\left(4 \, b x + 4 \, a\right) - 4 i \, d \sin\left(2 \, b x + 2 \, a\right) + 2 \, d\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-i \, b d x - i \, b c + {\left(-i \, b d x - i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 i \, b d x + 2 i \, b c\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \cos\left(b x + a\right) + 1\right) + {\left(i \, b d x + i \, b c + {\left(i \, b d x + i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-2 i \, b d x - 2 i \, b c\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \cos\left(b x + a\right) + 1\right) - 4 \, {\left(b d x + b c - i \, d\right)} \sin\left(3 \, b x + 3 \, a\right) - 4 \, {\left(b d x + b c + i \, d\right)} \sin\left(b x + a\right)}{-4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 8 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{2}}"," ",0,"-((2*b*d*x + 2*b*c + 2*(b*d*x + b*c)*cos(4*b*x + 4*a) - 4*(b*d*x + b*c)*cos(2*b*x + 2*a) + (2*I*b*d*x + 2*I*b*c)*sin(4*b*x + 4*a) + (-4*I*b*d*x - 4*I*b*c)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*b*c*cos(4*b*x + 4*a) - 4*b*c*cos(2*b*x + 2*a) + 2*I*b*c*sin(4*b*x + 4*a) - 4*I*b*c*sin(2*b*x + 2*a) + 2*b*c)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*b*d*x*cos(4*b*x + 4*a) - 4*b*d*x*cos(2*b*x + 2*a) + 2*I*b*d*x*sin(4*b*x + 4*a) - 4*I*b*d*x*sin(2*b*x + 2*a) + 2*b*d*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (4*I*b*d*x + 4*I*b*c + 4*d)*cos(3*b*x + 3*a) + (4*I*b*d*x + 4*I*b*c - 4*d)*cos(b*x + a) - (2*d*cos(4*b*x + 4*a) - 4*d*cos(2*b*x + 2*a) + 2*I*d*sin(4*b*x + 4*a) - 4*I*d*sin(2*b*x + 2*a) + 2*d)*dilog(-e^(I*b*x + I*a)) + (2*d*cos(4*b*x + 4*a) - 4*d*cos(2*b*x + 2*a) + 2*I*d*sin(4*b*x + 4*a) - 4*I*d*sin(2*b*x + 2*a) + 2*d)*dilog(e^(I*b*x + I*a)) + (-I*b*d*x - I*b*c + (-I*b*d*x - I*b*c)*cos(4*b*x + 4*a) + (2*I*b*d*x + 2*I*b*c)*cos(2*b*x + 2*a) + (b*d*x + b*c)*sin(4*b*x + 4*a) - 2*(b*d*x + b*c)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (I*b*d*x + I*b*c + (I*b*d*x + I*b*c)*cos(4*b*x + 4*a) + (-2*I*b*d*x - 2*I*b*c)*cos(2*b*x + 2*a) - (b*d*x + b*c)*sin(4*b*x + 4*a) + 2*(b*d*x + b*c)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 4*(b*d*x + b*c - I*d)*sin(3*b*x + 3*a) - 4*(b*d*x + b*c + I*d)*sin(b*x + a))/(-4*I*b^2*cos(4*b*x + 4*a) + 8*I*b^2*cos(2*b*x + 2*a) + 4*b^2*sin(4*b*x + 4*a) - 8*b^2*sin(2*b*x + 2*a) - 4*I*b^2)","B",0
36,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{{\left({\left(b d x + b c\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(b d x + b c\right)} \cos\left(b x + a\right) - d \sin\left(3 \, b x + 3 \, a\right) + d \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(b d x + b c - 2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, d \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left({\left(b d x + b c\right)} \cos\left(b x + a\right) + d \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b d x + b c\right)} \cos\left(b x + a\right) + \frac{1}{2} \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{{\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(b x + a\right)}\,{d x} + \frac{1}{2} \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{{\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(b x + a\right)}\,{d x} + {\left(d \cos\left(3 \, b x + 3 \, a\right) - d \cos\left(b x + a\right) + {\left(b d x + b c\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(b d x + b c\right)} \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(2 \, d \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right) - d\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(d \cos\left(b x + a\right) - {\left(b d x + b c\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) + d \sin\left(b x + a\right)}{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)}"," ",0,"(((b*d*x + b*c)*cos(3*b*x + 3*a) + (b*d*x + b*c)*cos(b*x + a) - d*sin(3*b*x + 3*a) + d*sin(b*x + a))*cos(4*b*x + 4*a) + (b*d*x + b*c - 2*(b*d*x + b*c)*cos(2*b*x + 2*a) - 2*d*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) - 2*((b*d*x + b*c)*cos(b*x + a) + d*sin(b*x + a))*cos(2*b*x + 2*a) + (b*d*x + b*c)*cos(b*x + a) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(4*b*x + 4*a)^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a)^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(4*b*x + 4*a)^2 - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(2*b*x + 2*a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a))*integrate(1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*d^2)*sin(b*x + a)/(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(b*x + a)^2 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(b*x + a)^2 + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(b*x + a)), x) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(4*b*x + 4*a)^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a)^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(4*b*x + 4*a)^2 - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(2*b*x + 2*a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a))*integrate(1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*d^2)*sin(b*x + a)/(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(b*x + a)^2 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(b*x + a)^2 - 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(b*x + a)), x) + (d*cos(3*b*x + 3*a) - d*cos(b*x + a) + (b*d*x + b*c)*sin(3*b*x + 3*a) + (b*d*x + b*c)*sin(b*x + a))*sin(4*b*x + 4*a) + (2*d*cos(2*b*x + 2*a) - 2*(b*d*x + b*c)*sin(2*b*x + 2*a) - d)*sin(3*b*x + 3*a) + 2*(d*cos(b*x + a) - (b*d*x + b*c)*sin(b*x + a))*sin(2*b*x + 2*a) + d*sin(b*x + a))/(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(4*b*x + 4*a)^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a)^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(4*b*x + 4*a)^2 - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(2*b*x + 2*a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a))","F",0
37,0,0,0,0.000000," ","integrate(csc(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left({\left(b d x + b c\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(b d x + b c\right)} \cos\left(b x + a\right) - 2 \, d \sin\left(3 \, b x + 3 \, a\right) + 2 \, d \sin\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(b d x + b c - 2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, d \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left({\left(b d x + b c\right)} \cos\left(b x + a\right) + 2 \, d \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b d x + b c\right)} \cos\left(b x + a\right) + \frac{1}{2} \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} - 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{{\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 6 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \cos\left(b x + a\right)}\,{d x} + \frac{1}{2} \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} - 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{{\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 6 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \sin\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4}\right)} \cos\left(b x + a\right)}\,{d x} + {\left(2 \, d \cos\left(3 \, b x + 3 \, a\right) - 2 \, d \cos\left(b x + a\right) + {\left(b d x + b c\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(b d x + b c\right)} \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 2 \, {\left(2 \, d \cos\left(2 \, b x + 2 \, a\right) - {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right) - d\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(2 \, d \cos\left(b x + a\right) - {\left(b d x + b c\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d \sin\left(b x + a\right)}{b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)^{2} - 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} - 2 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)}"," ",0,"(((b*d*x + b*c)*cos(3*b*x + 3*a) + (b*d*x + b*c)*cos(b*x + a) - 2*d*sin(3*b*x + 3*a) + 2*d*sin(b*x + a))*cos(4*b*x + 4*a) + (b*d*x + b*c - 2*(b*d*x + b*c)*cos(2*b*x + 2*a) - 4*d*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) - 2*((b*d*x + b*c)*cos(b*x + a) + 2*d*sin(b*x + a))*cos(2*b*x + 2*a) + (b*d*x + b*c)*cos(b*x + a) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(4*b*x + 4*a)^2 + 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a)^2 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(4*b*x + 4*a)^2 - 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(2*b*x + 2*a)^2 + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 - 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) - 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a))*integrate(1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 6*d^2)*sin(b*x + a)/(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*cos(b*x + a)^2 + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*sin(b*x + a)^2 + 2*(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*cos(b*x + a)), x) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(4*b*x + 4*a)^2 + 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a)^2 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(4*b*x + 4*a)^2 - 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(2*b*x + 2*a)^2 + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 - 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) - 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a))*integrate(1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 6*d^2)*sin(b*x + a)/(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*cos(b*x + a)^2 + (b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*sin(b*x + a)^2 - 2*(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4)*cos(b*x + a)), x) + (2*d*cos(3*b*x + 3*a) - 2*d*cos(b*x + a) + (b*d*x + b*c)*sin(3*b*x + 3*a) + (b*d*x + b*c)*sin(b*x + a))*sin(4*b*x + 4*a) + 2*(2*d*cos(2*b*x + 2*a) - (b*d*x + b*c)*sin(2*b*x + 2*a) - d)*sin(3*b*x + 3*a) + 2*(2*d*cos(b*x + a) - (b*d*x + b*c)*sin(b*x + a))*sin(2*b*x + 2*a) + 2*d*sin(b*x + a))/(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(4*b*x + 4*a)^2 + 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a)^2 + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(4*b*x + 4*a)^2 - 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sin(2*b*x + 2*a)^2 + 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 - 2*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a))*cos(4*b*x + 4*a) - 4*(b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cos(2*b*x + 2*a))","F",0
38,1,261,0,0.758605," ","integrate((d*x+c)^(5/2)*sin(b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(40 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) - 4 \, {\left(4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3} - 15 \, \sqrt{2} \sqrt{d x + c} b d^{2}\right)} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(15 i - 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(15 i + 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(15 i + 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(15 i - 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{32 \, b^{4}}"," ",0,"1/32*sqrt(2)*(40*sqrt(2)*(d*x + c)^(3/2)*b^2*d*sin(((d*x + c)*b - b*c + a*d)/d) - 4*(4*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*cos(((d*x + c)*b - b*c + a*d)/d) + ((15*I - 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (15*I + 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(15*I + 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (15*I - 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b^4","C",0
39,1,242,0,1.755347," ","integrate((d*x+c)^(3/2)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(8 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) - 12 \, \sqrt{2} \sqrt{d x + c} b d \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) - {\left(-\left(3 i + 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(3 i - 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(3 i - 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(3 i + 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{16 \, b^{3}}"," ",0,"-1/16*sqrt(2)*(8*sqrt(2)*(d*x + c)^(3/2)*b^2*cos(((d*x + c)*b - b*c + a*d)/d) - 12*sqrt(2)*sqrt(d*x + c)*b*d*sin(((d*x + c)*b - b*c + a*d)/d) - (-(3*I + 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (3*I - 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) - ((3*I - 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (3*I + 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b^3","C",0
40,1,196,0,1.381562," ","integrate((d*x+c)^(1/2)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{d x + c} b \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(i + 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(i + 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(i - 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{8 \, b^{2}}"," ",0,"-1/8*sqrt(2)*(4*sqrt(2)*sqrt(d*x + c)*b*cos(((d*x + c)*b - b*c + a*d)/d) + ((I - 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (I + 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(I + 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (I - 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b^2","C",0
41,1,159,0,0.847888," ","integrate(sin(b*x+a)/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(-\left(i + 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(i - 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(\left(i - 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(i + 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{4 \, b}"," ",0,"-1/4*sqrt(2)*((-(I + 1)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (I - 1)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((I - 1)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (I + 1)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b","C",0
42,1,129,0,1.522165," ","integrate(sin(b*x+a)/(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{{\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}}}{4 \, \sqrt{d x + c} d}"," ",0,"-1/4*(((I - 1)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((I + 1)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) - (I - 1)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*sqrt((d*x + c)*b/d)/(sqrt(d*x + c)*d)","C",0
43,1,129,0,1.960591," ","integrate(sin(b*x+a)/(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}}}{4 \, {\left(d x + c\right)}^{\frac{3}{2}} d}"," ",0,"-1/4*((-(I + 1)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2)/((d*x + c)^(3/2)*d)","C",0
44,1,129,0,1.055197," ","integrate(sin(b*x+a)/(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{{\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}}}{4 \, {\left(d x + c\right)}^{\frac{5}{2}} d}"," ",0,"1/4*(((I - 1)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((I + 1)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) - (I - 1)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2)/((d*x + c)^(5/2)*d)","C",0
45,1,295,0,1.476720," ","integrate((d*x+c)^(5/2)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{512 \, \sqrt{2} {\left(d x + c\right)}^{\frac{7}{2}} b^{4}}{d} - 1120 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(105 i + 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(105 i - 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) - {\left(-\left(105 i - 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(105 i + 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right) - 56 \, {\left(16 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3} - 15 \, \sqrt{2} \sqrt{d x + c} b d^{2}\right)} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)\right)}}{7168 \, b^{4}}"," ",0,"1/7168*sqrt(2)*(512*sqrt(2)*(d*x + c)^(7/2)*b^4/d - 1120*sqrt(2)*(d*x + c)^(3/2)*b^2*d*cos(2*((d*x + c)*b - b*c + a*d)/d) - ((105*I + 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (105*I - 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(105*I - 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (105*I + 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) - 56*(16*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*sin(2*((d*x + c)*b - b*c + a*d)/d))/b^4","C",0
46,1,274,0,0.512353," ","integrate((d*x+c)^(3/2)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{128 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3}}{d} - 160 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 120 \, \sqrt{2} \sqrt{d x + c} b d \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(15 i - 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(15 i + 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) - {\left(-\left(15 i + 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(15 i - 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right)\right)}}{1280 \, b^{3}}"," ",0,"1/1280*sqrt(2)*(128*sqrt(2)*(d*x + c)^(5/2)*b^3/d - 160*sqrt(2)*(d*x + c)^(3/2)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - 120*sqrt(2)*sqrt(d*x + c)*b*d*cos(2*((d*x + c)*b - b*c + a*d)/d) - ((15*I - 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (15*I + 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(15*I + 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (15*I - 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))/b^3","C",0
47,1,229,0,0.843585," ","integrate((d*x+c)^(1/2)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{32 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2}}{d} - 24 \, \sqrt{2} \sqrt{d x + c} b \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(3 i + 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(3 i - 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) - {\left(\left(3 i - 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(3 i + 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right)\right)}}{192 \, b^{2}}"," ",0,"1/192*sqrt(2)*(32*sqrt(2)*(d*x + c)^(3/2)*b^2/d - 24*sqrt(2)*sqrt(d*x + c)*b*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(3*I + 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (3*I - 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - ((3*I - 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (3*I + 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))/b^2","C",0
48,1,187,0,0.773734," ","integrate(sin(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left({\left(\left(i - 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(i + 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) + {\left(-\left(i + 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(i - 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right) + \frac{8 \, \sqrt{2} \sqrt{d x + c} b}{d}\right)}}{16 \, b}"," ",0,"1/16*sqrt(2)*(((I - 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (I + 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + (-(I + 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (I - 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) + 8*sqrt(2)*sqrt(d*x + c)*b/d)/b","C",0
49,1,135,0,1.923431," ","integrate(sin(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}} + 8}{8 \, \sqrt{d x + c} d}"," ",0,"-1/8*(sqrt(2)*((-(I + 1)*sqrt(2)*gamma(-1/2, 2*I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-1/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-1/2, 2*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-1/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*sqrt((d*x + c)*b/d) + 8)/(sqrt(d*x + c)*d)","C",0
50,1,135,0,1.200891," ","integrate(sin(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left({\left(\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}} - 4}{12 \, {\left(d x + c\right)}^{\frac{3}{2}} d}"," ",0,"1/12*(sqrt(2)*(((3*I - 3)*sqrt(2)*gamma(-3/2, 2*I*(d*x + c)*b/d) - (3*I + 3)*sqrt(2)*gamma(-3/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((3*I + 3)*sqrt(2)*gamma(-3/2, 2*I*(d*x + c)*b/d) - (3*I - 3)*sqrt(2)*gamma(-3/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2) - 4)/((d*x + c)^(3/2)*d)","C",0
51,1,135,0,1.973177," ","integrate(sin(b*x+a)^2/(d*x+c)^(7/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left({\left(-\left(5 i + 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) + \left(5 i - 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(5 i - 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(5 i + 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}} - 2}{10 \, {\left(d x + c\right)}^{\frac{5}{2}} d}"," ",0,"1/10*(sqrt(2)*((-(5*I + 5)*sqrt(2)*gamma(-5/2, 2*I*(d*x + c)*b/d) + (5*I - 5)*sqrt(2)*gamma(-5/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((5*I - 5)*sqrt(2)*gamma(-5/2, 2*I*(d*x + c)*b/d) - (5*I + 5)*sqrt(2)*gamma(-5/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2) - 2)/((d*x + c)^(5/2)*d)","C",0
52,1,135,0,1.045651," ","integrate(sin(b*x+a)^2/(d*x+c)^(9/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(\left(7 i - 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(7 i + 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(7 i + 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(7 i - 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{7}{2}} + 1}{7 \, {\left(d x + c\right)}^{\frac{7}{2}} d}"," ",0,"-1/7*(sqrt(2)*(((7*I - 7)*sqrt(2)*gamma(-7/2, 2*I*(d*x + c)*b/d) - (7*I + 7)*sqrt(2)*gamma(-7/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((7*I + 7)*sqrt(2)*gamma(-7/2, 2*I*(d*x + c)*b/d) - (7*I - 7)*sqrt(2)*gamma(-7/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*((d*x + c)*b/d)^(7/2) + 1)/((d*x + c)^(7/2)*d)","C",0
53,1,543,0,0.538796," ","integrate((d*x+c)^(5/2)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(240 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 6480 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) - 24 \, {\left(\frac{12 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 5 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 648 \, {\left(\frac{4 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(5 i - 5\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(5 i + 5\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{3 i \, b}{d}}\right) + {\left(-\left(1215 i - 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(1215 i + 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(\left(1215 i + 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(1215 i - 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(5 i + 5\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(5 i - 5\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{3456 \, b^{5}}"," ",0,"-1/3456*(240*(d*x + c)^(3/2)*b^3*sin(3*((d*x + c)*b - b*c + a*d)/d) - 6480*(d*x + c)^(3/2)*b^3*sin(((d*x + c)*b - b*c + a*d)/d) - 24*(12*(d*x + c)^(5/2)*b^4/d - 5*sqrt(d*x + c)*b^2*d)*cos(3*((d*x + c)*b - b*c + a*d)/d) + 648*(4*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(((d*x + c)*b - b*c + a*d)/d) + ((5*I - 5)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (5*I + 5)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(1215*I - 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (1215*I + 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((1215*I + 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (1215*I - 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(5*I + 5)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (5*I - 5)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^5","C",0
54,1,499,0,2.873703," ","integrate((d*x+c)^(3/2)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{48 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{432 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} - 24 \, \sqrt{d x + c} b^{2} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 648 \, \sqrt{d x + c} b^{2} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) - {\left(-\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{3 i \, b}{d}}\right) - {\left(\left(81 i + 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(81 i - 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(-\left(81 i - 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(81 i + 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - {\left(\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{576 \, b^{4}}"," ",0,"1/576*(48*(d*x + c)^(3/2)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d)/d - 432*(d*x + c)^(3/2)*b^3*cos(((d*x + c)*b - b*c + a*d)/d)/d - 24*sqrt(d*x + c)*b^2*sin(3*((d*x + c)*b - b*c + a*d)/d) + 648*sqrt(d*x + c)*b^2*sin(((d*x + c)*b - b*c + a*d)/d) - (-(I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) - ((81*I + 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (81*I - 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) - (-(81*I - 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (81*I + 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) - ((I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^4","C",0
55,1,422,0,1.032393," ","integrate((d*x+c)^(1/2)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{24 \, \sqrt{d x + c} b^{2} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{216 \, \sqrt{d x + c} b^{2} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} + {\left(\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{3 i \, b}{d}}\right) + {\left(-\left(27 i - 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(27 i + 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(\left(27 i + 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(27 i - 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{288 \, b^{3}}"," ",0,"1/288*(24*sqrt(d*x + c)*b^2*cos(3*((d*x + c)*b - b*c + a*d)/d)/d - 216*sqrt(d*x + c)*b^2*cos(((d*x + c)*b - b*c + a*d)/d)/d + ((I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(27*I - 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (27*I + 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((27*I + 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (27*I - 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^3","C",0
56,1,375,0,1.753461," ","integrate(sin(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""maxima"")","\frac{{\left({\left(-\frac{\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d} + \frac{\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{3 i \, b}{d}}\right) + {\left(\frac{\left(9 i + 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} - \frac{\left(9 i - 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\frac{\left(9 i - 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} + \frac{\left(9 i + 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(\frac{\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d} - \frac{\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{48 \, b^{2}}"," ",0,"1/48*((-(I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d + (I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + ((9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d - (9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d + (9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d - (I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^2","C",0
57,1,252,0,1.682749," ","integrate(sin(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}} + {\left({\left(-\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(-\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}}}{16 \, \sqrt{d x + c} d}"," ",0,"1/16*(sqrt(3)*(((I - 1)*sqrt(2)*gamma(-1/2, 3*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-1/2, -3*I*(d*x + c)*b/d))*cos(-3*(b*c - a*d)/d) + ((I + 1)*sqrt(2)*gamma(-1/2, 3*I*(d*x + c)*b/d) - (I - 1)*sqrt(2)*gamma(-1/2, -3*I*(d*x + c)*b/d))*sin(-3*(b*c - a*d)/d))*sqrt((d*x + c)*b/d) + ((-(3*I - 3)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) + (3*I + 3)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + (-(3*I + 3)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) + (3*I - 3)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*sqrt((d*x + c)*b/d))/(sqrt(d*x + c)*d)","C",0
58,1,253,0,1.023870," ","integrate(sin(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""maxima"")","\frac{3 \, \sqrt{3} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}} + {\left({\left(\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(-\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}}}{16 \, {\left(d x + c\right)}^{\frac{3}{2}} d}"," ",0,"1/16*(3*sqrt(3)*((-(I + 1)*sqrt(2)*gamma(-3/2, 3*I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-3/2, -3*I*(d*x + c)*b/d))*cos(-3*(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-3/2, 3*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-3/2, -3*I*(d*x + c)*b/d))*sin(-3*(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2) + (((3*I + 3)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) - (3*I - 3)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + (-(3*I - 3)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) + (3*I + 3)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2))/((d*x + c)^(3/2)*d)","C",0
59,1,253,0,2.398553," ","integrate(sin(b*x+a)^3/(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{9 \, \sqrt{3} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}} + {\left({\left(-\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(-\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}}}{16 \, {\left(d x + c\right)}^{\frac{5}{2}} d}"," ",0,"-1/16*(9*sqrt(3)*(((I - 1)*sqrt(2)*gamma(-5/2, 3*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-5/2, -3*I*(d*x + c)*b/d))*cos(-3*(b*c - a*d)/d) + ((I + 1)*sqrt(2)*gamma(-5/2, 3*I*(d*x + c)*b/d) - (I - 1)*sqrt(2)*gamma(-5/2, -3*I*(d*x + c)*b/d))*sin(-3*(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2) + ((-(3*I - 3)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) + (3*I + 3)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + (-(3*I + 3)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) + (3*I - 3)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2))/((d*x + c)^(5/2)*d)","C",0
60,1,106,0,1.693172," ","integrate((d*x)^(3/2)*sin(f*x),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(8 \, \sqrt{2} \left(d x\right)^{\frac{3}{2}} f^{2} \cos\left(f x\right) - 12 \, \sqrt{2} \sqrt{d x} d f \sin\left(f x\right) + \left(3 i + 3\right) \, \sqrt{\pi} d^{2} \left(\frac{f^{2}}{d^{2}}\right)^{\frac{1}{4}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{i \, f}{d}}\right) - \left(3 i - 3\right) \, \sqrt{\pi} d^{2} \left(\frac{f^{2}}{d^{2}}\right)^{\frac{1}{4}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{i \, f}{d}}\right)\right)}}{16 \, f^{3}}"," ",0,"-1/16*sqrt(2)*(8*sqrt(2)*(d*x)^(3/2)*f^2*cos(f*x) - 12*sqrt(2)*sqrt(d*x)*d*f*sin(f*x) + (3*I + 3)*sqrt(pi)*d^2*(f^2/d^2)^(1/4)*erf(sqrt(d*x)*sqrt(I*f/d)) - (3*I - 3)*sqrt(pi)*d^2*(f^2/d^2)^(1/4)*erf(sqrt(d*x)*sqrt(-I*f/d)))/f^3","C",0
61,1,84,0,0.522043," ","integrate((d*x)^(1/2)*sin(f*x),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{d x} f \cos\left(f x\right) + \left(i - 1\right) \, \sqrt{\pi} d \left(\frac{f^{2}}{d^{2}}\right)^{\frac{1}{4}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{i \, f}{d}}\right) - \left(i + 1\right) \, \sqrt{\pi} d \left(\frac{f^{2}}{d^{2}}\right)^{\frac{1}{4}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{i \, f}{d}}\right)\right)}}{8 \, f^{2}}"," ",0,"-1/8*sqrt(2)*(4*sqrt(2)*sqrt(d*x)*f*cos(f*x) + (I - 1)*sqrt(pi)*d*(f^2/d^2)^(1/4)*erf(sqrt(d*x)*sqrt(I*f/d)) - (I + 1)*sqrt(pi)*d*(f^2/d^2)^(1/4)*erf(sqrt(d*x)*sqrt(-I*f/d)))/f^2","C",0
62,1,67,0,0.654699," ","integrate(sin(f*x)/(d*x)^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\left(i + 1\right) \, \sqrt{\pi} \left(\frac{f^{2}}{d^{2}}\right)^{\frac{1}{4}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{i \, f}{d}}\right) - \left(i - 1\right) \, \sqrt{\pi} \left(\frac{f^{2}}{d^{2}}\right)^{\frac{1}{4}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{i \, f}{d}}\right)\right)}}{4 \, f}"," ",0,"1/4*sqrt(2)*((I + 1)*sqrt(pi)*(f^2/d^2)^(1/4)*erf(sqrt(d*x)*sqrt(I*f/d)) - (I - 1)*sqrt(pi)*(f^2/d^2)^(1/4)*erf(sqrt(d*x)*sqrt(-I*f/d)))/f","C",0
63,1,38,0,2.392800," ","integrate(sin(f*x)/(d*x)^(3/2),x, algorithm=""maxima"")","-\frac{\sqrt{f x} {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, f x\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, f x\right)\right)}}{4 \, \sqrt{d x} d}"," ",0,"-1/4*sqrt(f*x)*((I - 1)*sqrt(2)*gamma(-1/2, I*f*x) - (I + 1)*sqrt(2)*gamma(-1/2, -I*f*x))/(sqrt(d*x)*d)","C",0
64,1,38,0,1.066381," ","integrate(sin(f*x)/(d*x)^(5/2),x, algorithm=""maxima"")","-\frac{\left(f x\right)^{\frac{3}{2}} {\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, i \, f x\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -i \, f x\right)\right)}}{4 \, \left(d x\right)^{\frac{3}{2}} d}"," ",0,"-1/4*(f*x)^(3/2)*(-(I + 1)*sqrt(2)*gamma(-3/2, I*f*x) + (I - 1)*sqrt(2)*gamma(-3/2, -I*f*x))/((d*x)^(3/2)*d)","C",0
65,0,0,0,0.000000," ","integrate(csc(b*x+a)*(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \sqrt{d x + c} \csc\left(b x + a\right)\,{d x}"," ",0,"integrate(sqrt(d*x + c)*csc(b*x + a), x)","F",0
66,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*x+c)^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right)}{\sqrt{d x + c}}\,{d x}"," ",0,"integrate(csc(b*x + a)/sqrt(d*x + c), x)","F",0
67,0,0,0,0.000000," ","integrate(x/sin(f*x+e)^(3/2)+x*sin(f*x+e)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\sin\left(f x + e\right)} + \frac{x}{\sin\left(f x + e\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sqrt(sin(f*x + e)) + x/sin(f*x + e)^(3/2), x)","F",0
68,0,0,0,0.000000," ","integrate(x^2/sin(f*x+e)^(3/2)+x^2*sin(f*x+e)^(1/2),x, algorithm=""maxima"")","\int x^{2} \sqrt{\sin\left(f x + e\right)} + \frac{x^{2}}{\sin\left(f x + e\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*sqrt(sin(f*x + e)) + x^2/sin(f*x + e)^(3/2), x)","F",0
69,0,0,0,0.000000," ","integrate(x/sin(f*x+e)^(5/2)-1/3*x/sin(f*x+e)^(1/2),x, algorithm=""maxima"")","\int -\frac{x}{3 \, \sqrt{\sin\left(f x + e\right)}} + \frac{x}{\sin\left(f x + e\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-1/3*x/sqrt(sin(f*x + e)) + x/sin(f*x + e)^(5/2), x)","F",0
70,0,0,0,0.000000," ","integrate(x/sin(f*x+e)^(7/2)+3/5*x*sin(f*x+e)^(1/2),x, algorithm=""maxima"")","\int \frac{3}{5} \, x \sqrt{\sin\left(f x + e\right)} + \frac{x}{\sin\left(f x + e\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(3/5*x*sqrt(sin(f*x + e)) + x/sin(f*x + e)^(7/2), x)","F",0
71,0,0,0,0.000000," ","integrate((d*x+c)^m*(b*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \left(b \sin\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(b*sin(f*x + e))^n, x)","F",0
72,0,0,0,0.000000," ","integrate((d*x+c)^m*sin(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*sin(b*x + a)^3, x)","F",0
73,0,0,0,0.000000," ","integrate((d*x+c)^m*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} - e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)}}{2 \, {\left(d m + d\right)}}"," ",0,"-1/2*((d*m + d)*integrate((d*x + c)^m*cos(2*b*x + 2*a), x) - e^(m*log(d*x + c) + log(d*x + c)))/(d*m + d)","F",0
74,0,0,0,0.000000," ","integrate((d*x+c)^m*sin(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*sin(b*x + a), x)","F",0
75,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a), x)","F",0
76,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^2, x)","F",0
77,0,0,0,0.000000," ","integrate(x^(3+m)*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m + 3} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 3)*sin(b*x + a), x)","F",0
78,0,0,0,0.000000," ","integrate(x^(2+m)*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m + 2} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 2)*sin(b*x + a), x)","F",0
79,0,0,0,0.000000," ","integrate(x^(1+m)*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m + 1} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 1)*sin(b*x + a), x)","F",0
80,0,0,0,0.000000," ","integrate(x^m*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^m*sin(b*x + a), x)","F",0
81,0,0,0,0.000000," ","integrate(x^(-1+m)*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m - 1} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 1)*sin(b*x + a), x)","F",0
82,0,0,0,0.000000," ","integrate(x^(-2+m)*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m - 2} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 2)*sin(b*x + a), x)","F",0
83,0,0,0,0.000000," ","integrate(x^(-3+m)*sin(b*x+a),x, algorithm=""maxima"")","\int x^{m - 3} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 3)*sin(b*x + a), x)","F",0
84,0,0,0,0.000000," ","integrate(x^(3+m)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(m + 4\right)} \int x^{3} x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} - e^{\left(m \log\left(x\right) + 4 \, \log\left(x\right)\right)}}{2 \, {\left(m + 4\right)}}"," ",0,"-1/2*((m + 4)*integrate(x^3*x^m*cos(2*b*x + 2*a), x) - e^(m*log(x) + 4*log(x)))/(m + 4)","F",0
85,0,0,0,0.000000," ","integrate(x^(2+m)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(m + 3\right)} \int x^{2} x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} - e^{\left(m \log\left(x\right) + 3 \, \log\left(x\right)\right)}}{2 \, {\left(m + 3\right)}}"," ",0,"-1/2*((m + 3)*integrate(x^2*x^m*cos(2*b*x + 2*a), x) - e^(m*log(x) + 3*log(x)))/(m + 3)","F",0
86,0,0,0,0.000000," ","integrate(x^(1+m)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(m + 2\right)} \int x x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} - e^{\left(m \log\left(x\right) + 2 \, \log\left(x\right)\right)}}{2 \, {\left(m + 2\right)}}"," ",0,"-1/2*((m + 2)*integrate(x*x^m*cos(2*b*x + 2*a), x) - e^(m*log(x) + 2*log(x)))/(m + 2)","F",0
87,0,0,0,0.000000," ","integrate(x^m*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(m + 1\right)} \int x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} - e^{\left(m \log\left(x\right) + \log\left(x\right)\right)}}{2 \, {\left(m + 1\right)}}"," ",0,"-1/2*((m + 1)*integrate(x^m*cos(2*b*x + 2*a), x) - e^(m*log(x) + log(x)))/(m + 1)","F",0
88,0,0,0,0.000000," ","integrate(x^(-1+m)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{m \int \frac{x^{m} \cos\left(2 \, b x + 2 \, a\right)}{x}\,{d x} - x^{m}}{2 \, m}"," ",0,"-1/2*(m*integrate(x^m*cos(2*b*x + 2*a)/x, x) - x^m)/m","F",0
89,0,0,0,0.000000," ","integrate(x^(-2+m)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(m - 1\right)} x \int \frac{x^{m} \cos\left(2 \, b x + 2 \, a\right)}{x^{2}}\,{d x} - x^{m}}{2 \, {\left(m - 1\right)} x}"," ",0,"-1/2*((m - 1)*x*integrate(x^m*cos(2*b*x + 2*a)/x^2, x) - x^m)/((m - 1)*x)","F",0
90,0,0,0,0.000000," ","integrate(x^(-3+m)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(m - 2\right)} x^{2} \int \frac{x^{m} \cos\left(2 \, b x + 2 \, a\right)}{x^{3}}\,{d x} - x^{m}}{2 \, {\left(m - 2\right)} x^{2}}"," ",0,"-1/2*((m - 2)*x^2*integrate(x^m*cos(2*b*x + 2*a)/x^3, x) - x^m)/((m - 2)*x^2)","F",0
91,0,0,0,0.000000," ","integrate(x/csc(f*x+e)^(3/2)-1/3*x*csc(f*x+e)^(1/2),x, algorithm=""maxima"")","\int -\frac{1}{3} \, x \sqrt{\csc\left(f x + e\right)} + \frac{x}{\csc\left(f x + e\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/3*x*sqrt(csc(f*x + e)) + x/csc(f*x + e)^(3/2), x)","F",0
92,0,0,0,0.000000," ","integrate(x^2/csc(f*x+e)^(3/2)-1/3*x^2*csc(f*x+e)^(1/2),x, algorithm=""maxima"")","\int -\frac{1}{3} \, x^{2} \sqrt{\csc\left(f x + e\right)} + \frac{x^{2}}{\csc\left(f x + e\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/3*x^2*sqrt(csc(f*x + e)) + x^2/csc(f*x + e)^(3/2), x)","F",0
93,0,0,0,0.000000," ","integrate(x/csc(f*x+e)^(5/2)-3/5*x/csc(f*x+e)^(1/2),x, algorithm=""maxima"")","\int -\frac{3 \, x}{5 \, \sqrt{\csc\left(f x + e\right)}} + \frac{x}{\csc\left(f x + e\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-3/5*x/sqrt(csc(f*x + e)) + x/csc(f*x + e)^(5/2), x)","F",0
94,0,0,0,0.000000," ","integrate(x/csc(f*x+e)^(7/2)-5/21*x*csc(f*x+e)^(1/2),x, algorithm=""maxima"")","\int -\frac{5}{21} \, x \sqrt{\csc\left(f x + e\right)} + \frac{x}{\csc\left(f x + e\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-5/21*x*sqrt(csc(f*x + e)) + x/csc(f*x + e)^(7/2), x)","F",0
95,1,462,0,0.335038," ","integrate((d*x+c)^3*(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c^{3} + \frac{{\left(f x + e\right)}^{4} a d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a c^{2} d e}{f} - 4 \, a c^{3} \cos\left(f x + e\right) + \frac{4 \, a d^{3} e^{3} \cos\left(f x + e\right)}{f^{3}} - \frac{12 \, a c d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{12 \, a c^{2} d e \cos\left(f x + e\right)}{f} - \frac{12 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a d^{3} e^{2}}{f^{3}} + \frac{24 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a c d^{2} e}{f^{2}} - \frac{12 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a c^{2} d}{f} + \frac{12 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a d^{3} e}{f^{3}} - \frac{12 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a c d^{2}}{f^{2}} - \frac{4 \, {\left({\left({\left(f x + e\right)}^{3} - 6 \, f x - 6 \, e\right)} \cos\left(f x + e\right) - 3 \, {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a d^{3}}{f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c^3 + (f*x + e)^4*a*d^3/f^3 - 4*(f*x + e)^3*a*d^3*e/f^3 + 6*(f*x + e)^2*a*d^3*e^2/f^3 - 4*(f*x + e)*a*d^3*e^3/f^3 + 4*(f*x + e)^3*a*c*d^2/f^2 - 12*(f*x + e)^2*a*c*d^2*e/f^2 + 12*(f*x + e)*a*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c^2*d/f - 12*(f*x + e)*a*c^2*d*e/f - 4*a*c^3*cos(f*x + e) + 4*a*d^3*e^3*cos(f*x + e)/f^3 - 12*a*c*d^2*e^2*cos(f*x + e)/f^2 + 12*a*c^2*d*e*cos(f*x + e)/f - 12*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*d^3*e^2/f^3 + 24*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*c*d^2*e/f^2 - 12*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*c^2*d/f + 12*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a*d^3*e/f^3 - 12*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a*c*d^2/f^2 - 4*(((f*x + e)^3 - 6*f*x - 6*e)*cos(f*x + e) - 3*((f*x + e)^2 - 2)*sin(f*x + e))*a*d^3/f^3)/f","B",0
96,1,239,0,0.319439," ","integrate((d*x+c)^2*(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a c^{2} + \frac{{\left(f x + e\right)}^{3} a d^{2}}{f^{2}} - \frac{3 \, {\left(f x + e\right)}^{2} a d^{2} e}{f^{2}} + \frac{3 \, {\left(f x + e\right)} a d^{2} e^{2}}{f^{2}} + \frac{3 \, {\left(f x + e\right)}^{2} a c d}{f} - \frac{6 \, {\left(f x + e\right)} a c d e}{f} - 3 \, a c^{2} \cos\left(f x + e\right) - \frac{3 \, a d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{6 \, a c d e \cos\left(f x + e\right)}{f} + \frac{6 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a d^{2} e}{f^{2}} - \frac{6 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a c d}{f} - \frac{3 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a d^{2}}{f^{2}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a*c^2 + (f*x + e)^3*a*d^2/f^2 - 3*(f*x + e)^2*a*d^2*e/f^2 + 3*(f*x + e)*a*d^2*e^2/f^2 + 3*(f*x + e)^2*a*c*d/f - 6*(f*x + e)*a*c*d*e/f - 3*a*c^2*cos(f*x + e) - 3*a*d^2*e^2*cos(f*x + e)/f^2 + 6*a*c*d*e*cos(f*x + e)/f + 6*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*d^2*e/f^2 - 6*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*c*d/f - 3*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a*d^2/f^2)/f","B",0
97,1,93,0,0.439401," ","integrate((d*x+c)*(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} a c + \frac{{\left(f x + e\right)}^{2} a d}{f} - \frac{2 \, {\left(f x + e\right)} a d e}{f} - 2 \, a c \cos\left(f x + e\right) + \frac{2 \, a d e \cos\left(f x + e\right)}{f} - \frac{2 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a d}{f}}{2 \, f}"," ",0,"1/2*(2*(f*x + e)*a*c + (f*x + e)^2*a*d/f - 2*(f*x + e)*a*d*e/f - 2*a*c*cos(f*x + e) + 2*a*d*e*cos(f*x + e)/f - 2*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*d/f)/f","B",0
98,1,171,0,0.511442," ","integrate((a+a*sin(f*x+e))/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{2 \, a f \log\left(c + \frac{{\left(f x + e\right)} d}{f} - \frac{d e}{f}\right)}{d} + \frac{{\left(f {\left(-i \, E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f {\left(E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a}{d}}{2 \, f}"," ",0,"1/2*(2*a*f*log(c + (f*x + e)*d/f - d*e/f)/d + (f*(-I*exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f*(exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a/d)/f","C",0
99,1,196,0,0.626588," ","integrate((a+a*sin(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, a f^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} - \frac{{\left(f^{2} {\left(-i \, E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{2} {\left(E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f}}{2 \, f}"," ",0,"-1/2*(2*a*f^2/((f*x + e)*d^2 - d^2*e + c*d*f) - (f^2*(-I*exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^2*(exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a/((f*x + e)*d^2 - d^2*e + c*d*f))/f","C",0
100,1,265,0,0.721162," ","integrate((a+a*sin(f*x+e))/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{a f^{3}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}} - \frac{{\left(f^{3} {\left(-i \, E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{3} {\left(E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}}}{2 \, f}"," ",0,"-1/2*(a*f^3/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)) - (f^3*(-I*exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^3*(exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)))/f","C",0
101,1,969,0,0.507584," ","integrate((d*x+c)^3*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{3} + 16 \, {\left(f x + e\right)} a^{2} c^{3} + \frac{4 \, {\left(f x + e\right)}^{4} a^{2} d^{3}}{f^{3}} - \frac{16 \, {\left(f x + e\right)}^{3} a^{2} d^{3} e}{f^{3}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} e^{3}}{f^{3}} - \frac{16 \, {\left(f x + e\right)} a^{2} d^{3} e^{3}}{f^{3}} + \frac{16 \, {\left(f x + e\right)}^{3} a^{2} c d^{2}}{f^{2}} - \frac{48 \, {\left(f x + e\right)}^{2} a^{2} c d^{2} e}{f^{2}} + \frac{12 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{48 \, {\left(f x + e\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} c^{2} d}{f} - \frac{12 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d e}{f} - \frac{48 \, {\left(f x + e\right)} a^{2} c^{2} d e}{f} - 32 \, a^{2} c^{3} \cos\left(f x + e\right) + \frac{32 \, a^{2} d^{3} e^{3} \cos\left(f x + e\right)}{f^{3}} - \frac{96 \, a^{2} c d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{96 \, a^{2} c^{2} d e \cos\left(f x + e\right)}{f} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} e^{2}}{f^{3}} - \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a^{2} d^{3} e^{2}}{f^{3}} - \frac{12 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} e}{f^{2}} + \frac{192 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a^{2} c d^{2} e}{f^{2}} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d}{f} - \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a^{2} c^{2} d}{f} - \frac{2 \, {\left(4 \, {\left(f x + e\right)}^{3} - 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} e}{f^{3}} + \frac{96 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a^{2} d^{3} e}{f^{3}} + \frac{2 \, {\left(4 \, {\left(f x + e\right)}^{3} - 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2}}{f^{2}} - \frac{96 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a^{2} c d^{2}}{f^{2}} + \frac{{\left(2 \, {\left(f x + e\right)}^{4} - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(2 \, {\left(f x + e\right)}^{3} - 3 \, f x - 3 \, e\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3}}{f^{3}} - \frac{32 \, {\left({\left({\left(f x + e\right)}^{3} - 6 \, f x - 6 \, e\right)} \cos\left(f x + e\right) - 3 \, {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a^{2} d^{3}}{f^{3}}}{16 \, f}"," ",0,"1/16*(4*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^3 + 16*(f*x + e)*a^2*c^3 + 4*(f*x + e)^4*a^2*d^3/f^3 - 16*(f*x + e)^3*a^2*d^3*e/f^3 + 24*(f*x + e)^2*a^2*d^3*e^2/f^3 - 4*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*d^3*e^3/f^3 - 16*(f*x + e)*a^2*d^3*e^3/f^3 + 16*(f*x + e)^3*a^2*c*d^2/f^2 - 48*(f*x + e)^2*a^2*c*d^2*e/f^2 + 12*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c*d^2*e^2/f^2 + 48*(f*x + e)*a^2*c*d^2*e^2/f^2 + 24*(f*x + e)^2*a^2*c^2*d/f - 12*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^2*d*e/f - 48*(f*x + e)*a^2*c^2*d*e/f - 32*a^2*c^3*cos(f*x + e) + 32*a^2*d^3*e^3*cos(f*x + e)/f^3 - 96*a^2*c*d^2*e^2*cos(f*x + e)/f^2 + 96*a^2*c^2*d*e*cos(f*x + e)/f + 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*a^2*d^3*e^2/f^3 - 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a^2*d^3*e^2/f^3 - 12*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*a^2*c*d^2*e/f^2 + 192*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a^2*c*d^2*e/f^2 + 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*a^2*c^2*d/f - 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a^2*c^2*d/f - 2*(4*(f*x + e)^3 - 6*(f*x + e)*cos(2*f*x + 2*e) - 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*a^2*d^3*e/f^3 + 96*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a^2*d^3*e/f^3 + 2*(4*(f*x + e)^3 - 6*(f*x + e)*cos(2*f*x + 2*e) - 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*a^2*c*d^2/f^2 - 96*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a^2*c*d^2/f^2 + (2*(f*x + e)^4 - 3*(2*(f*x + e)^2 - 1)*cos(2*f*x + 2*e) - 2*(2*(f*x + e)^3 - 3*f*x - 3*e)*sin(2*f*x + 2*e))*a^2*d^3/f^3 - 32*(((f*x + e)^3 - 6*f*x - 6*e)*cos(f*x + e) - 3*((f*x + e)^2 - 2)*sin(f*x + e))*a^2*d^3/f^3)/f","B",0
102,1,508,0,0.460359," ","integrate((d*x+c)^2*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} + 24 \, {\left(f x + e\right)} a^{2} c^{2} + \frac{8 \, {\left(f x + e\right)}^{3} a^{2} d^{2}}{f^{2}} - \frac{24 \, {\left(f x + e\right)}^{2} a^{2} d^{2} e}{f^{2}} + \frac{6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} c d}{f} - \frac{12 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d e}{f} - \frac{48 \, {\left(f x + e\right)} a^{2} c d e}{f} - 48 \, a^{2} c^{2} \cos\left(f x + e\right) - \frac{48 \, a^{2} d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{96 \, a^{2} c d e \cos\left(f x + e\right)}{f} - \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} e}{f^{2}} + \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a^{2} d^{2} e}{f^{2}} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d}{f} - \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a^{2} c d}{f} + \frac{{\left(4 \, {\left(f x + e\right)}^{3} - 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2}}{f^{2}} - \frac{48 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a^{2} d^{2}}{f^{2}}}{24 \, f}"," ",0,"1/24*(6*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c^2 + 24*(f*x + e)*a^2*c^2 + 8*(f*x + e)^3*a^2*d^2/f^2 - 24*(f*x + e)^2*a^2*d^2*e/f^2 + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*d^2*e^2/f^2 + 24*(f*x + e)*a^2*d^2*e^2/f^2 + 24*(f*x + e)^2*a^2*c*d/f - 12*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c*d*e/f - 48*(f*x + e)*a^2*c*d*e/f - 48*a^2*c^2*cos(f*x + e) - 48*a^2*d^2*e^2*cos(f*x + e)/f^2 + 96*a^2*c*d*e*cos(f*x + e)/f - 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*a^2*d^2*e/f^2 + 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a^2*d^2*e/f^2 + 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*a^2*c*d/f - 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a^2*c*d/f + (4*(f*x + e)^3 - 6*(f*x + e)*cos(2*f*x + 2*e) - 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*a^2*d^2/f^2 - 48*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a^2*d^2/f^2)/f","B",0
103,1,205,0,0.452664," ","integrate((d*x+c)*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c + 8 \, {\left(f x + e\right)} a^{2} c + \frac{4 \, {\left(f x + e\right)}^{2} a^{2} d}{f} - \frac{2 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d e}{f} - \frac{8 \, {\left(f x + e\right)} a^{2} d e}{f} - 16 \, a^{2} c \cos\left(f x + e\right) + \frac{16 \, a^{2} d e \cos\left(f x + e\right)}{f} + \frac{{\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} d}{f} - \frac{16 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a^{2} d}{f}}{8 \, f}"," ",0,"1/8*(2*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c + 8*(f*x + e)*a^2*c + 4*(f*x + e)^2*a^2*d/f - 2*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*d*e/f - 8*(f*x + e)*a^2*d*e/f - 16*a^2*c*cos(f*x + e) + 16*a^2*d*e*cos(f*x + e)/f + (2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*a^2*d/f - 16*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a^2*d/f)/f","A",0
104,1,335,0,0.717465," ","integrate((a+a*sin(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{4 \, a^{2} f \log\left(c + \frac{{\left(f x + e\right)} d}{f} - \frac{d e}{f}\right)}{d} + \frac{4 \, {\left(f {\left(-i \, E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f {\left(E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a^{2}}{d} + \frac{{\left(f {\left(E_{1}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f {\left(i \, E_{1}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - i \, E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, f \log\left({\left(f x + e\right)} d - d e + c f\right)\right)} a^{2}}{d}}{4 \, f}"," ",0,"1/4*(4*a^2*f*log(c + (f*x + e)*d/f - d*e/f)/d + 4*(f*(-I*exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f*(exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a^2/d + (f*(exp_integral_e(1, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f*(I*exp_integral_e(1, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - I*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) + 2*f*log((f*x + e)*d - d*e + c*f))*a^2/d)/f","C",0
105,1,370,0,0.607602," ","integrate((a+a*sin(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{\frac{64 \, a^{2} f^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} - \frac{64 \, {\left(f^{2} {\left(-i \, E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{2} {\left(E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} - \frac{{\left(16 \, f^{2} {\left(E_{2}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f^{2} {\left(16 i \, E_{2}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 16 i \, E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 32 \, f^{2}\right)} a^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f}}{64 \, f}"," ",0,"-1/64*(64*a^2*f^2/((f*x + e)*d^2 - d^2*e + c*d*f) - 64*(f^2*(-I*exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^2*(exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a^2/((f*x + e)*d^2 - d^2*e + c*d*f) - (16*f^2*(exp_integral_e(2, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f^2*(16*I*exp_integral_e(2, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 16*I*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) - 32*f^2)*a^2/((f*x + e)*d^2 - d^2*e + c*d*f))/f","C",0
106,1,475,0,1.091452," ","integrate((a+a*sin(f*x+e))^2/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{32 \, a^{2} f^{3}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}} - \frac{64 \, {\left(f^{3} {\left(-i \, E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{3} {\left(E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a^{2}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}} - \frac{{\left(16 \, f^{3} {\left(E_{3}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{3}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f^{3} {\left(16 i \, E_{3}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 16 i \, E_{3}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 16 \, f^{3}\right)} a^{2}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}}}{64 \, f}"," ",0,"-1/64*(32*a^2*f^3/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)) - 64*(f^3*(-I*exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^3*(exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a^2/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)) - (16*f^3*(exp_integral_e(3, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(3, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f^3*(16*I*exp_integral_e(3, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 16*I*exp_integral_e(3, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) - 16*f^3)*a^2/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)))/f","C",0
107,1,974,0,0.697553," ","integrate((d*x+c)^3/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right)\right)} c d^{2} e}{a f^{2} \cos\left(f x + e\right)^{2} + a f^{2} \sin\left(f x + e\right)^{2} + 2 \, a f^{2} \sin\left(f x + e\right) + a f^{2}} - \frac{6 \, c d^{2} e^{2}}{a f^{2} + \frac{a f^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{3 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right)\right)} c^{2} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} + 2 \, a f \sin\left(f x + e\right) + a f} + \frac{6 \, c^{2} d e}{a f + \frac{a f \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 \, c^{3}}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} + \frac{-2 i \, d^{3} e^{3} + {\left(6 \, d^{3} e^{2} \cos\left(f x + e\right) + 6 i \, d^{3} e^{2} \sin\left(f x + e\right) + 6 i \, d^{3} e^{2}\right)} \arctan\left(\sin\left(f x + e\right) + 1, \cos\left(f x + e\right)\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(12 i \, d^{3} e - 12 i \, c d^{2} f\right)} {\left(f x + e\right)} - 6 \, {\left({\left(f x + e\right)}^{2} d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(12 i \, d^{3} e - 12 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - 2 \, {\left({\left(f x + e\right)}^{3} d^{3} + 3 \, {\left(f x + e\right)} d^{3} e^{2} - 3 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f - 12 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(3 \, {\left(f x + e\right)}^{2} d^{3} + 3 \, d^{3} e^{2} - 6 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + 3 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-12 i \, d^{3} \cos\left(f x + e\right) + 12 \, d^{3} \sin\left(f x + e\right) + 12 \, d^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{3} d^{3} - 6 i \, {\left(f x + e\right)} d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) + a f^{3}}}{f}"," ",0,"(6*(2*(f*x + e)*cos(f*x + e) - (cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1))*c*d^2*e/(a*f^2*cos(f*x + e)^2 + a*f^2*sin(f*x + e)^2 + 2*a*f^2*sin(f*x + e) + a*f^2) - 6*c*d^2*e^2/(a*f^2 + a*f^2*sin(f*x + e)/(cos(f*x + e) + 1)) - 3*(2*(f*x + e)*cos(f*x + e) - (cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1))*c^2*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 + 2*a*f*sin(f*x + e) + a*f) + 6*c^2*d*e/(a*f + a*f*sin(f*x + e)/(cos(f*x + e) + 1)) - 2*c^3/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)) + (-2*I*d^3*e^3 + (6*d^3*e^2*cos(f*x + e) + 6*I*d^3*e^2*sin(f*x + e) + 6*I*d^3*e^2)*arctan2(sin(f*x + e) + 1, cos(f*x + e)) + (-6*I*(f*x + e)^2*d^3 + (12*I*d^3*e - 12*I*c*d^2*f)*(f*x + e) - 6*((f*x + e)^2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (-6*I*(f*x + e)^2*d^3 + (12*I*d^3*e - 12*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) - 2*((f*x + e)^3*d^3 + 3*(f*x + e)*d^3*e^2 - 3*(d^3*e - c*d^2*f)*(f*x + e)^2)*cos(f*x + e) + (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f - 12*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) + (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f)*sin(f*x + e))*dilog(I*e^(I*f*x + I*e)) + (3*(f*x + e)^2*d^3 + 3*d^3*e^2 - 6*(d^3*e - c*d^2*f)*(f*x + e) + (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e))*cos(f*x + e) + 3*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (-12*I*d^3*cos(f*x + e) + 12*d^3*sin(f*x + e) + 12*d^3)*polylog(3, I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^3*d^3 - 6*I*(f*x + e)*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e)^2)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) + a*f^3))/f","B",0
108,1,312,0,0.690016," ","integrate((d*x+c)^2/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 i \, c^{2} f^{2} + {\left(4 \, c d f \cos\left(f x + e\right) + 4 i \, c d f \sin\left(f x + e\right) + 4 i \, c d f\right)} \arctan\left(\sin\left(f x + e\right) + 1, \cos\left(f x + e\right)\right) - {\left(4 \, d^{2} f x \cos\left(f x + e\right) + 4 i \, d^{2} f x \sin\left(f x + e\right) + 4 i \, d^{2} f x\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x\right)} \cos\left(f x + e\right) - {\left(4 \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} \sin\left(f x + e\right) + 4 i \, d^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) + {\left(2 \, d^{2} f x + 2 \, c d f + {\left(-2 i \, d^{2} f x - 2 i \, c d f\right)} \cos\left(f x + e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) + a f^{3}}"," ",0,"(2*I*c^2*f^2 + (4*c*d*f*cos(f*x + e) + 4*I*c*d*f*sin(f*x + e) + 4*I*c*d*f)*arctan2(sin(f*x + e) + 1, cos(f*x + e)) - (4*d^2*f*x*cos(f*x + e) + 4*I*d^2*f*x*sin(f*x + e) + 4*I*d^2*f*x)*arctan2(cos(f*x + e), sin(f*x + e) + 1) - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x)*cos(f*x + e) - (4*d^2*cos(f*x + e) + 4*I*d^2*sin(f*x + e) + 4*I*d^2)*dilog(I*e^(I*f*x + I*e)) + (2*d^2*f*x + 2*c*d*f + (-2*I*d^2*f*x - 2*I*c*d*f)*cos(f*x + e) + 2*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) + a*f^3)","B",0
109,1,169,0,0.334974," ","integrate((d*x+c)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{{\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) - {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right)\right)} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} + 2 \, a f \sin\left(f x + e\right) + a f} - \frac{2 \, d e}{a f + \frac{a f \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} + \frac{2 \, c}{a + \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"-((2*(f*x + e)*cos(f*x + e) - (cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1))*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 + 2*a*f*sin(f*x + e) + a*f) - 2*d*e/(a*f + a*f*sin(f*x + e)/(cos(f*x + e) + 1)) + 2*c/(a + a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
110,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,1,3580,0,6.100821," ","integrate((d*x+c)^3/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{6 \, c d^{2} e^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} f^{2} + \frac{3 \, a^{2} f^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} f^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} f^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{6 \, {\left(2 \, {\left(f x + 3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + e + \cos\left(f x + e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 2 \, {\left(9 \, {\left(f x + e\right)} \cos\left(f x + e\right) - 6 \, \sin\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 6 \, \cos\left(f x + e\right)^{2} - {\left(6 \, {\left(\cos\left(f x + e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \sin\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 9 \, \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) - 3 \, \sin\left(f x + e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - \sin\left(3 \, f x + 3 \, e\right)^{2} - 18 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} - 9 \, \sin\left(f x + e\right)^{2} - 6 \, \sin\left(f x + e\right) - 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - 2 \, {\left(3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + \cos\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + 3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + e + 2 \, \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) - 6 \, \sin\left(2 \, f x + 2 \, e\right)^{2} - 6 \, \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right)\right)} c d^{2} e}{a^{2} f^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f^{2} \cos\left(f x + e\right)^{2} + a^{2} f^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, a^{2} f^{2} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f^{2} \sin\left(f x + e\right)^{2} + 6 \, a^{2} f^{2} \sin\left(f x + e\right) + a^{2} f^{2} - 6 \, {\left(a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(3 \, a^{2} f^{2} \sin\left(f x + e\right) + a^{2} f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a^{2} f^{2} \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} f^{2} \sin\left(f x + e\right) - a^{2} f^{2}\right)} \sin\left(3 \, f x + 3 \, e\right)} - \frac{6 \, c^{2} d e {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} f + \frac{3 \, a^{2} f \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} f \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} f \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{3 \, {\left(2 \, {\left(f x + 3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + e + \cos\left(f x + e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 2 \, {\left(9 \, {\left(f x + e\right)} \cos\left(f x + e\right) - 6 \, \sin\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 6 \, \cos\left(f x + e\right)^{2} - {\left(6 \, {\left(\cos\left(f x + e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \sin\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 9 \, \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) - 3 \, \sin\left(f x + e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - \sin\left(3 \, f x + 3 \, e\right)^{2} - 18 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} - 9 \, \sin\left(f x + e\right)^{2} - 6 \, \sin\left(f x + e\right) - 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - 2 \, {\left(3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + \cos\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + 3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + e + 2 \, \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) - 6 \, \sin\left(2 \, f x + 2 \, e\right)^{2} - 6 \, \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right)\right)} c^{2} d}{a^{2} f \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, a^{2} f \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \sin\left(f x + e\right)^{2} + 6 \, a^{2} f \sin\left(f x + e\right) + a^{2} f - 6 \, {\left(a^{2} f \cos\left(f x + e\right) + a^{2} f \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(3 \, a^{2} f \sin\left(f x + e\right) + a^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} f \sin\left(f x + e\right) - a^{2} f\right)} \sin\left(3 \, f x + 3 \, e\right)} + \frac{2 \, c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} - \frac{3 \, {\left(2 i \, d^{3} e^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f + {\left(-6 i \, d^{3} e^{2} - 12 i \, d^{3} + 6 \, {\left(d^{3} e^{2} + 2 \, d^{3}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(18 i \, d^{3} e^{2} + 36 i \, d^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) - 18 \, {\left(d^{3} e^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(6 i \, d^{3} e^{2} + 12 i \, d^{3}\right)} \sin\left(3 \, f x + 3 \, e\right) - 18 \, {\left(d^{3} e^{2} + 2 \, d^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(-18 i \, d^{3} e^{2} - 36 i \, d^{3}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right) + 1, \cos\left(f x + e\right)\right) + {\left(6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f\right)} {\left(f x + e\right)} - 6 \, {\left({\left(f x + e\right)}^{2} d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-18 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(36 i \, d^{3} e - 36 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left({\left(f x + e\right)}^{2} d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(12 i \, d^{3} e - 12 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) + 18 \, {\left({\left(f x + e\right)}^{2} d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(18 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(-36 i \, d^{3} e + 36 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - 2 \, {\left({\left(f x + e\right)}^{3} d^{3} - 3 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(d^{3} e^{2} + 2 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-6 i \, {\left(f x + e\right)}^{3} d^{3} - 6 \, d^{3} e^{2} - 12 i \, d^{3} e + 12 i \, c d^{2} f + {\left(18 i \, d^{3} e - 18 i \, c d^{2} f - 6 \, d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-18 i \, d^{3} e^{2} + 12 \, d^{3} e - 12 \, c d^{2} f - 24 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, d^{3} e^{3} - 6 i \, {\left(f x + e\right)}^{2} d^{3} - 6 i \, d^{3} e^{2} + 24 \, d^{3} e - 24 \, c d^{2} f + {\left(12 i \, d^{3} e - 12 i \, c d^{2} f + 12 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(12 i \, {\left(f x + e\right)} d^{3} - 12 i \, d^{3} e + 12 i \, c d^{2} f - 12 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-36 i \, {\left(f x + e\right)} d^{3} + 36 i \, d^{3} e - 36 i \, c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 36 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f\right)} \sin\left(3 \, f x + 3 \, e\right) + 36 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(36 i \, {\left(f x + e\right)} d^{3} - 36 i \, d^{3} e + 36 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(3 \, {\left(f x + e\right)}^{2} d^{3} + 3 \, d^{3} e^{2} + 6 \, d^{3} - 6 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} - {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} - 6 i \, d^{3} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) - 9 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(9 i \, {\left(f x + e\right)}^{2} d^{3} + 9 i \, d^{3} e^{2} + 18 i \, d^{3} + {\left(-18 i \, d^{3} e + 18 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) - 3 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(9 i \, {\left(f x + e\right)}^{2} d^{3} + 9 i \, d^{3} e^{2} + 18 i \, d^{3} + {\left(-18 i \, d^{3} e + 18 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + 9 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-12 i \, d^{3} \cos\left(3 \, f x + 3 \, e\right) + 36 \, d^{3} \cos\left(2 \, f x + 2 \, e\right) + 36 i \, d^{3} \cos\left(f x + e\right) + 12 \, d^{3} \sin\left(3 \, f x + 3 \, e\right) + 36 i \, d^{3} \sin\left(2 \, f x + 2 \, e\right) - 36 \, d^{3} \sin\left(f x + e\right) - 12 \, d^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{3} d^{3} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, d^{3} e^{2} - 12 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(6 \, {\left(f x + e\right)}^{3} d^{3} - 6 i \, d^{3} e^{2} + 12 \, d^{3} e - 12 \, c d^{2} f - 6 \, {\left(3 \, d^{3} e - 3 \, c d^{2} f + i \, d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(18 \, d^{3} e^{2} + 12 i \, d^{3} e - 12 i \, c d^{2} f + 24 \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(6 i \, d^{3} e^{3} + 6 \, {\left(f x + e\right)}^{2} d^{3} + 6 \, d^{3} e^{2} + 24 i \, d^{3} e - 24 i \, c d^{2} f - 12 \, {\left(d^{3} e - c d^{2} f - i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)}}{-3 i \, a^{2} f^{3} \cos\left(3 \, f x + 3 \, e\right) + 9 \, a^{2} f^{3} \cos\left(2 \, f x + 2 \, e\right) + 9 i \, a^{2} f^{3} \cos\left(f x + e\right) + 3 \, a^{2} f^{3} \sin\left(3 \, f x + 3 \, e\right) + 9 i \, a^{2} f^{3} \sin\left(2 \, f x + 2 \, e\right) - 9 \, a^{2} f^{3} \sin\left(f x + e\right) - 3 \, a^{2} f^{3}}}{3 \, f}"," ",0,"-1/3*(6*c*d^2*e^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2*f^2 + 3*a^2*f^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*f^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*f^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + 6*(2*(f*x + 3*(f*x + e)*sin(f*x + e) + e + cos(f*x + e) + sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 2*(9*(f*x + e)*cos(f*x + e) - 6*sin(f*x + e) - 1)*cos(2*f*x + 2*e) - 6*cos(2*f*x + 2*e)^2 - 6*cos(f*x + e)^2 - (6*(cos(f*x + e) + sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - cos(3*f*x + 3*e)^2 + 6*(3*sin(f*x + e) + 1)*cos(2*f*x + 2*e) - 9*cos(2*f*x + 2*e)^2 - 9*cos(f*x + e)^2 - 2*(3*cos(2*f*x + 2*e) - 3*sin(f*x + e) - 1)*sin(3*f*x + 3*e) - sin(3*f*x + 3*e)^2 - 18*cos(f*x + e)*sin(2*f*x + 2*e) - 9*sin(2*f*x + 2*e)^2 - 9*sin(f*x + e)^2 - 6*sin(f*x + e) - 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 2*(3*(f*x + e)*cos(f*x + e) + cos(2*f*x + 2*e) - sin(f*x + e))*sin(3*f*x + 3*e) - 6*(f*x + 3*(f*x + e)*sin(f*x + e) + e + 2*cos(f*x + e))*sin(2*f*x + 2*e) - 6*sin(2*f*x + 2*e)^2 - 6*sin(f*x + e)^2 - 2*sin(f*x + e))*c*d^2*e/(a^2*f^2*cos(3*f*x + 3*e)^2 + 9*a^2*f^2*cos(2*f*x + 2*e)^2 + 9*a^2*f^2*cos(f*x + e)^2 + a^2*f^2*sin(3*f*x + 3*e)^2 + 18*a^2*f^2*cos(f*x + e)*sin(2*f*x + 2*e) + 9*a^2*f^2*sin(2*f*x + 2*e)^2 + 9*a^2*f^2*sin(f*x + e)^2 + 6*a^2*f^2*sin(f*x + e) + a^2*f^2 - 6*(a^2*f^2*cos(f*x + e) + a^2*f^2*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(3*a^2*f^2*sin(f*x + e) + a^2*f^2)*cos(2*f*x + 2*e) + 2*(3*a^2*f^2*cos(2*f*x + 2*e) - 3*a^2*f^2*sin(f*x + e) - a^2*f^2)*sin(3*f*x + 3*e)) - 6*c^2*d*e*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2*f + 3*a^2*f*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*f*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*f*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 3*(2*(f*x + 3*(f*x + e)*sin(f*x + e) + e + cos(f*x + e) + sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 2*(9*(f*x + e)*cos(f*x + e) - 6*sin(f*x + e) - 1)*cos(2*f*x + 2*e) - 6*cos(2*f*x + 2*e)^2 - 6*cos(f*x + e)^2 - (6*(cos(f*x + e) + sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - cos(3*f*x + 3*e)^2 + 6*(3*sin(f*x + e) + 1)*cos(2*f*x + 2*e) - 9*cos(2*f*x + 2*e)^2 - 9*cos(f*x + e)^2 - 2*(3*cos(2*f*x + 2*e) - 3*sin(f*x + e) - 1)*sin(3*f*x + 3*e) - sin(3*f*x + 3*e)^2 - 18*cos(f*x + e)*sin(2*f*x + 2*e) - 9*sin(2*f*x + 2*e)^2 - 9*sin(f*x + e)^2 - 6*sin(f*x + e) - 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 2*(3*(f*x + e)*cos(f*x + e) + cos(2*f*x + 2*e) - sin(f*x + e))*sin(3*f*x + 3*e) - 6*(f*x + 3*(f*x + e)*sin(f*x + e) + e + 2*cos(f*x + e))*sin(2*f*x + 2*e) - 6*sin(2*f*x + 2*e)^2 - 6*sin(f*x + e)^2 - 2*sin(f*x + e))*c^2*d/(a^2*f*cos(3*f*x + 3*e)^2 + 9*a^2*f*cos(2*f*x + 2*e)^2 + 9*a^2*f*cos(f*x + e)^2 + a^2*f*sin(3*f*x + 3*e)^2 + 18*a^2*f*cos(f*x + e)*sin(2*f*x + 2*e) + 9*a^2*f*sin(2*f*x + 2*e)^2 + 9*a^2*f*sin(f*x + e)^2 + 6*a^2*f*sin(f*x + e) + a^2*f - 6*(a^2*f*cos(f*x + e) + a^2*f*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(3*a^2*f*sin(f*x + e) + a^2*f)*cos(2*f*x + 2*e) + 2*(3*a^2*f*cos(2*f*x + 2*e) - 3*a^2*f*sin(f*x + e) - a^2*f)*sin(3*f*x + 3*e)) + 2*c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) - 3*(2*I*d^3*e^3 + 12*I*d^3*e - 12*I*c*d^2*f + (-6*I*d^3*e^2 - 12*I*d^3 + 6*(d^3*e^2 + 2*d^3)*cos(3*f*x + 3*e) + (18*I*d^3*e^2 + 36*I*d^3)*cos(2*f*x + 2*e) - 18*(d^3*e^2 + 2*d^3)*cos(f*x + e) + (6*I*d^3*e^2 + 12*I*d^3)*sin(3*f*x + 3*e) - 18*(d^3*e^2 + 2*d^3)*sin(2*f*x + 2*e) + (-18*I*d^3*e^2 - 36*I*d^3)*sin(f*x + e))*arctan2(sin(f*x + e) + 1, cos(f*x + e)) + (6*I*(f*x + e)^2*d^3 + (-12*I*d^3*e + 12*I*c*d^2*f)*(f*x + e) - 6*((f*x + e)^2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(3*f*x + 3*e) + (-18*I*(f*x + e)^2*d^3 + (36*I*d^3*e - 36*I*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + 18*((f*x + e)^2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (-6*I*(f*x + e)^2*d^3 + (12*I*d^3*e - 12*I*c*d^2*f)*(f*x + e))*sin(3*f*x + 3*e) + 18*((f*x + e)^2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e) + (18*I*(f*x + e)^2*d^3 + (-36*I*d^3*e + 36*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(cos(f*x + e), sin(f*x + e) + 1) - 2*((f*x + e)^3*d^3 - 3*(d^3*e - c*d^2*f)*(f*x + e)^2 + 3*(d^3*e^2 + 2*d^3)*(f*x + e))*cos(3*f*x + 3*e) + (-6*I*(f*x + e)^3*d^3 - 6*d^3*e^2 - 12*I*d^3*e + 12*I*c*d^2*f + (18*I*d^3*e - 18*I*c*d^2*f - 6*d^3)*(f*x + e)^2 + (-18*I*d^3*e^2 + 12*d^3*e - 12*c*d^2*f - 24*I*d^3)*(f*x + e))*cos(2*f*x + 2*e) + (6*d^3*e^3 - 6*I*(f*x + e)^2*d^3 - 6*I*d^3*e^2 + 24*d^3*e - 24*c*d^2*f + (12*I*d^3*e - 12*I*c*d^2*f + 12*d^3)*(f*x + e))*cos(f*x + e) + (12*I*(f*x + e)*d^3 - 12*I*d^3*e + 12*I*c*d^2*f - 12*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(3*f*x + 3*e) + (-36*I*(f*x + e)*d^3 + 36*I*d^3*e - 36*I*c*d^2*f)*cos(2*f*x + 2*e) + 36*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) + (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f)*sin(3*f*x + 3*e) + 36*((f*x + e)*d^3 - d^3*e + c*d^2*f)*sin(2*f*x + 2*e) + (36*I*(f*x + e)*d^3 - 36*I*d^3*e + 36*I*c*d^2*f)*sin(f*x + e))*dilog(I*e^(I*f*x + I*e)) - (3*(f*x + e)^2*d^3 + 3*d^3*e^2 + 6*d^3 - 6*(d^3*e - c*d^2*f)*(f*x + e) - (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 - 6*I*d^3 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e))*cos(3*f*x + 3*e) - 9*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) - (9*I*(f*x + e)^2*d^3 + 9*I*d^3*e^2 + 18*I*d^3 + (-18*I*d^3*e + 18*I*c*d^2*f)*(f*x + e))*cos(f*x + e) - 3*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(3*f*x + 3*e) - (9*I*(f*x + e)^2*d^3 + 9*I*d^3*e^2 + 18*I*d^3 + (-18*I*d^3*e + 18*I*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e) + 9*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (-12*I*d^3*cos(3*f*x + 3*e) + 36*d^3*cos(2*f*x + 2*e) + 36*I*d^3*cos(f*x + e) + 12*d^3*sin(3*f*x + 3*e) + 36*I*d^3*sin(2*f*x + 2*e) - 36*d^3*sin(f*x + e) - 12*d^3)*polylog(3, I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^3*d^3 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e)^2 + (-6*I*d^3*e^2 - 12*I*d^3)*(f*x + e))*sin(3*f*x + 3*e) + (6*(f*x + e)^3*d^3 - 6*I*d^3*e^2 + 12*d^3*e - 12*c*d^2*f - 6*(3*d^3*e - 3*c*d^2*f + I*d^3)*(f*x + e)^2 + (18*d^3*e^2 + 12*I*d^3*e - 12*I*c*d^2*f + 24*d^3)*(f*x + e))*sin(2*f*x + 2*e) + (6*I*d^3*e^3 + 6*(f*x + e)^2*d^3 + 6*d^3*e^2 + 24*I*d^3*e - 24*I*c*d^2*f - 12*(d^3*e - c*d^2*f - I*d^3)*(f*x + e))*sin(f*x + e))/(-3*I*a^2*f^3*cos(3*f*x + 3*e) + 9*a^2*f^3*cos(2*f*x + 2*e) + 9*I*a^2*f^3*cos(f*x + e) + 3*a^2*f^3*sin(3*f*x + 3*e) + 9*I*a^2*f^3*sin(2*f*x + 2*e) - 9*a^2*f^3*sin(f*x + e) - 3*a^2*f^3))/f","B",0
113,1,832,0,1.414297," ","integrate((d*x+c)^2/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{-2 i \, c^{2} f^{2} - 4 i \, d^{2} + {\left(4 \, c d f \cos\left(3 \, f x + 3 \, e\right) + 12 i \, c d f \cos\left(2 \, f x + 2 \, e\right) - 12 \, c d f \cos\left(f x + e\right) + 4 i \, c d f \sin\left(3 \, f x + 3 \, e\right) - 12 \, c d f \sin\left(2 \, f x + 2 \, e\right) - 12 i \, c d f \sin\left(f x + e\right) - 4 i \, c d f\right)} \arctan\left(\sin\left(f x + e\right) + 1, \cos\left(f x + e\right)\right) - {\left(4 \, d^{2} f x \cos\left(3 \, f x + 3 \, e\right) + 12 i \, d^{2} f x \cos\left(2 \, f x + 2 \, e\right) - 12 \, d^{2} f x \cos\left(f x + e\right) + 4 i \, d^{2} f x \sin\left(3 \, f x + 3 \, e\right) - 12 \, d^{2} f x \sin\left(2 \, f x + 2 \, e\right) - 12 i \, d^{2} f x \sin\left(f x + e\right) - 4 i \, d^{2} f x\right)} \arctan\left(\cos\left(f x + e\right), \sin\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-6 i \, d^{2} f^{2} x^{2} - 4 \, c d f + 4 i \, d^{2} - 4 \, {\left(3 i \, c d f^{2} + d^{2} f\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(6 \, c^{2} f^{2} + 4 i \, d^{2} f x + 4 i \, c d f + 8 \, d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, d^{2} \cos\left(3 \, f x + 3 \, e\right) + 12 i \, d^{2} \cos\left(2 \, f x + 2 \, e\right) - 12 \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} \sin\left(3 \, f x + 3 \, e\right) - 12 \, d^{2} \sin\left(2 \, f x + 2 \, e\right) - 12 i \, d^{2} \sin\left(f x + e\right) - 4 i \, d^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(2 \, d^{2} f x + 2 \, c d f - {\left(-2 i \, d^{2} f x - 2 i \, c d f\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(6 i \, d^{2} f x + 6 i \, c d f\right)} \cos\left(f x + e\right) - 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(6 i \, d^{2} f x + 6 i \, c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(6 \, d^{2} f^{2} x^{2} - 4 i \, c d f - 4 \, d^{2} + {\left(12 \, c d f^{2} - 4 i \, d^{2} f\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(-6 i \, c^{2} f^{2} + 4 \, d^{2} f x + 4 \, c d f - 8 i \, d^{2}\right)} \sin\left(f x + e\right)}{-3 i \, a^{2} f^{3} \cos\left(3 \, f x + 3 \, e\right) + 9 \, a^{2} f^{3} \cos\left(2 \, f x + 2 \, e\right) + 9 i \, a^{2} f^{3} \cos\left(f x + e\right) + 3 \, a^{2} f^{3} \sin\left(3 \, f x + 3 \, e\right) + 9 i \, a^{2} f^{3} \sin\left(2 \, f x + 2 \, e\right) - 9 \, a^{2} f^{3} \sin\left(f x + e\right) - 3 \, a^{2} f^{3}}"," ",0,"(-2*I*c^2*f^2 - 4*I*d^2 + (4*c*d*f*cos(3*f*x + 3*e) + 12*I*c*d*f*cos(2*f*x + 2*e) - 12*c*d*f*cos(f*x + e) + 4*I*c*d*f*sin(3*f*x + 3*e) - 12*c*d*f*sin(2*f*x + 2*e) - 12*I*c*d*f*sin(f*x + e) - 4*I*c*d*f)*arctan2(sin(f*x + e) + 1, cos(f*x + e)) - (4*d^2*f*x*cos(3*f*x + 3*e) + 12*I*d^2*f*x*cos(2*f*x + 2*e) - 12*d^2*f*x*cos(f*x + e) + 4*I*d^2*f*x*sin(3*f*x + 3*e) - 12*d^2*f*x*sin(2*f*x + 2*e) - 12*I*d^2*f*x*sin(f*x + e) - 4*I*d^2*f*x)*arctan2(cos(f*x + e), sin(f*x + e) + 1) - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x)*cos(3*f*x + 3*e) + (-6*I*d^2*f^2*x^2 - 4*c*d*f + 4*I*d^2 - 4*(3*I*c*d*f^2 + d^2*f)*x)*cos(2*f*x + 2*e) - (6*c^2*f^2 + 4*I*d^2*f*x + 4*I*c*d*f + 8*d^2)*cos(f*x + e) - (4*d^2*cos(3*f*x + 3*e) + 12*I*d^2*cos(2*f*x + 2*e) - 12*d^2*cos(f*x + e) + 4*I*d^2*sin(3*f*x + 3*e) - 12*d^2*sin(2*f*x + 2*e) - 12*I*d^2*sin(f*x + e) - 4*I*d^2)*dilog(I*e^(I*f*x + I*e)) - (2*d^2*f*x + 2*c*d*f - (-2*I*d^2*f*x - 2*I*c*d*f)*cos(3*f*x + 3*e) - 6*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e) - (6*I*d^2*f*x + 6*I*c*d*f)*cos(f*x + e) - 2*(d^2*f*x + c*d*f)*sin(3*f*x + 3*e) - (6*I*d^2*f*x + 6*I*c*d*f)*sin(2*f*x + 2*e) + 6*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) + (-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x)*sin(3*f*x + 3*e) + (6*d^2*f^2*x^2 - 4*I*c*d*f - 4*d^2 + (12*c*d*f^2 - 4*I*d^2*f)*x)*sin(2*f*x + 2*e) + (-6*I*c^2*f^2 + 4*d^2*f*x + 4*c*d*f - 8*I*d^2)*sin(f*x + e))/(-3*I*a^2*f^3*cos(3*f*x + 3*e) + 9*a^2*f^3*cos(2*f*x + 2*e) + 9*I*a^2*f^3*cos(f*x + e) + 3*a^2*f^3*sin(3*f*x + 3*e) + 9*I*a^2*f^3*sin(2*f*x + 2*e) - 9*a^2*f^3*sin(f*x + e) - 3*a^2*f^3)","B",0
114,1,910,0,1.791361," ","integrate((d*x+c)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, d e {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} f + \frac{3 \, a^{2} f \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} f \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} f \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}} + \frac{{\left(2 \, {\left(f x + 3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + e + \cos\left(f x + e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 2 \, {\left(9 \, {\left(f x + e\right)} \cos\left(f x + e\right) - 6 \, \sin\left(f x + e\right) - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 6 \, \cos\left(f x + e\right)^{2} - {\left(6 \, {\left(\cos\left(f x + e\right) + \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \sin\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} - 9 \, \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) - 3 \, \sin\left(f x + e\right) - 1\right)} \sin\left(3 \, f x + 3 \, e\right) - \sin\left(3 \, f x + 3 \, e\right)^{2} - 18 \, \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) - 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} - 9 \, \sin\left(f x + e\right)^{2} - 6 \, \sin\left(f x + e\right) - 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) + 1\right) - 2 \, {\left(3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + \cos\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + 3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + e + 2 \, \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) - 6 \, \sin\left(2 \, f x + 2 \, e\right)^{2} - 6 \, \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right)\right)} d}{a^{2} f \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, a^{2} f \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \sin\left(f x + e\right)^{2} + 6 \, a^{2} f \sin\left(f x + e\right) + a^{2} f - 6 \, {\left(a^{2} f \cos\left(f x + e\right) + a^{2} f \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(3 \, a^{2} f \sin\left(f x + e\right) + a^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(3 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right) - 3 \, a^{2} f \sin\left(f x + e\right) - a^{2} f\right)} \sin\left(3 \, f x + 3 \, e\right)} - \frac{2 \, c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{2} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}}{3 \, f}"," ",0,"1/3*(2*d*e*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2*f + 3*a^2*f*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*f*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*f*sin(f*x + e)^3/(cos(f*x + e) + 1)^3) + (2*(f*x + 3*(f*x + e)*sin(f*x + e) + e + cos(f*x + e) + sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 2*(9*(f*x + e)*cos(f*x + e) - 6*sin(f*x + e) - 1)*cos(2*f*x + 2*e) - 6*cos(2*f*x + 2*e)^2 - 6*cos(f*x + e)^2 - (6*(cos(f*x + e) + sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - cos(3*f*x + 3*e)^2 + 6*(3*sin(f*x + e) + 1)*cos(2*f*x + 2*e) - 9*cos(2*f*x + 2*e)^2 - 9*cos(f*x + e)^2 - 2*(3*cos(2*f*x + 2*e) - 3*sin(f*x + e) - 1)*sin(3*f*x + 3*e) - sin(3*f*x + 3*e)^2 - 18*cos(f*x + e)*sin(2*f*x + 2*e) - 9*sin(2*f*x + 2*e)^2 - 9*sin(f*x + e)^2 - 6*sin(f*x + e) - 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*sin(f*x + e) + 1) - 2*(3*(f*x + e)*cos(f*x + e) + cos(2*f*x + 2*e) - sin(f*x + e))*sin(3*f*x + 3*e) - 6*(f*x + 3*(f*x + e)*sin(f*x + e) + e + 2*cos(f*x + e))*sin(2*f*x + 2*e) - 6*sin(2*f*x + 2*e)^2 - 6*sin(f*x + e)^2 - 2*sin(f*x + e))*d/(a^2*f*cos(3*f*x + 3*e)^2 + 9*a^2*f*cos(2*f*x + 2*e)^2 + 9*a^2*f*cos(f*x + e)^2 + a^2*f*sin(3*f*x + 3*e)^2 + 18*a^2*f*cos(f*x + e)*sin(2*f*x + 2*e) + 9*a^2*f*sin(2*f*x + 2*e)^2 + 9*a^2*f*sin(f*x + e)^2 + 6*a^2*f*sin(f*x + e) + a^2*f - 6*(a^2*f*cos(f*x + e) + a^2*f*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(3*a^2*f*sin(f*x + e) + a^2*f)*cos(2*f*x + 2*e) + 2*(3*a^2*f*cos(2*f*x + 2*e) - 3*a^2*f*sin(f*x + e) - a^2*f)*sin(3*f*x + 3*e)) - 2*c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 2)/(a^2 + 3*a^2*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^2*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a^2*sin(f*x + e)^3/(cos(f*x + e) + 1)^3))/f","B",0
115,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{6 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - 4 \, d^{2} \cos\left(f x + e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} - 2 \, d^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 \, d^{2} - {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) - {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 4 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 2 \, {\left(d^{2} f x + c d f + 3 \, {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 2 \, d^{2}\right)} \cos\left(f x + e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right) + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} - 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \int \frac{{\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 6 \, d^{3}\right)} \cos\left(f x + e\right)}{a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)}\,{d x} - 2 \, {\left(2 \, d^{2} \sin\left(2 \, f x + 2 \, e\right) - {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 4 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 2 \, {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 4 \, d^{2} - 6 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + 3 \, {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 2 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right) + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} - 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(6*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 - 4*d^2*cos(f*x + e) + 6*(d^2*f*x + c*d*f)*cos(f*x + e)^2 + 6*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 6*(d^2*f*x + c*d*f)*sin(f*x + e)^2 + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 - 2*d^2*cos(2*f*x + 2*e) + 2*d^2 - (d^2*f*x + c*d*f)*cos(f*x + e) - (d^2*f*x + c*d*f)*sin(2*f*x + 2*e) + (3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 4*d^2)*sin(f*x + e))*cos(3*f*x + 3*e) - 2*(d^2*f*x + c*d*f + 3*(3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 2*d^2)*cos(f*x + e) + 6*(d^2*f*x + c*d*f)*sin(f*x + e))*cos(2*f*x + 2*e) - 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e)^2 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(3*f*x + 3*e)^2 + 18*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e)*sin(2*f*x + 2*e) + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e)^2 - 6*((a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e) + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*cos(2*f*x + 2*e) - 2*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 - 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*sin(3*f*x + 3*e) + 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*integrate(2/3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 6*d^3)*cos(f*x + e)/(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)), x) - 2*(2*d^2*sin(2*f*x + 2*e) - (d^2*f*x + c*d*f)*cos(2*f*x + 2*e) + (3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 4*d^2)*cos(f*x + e) + (d^2*f*x + c*d*f)*sin(f*x + e))*sin(3*f*x + 3*e) - 2*(3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 4*d^2 - 6*(d^2*f*x + c*d*f)*cos(f*x + e) + 3*(3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 2*d^2)*sin(f*x + e))*sin(2*f*x + 2*e) + 2*(d^2*f*x + c*d*f)*sin(f*x + e))/(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e)^2 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(3*f*x + 3*e)^2 + 18*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e)*sin(2*f*x + 2*e) + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e)^2 - 6*((a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e) + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*cos(2*f*x + 2*e) - 2*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 - 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*sin(3*f*x + 3*e) + 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))","F",0
116,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{12 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} - 12 \, d^{2} \cos\left(f x + e\right) + 12 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 12 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 12 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} - 6 \, d^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 \, d^{2} - 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) - 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 4 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 2 \, {\left(2 \, d^{2} f x + 2 \, c d f + 9 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2}\right)} \cos\left(f x + e\right) + 12 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 4 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right) + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} - 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \int \frac{{\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 12 \, d^{3}\right)} \cos\left(f x + e\right)}{a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3} + {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \sin\left(f x + e\right)}\,{d x} - 2 \, {\left(6 \, d^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 4 \, d^{2}\right)} \cos\left(f x + e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 4 \, d^{2} - 4 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 18 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} - 6 \, {\left({\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right) + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) - 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} - 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(12*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 - 12*d^2*cos(f*x + e) + 12*(d^2*f*x + c*d*f)*cos(f*x + e)^2 + 12*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 12*(d^2*f*x + c*d*f)*sin(f*x + e)^2 + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 - 6*d^2*cos(2*f*x + 2*e) + 6*d^2 - 2*(d^2*f*x + c*d*f)*cos(f*x + e) - 2*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e) + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 4*d^2)*sin(f*x + e))*cos(3*f*x + 3*e) - 2*(2*d^2*f*x + 2*c*d*f + 9*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2)*cos(f*x + e) + 12*(d^2*f*x + c*d*f)*sin(f*x + e))*cos(2*f*x + 2*e) - 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(3*f*x + 3*e)^2 + 18*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)*sin(2*f*x + 2*e) + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 - 6*((a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e) + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*cos(2*f*x + 2*e) - 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 - 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*sin(3*f*x + 3*e) + 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*integrate(4/3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 12*d^3)*cos(f*x + e)/(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3 + (a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*cos(f*x + e)^2 + (a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*sin(f*x + e)^2 + 2*(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*sin(f*x + e)), x) - 2*(6*d^2*sin(2*f*x + 2*e) - 2*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e) + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 4*d^2)*cos(f*x + e) + 2*(d^2*f*x + c*d*f)*sin(f*x + e))*sin(3*f*x + 3*e) - 6*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 4*d^2 - 4*(d^2*f*x + c*d*f)*cos(f*x + e) + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2)*sin(f*x + e))*sin(2*f*x + 2*e) + 4*(d^2*f*x + c*d*f)*sin(f*x + e))/(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(3*f*x + 3*e)^2 + 18*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)*sin(2*f*x + 2*e) + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 - 6*((a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e) + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e))*cos(3*f*x + 3*e) - 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*cos(2*f*x + 2*e) - 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 - 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*sin(3*f*x + 3*e) + 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))","F",0
117,1,982,0,0.694604," ","integrate((d*x+c)^3/(a-a*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)} c d^{2} e}{a f^{2} \cos\left(f x + e\right)^{2} + a f^{2} \sin\left(f x + e\right)^{2} - 2 \, a f^{2} \sin\left(f x + e\right) + a f^{2}} - \frac{6 \, c d^{2} e^{2}}{a f^{2} - \frac{a f^{2} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{3 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)} c^{2} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} - 2 \, a f \sin\left(f x + e\right) + a f} + \frac{6 \, c^{2} d e}{a f - \frac{a f \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 \, c^{3}}{a - \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 i \, d^{3} e^{3} + {\left(6 \, d^{3} e^{2} \cos\left(f x + e\right) + 6 i \, d^{3} e^{2} \sin\left(f x + e\right) - 6 i \, d^{3} e^{2}\right)} \arctan\left(\sin\left(f x + e\right) - 1, \cos\left(f x + e\right)\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(12 i \, d^{3} e - 12 i \, c d^{2} f\right)} {\left(f x + e\right)} + 6 \, {\left({\left(f x + e\right)}^{2} d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) - 2 \, {\left({\left(f x + e\right)}^{3} d^{3} + 3 \, {\left(f x + e\right)} d^{3} e^{2} - 3 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \cos\left(f x + e\right) + {\left(12 i \, {\left(f x + e\right)} d^{3} - 12 i \, d^{3} e + 12 i \, c d^{2} f - 12 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(3 \, {\left(f x + e\right)}^{2} d^{3} + 3 \, d^{3} e^{2} - 6 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} - {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) - 3 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-12 i \, d^{3} \cos\left(f x + e\right) + 12 \, d^{3} \sin\left(f x + e\right) - 12 \, d^{3}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{3} d^{3} - 6 i \, {\left(f x + e\right)} d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) - a f^{3}}}{f}"," ",0,"-(6*(2*(f*x + e)*cos(f*x + e) + (cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))*c*d^2*e/(a*f^2*cos(f*x + e)^2 + a*f^2*sin(f*x + e)^2 - 2*a*f^2*sin(f*x + e) + a*f^2) - 6*c*d^2*e^2/(a*f^2 - a*f^2*sin(f*x + e)/(cos(f*x + e) + 1)) - 3*(2*(f*x + e)*cos(f*x + e) + (cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))*c^2*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 - 2*a*f*sin(f*x + e) + a*f) + 6*c^2*d*e/(a*f - a*f*sin(f*x + e)/(cos(f*x + e) + 1)) - 2*c^3/(a - a*sin(f*x + e)/(cos(f*x + e) + 1)) - (2*I*d^3*e^3 + (6*d^3*e^2*cos(f*x + e) + 6*I*d^3*e^2*sin(f*x + e) - 6*I*d^3*e^2)*arctan2(sin(f*x + e) - 1, cos(f*x + e)) + (-6*I*(f*x + e)^2*d^3 + (12*I*d^3*e - 12*I*c*d^2*f)*(f*x + e) + 6*((f*x + e)^2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (6*I*(f*x + e)^2*d^3 + (-12*I*d^3*e + 12*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(cos(f*x + e), -sin(f*x + e) + 1) - 2*((f*x + e)^3*d^3 + 3*(f*x + e)*d^3*e^2 - 3*(d^3*e - c*d^2*f)*(f*x + e)^2)*cos(f*x + e) + (12*I*(f*x + e)*d^3 - 12*I*d^3*e + 12*I*c*d^2*f - 12*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) + (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f)*sin(f*x + e))*dilog(-I*e^(I*f*x + I*e)) - (3*(f*x + e)^2*d^3 + 3*d^3*e^2 - 6*(d^3*e - c*d^2*f)*(f*x + e) - (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e))*cos(f*x + e) - 3*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + (-12*I*d^3*cos(f*x + e) + 12*d^3*sin(f*x + e) - 12*d^3)*polylog(3, -I*e^(I*f*x + I*e)) + (-2*I*(f*x + e)^3*d^3 - 6*I*(f*x + e)*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e)^2)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) - a*f^3))/f","B",0
118,1,316,0,0.506953," ","integrate((d*x+c)^2/(a-a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{-2 i \, c^{2} f^{2} + {\left(4 \, c d f \cos\left(f x + e\right) + 4 i \, c d f \sin\left(f x + e\right) - 4 i \, c d f\right)} \arctan\left(\sin\left(f x + e\right) - 1, \cos\left(f x + e\right)\right) + {\left(4 \, d^{2} f x \cos\left(f x + e\right) + 4 i \, d^{2} f x \sin\left(f x + e\right) - 4 i \, d^{2} f x\right)} \arctan\left(\cos\left(f x + e\right), -\sin\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x\right)} \cos\left(f x + e\right) - {\left(4 \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} \sin\left(f x + e\right) - 4 i \, d^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, f x + i \, e\right)}\right) - {\left(2 \, d^{2} f x + 2 \, c d f - {\left(-2 i \, d^{2} f x - 2 i \, c d f\right)} \cos\left(f x + e\right) - 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) - a f^{3}}"," ",0,"(-2*I*c^2*f^2 + (4*c*d*f*cos(f*x + e) + 4*I*c*d*f*sin(f*x + e) - 4*I*c*d*f)*arctan2(sin(f*x + e) - 1, cos(f*x + e)) + (4*d^2*f*x*cos(f*x + e) + 4*I*d^2*f*x*sin(f*x + e) - 4*I*d^2*f*x)*arctan2(cos(f*x + e), -sin(f*x + e) + 1) - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x)*cos(f*x + e) - (4*d^2*cos(f*x + e) + 4*I*d^2*sin(f*x + e) - 4*I*d^2)*dilog(-I*e^(I*f*x + I*e)) - (2*d^2*f*x + 2*c*d*f - (-2*I*d^2*f*x - 2*I*c*d*f)*cos(f*x + e) - 2*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1) + (-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) - a*f^3)","B",0
119,1,169,0,1.175525," ","integrate((d*x+c)/(a-a*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) + 1\right)\right)} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} - 2 \, a f \sin\left(f x + e\right) + a f} - \frac{2 \, d e}{a f - \frac{a f \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} + \frac{2 \, c}{a - \frac{a \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{f}"," ",0,"((2*(f*x + e)*cos(f*x + e) + (cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*sin(f*x + e) + 1))*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 - 2*a*f*sin(f*x + e) + a*f) - 2*d*e/(a*f - a*f*sin(f*x + e)/(cos(f*x + e) + 1)) + 2*c/(a - a*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
120,-1,0,0,0.000000," ","integrate(1/(d*x+c)/(a-a*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a-a*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,0,0,0,0.000000," ","integrate(x^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} x^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*x^3, x)","F",0
123,0,0,0,0.000000," ","integrate(x^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} x^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*x^2, x)","F",0
124,0,0,0,0.000000," ","integrate(x*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} x\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*x, x)","F",0
125,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(d x + c\right) + a}}{x}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)/x, x)","F",0
126,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(d x + c\right) + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)/x^2, x)","F",0
127,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(d x + c\right) + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)/x^3, x)","F",0
128,0,0,0,0.000000," ","integrate(x^3*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} x^{3}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*x^3, x)","F",0
129,0,0,0,0.000000," ","integrate(x^2*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} x^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*x^2, x)","F",0
130,0,0,0,0.000000," ","integrate(x*(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} x\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*x, x)","F",0
131,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/x,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/x, x)","F",0
132,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/x^2,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{x^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/x^2, x)","F",0
133,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)/x^3, x)","F",0
134,0,0,0,0.000000," ","integrate(x^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(a*sin(d*x + c) + a), x)","F",0
135,0,0,0,0.000000," ","integrate(x^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(a*sin(d*x + c) + a), x)","F",0
136,0,0,0,0.000000," ","integrate(x/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(a*sin(d*x + c) + a), x)","F",0
137,0,0,0,0.000000," ","integrate(1/x/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(d x + c\right) + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(d*x + c) + a)*x), x)","F",0
138,0,0,0,0.000000," ","integrate(1/x^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(d x + c\right) + a} x^{2}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(d*x + c) + a)*x^2), x)","F",0
139,0,0,0,0.000000," ","integrate(x^3/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(a*sin(f*x + e) + a)^(3/2), x)","F",0
140,0,0,0,0.000000," ","integrate(x^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
141,0,0,0,0.000000," ","integrate(x/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{x}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(a*sin(f*x + e) + a)^(3/2), x)","F",0
142,0,0,0,0.000000," ","integrate(1/x/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*x), x)","F",0
143,0,0,0,0.000000," ","integrate(1/x^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} x^{2}}\,{d x}"," ",0,"integrate(1/((a*sin(f*x + e) + a)^(3/2)*x^2), x)","F",0
144,0,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/3)/x,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(1/3)/x, x)","F",0
145,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} {\left(a \sin\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(a*sin(f*x + e) + a)^n, x)","F",0
146,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \frac{6 \, a^{3} e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)} - 6 \, {\left(a^{3} d m + a^{3} d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} - {\left(a^{3} d m + a^{3} d\right)} \int {\left(d x + c\right)}^{m} \sin\left(3 \, f x + 3 \, e\right)\,{d x} + 15 \, {\left(a^{3} d m + a^{3} d\right)} \int {\left(d x + c\right)}^{m} \sin\left(f x + e\right)\,{d x}}{4 \, {\left(d m + d\right)}}"," ",0,"(d*x + c)^(m + 1)*a^3/(d*(m + 1)) + 1/4*(6*a^3*e^(m*log(d*x + c) + log(d*x + c)) - 6*(a^3*d*m + a^3*d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) - (a^3*d*m + a^3*d)*integrate((d*x + c)^m*sin(3*f*x + 3*e), x) + 15*(a^3*d*m + a^3*d)*integrate((d*x + c)^m*sin(f*x + e), x))/(d*m + d)","F",0
147,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \frac{a^{2} e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)} - {\left(a^{2} d m + a^{2} d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} + 4 \, {\left(a^{2} d m + a^{2} d\right)} \int {\left(d x + c\right)}^{m} \sin\left(f x + e\right)\,{d x}}{2 \, {\left(d m + d\right)}}"," ",0,"(d*x + c)^(m + 1)*a^2/(d*(m + 1)) + 1/2*(a^2*e^(m*log(d*x + c) + log(d*x + c)) - (a^2*d*m + a^2*d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) + 4*(a^2*d*m + a^2*d)*integrate((d*x + c)^m*sin(f*x + e), x))/(d*m + d)","F",0
148,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+a*sin(f*x+e)),x, algorithm=""maxima"")","a \int {\left(d x + c\right)}^{m} \sin\left(f x + e\right)\,{d x} + \frac{{\left(d x + c\right)}^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"a*integrate((d*x + c)^m*sin(f*x + e), x) + (d*x + c)^(m + 1)*a/(d*(m + 1))","F",0
149,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{a \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^m/(a*sin(f*x + e) + a), x)","F",0
150,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^m/(a*sin(f*x + e) + a)^2, x)","F",0
151,1,462,0,0.429854," ","integrate((d*x+c)^3*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c^{3} + \frac{{\left(f x + e\right)}^{4} a d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a c^{2} d e}{f} - 4 \, b c^{3} \cos\left(f x + e\right) + \frac{4 \, b d^{3} e^{3} \cos\left(f x + e\right)}{f^{3}} - \frac{12 \, b c d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{12 \, b c^{2} d e \cos\left(f x + e\right)}{f} - \frac{12 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} b d^{3} e^{2}}{f^{3}} + \frac{24 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} b c d^{2} e}{f^{2}} - \frac{12 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} b c^{2} d}{f} + \frac{12 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} b d^{3} e}{f^{3}} - \frac{12 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} b c d^{2}}{f^{2}} - \frac{4 \, {\left({\left({\left(f x + e\right)}^{3} - 6 \, f x - 6 \, e\right)} \cos\left(f x + e\right) - 3 \, {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} b d^{3}}{f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c^3 + (f*x + e)^4*a*d^3/f^3 - 4*(f*x + e)^3*a*d^3*e/f^3 + 6*(f*x + e)^2*a*d^3*e^2/f^3 - 4*(f*x + e)*a*d^3*e^3/f^3 + 4*(f*x + e)^3*a*c*d^2/f^2 - 12*(f*x + e)^2*a*c*d^2*e/f^2 + 12*(f*x + e)*a*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c^2*d/f - 12*(f*x + e)*a*c^2*d*e/f - 4*b*c^3*cos(f*x + e) + 4*b*d^3*e^3*cos(f*x + e)/f^3 - 12*b*c*d^2*e^2*cos(f*x + e)/f^2 + 12*b*c^2*d*e*cos(f*x + e)/f - 12*((f*x + e)*cos(f*x + e) - sin(f*x + e))*b*d^3*e^2/f^3 + 24*((f*x + e)*cos(f*x + e) - sin(f*x + e))*b*c*d^2*e/f^2 - 12*((f*x + e)*cos(f*x + e) - sin(f*x + e))*b*c^2*d/f + 12*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*b*d^3*e/f^3 - 12*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*b*c*d^2/f^2 - 4*(((f*x + e)^3 - 6*f*x - 6*e)*cos(f*x + e) - 3*((f*x + e)^2 - 2)*sin(f*x + e))*b*d^3/f^3)/f","B",0
152,1,239,0,0.347268," ","integrate((d*x+c)^2*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a c^{2} + \frac{{\left(f x + e\right)}^{3} a d^{2}}{f^{2}} - \frac{3 \, {\left(f x + e\right)}^{2} a d^{2} e}{f^{2}} + \frac{3 \, {\left(f x + e\right)} a d^{2} e^{2}}{f^{2}} + \frac{3 \, {\left(f x + e\right)}^{2} a c d}{f} - \frac{6 \, {\left(f x + e\right)} a c d e}{f} - 3 \, b c^{2} \cos\left(f x + e\right) - \frac{3 \, b d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{6 \, b c d e \cos\left(f x + e\right)}{f} + \frac{6 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} b d^{2} e}{f^{2}} - \frac{6 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} b c d}{f} - \frac{3 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} b d^{2}}{f^{2}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a*c^2 + (f*x + e)^3*a*d^2/f^2 - 3*(f*x + e)^2*a*d^2*e/f^2 + 3*(f*x + e)*a*d^2*e^2/f^2 + 3*(f*x + e)^2*a*c*d/f - 6*(f*x + e)*a*c*d*e/f - 3*b*c^2*cos(f*x + e) - 3*b*d^2*e^2*cos(f*x + e)/f^2 + 6*b*c*d*e*cos(f*x + e)/f + 6*((f*x + e)*cos(f*x + e) - sin(f*x + e))*b*d^2*e/f^2 - 6*((f*x + e)*cos(f*x + e) - sin(f*x + e))*b*c*d/f - 3*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*b*d^2/f^2)/f","B",0
153,1,93,0,0.348478," ","integrate((d*x+c)*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} a c + \frac{{\left(f x + e\right)}^{2} a d}{f} - \frac{2 \, {\left(f x + e\right)} a d e}{f} - 2 \, b c \cos\left(f x + e\right) + \frac{2 \, b d e \cos\left(f x + e\right)}{f} - \frac{2 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} b d}{f}}{2 \, f}"," ",0,"1/2*(2*(f*x + e)*a*c + (f*x + e)^2*a*d/f - 2*(f*x + e)*a*d*e/f - 2*b*c*cos(f*x + e) + 2*b*d*e*cos(f*x + e)/f - 2*((f*x + e)*cos(f*x + e) - sin(f*x + e))*b*d/f)/f","B",0
154,1,171,0,0.597612," ","integrate((a+b*sin(f*x+e))/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{2 \, a f \log\left(c + \frac{{\left(f x + e\right)} d}{f} - \frac{d e}{f}\right)}{d} + \frac{{\left(f {\left(-i \, E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f {\left(E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} b}{d}}{2 \, f}"," ",0,"1/2*(2*a*f*log(c + (f*x + e)*d/f - d*e/f)/d + (f*(-I*exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f*(exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*b/d)/f","C",0
155,1,196,0,0.495302," ","integrate((a+b*sin(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, a f^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} - \frac{{\left(f^{2} {\left(-i \, E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{2} {\left(E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} b}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f}}{2 \, f}"," ",0,"-1/2*(2*a*f^2/((f*x + e)*d^2 - d^2*e + c*d*f) - (f^2*(-I*exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^2*(exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*b/((f*x + e)*d^2 - d^2*e + c*d*f))/f","C",0
156,1,265,0,0.949914," ","integrate((a+b*sin(f*x+e))/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{a f^{3}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}} - \frac{{\left(f^{3} {\left(-i \, E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{3} {\left(E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} b}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}}}{2 \, f}"," ",0,"-1/2*(a*f^3/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)) - (f^3*(-I*exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^3*(exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*b/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)))/f","C",0
157,1,959,0,0.466553," ","integrate((d*x+c)^3*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(f x + e\right)} a^{2} c^{3} + 4 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c^{3} + \frac{4 \, {\left(f x + e\right)}^{4} a^{2} d^{3}}{f^{3}} - \frac{16 \, {\left(f x + e\right)}^{3} a^{2} d^{3} e}{f^{3}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} d^{3} e^{2}}{f^{3}} - \frac{16 \, {\left(f x + e\right)} a^{2} d^{3} e^{3}}{f^{3}} - \frac{4 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{3} e^{3}}{f^{3}} + \frac{16 \, {\left(f x + e\right)}^{3} a^{2} c d^{2}}{f^{2}} - \frac{48 \, {\left(f x + e\right)}^{2} a^{2} c d^{2} e}{f^{2}} + \frac{48 \, {\left(f x + e\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{12 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} c^{2} d}{f} - \frac{48 \, {\left(f x + e\right)} a^{2} c^{2} d e}{f} - \frac{12 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c^{2} d e}{f} - 32 \, a b c^{3} \cos\left(f x + e\right) + \frac{32 \, a b d^{3} e^{3} \cos\left(f x + e\right)}{f^{3}} - \frac{96 \, a b c d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{96 \, a b c^{2} d e \cos\left(f x + e\right)}{f} - \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a b d^{3} e^{2}}{f^{3}} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{3} e^{2}}{f^{3}} + \frac{192 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a b c d^{2} e}{f^{2}} - \frac{12 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} b^{2} c d^{2} e}{f^{2}} - \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a b c^{2} d}{f} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} b^{2} c^{2} d}{f} + \frac{96 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a b d^{3} e}{f^{3}} - \frac{2 \, {\left(4 \, {\left(f x + e\right)}^{3} - 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{3} e}{f^{3}} - \frac{96 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a b c d^{2}}{f^{2}} + \frac{2 \, {\left(4 \, {\left(f x + e\right)}^{3} - 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c d^{2}}{f^{2}} - \frac{32 \, {\left({\left({\left(f x + e\right)}^{3} - 6 \, f x - 6 \, e\right)} \cos\left(f x + e\right) - 3 \, {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a b d^{3}}{f^{3}} + \frac{{\left(2 \, {\left(f x + e\right)}^{4} - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(2 \, {\left(f x + e\right)}^{3} - 3 \, f x - 3 \, e\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{3}}{f^{3}}}{16 \, f}"," ",0,"1/16*(16*(f*x + e)*a^2*c^3 + 4*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c^3 + 4*(f*x + e)^4*a^2*d^3/f^3 - 16*(f*x + e)^3*a^2*d^3*e/f^3 + 24*(f*x + e)^2*a^2*d^3*e^2/f^3 - 16*(f*x + e)*a^2*d^3*e^3/f^3 - 4*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*d^3*e^3/f^3 + 16*(f*x + e)^3*a^2*c*d^2/f^2 - 48*(f*x + e)^2*a^2*c*d^2*e/f^2 + 48*(f*x + e)*a^2*c*d^2*e^2/f^2 + 12*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c*d^2*e^2/f^2 + 24*(f*x + e)^2*a^2*c^2*d/f - 48*(f*x + e)*a^2*c^2*d*e/f - 12*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c^2*d*e/f - 32*a*b*c^3*cos(f*x + e) + 32*a*b*d^3*e^3*cos(f*x + e)/f^3 - 96*a*b*c*d^2*e^2*cos(f*x + e)/f^2 + 96*a*b*c^2*d*e*cos(f*x + e)/f - 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*b*d^3*e^2/f^3 + 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*b^2*d^3*e^2/f^3 + 192*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*b*c*d^2*e/f^2 - 12*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*b^2*c*d^2*e/f^2 - 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*b*c^2*d/f + 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*b^2*c^2*d/f + 96*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a*b*d^3*e/f^3 - 2*(4*(f*x + e)^3 - 6*(f*x + e)*cos(2*f*x + 2*e) - 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*b^2*d^3*e/f^3 - 96*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a*b*c*d^2/f^2 + 2*(4*(f*x + e)^3 - 6*(f*x + e)*cos(2*f*x + 2*e) - 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*b^2*c*d^2/f^2 - 32*(((f*x + e)^3 - 6*f*x - 6*e)*cos(f*x + e) - 3*((f*x + e)^2 - 2)*sin(f*x + e))*a*b*d^3/f^3 + (2*(f*x + e)^4 - 3*(2*(f*x + e)^2 - 1)*cos(2*f*x + 2*e) - 2*(2*(f*x + e)^3 - 3*f*x - 3*e)*sin(2*f*x + 2*e))*b^2*d^3/f^3)/f","B",0
158,1,502,0,0.441613," ","integrate((d*x+c)^2*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{24 \, {\left(f x + e\right)} a^{2} c^{2} + 6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c^{2} + \frac{8 \, {\left(f x + e\right)}^{3} a^{2} d^{2}}{f^{2}} - \frac{24 \, {\left(f x + e\right)}^{2} a^{2} d^{2} e}{f^{2}} + \frac{24 \, {\left(f x + e\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} c d}{f} - \frac{48 \, {\left(f x + e\right)} a^{2} c d e}{f} - \frac{12 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c d e}{f} - 48 \, a b c^{2} \cos\left(f x + e\right) - \frac{48 \, a b d^{2} e^{2} \cos\left(f x + e\right)}{f^{2}} + \frac{96 \, a b c d e \cos\left(f x + e\right)}{f} + \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a b d^{2} e}{f^{2}} - \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{2} e}{f^{2}} - \frac{96 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a b c d}{f} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} b^{2} c d}{f} - \frac{48 \, {\left({\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} a b d^{2}}{f^{2}} + \frac{{\left(4 \, {\left(f x + e\right)}^{3} - 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) - 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d^{2}}{f^{2}}}{24 \, f}"," ",0,"1/24*(24*(f*x + e)*a^2*c^2 + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c^2 + 8*(f*x + e)^3*a^2*d^2/f^2 - 24*(f*x + e)^2*a^2*d^2*e/f^2 + 24*(f*x + e)*a^2*d^2*e^2/f^2 + 6*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*d^2*e^2/f^2 + 24*(f*x + e)^2*a^2*c*d/f - 48*(f*x + e)*a^2*c*d*e/f - 12*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c*d*e/f - 48*a*b*c^2*cos(f*x + e) - 48*a*b*d^2*e^2*cos(f*x + e)/f^2 + 96*a*b*c*d*e*cos(f*x + e)/f + 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*b*d^2*e/f^2 - 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*b^2*d^2*e/f^2 - 96*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*b*c*d/f + 6*(2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*b^2*c*d/f - 48*(((f*x + e)^2 - 2)*cos(f*x + e) - 2*(f*x + e)*sin(f*x + e))*a*b*d^2/f^2 + (4*(f*x + e)^3 - 6*(f*x + e)*cos(2*f*x + 2*e) - 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*b^2*d^2/f^2)/f","B",0
159,1,202,0,0.557360," ","integrate((d*x+c)*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{8 \, {\left(f x + e\right)} a^{2} c + 2 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} c + \frac{4 \, {\left(f x + e\right)}^{2} a^{2} d}{f} - \frac{8 \, {\left(f x + e\right)} a^{2} d e}{f} - \frac{2 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} b^{2} d e}{f} - 16 \, a b c \cos\left(f x + e\right) + \frac{16 \, a b d e \cos\left(f x + e\right)}{f} - \frac{16 \, {\left({\left(f x + e\right)} \cos\left(f x + e\right) - \sin\left(f x + e\right)\right)} a b d}{f} + \frac{{\left(2 \, {\left(f x + e\right)}^{2} - 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) - \cos\left(2 \, f x + 2 \, e\right)\right)} b^{2} d}{f}}{8 \, f}"," ",0,"1/8*(8*(f*x + e)*a^2*c + 2*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*c + 4*(f*x + e)^2*a^2*d/f - 8*(f*x + e)*a^2*d*e/f - 2*(2*f*x + 2*e - sin(2*f*x + 2*e))*b^2*d*e/f - 16*a*b*c*cos(f*x + e) + 16*a*b*d*e*cos(f*x + e)/f - 16*((f*x + e)*cos(f*x + e) - sin(f*x + e))*a*b*d/f + (2*(f*x + e)^2 - 2*(f*x + e)*sin(2*f*x + 2*e) - cos(2*f*x + 2*e))*b^2*d/f)/f","A",0
160,1,334,0,0.718522," ","integrate((a+b*sin(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{4 \, a^{2} f \log\left(c + \frac{{\left(f x + e\right)} d}{f} - \frac{d e}{f}\right)}{d} + \frac{4 \, {\left(f {\left(-i \, E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f {\left(E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a b}{d} + \frac{{\left(f {\left(E_{1}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f {\left(i \, E_{1}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - i \, E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, f \log\left({\left(f x + e\right)} d - d e + c f\right)\right)} b^{2}}{d}}{4 \, f}"," ",0,"1/4*(4*a^2*f*log(c + (f*x + e)*d/f - d*e/f)/d + 4*(f*(-I*exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f*(exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a*b/d + (f*(exp_integral_e(1, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f*(I*exp_integral_e(1, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - I*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) + 2*f*log((f*x + e)*d - d*e + c*f))*b^2/d)/f","C",0
161,1,369,0,0.594608," ","integrate((a+b*sin(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{\frac{64 \, a^{2} f^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} - \frac{64 \, {\left(f^{2} {\left(-i \, E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{2} {\left(E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a b}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} - \frac{{\left(16 \, f^{2} {\left(E_{2}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f^{2} {\left(16 i \, E_{2}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 16 i \, E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 32 \, f^{2}\right)} b^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f}}{64 \, f}"," ",0,"-1/64*(64*a^2*f^2/((f*x + e)*d^2 - d^2*e + c*d*f) - 64*(f^2*(-I*exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^2*(exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a*b/((f*x + e)*d^2 - d^2*e + c*d*f) - (16*f^2*(exp_integral_e(2, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f^2*(16*I*exp_integral_e(2, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 16*I*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) - 32*f^2)*b^2/((f*x + e)*d^2 - d^2*e + c*d*f))/f","C",0
162,1,474,0,0.722131," ","integrate((a+b*sin(f*x+e))^2/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{\frac{32 \, a^{2} f^{3}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}} - \frac{64 \, {\left(f^{3} {\left(-i \, E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + i \, E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{3} {\left(E_{3}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{3}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a b}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}} - \frac{{\left(16 \, f^{3} {\left(E_{3}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{3}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f^{3} {\left(16 i \, E_{3}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 16 i \, E_{3}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 16 \, f^{3}\right)} b^{2}}{{\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}}}{64 \, f}"," ",0,"-1/64*(32*a^2*f^3/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)) - 64*(f^3*(-I*exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + I*exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^3*(exp_integral_e(3, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(3, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a*b/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)) - (16*f^3*(exp_integral_e(3, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(3, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f^3*(16*I*exp_integral_e(3, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 16*I*exp_integral_e(3, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) - 16*f^3)*b^2/((f*x + e)^2*d^3 + d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*(d^3*e - c*d^2*f)*(f*x + e)))/f","C",0
163,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
164,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
165,-2,0,0,0.000000," ","integrate((d*x+c)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
166,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x + c\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x + c)*(b*sin(f*x + e) + a)), x)","F",0
167,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{{\left(d x + c\right)}^{2} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x + c)^2*(b*sin(f*x + e) + a)), x)","F",0
168,-2,0,0,0.000000," ","integrate((d*x+c)^3/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
169,-2,0,0,0.000000," ","integrate((d*x+c)^2/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
170,-2,0,0,0.000000," ","integrate((d*x+c)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
171,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + 2 \, a b \cos\left(f x + e\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)\right)} \int \frac{a b d \cos\left(f x + e\right) + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(f x + e\right)^{2} + {\left(a b d \cos\left(f x + e\right) - {\left(a b d f x + a b c f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(a b d \sin\left(f x + e\right) + b^{2} d + {\left(a b d f x + a b c f\right)} \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a b d f x + a b c f\right)} \sin\left(f x + e\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \sin\left(f x + e\right)}\,{d x} + 2 \, {\left(a b \sin\left(f x + e\right) + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} c f\right)} \sin\left(f x + e\right)}"," ",0,"(2*a*b*cos(2*f*x + 2*e)*cos(f*x + e) + 2*a*b*cos(f*x + e) - ((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f + ((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*cos(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*cos(f*x + e)^2 + 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*cos(f*x + e)*sin(2*f*x + 2*e) + ((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*sin(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*sin(f*x + e)^2 - 2*((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f + 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*sin(f*x + e))*integrate(-2*(a*b*d*cos(f*x + e) + 2*(a^2*d*f*x + a^2*c*f)*cos(f*x + e)^2 + 2*(a^2*d*f*x + a^2*c*f)*sin(f*x + e)^2 + (a*b*d*cos(f*x + e) - (a*b*d*f*x + a*b*c*f)*sin(f*x + e))*cos(2*f*x + 2*e) + (a*b*d*sin(f*x + e) + b^2*d + (a*b*d*f*x + a*b*c*f)*cos(f*x + e))*sin(2*f*x + 2*e) + (a*b*d*f*x + a*b*c*f)*sin(f*x + e))/((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f + ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f)*cos(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^2*f*x^2 + 2*(a^4 - a^2*b^2)*c*d*f*x + (a^4 - a^2*b^2)*c^2*f)*cos(f*x + e)^2 + 4*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*cos(f*x + e)*sin(2*f*x + 2*e) + ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f)*sin(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^2*f*x^2 + 2*(a^4 - a^2*b^2)*c*d*f*x + (a^4 - a^2*b^2)*c^2*f)*sin(f*x + e)^2 - 2*((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f + 2*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*sin(f*x + e)), x) + 2*(a*b*sin(f*x + e) + b^2)*sin(2*f*x + 2*e))/((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f + ((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*cos(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*cos(f*x + e)^2 + 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*cos(f*x + e)*sin(2*f*x + 2*e) + ((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f)*sin(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d*f*x + (a^4 - a^2*b^2)*c*f)*sin(f*x + e)^2 - 2*((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*c*f + 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*c*f)*sin(f*x + e))","F",0
172,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, a b \cos\left(2 \, f x + 2 \, e\right) \cos\left(f x + e\right) + 2 \, a b \cos\left(f x + e\right) + 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \sin\left(f x + e\right)\right)} \int \frac{2 \, a b d \cos\left(f x + e\right) + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(f x + e\right)^{2} + {\left(2 \, a b d \cos\left(f x + e\right) - {\left(a b d f x + a b c f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(2 \, a b d \sin\left(f x + e\right) + 2 \, b^{2} d + {\left(a b d f x + a b c f\right)} \cos\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a b d f x + a b c f\right)} \sin\left(f x + e\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d^{3} f x^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{3} f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{3} f x^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{3} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{3} f x^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{3} f\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} f x^{3} + 3 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d f x + {\left(a^{3} b - a b^{3}\right)} c^{3} f\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{3} f x^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{3} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{3} f x^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{3} f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{3} f x^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} c^{2} d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{3} f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} f x^{3} + 3 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d f x + {\left(a^{3} b - a b^{3}\right)} c^{3} f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} f x^{3} + 3 \, {\left(a^{3} b - a b^{3}\right)} c d^{2} f x^{2} + 3 \, {\left(a^{3} b - a b^{3}\right)} c^{2} d f x + {\left(a^{3} b - a b^{3}\right)} c^{3} f\right)} \sin\left(f x + e\right)}\,{d x} + 2 \, {\left(a b \sin\left(f x + e\right) + b^{2}\right)} \sin\left(2 \, f x + 2 \, e\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \cos\left(f x + e\right) \sin\left(2 \, f x + 2 \, e\right) + {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c d f x + {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} c d f x + {\left(a^{2} b^{2} - b^{4}\right)} c^{2} f + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} c d f x + {\left(a^{3} b - a b^{3}\right)} c^{2} f\right)} \sin\left(f x + e\right)}"," ",0,"(2*a*b*cos(2*f*x + 2*e)*cos(f*x + e) + 2*a*b*cos(f*x + e) - ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f + ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f)*cos(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^2*f*x^2 + 2*(a^4 - a^2*b^2)*c*d*f*x + (a^4 - a^2*b^2)*c^2*f)*cos(f*x + e)^2 + 4*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*cos(f*x + e)*sin(2*f*x + 2*e) + ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f)*sin(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^2*f*x^2 + 2*(a^4 - a^2*b^2)*c*d*f*x + (a^4 - a^2*b^2)*c^2*f)*sin(f*x + e)^2 - 2*((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f + 2*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*sin(f*x + e))*integrate(-2*(2*a*b*d*cos(f*x + e) + 2*(a^2*d*f*x + a^2*c*f)*cos(f*x + e)^2 + 2*(a^2*d*f*x + a^2*c*f)*sin(f*x + e)^2 + (2*a*b*d*cos(f*x + e) - (a*b*d*f*x + a*b*c*f)*sin(f*x + e))*cos(2*f*x + 2*e) + (2*a*b*d*sin(f*x + e) + 2*b^2*d + (a*b*d*f*x + a*b*c*f)*cos(f*x + e))*sin(2*f*x + 2*e) + (a*b*d*f*x + a*b*c*f)*sin(f*x + e))/((a^2*b^2 - b^4)*d^3*f*x^3 + 3*(a^2*b^2 - b^4)*c*d^2*f*x^2 + 3*(a^2*b^2 - b^4)*c^2*d*f*x + (a^2*b^2 - b^4)*c^3*f + ((a^2*b^2 - b^4)*d^3*f*x^3 + 3*(a^2*b^2 - b^4)*c*d^2*f*x^2 + 3*(a^2*b^2 - b^4)*c^2*d*f*x + (a^2*b^2 - b^4)*c^3*f)*cos(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^3*f*x^3 + 3*(a^4 - a^2*b^2)*c*d^2*f*x^2 + 3*(a^4 - a^2*b^2)*c^2*d*f*x + (a^4 - a^2*b^2)*c^3*f)*cos(f*x + e)^2 + 4*((a^3*b - a*b^3)*d^3*f*x^3 + 3*(a^3*b - a*b^3)*c*d^2*f*x^2 + 3*(a^3*b - a*b^3)*c^2*d*f*x + (a^3*b - a*b^3)*c^3*f)*cos(f*x + e)*sin(2*f*x + 2*e) + ((a^2*b^2 - b^4)*d^3*f*x^3 + 3*(a^2*b^2 - b^4)*c*d^2*f*x^2 + 3*(a^2*b^2 - b^4)*c^2*d*f*x + (a^2*b^2 - b^4)*c^3*f)*sin(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^3*f*x^3 + 3*(a^4 - a^2*b^2)*c*d^2*f*x^2 + 3*(a^4 - a^2*b^2)*c^2*d*f*x + (a^4 - a^2*b^2)*c^3*f)*sin(f*x + e)^2 - 2*((a^2*b^2 - b^4)*d^3*f*x^3 + 3*(a^2*b^2 - b^4)*c*d^2*f*x^2 + 3*(a^2*b^2 - b^4)*c^2*d*f*x + (a^2*b^2 - b^4)*c^3*f + 2*((a^3*b - a*b^3)*d^3*f*x^3 + 3*(a^3*b - a*b^3)*c*d^2*f*x^2 + 3*(a^3*b - a*b^3)*c^2*d*f*x + (a^3*b - a*b^3)*c^3*f)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*((a^3*b - a*b^3)*d^3*f*x^3 + 3*(a^3*b - a*b^3)*c*d^2*f*x^2 + 3*(a^3*b - a*b^3)*c^2*d*f*x + (a^3*b - a*b^3)*c^3*f)*sin(f*x + e)), x) + 2*(a*b*sin(f*x + e) + b^2)*sin(2*f*x + 2*e))/((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f + ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f)*cos(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^2*f*x^2 + 2*(a^4 - a^2*b^2)*c*d*f*x + (a^4 - a^2*b^2)*c^2*f)*cos(f*x + e)^2 + 4*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*cos(f*x + e)*sin(2*f*x + 2*e) + ((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f)*sin(2*f*x + 2*e)^2 + 4*((a^4 - a^2*b^2)*d^2*f*x^2 + 2*(a^4 - a^2*b^2)*c*d*f*x + (a^4 - a^2*b^2)*c^2*f)*sin(f*x + e)^2 - 2*((a^2*b^2 - b^4)*d^2*f*x^2 + 2*(a^2*b^2 - b^4)*c*d*f*x + (a^2*b^2 - b^4)*c^2*f + 2*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*((a^3*b - a*b^3)*d^2*f*x^2 + 2*(a^3*b - a*b^3)*c*d*f*x + (a^3*b - a*b^3)*c^2*f)*sin(f*x + e))","F",0
173,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+b*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} {\left(b \sin\left(f x + e\right) + a\right)}^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(b*sin(f*x + e) + a)^n, x)","F",0
174,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+b*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{m + 1} a^{3}}{d {\left(m + 1\right)}} + \frac{6 \, a b^{2} e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)} - 6 \, {\left(a b^{2} d m + a b^{2} d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} - {\left(b^{3} d m + b^{3} d\right)} \int {\left(d x + c\right)}^{m} \sin\left(3 \, f x + 3 \, e\right)\,{d x} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} \int {\left(d x + c\right)}^{m} \sin\left(f x + e\right)\,{d x}}{4 \, {\left(d m + d\right)}}"," ",0,"(d*x + c)^(m + 1)*a^3/(d*(m + 1)) + 1/4*(6*a*b^2*e^(m*log(d*x + c) + log(d*x + c)) - 6*(a*b^2*d*m + a*b^2*d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) - (b^3*d*m + b^3*d)*integrate((d*x + c)^m*sin(3*f*x + 3*e), x) + 3*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*integrate((d*x + c)^m*sin(f*x + e), x))/(d*m + d)","F",0
175,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{m + 1} a^{2}}{d {\left(m + 1\right)}} + \frac{b^{2} e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)} - {\left(b^{2} d m + b^{2} d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, f x + 2 \, e\right)\,{d x} + 4 \, {\left(a b d m + a b d\right)} \int {\left(d x + c\right)}^{m} \sin\left(f x + e\right)\,{d x}}{2 \, {\left(d m + d\right)}}"," ",0,"(d*x + c)^(m + 1)*a^2/(d*(m + 1)) + 1/2*(b^2*e^(m*log(d*x + c) + log(d*x + c)) - (b^2*d*m + b^2*d)*integrate((d*x + c)^m*cos(2*f*x + 2*e), x) + 4*(a*b*d*m + a*b*d)*integrate((d*x + c)^m*sin(f*x + e), x))/(d*m + d)","F",0
176,0,0,0,0.000000," ","integrate((d*x+c)^m*(a+b*sin(f*x+e)),x, algorithm=""maxima"")","b \int {\left(d x + c\right)}^{m} \sin\left(f x + e\right)\,{d x} + \frac{{\left(d x + c\right)}^{m + 1} a}{d {\left(m + 1\right)}}"," ",0,"b*integrate((d*x + c)^m*sin(f*x + e), x) + (d*x + c)^(m + 1)*a/(d*(m + 1))","F",0
177,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^m/(b*sin(f*x + e) + a), x)","F",0
178,0,0,0,0.000000," ","integrate((d*x+c)^m/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d x + c\right)}^{m}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^m/(b*sin(f*x + e) + a)^2, x)","F",0
179,1,1307,0,0.628611," ","integrate((f*x+e)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, c^{2} e f^{2} {\left(\frac{1}{a d^{2} + \frac{a d^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d^{2}}\right)} - 12 \, c e^{2} f {\left(\frac{1}{a d + \frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - \frac{6 \, {\left({\left(d x + c\right)}^{2} \cos\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} \sin\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)}^{2} \sin\left(d x + c\right) + {\left(d x + c\right)}^{2} + 4 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)\right)} c e f^{2}}{a d^{2} \cos\left(d x + c\right)^{2} + a d^{2} \sin\left(d x + c\right)^{2} + 2 \, a d^{2} \sin\left(d x + c\right) + a d^{2}} + 4 \, e^{3} {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right)} + \frac{3 \, {\left({\left(d x + c\right)}^{2} \cos\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} \sin\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)}^{2} \sin\left(d x + c\right) + {\left(d x + c\right)}^{2} + 4 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)\right)} e^{2} f}{a d \cos\left(d x + c\right)^{2} + a d \sin\left(d x + c\right)^{2} + 2 \, a d \sin\left(d x + c\right) + a d} + \frac{2 \, {\left({\left(d x + c\right)}^{4} f^{3} + 6 \, {\left(d x + c\right)}^{2} c^{2} f^{3} - 4 \, {\left(d x + c\right)} c^{3} f^{3} + 8 i \, c^{3} f^{3} + 4 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{3} - {\left(24 \, c^{2} f^{3} \cos\left(d x + c\right) + 24 i \, c^{2} f^{3} \sin\left(d x + c\right) + 24 i \, c^{2} f^{3}\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(-24 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-48 i \, d e f^{2} + 48 i \, c f^{3}\right)} {\left(d x + c\right)} - 24 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-24 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-48 i \, d e f^{2} + 48 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(i \, {\left(d x + c\right)}^{4} f^{3} + {\left(-4 i \, c^{3} - 24 \, c^{2}\right)} {\left(d x + c\right)} f^{3} + {\left(4 i \, d e f^{2} - 4 \, {\left(i \, c + 2\right)} f^{3}\right)} {\left(d x + c\right)}^{3} - {\left(24 \, d e f^{2} - {\left(6 i \, c^{2} + 24 \, c\right)} f^{3}\right)} {\left(d x + c\right)}^{2}\right)} \cos\left(d x + c\right) - {\left(-48 i \, d e f^{2} - 48 i \, {\left(d x + c\right)} f^{3} + 48 i \, c f^{3} - 48 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) + {\left(-48 i \, d e f^{2} - 48 i \, {\left(d x + c\right)} f^{3} + 48 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(12 \, {\left(d x + c\right)}^{2} f^{3} + 12 \, c^{2} f^{3} + 24 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} - 12 i \, c^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + 48 \, {\left(i \, f^{3} \cos\left(d x + c\right) - f^{3} \sin\left(d x + c\right) - f^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left({\left(d x + c\right)}^{4} f^{3} - 4 \, {\left(c^{3} - 6 i \, c^{2}\right)} {\left(d x + c\right)} f^{3} + {\left(4 \, d e f^{2} - {\left(4 \, c - 8 i\right)} f^{3}\right)} {\left(d x + c\right)}^{3} + 6 \, {\left(4 i \, d e f^{2} + {\left(c^{2} - 4 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}^{2}\right)} \sin\left(d x + c\right)\right)}}{-4 i \, a d^{3} \cos\left(d x + c\right) + 4 \, a d^{3} \sin\left(d x + c\right) + 4 \, a d^{3}}}{2 \, d}"," ",0,"1/2*(12*c^2*e*f^2*(1/(a*d^2 + a*d^2*sin(d*x + c)/(cos(d*x + c) + 1)) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d^2)) - 12*c*e^2*f*(1/(a*d + a*d*sin(d*x + c)/(cos(d*x + c) + 1)) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - 6*((d*x + c)^2*cos(d*x + c)^2 + (d*x + c)^2*sin(d*x + c)^2 + 2*(d*x + c)^2*sin(d*x + c) + (d*x + c)^2 + 4*(d*x + c)*cos(d*x + c) - 2*(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1))*c*e*f^2/(a*d^2*cos(d*x + c)^2 + a*d^2*sin(d*x + c)^2 + 2*a*d^2*sin(d*x + c) + a*d^2) + 4*e^3*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)/(cos(d*x + c) + 1))) + 3*((d*x + c)^2*cos(d*x + c)^2 + (d*x + c)^2*sin(d*x + c)^2 + 2*(d*x + c)^2*sin(d*x + c) + (d*x + c)^2 + 4*(d*x + c)*cos(d*x + c) - 2*(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1))*e^2*f/(a*d*cos(d*x + c)^2 + a*d*sin(d*x + c)^2 + 2*a*d*sin(d*x + c) + a*d) + 2*((d*x + c)^4*f^3 + 6*(d*x + c)^2*c^2*f^3 - 4*(d*x + c)*c^3*f^3 + 8*I*c^3*f^3 + 4*(d*e*f^2 - c*f^3)*(d*x + c)^3 - (24*c^2*f^3*cos(d*x + c) + 24*I*c^2*f^3*sin(d*x + c) + 24*I*c^2*f^3)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (-24*I*(d*x + c)^2*f^3 + (-48*I*d*e*f^2 + 48*I*c*f^3)*(d*x + c) - 24*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + (-24*I*(d*x + c)^2*f^3 + (-48*I*d*e*f^2 + 48*I*c*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (I*(d*x + c)^4*f^3 + (-4*I*c^3 - 24*c^2)*(d*x + c)*f^3 + (4*I*d*e*f^2 - 4*(I*c + 2)*f^3)*(d*x + c)^3 - (24*d*e*f^2 - (6*I*c^2 + 24*c)*f^3)*(d*x + c)^2)*cos(d*x + c) - (-48*I*d*e*f^2 - 48*I*(d*x + c)*f^3 + 48*I*c*f^3 - 48*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) + (-48*I*d*e*f^2 - 48*I*(d*x + c)*f^3 + 48*I*c*f^3)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) - (12*(d*x + c)^2*f^3 + 12*c^2*f^3 + 24*(d*e*f^2 - c*f^3)*(d*x + c) + (-12*I*(d*x + c)^2*f^3 - 12*I*c^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*cos(d*x + c) + 12*((d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + 48*(I*f^3*cos(d*x + c) - f^3*sin(d*x + c) - f^3)*polylog(3, I*e^(I*d*x + I*c)) + ((d*x + c)^4*f^3 - 4*(c^3 - 6*I*c^2)*(d*x + c)*f^3 + (4*d*e*f^2 - (4*c - 8*I)*f^3)*(d*x + c)^3 + 6*(4*I*d*e*f^2 + (c^2 - 4*I*c)*f^3)*(d*x + c)^2)*sin(d*x + c))/(-4*I*a*d^3*cos(d*x + c) + 4*a*d^3*sin(d*x + c) + 4*a*d^3))/d","B",0
180,1,404,0,0.560242," ","integrate((f*x+e)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x - 6 i \, d^{2} e^{2} - {\left(12 \, d e f \cos\left(d x + c\right) + 12 i \, d e f \sin\left(d x + c\right) + 12 i \, d e f\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(12 \, d f^{2} x \cos\left(d x + c\right) + 12 i \, d f^{2} x \sin\left(d x + c\right) + 12 i \, d f^{2} x\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(i \, d^{3} f^{2} x^{3} - 3 \, {\left(-i \, d^{3} e f + 2 \, d^{2} f^{2}\right)} x^{2} + {\left(3 i \, d^{3} e^{2} - 12 \, d^{2} e f\right)} x\right)} \cos\left(d x + c\right) + {\left(12 \, f^{2} \cos\left(d x + c\right) + 12 i \, f^{2} \sin\left(d x + c\right) + 12 i \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(6 \, d f^{2} x + 6 \, d e f + {\left(-6 i \, d f^{2} x - 6 i \, d e f\right)} \cos\left(d x + c\right) + 6 \, {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(d^{3} f^{2} x^{3} + {\left(3 \, d^{3} e f + 6 i \, d^{2} f^{2}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} + 4 i \, d^{2} e f\right)} x\right)} \sin\left(d x + c\right)}{-3 i \, a d^{3} \cos\left(d x + c\right) + 3 \, a d^{3} \sin\left(d x + c\right) + 3 \, a d^{3}}"," ",0,"(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x - 6*I*d^2*e^2 - (12*d*e*f*cos(d*x + c) + 12*I*d*e*f*sin(d*x + c) + 12*I*d*e*f)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (12*d*f^2*x*cos(d*x + c) + 12*I*d*f^2*x*sin(d*x + c) + 12*I*d*f^2*x)*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (I*d^3*f^2*x^3 - 3*(-I*d^3*e*f + 2*d^2*f^2)*x^2 + (3*I*d^3*e^2 - 12*d^2*e*f)*x)*cos(d*x + c) + (12*f^2*cos(d*x + c) + 12*I*f^2*sin(d*x + c) + 12*I*f^2)*dilog(I*e^(I*d*x + I*c)) - (6*d*f^2*x + 6*d*e*f + (-6*I*d*f^2*x - 6*I*d*e*f)*cos(d*x + c) + 6*(d*f^2*x + d*e*f)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (d^3*f^2*x^3 + (3*d^3*e*f + 6*I*d^2*f^2)*x^2 + 3*(d^3*e^2 + 4*I*d^2*e*f)*x)*sin(d*x + c))/(-3*I*a*d^3*cos(d*x + c) + 3*a*d^3*sin(d*x + c) + 3*a*d^3)","B",0
181,1,273,0,0.420990," ","integrate((f*x+e)*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, c f {\left(\frac{1}{a d + \frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - 4 \, e {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right)} - \frac{{\left({\left(d x + c\right)}^{2} \cos\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} \sin\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)}^{2} \sin\left(d x + c\right) + {\left(d x + c\right)}^{2} + 4 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)\right)} f}{a d \cos\left(d x + c\right)^{2} + a d \sin\left(d x + c\right)^{2} + 2 \, a d \sin\left(d x + c\right) + a d}}{2 \, d}"," ",0,"-1/2*(4*c*f*(1/(a*d + a*d*sin(d*x + c)/(cos(d*x + c) + 1)) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - 4*e*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)/(cos(d*x + c) + 1))) - ((d*x + c)^2*cos(d*x + c)^2 + (d*x + c)^2*sin(d*x + c)^2 + 2*(d*x + c)^2*sin(d*x + c) + (d*x + c)^2 + 4*(d*x + c)*cos(d*x + c) - 2*(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1))*f/(a*d*cos(d*x + c)^2 + a*d*sin(d*x + c)^2 + 2*a*d*sin(d*x + c) + a*d))/d","B",0
182,1,50,0,0.409252," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right)}}{d}"," ",0,"2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
183,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate(sin(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,1,4598,0,1.971931," ","integrate((f*x+e)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, c^{2} e f^{2} {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 2}{a d^{2} + \frac{a d^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a d^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a d^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d^{2}}\right)} - 12 \, c e^{2} f {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 2}{a d + \frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a d \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - \frac{6 \, {\left({\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{4} + {\left({\left(d x + c\right)}^{2} - 1\right)} \sin\left(d x + c\right)^{4} + {\left({\left(d x + c\right)} \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 7 \, {\left(d x + c\right)} \cos\left(d x + c\right)^{3} + {\left(d x + {\left(d x + c\right)} \sin\left(d x + c\right) + c - \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{3} + {\left({\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + 6 \, {\left(d x + c\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(d x + c\right)}^{2} - {\left(d x + c\right)} \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left({\left({\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 1\right)} \sin\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + {\left({\left(d x + c\right)} \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(d x + c\right)}^{2} + {\left(d x + c\right)} \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) - 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + 7 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 3\right)} \sin\left(d x + c\right)^{2} + {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{3} - {\left(4 \, {\left(d x + c\right)}^{2} - {\left(d x + c\right)} \cos\left(d x + c\right) - 6\right)} \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)^{2} - {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)}^{2} + 12 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{4} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right)^{3} - 2 \, {\left(\sin\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 2 \, \sin\left(d x + c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(d x + c\right)^{2} + 2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right) \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{3} + {\left(d x + c\right)} \sin\left(d x + c\right)^{3} + {\left(d x + {\left(d x + c\right)} \sin\left(d x + c\right) + c - \cos\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 14 \, {\left(d x + c\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, d x + {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right) + 2 \, c\right)} \sin\left(d x + c\right)^{2} + d x + 2 \, {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{2} - {\left(d x + c\right)} \sin\left(d x + c\right)^{2} - {\left(d x + c - 2 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{2} + 2 \, d x + 4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right) + 2 \, c\right)} \sin\left(d x + c\right) + c\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)\right)} c e f^{2}}{a d^{2} \cos\left(d x + c\right)^{4} + a d^{2} \sin\left(d x + c\right)^{4} + 2 \, a d^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 2 \, a d^{2} \sin\left(d x + c\right)^{3} + a d^{2} \cos\left(d x + c\right)^{2} + {\left(a d^{2} \cos\left(d x + c\right)^{2} + a d^{2} \sin\left(d x + c\right)^{2} + 2 \, a d^{2} \sin\left(d x + c\right) + a d^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a d^{2} \cos\left(d x + c\right)^{2} + a d^{2} \sin\left(d x + c\right)^{2} + 2 \, a d^{2} \sin\left(d x + c\right) + a d^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, a d^{2} \cos\left(d x + c\right)^{2} + a d^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} \sin\left(d x + c\right)^{3} + 2 \, a d^{2} \sin\left(d x + c\right)^{2} + {\left(a d^{2} \cos\left(d x + c\right)^{2} + a d^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a d^{2} \cos\left(d x + c\right)^{3} + a d^{2} \cos\left(d x + c\right) \sin\left(d x + c\right)^{2} + 2 \, a d^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + a d^{2} \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)} + 4 \, e^{3} {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)} + \frac{3 \, {\left({\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{4} + {\left({\left(d x + c\right)}^{2} - 1\right)} \sin\left(d x + c\right)^{4} + {\left({\left(d x + c\right)} \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 7 \, {\left(d x + c\right)} \cos\left(d x + c\right)^{3} + {\left(d x + {\left(d x + c\right)} \sin\left(d x + c\right) + c - \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{3} + {\left({\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + 6 \, {\left(d x + c\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(d x + c\right)}^{2} - {\left(d x + c\right)} \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left({\left({\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 1\right)} \sin\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + {\left({\left(d x + c\right)} \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(d x + c\right)}^{2} + {\left(d x + c\right)} \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) - 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + 7 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 3\right)} \sin\left(d x + c\right)^{2} + {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{3} - {\left(4 \, {\left(d x + c\right)}^{2} - {\left(d x + c\right)} \cos\left(d x + c\right) - 6\right)} \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)^{2} - {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)}^{2} + 12 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{4} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right)^{3} - 2 \, {\left(\sin\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 2 \, \sin\left(d x + c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(d x + c\right)^{2} + 2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right) \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{3} + {\left(d x + c\right)} \sin\left(d x + c\right)^{3} + {\left(d x + {\left(d x + c\right)} \sin\left(d x + c\right) + c - \cos\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 14 \, {\left(d x + c\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, d x + {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right) + 2 \, c\right)} \sin\left(d x + c\right)^{2} + d x + 2 \, {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{2} - {\left(d x + c\right)} \sin\left(d x + c\right)^{2} - {\left(d x + c - 2 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{2} + 2 \, d x + 4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right) + 2 \, c\right)} \sin\left(d x + c\right) + c\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)\right)} e^{2} f}{a d \cos\left(d x + c\right)^{4} + a d \sin\left(d x + c\right)^{4} + 2 \, a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 2 \, a d \sin\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} + {\left(a d \cos\left(d x + c\right)^{2} + a d \sin\left(d x + c\right)^{2} + 2 \, a d \sin\left(d x + c\right) + a d\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a d \cos\left(d x + c\right)^{2} + a d \sin\left(d x + c\right)^{2} + 2 \, a d \sin\left(d x + c\right) + a d\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d \sin\left(d x + c\right)^{3} + 2 \, a d \sin\left(d x + c\right)^{2} + {\left(a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right) \sin\left(d x + c\right)^{2} + 2 \, a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)} + \frac{2 \, {\left({\left(d x + c\right)}^{4} f^{3} + {\left(4 \, d e f^{2} - {\left(4 \, c + 2 i\right)} f^{3}\right)} {\left(d x + c\right)}^{3} + 12 i \, d e f^{2} - {\left(-10 i \, c^{3} + 6 \, c^{2} + 12 i \, c - 12\right)} f^{3} + 6 \, {\left(-i \, d e f^{2} + {\left(c^{2} + i \, c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} - {\left(12 \, d e f^{2} + {\left(4 \, c^{3} + 6 i \, c^{2} - 12 \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)} - {\left(24 \, c^{2} f^{3} \cos\left(d x + c\right) + 24 i \, c^{2} f^{3} \sin\left(d x + c\right) + 24 i \, c^{2} f^{3}\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(-24 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-48 i \, d e f^{2} + 48 i \, c f^{3}\right)} {\left(d x + c\right)} - 24 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-24 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-48 i \, d e f^{2} + 48 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} - 12 i \, d e f^{2} + {\left(-2 i \, c^{3} - 6 \, c^{2} + 12 i \, c + 12\right)} f^{3} + {\left(6 i \, d e f^{2} - 6 \, {\left(i \, c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} - {\left(12 \, d e f^{2} - {\left(6 i \, c^{2} + 12 \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(i \, {\left(d x + c\right)}^{4} f^{3} - 2 \, {\left(-2 i \, d e f^{2} + {\left(2 i \, c + 5\right)} f^{3}\right)} {\left(d x + c\right)}^{3} + 12 \, d e f^{2} + {\left(2 \, c^{3} - 6 i \, c^{2} - 12 \, c + 12 i\right)} f^{3} - {\left(30 \, d e f^{2} - {\left(6 i \, c^{2} + 30 \, c - 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, d e f^{2} + {\left(-4 i \, c^{3} - 30 \, c^{2} + 12 i \, c + 12\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(-48 i \, d e f^{2} - 48 i \, {\left(d x + c\right)} f^{3} + 48 i \, c f^{3} - 48 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) + {\left(-48 i \, d e f^{2} - 48 i \, {\left(d x + c\right)} f^{3} + 48 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(12 \, {\left(d x + c\right)}^{2} f^{3} + 12 \, c^{2} f^{3} + 24 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} - 12 i \, c^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + 48 \, {\left(i \, f^{3} \cos\left(d x + c\right) - f^{3} \sin\left(d x + c\right) - f^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left(2 \, {\left(d x + c\right)}^{3} f^{3} - 12 \, d e f^{2} - {\left(2 \, c^{3} - 6 i \, c^{2} - 12 \, c + 12 i\right)} f^{3} + {\left(6 \, d e f^{2} - {\left(6 \, c - 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 6 \, {\left(2 i \, d e f^{2} + {\left(c^{2} - 2 i \, c - 2\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(d x + c\right)}^{4} f^{3} + {\left(4 \, d e f^{2} - {\left(4 \, c - 10 i\right)} f^{3}\right)} {\left(d x + c\right)}^{3} - 12 i \, d e f^{2} - {\left(2 i \, c^{3} + 6 \, c^{2} - 12 i \, c - 12\right)} f^{3} + 6 \, {\left(5 i \, d e f^{2} + {\left(c^{2} - 5 i \, c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} - {\left(12 \, d e f^{2} + {\left(4 \, c^{3} - 30 i \, c^{2} - 12 \, c + 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-4 i \, a d^{3} \cos\left(d x + c\right) + 4 \, a d^{3} \sin\left(d x + c\right) + 4 \, a d^{3}}}{2 \, d}"," ",0,"-1/2*(12*c^2*e*f^2*((sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2)/(a*d^2 + a*d^2*sin(d*x + c)/(cos(d*x + c) + 1) + a*d^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*d^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d^2)) - 12*c*e^2*f*((sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2)/(a*d + a*d*sin(d*x + c)/(cos(d*x + c) + 1) + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*d*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - 6*(((d*x + c)^2 - 1)*cos(d*x + c)^4 + ((d*x + c)^2 - 1)*sin(d*x + c)^4 + ((d*x + c)*cos(d*x + c) + sin(d*x + c) + 1)*cos(2*d*x + 2*c)^3 + 7*(d*x + c)*cos(d*x + c)^3 + (d*x + (d*x + c)*sin(d*x + c) + c - cos(d*x + c))*sin(2*d*x + 2*c)^3 + (2*(d*x + c)^2 - 3)*sin(d*x + c)^3 + (((d*x + c)^2 - 1)*cos(d*x + c)^2 + ((d*x + c)^2 - 3)*sin(d*x + c)^2 + (d*x + c)^2 + 6*(d*x + c)*cos(d*x + c) + 2*((d*x + c)^2 - (d*x + c)*cos(d*x + c) - 2)*sin(d*x + c) - 1)*cos(2*d*x + 2*c)^2 + ((d*x + c)^2 - 1)*cos(d*x + c)^2 + (((d*x + c)^2 - 3)*cos(d*x + c)^2 + ((d*x + c)^2 - 1)*sin(d*x + c)^2 + (d*x + c)^2 + ((d*x + c)*cos(d*x + c) + sin(d*x + c) + 1)*cos(2*d*x + 2*c) + 8*(d*x + c)*cos(d*x + c) + 2*((d*x + c)^2 + (d*x + c)*cos(d*x + c) - 1)*sin(d*x + c) - 1)*sin(2*d*x + 2*c)^2 + (2*((d*x + c)^2 - 1)*cos(d*x + c)^2 + (d*x + c)^2 + 7*(d*x + c)*cos(d*x + c) - 3)*sin(d*x + c)^2 + ((d*x + c)*cos(d*x + c)^3 - (2*(d*x + c)^2 - 3)*sin(d*x + c)^3 - (4*(d*x + c)^2 - (d*x + c)*cos(d*x + c) - 6)*sin(d*x + c)^2 + 2*cos(d*x + c)^2 - ((2*(d*x + c)^2 - 3)*cos(d*x + c)^2 + 2*(d*x + c)^2 + 12*(d*x + c)*cos(d*x + c) - 4)*sin(d*x + c) + 1)*cos(2*d*x + 2*c) + (d*x + c)*cos(d*x + c) - 2*(cos(d*x + c)^4 + sin(d*x + c)^4 + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 2*cos(d*x + c)^2*sin(d*x + c) + (2*cos(d*x + c)^2 + 1)*sin(d*x + c)^2 + 2*sin(d*x + c)^3 - 2*(sin(d*x + c)^3 + (cos(d*x + c)^2 + 1)*sin(d*x + c) + 2*sin(d*x + c)^2)*cos(2*d*x + 2*c) + cos(d*x + c)^2 + 2*(cos(d*x + c)^3 + cos(d*x + c)*sin(d*x + c)^2 + 2*cos(d*x + c)*sin(d*x + c) + cos(d*x + c))*sin(2*d*x + 2*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + ((2*(d*x + c)^2 - 3)*cos(d*x + c)^3 + (d*x + c)*sin(d*x + c)^3 + (d*x + (d*x + c)*sin(d*x + c) + c - cos(d*x + c))*cos(2*d*x + 2*c)^2 + 14*(d*x + c)*cos(d*x + c)^2 + (2*d*x + (2*(d*x + c)^2 - 3)*cos(d*x + c) + 2*c)*sin(d*x + c)^2 + d*x + 2*((d*x + c)*cos(d*x + c)^2 - (d*x + c)*sin(d*x + c)^2 - (d*x + c - 2*cos(d*x + c))*sin(d*x + c) + cos(d*x + c))*cos(2*d*x + 2*c) + 2*((d*x + c)^2 - 1)*cos(d*x + c) + ((d*x + c)*cos(d*x + c)^2 + 2*d*x + 4*((d*x + c)^2 - 1)*cos(d*x + c) + 2*c)*sin(d*x + c) + c)*sin(2*d*x + 2*c) + ((2*(d*x + c)^2 - 3)*cos(d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 1)*sin(d*x + c))*c*e*f^2/(a*d^2*cos(d*x + c)^4 + a*d^2*sin(d*x + c)^4 + 2*a*d^2*cos(d*x + c)^2*sin(d*x + c) + 2*a*d^2*sin(d*x + c)^3 + a*d^2*cos(d*x + c)^2 + (a*d^2*cos(d*x + c)^2 + a*d^2*sin(d*x + c)^2 + 2*a*d^2*sin(d*x + c) + a*d^2)*cos(2*d*x + 2*c)^2 + (a*d^2*cos(d*x + c)^2 + a*d^2*sin(d*x + c)^2 + 2*a*d^2*sin(d*x + c) + a*d^2)*sin(2*d*x + 2*c)^2 + (2*a*d^2*cos(d*x + c)^2 + a*d^2)*sin(d*x + c)^2 - 2*(a*d^2*sin(d*x + c)^3 + 2*a*d^2*sin(d*x + c)^2 + (a*d^2*cos(d*x + c)^2 + a*d^2)*sin(d*x + c))*cos(2*d*x + 2*c) + 2*(a*d^2*cos(d*x + c)^3 + a*d^2*cos(d*x + c)*sin(d*x + c)^2 + 2*a*d^2*cos(d*x + c)*sin(d*x + c) + a*d^2*cos(d*x + c))*sin(2*d*x + 2*c)) + 4*e^3*((sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2)/(a + a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a) + 3*(((d*x + c)^2 - 1)*cos(d*x + c)^4 + ((d*x + c)^2 - 1)*sin(d*x + c)^4 + ((d*x + c)*cos(d*x + c) + sin(d*x + c) + 1)*cos(2*d*x + 2*c)^3 + 7*(d*x + c)*cos(d*x + c)^3 + (d*x + (d*x + c)*sin(d*x + c) + c - cos(d*x + c))*sin(2*d*x + 2*c)^3 + (2*(d*x + c)^2 - 3)*sin(d*x + c)^3 + (((d*x + c)^2 - 1)*cos(d*x + c)^2 + ((d*x + c)^2 - 3)*sin(d*x + c)^2 + (d*x + c)^2 + 6*(d*x + c)*cos(d*x + c) + 2*((d*x + c)^2 - (d*x + c)*cos(d*x + c) - 2)*sin(d*x + c) - 1)*cos(2*d*x + 2*c)^2 + ((d*x + c)^2 - 1)*cos(d*x + c)^2 + (((d*x + c)^2 - 3)*cos(d*x + c)^2 + ((d*x + c)^2 - 1)*sin(d*x + c)^2 + (d*x + c)^2 + ((d*x + c)*cos(d*x + c) + sin(d*x + c) + 1)*cos(2*d*x + 2*c) + 8*(d*x + c)*cos(d*x + c) + 2*((d*x + c)^2 + (d*x + c)*cos(d*x + c) - 1)*sin(d*x + c) - 1)*sin(2*d*x + 2*c)^2 + (2*((d*x + c)^2 - 1)*cos(d*x + c)^2 + (d*x + c)^2 + 7*(d*x + c)*cos(d*x + c) - 3)*sin(d*x + c)^2 + ((d*x + c)*cos(d*x + c)^3 - (2*(d*x + c)^2 - 3)*sin(d*x + c)^3 - (4*(d*x + c)^2 - (d*x + c)*cos(d*x + c) - 6)*sin(d*x + c)^2 + 2*cos(d*x + c)^2 - ((2*(d*x + c)^2 - 3)*cos(d*x + c)^2 + 2*(d*x + c)^2 + 12*(d*x + c)*cos(d*x + c) - 4)*sin(d*x + c) + 1)*cos(2*d*x + 2*c) + (d*x + c)*cos(d*x + c) - 2*(cos(d*x + c)^4 + sin(d*x + c)^4 + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 2*cos(d*x + c)^2*sin(d*x + c) + (2*cos(d*x + c)^2 + 1)*sin(d*x + c)^2 + 2*sin(d*x + c)^3 - 2*(sin(d*x + c)^3 + (cos(d*x + c)^2 + 1)*sin(d*x + c) + 2*sin(d*x + c)^2)*cos(2*d*x + 2*c) + cos(d*x + c)^2 + 2*(cos(d*x + c)^3 + cos(d*x + c)*sin(d*x + c)^2 + 2*cos(d*x + c)*sin(d*x + c) + cos(d*x + c))*sin(2*d*x + 2*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + ((2*(d*x + c)^2 - 3)*cos(d*x + c)^3 + (d*x + c)*sin(d*x + c)^3 + (d*x + (d*x + c)*sin(d*x + c) + c - cos(d*x + c))*cos(2*d*x + 2*c)^2 + 14*(d*x + c)*cos(d*x + c)^2 + (2*d*x + (2*(d*x + c)^2 - 3)*cos(d*x + c) + 2*c)*sin(d*x + c)^2 + d*x + 2*((d*x + c)*cos(d*x + c)^2 - (d*x + c)*sin(d*x + c)^2 - (d*x + c - 2*cos(d*x + c))*sin(d*x + c) + cos(d*x + c))*cos(2*d*x + 2*c) + 2*((d*x + c)^2 - 1)*cos(d*x + c) + ((d*x + c)*cos(d*x + c)^2 + 2*d*x + 4*((d*x + c)^2 - 1)*cos(d*x + c) + 2*c)*sin(d*x + c) + c)*sin(2*d*x + 2*c) + ((2*(d*x + c)^2 - 3)*cos(d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 1)*sin(d*x + c))*e^2*f/(a*d*cos(d*x + c)^4 + a*d*sin(d*x + c)^4 + 2*a*d*cos(d*x + c)^2*sin(d*x + c) + 2*a*d*sin(d*x + c)^3 + a*d*cos(d*x + c)^2 + (a*d*cos(d*x + c)^2 + a*d*sin(d*x + c)^2 + 2*a*d*sin(d*x + c) + a*d)*cos(2*d*x + 2*c)^2 + (a*d*cos(d*x + c)^2 + a*d*sin(d*x + c)^2 + 2*a*d*sin(d*x + c) + a*d)*sin(2*d*x + 2*c)^2 + (2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c)^2 - 2*(a*d*sin(d*x + c)^3 + 2*a*d*sin(d*x + c)^2 + (a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))*cos(2*d*x + 2*c) + 2*(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)*sin(d*x + c)^2 + 2*a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))*sin(2*d*x + 2*c)) + 2*((d*x + c)^4*f^3 + (4*d*e*f^2 - (4*c + 2*I)*f^3)*(d*x + c)^3 + 12*I*d*e*f^2 - (-10*I*c^3 + 6*c^2 + 12*I*c - 12)*f^3 + 6*(-I*d*e*f^2 + (c^2 + I*c - 1)*f^3)*(d*x + c)^2 - (12*d*e*f^2 + (4*c^3 + 6*I*c^2 - 12*c - 12*I)*f^3)*(d*x + c) - (24*c^2*f^3*cos(d*x + c) + 24*I*c^2*f^3*sin(d*x + c) + 24*I*c^2*f^3)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (-24*I*(d*x + c)^2*f^3 + (-48*I*d*e*f^2 + 48*I*c*f^3)*(d*x + c) - 24*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + (-24*I*(d*x + c)^2*f^3 + (-48*I*d*e*f^2 + 48*I*c*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (2*I*(d*x + c)^3*f^3 - 12*I*d*e*f^2 + (-2*I*c^3 - 6*c^2 + 12*I*c + 12)*f^3 + (6*I*d*e*f^2 - 6*(I*c + 1)*f^3)*(d*x + c)^2 - (12*d*e*f^2 - (6*I*c^2 + 12*c - 12*I)*f^3)*(d*x + c))*cos(2*d*x + 2*c) - (I*(d*x + c)^4*f^3 - 2*(-2*I*d*e*f^2 + (2*I*c + 5)*f^3)*(d*x + c)^3 + 12*d*e*f^2 + (2*c^3 - 6*I*c^2 - 12*c + 12*I)*f^3 - (30*d*e*f^2 - (6*I*c^2 + 30*c - 6*I)*f^3)*(d*x + c)^2 + (-12*I*d*e*f^2 + (-4*I*c^3 - 30*c^2 + 12*I*c + 12)*f^3)*(d*x + c))*cos(d*x + c) - (-48*I*d*e*f^2 - 48*I*(d*x + c)*f^3 + 48*I*c*f^3 - 48*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) + (-48*I*d*e*f^2 - 48*I*(d*x + c)*f^3 + 48*I*c*f^3)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) - (12*(d*x + c)^2*f^3 + 12*c^2*f^3 + 24*(d*e*f^2 - c*f^3)*(d*x + c) + (-12*I*(d*x + c)^2*f^3 - 12*I*c^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*cos(d*x + c) + 12*((d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + 48*(I*f^3*cos(d*x + c) - f^3*sin(d*x + c) - f^3)*polylog(3, I*e^(I*d*x + I*c)) + (2*(d*x + c)^3*f^3 - 12*d*e*f^2 - (2*c^3 - 6*I*c^2 - 12*c + 12*I)*f^3 + (6*d*e*f^2 - (6*c - 6*I)*f^3)*(d*x + c)^2 + 6*(2*I*d*e*f^2 + (c^2 - 2*I*c - 2)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + ((d*x + c)^4*f^3 + (4*d*e*f^2 - (4*c - 10*I)*f^3)*(d*x + c)^3 - 12*I*d*e*f^2 - (2*I*c^3 + 6*c^2 - 12*I*c - 12)*f^3 + 6*(5*I*d*e*f^2 + (c^2 - 5*I*c - 1)*f^3)*(d*x + c)^2 - (12*d*e*f^2 + (4*c^3 - 30*I*c^2 - 12*c + 12*I)*f^3)*(d*x + c))*sin(d*x + c))/(-4*I*a*d^3*cos(d*x + c) + 4*a*d^3*sin(d*x + c) + 4*a*d^3))/d","B",0
186,1,603,0,1.628176," ","integrate((f*x+e)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, d^{3} f^{2} x^{3} - 15 i \, d^{2} e^{2} - 6 \, d e f + {\left(6 \, d^{3} e f - 3 i \, d^{2} f^{2}\right)} x^{2} + 6 i \, f^{2} + 6 \, {\left(d^{3} e^{2} - i \, d^{2} e f - d f^{2}\right)} x - {\left(24 \, d e f \cos\left(d x + c\right) + 24 i \, d e f \sin\left(d x + c\right) + 24 i \, d e f\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(24 \, d f^{2} x \cos\left(d x + c\right) + 24 i \, d f^{2} x \sin\left(d x + c\right) + 24 i \, d f^{2} x\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(3 i \, d^{2} f^{2} x^{2} + 3 i \, d^{2} e^{2} - 6 \, d e f - 6 i \, f^{2} - 6 \, {\left(-i \, d^{2} e f + d f^{2}\right)} x\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(2 i \, d^{3} f^{2} x^{3} - 3 \, d^{2} e^{2} - 6 i \, d e f - 3 \, {\left(-2 i \, d^{3} e f + 5 \, d^{2} f^{2}\right)} x^{2} + 6 \, f^{2} + {\left(6 i \, d^{3} e^{2} - 30 \, d^{2} e f - 6 i \, d f^{2}\right)} x\right)} \cos\left(d x + c\right) + {\left(24 \, f^{2} \cos\left(d x + c\right) + 24 i \, f^{2} \sin\left(d x + c\right) + 24 i \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(12 \, d f^{2} x + 12 \, d e f + {\left(-12 i \, d f^{2} x - 12 i \, d e f\right)} \cos\left(d x + c\right) + 12 \, {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 6 i \, d e f - 6 \, f^{2} + {\left(6 \, d^{2} e f + 6 i \, d f^{2}\right)} x\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(2 \, d^{3} f^{2} x^{3} + 3 i \, d^{2} e^{2} - 6 \, d e f + {\left(6 \, d^{3} e f + 15 i \, d^{2} f^{2}\right)} x^{2} - 6 i \, f^{2} + 6 \, {\left(d^{3} e^{2} + 5 i \, d^{2} e f - d f^{2}\right)} x\right)} \sin\left(d x + c\right)}{-6 i \, a d^{3} \cos\left(d x + c\right) + 6 \, a d^{3} \sin\left(d x + c\right) + 6 \, a d^{3}}"," ",0,"-(2*d^3*f^2*x^3 - 15*I*d^2*e^2 - 6*d*e*f + (6*d^3*e*f - 3*I*d^2*f^2)*x^2 + 6*I*f^2 + 6*(d^3*e^2 - I*d^2*e*f - d*f^2)*x - (24*d*e*f*cos(d*x + c) + 24*I*d*e*f*sin(d*x + c) + 24*I*d*e*f)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (24*d*f^2*x*cos(d*x + c) + 24*I*d*f^2*x*sin(d*x + c) + 24*I*d*f^2*x)*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (3*I*d^2*f^2*x^2 + 3*I*d^2*e^2 - 6*d*e*f - 6*I*f^2 - 6*(-I*d^2*e*f + d*f^2)*x)*cos(2*d*x + 2*c) - (2*I*d^3*f^2*x^3 - 3*d^2*e^2 - 6*I*d*e*f - 3*(-2*I*d^3*e*f + 5*d^2*f^2)*x^2 + 6*f^2 + (6*I*d^3*e^2 - 30*d^2*e*f - 6*I*d*f^2)*x)*cos(d*x + c) + (24*f^2*cos(d*x + c) + 24*I*f^2*sin(d*x + c) + 24*I*f^2)*dilog(I*e^(I*d*x + I*c)) - (12*d*f^2*x + 12*d*e*f + (-12*I*d*f^2*x - 12*I*d*e*f)*cos(d*x + c) + 12*(d*f^2*x + d*e*f)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (3*d^2*f^2*x^2 + 3*d^2*e^2 + 6*I*d*e*f - 6*f^2 + (6*d^2*e*f + 6*I*d*f^2)*x)*sin(2*d*x + 2*c) + (2*d^3*f^2*x^3 + 3*I*d^2*e^2 - 6*d*e*f + (6*d^3*e*f + 15*I*d^2*f^2)*x^2 - 6*I*f^2 + 6*(d^3*e^2 + 5*I*d^2*e*f - d*f^2)*x)*sin(d*x + c))/(-6*I*a*d^3*cos(d*x + c) + 6*a*d^3*sin(d*x + c) + 6*a*d^3)","B",0
187,1,1762,0,1.115236," ","integrate((f*x+e)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, c f {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 2}{a d + \frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a d \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - 4 \, e {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)} - \frac{{\left({\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{4} + {\left({\left(d x + c\right)}^{2} - 1\right)} \sin\left(d x + c\right)^{4} + {\left({\left(d x + c\right)} \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{3} + 7 \, {\left(d x + c\right)} \cos\left(d x + c\right)^{3} + {\left(d x + {\left(d x + c\right)} \sin\left(d x + c\right) + c - \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)^{3} + {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{3} + {\left({\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + 6 \, {\left(d x + c\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(d x + c\right)}^{2} - {\left(d x + c\right)} \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left({\left({\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + {\left({\left(d x + c\right)}^{2} - 1\right)} \sin\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + {\left({\left(d x + c\right)} \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(d x + c\right)}^{2} + {\left(d x + c\right)} \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) - 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right)^{2} + {\left(d x + c\right)}^{2} + 7 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 3\right)} \sin\left(d x + c\right)^{2} + {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \sin\left(d x + c\right)^{3} - {\left(4 \, {\left(d x + c\right)}^{2} - {\left(d x + c\right)} \cos\left(d x + c\right) - 6\right)} \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)^{2} - {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)}^{2} + 12 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(\cos\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{4} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 2 \, \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right)^{3} - 2 \, {\left(\sin\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 2 \, \sin\left(d x + c\right)^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + \cos\left(d x + c\right)^{2} + 2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right) \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{3} + {\left(d x + c\right)} \sin\left(d x + c\right)^{3} + {\left(d x + {\left(d x + c\right)} \sin\left(d x + c\right) + c - \cos\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 14 \, {\left(d x + c\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, d x + {\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right) + 2 \, c\right)} \sin\left(d x + c\right)^{2} + d x + 2 \, {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{2} - {\left(d x + c\right)} \sin\left(d x + c\right)^{2} - {\left(d x + c - 2 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)} \cos\left(d x + c\right)^{2} + 2 \, d x + 4 \, {\left({\left(d x + c\right)}^{2} - 1\right)} \cos\left(d x + c\right) + 2 \, c\right)} \sin\left(d x + c\right) + c\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(2 \, {\left(d x + c\right)}^{2} - 3\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right)\right)} f}{a d \cos\left(d x + c\right)^{4} + a d \sin\left(d x + c\right)^{4} + 2 \, a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 2 \, a d \sin\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} + {\left(a d \cos\left(d x + c\right)^{2} + a d \sin\left(d x + c\right)^{2} + 2 \, a d \sin\left(d x + c\right) + a d\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + {\left(a d \cos\left(d x + c\right)^{2} + a d \sin\left(d x + c\right)^{2} + 2 \, a d \sin\left(d x + c\right) + a d\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + {\left(2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d \sin\left(d x + c\right)^{3} + 2 \, a d \sin\left(d x + c\right)^{2} + {\left(a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right) \sin\left(d x + c\right)^{2} + 2 \, a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)} \sin\left(2 \, d x + 2 \, c\right)}}{2 \, d}"," ",0,"1/2*(4*c*f*((sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2)/(a*d + a*d*sin(d*x + c)/(cos(d*x + c) + 1) + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*d*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - 4*e*((sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2)/(a + a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a) - (((d*x + c)^2 - 1)*cos(d*x + c)^4 + ((d*x + c)^2 - 1)*sin(d*x + c)^4 + ((d*x + c)*cos(d*x + c) + sin(d*x + c) + 1)*cos(2*d*x + 2*c)^3 + 7*(d*x + c)*cos(d*x + c)^3 + (d*x + (d*x + c)*sin(d*x + c) + c - cos(d*x + c))*sin(2*d*x + 2*c)^3 + (2*(d*x + c)^2 - 3)*sin(d*x + c)^3 + (((d*x + c)^2 - 1)*cos(d*x + c)^2 + ((d*x + c)^2 - 3)*sin(d*x + c)^2 + (d*x + c)^2 + 6*(d*x + c)*cos(d*x + c) + 2*((d*x + c)^2 - (d*x + c)*cos(d*x + c) - 2)*sin(d*x + c) - 1)*cos(2*d*x + 2*c)^2 + ((d*x + c)^2 - 1)*cos(d*x + c)^2 + (((d*x + c)^2 - 3)*cos(d*x + c)^2 + ((d*x + c)^2 - 1)*sin(d*x + c)^2 + (d*x + c)^2 + ((d*x + c)*cos(d*x + c) + sin(d*x + c) + 1)*cos(2*d*x + 2*c) + 8*(d*x + c)*cos(d*x + c) + 2*((d*x + c)^2 + (d*x + c)*cos(d*x + c) - 1)*sin(d*x + c) - 1)*sin(2*d*x + 2*c)^2 + (2*((d*x + c)^2 - 1)*cos(d*x + c)^2 + (d*x + c)^2 + 7*(d*x + c)*cos(d*x + c) - 3)*sin(d*x + c)^2 + ((d*x + c)*cos(d*x + c)^3 - (2*(d*x + c)^2 - 3)*sin(d*x + c)^3 - (4*(d*x + c)^2 - (d*x + c)*cos(d*x + c) - 6)*sin(d*x + c)^2 + 2*cos(d*x + c)^2 - ((2*(d*x + c)^2 - 3)*cos(d*x + c)^2 + 2*(d*x + c)^2 + 12*(d*x + c)*cos(d*x + c) - 4)*sin(d*x + c) + 1)*cos(2*d*x + 2*c) + (d*x + c)*cos(d*x + c) - 2*(cos(d*x + c)^4 + sin(d*x + c)^4 + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*cos(2*d*x + 2*c)^2 + (cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1)*sin(2*d*x + 2*c)^2 + 2*cos(d*x + c)^2*sin(d*x + c) + (2*cos(d*x + c)^2 + 1)*sin(d*x + c)^2 + 2*sin(d*x + c)^3 - 2*(sin(d*x + c)^3 + (cos(d*x + c)^2 + 1)*sin(d*x + c) + 2*sin(d*x + c)^2)*cos(2*d*x + 2*c) + cos(d*x + c)^2 + 2*(cos(d*x + c)^3 + cos(d*x + c)*sin(d*x + c)^2 + 2*cos(d*x + c)*sin(d*x + c) + cos(d*x + c))*sin(2*d*x + 2*c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + ((2*(d*x + c)^2 - 3)*cos(d*x + c)^3 + (d*x + c)*sin(d*x + c)^3 + (d*x + (d*x + c)*sin(d*x + c) + c - cos(d*x + c))*cos(2*d*x + 2*c)^2 + 14*(d*x + c)*cos(d*x + c)^2 + (2*d*x + (2*(d*x + c)^2 - 3)*cos(d*x + c) + 2*c)*sin(d*x + c)^2 + d*x + 2*((d*x + c)*cos(d*x + c)^2 - (d*x + c)*sin(d*x + c)^2 - (d*x + c - 2*cos(d*x + c))*sin(d*x + c) + cos(d*x + c))*cos(2*d*x + 2*c) + 2*((d*x + c)^2 - 1)*cos(d*x + c) + ((d*x + c)*cos(d*x + c)^2 + 2*d*x + 4*((d*x + c)^2 - 1)*cos(d*x + c) + 2*c)*sin(d*x + c) + c)*sin(2*d*x + 2*c) + ((2*(d*x + c)^2 - 3)*cos(d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 1)*sin(d*x + c))*f/(a*d*cos(d*x + c)^4 + a*d*sin(d*x + c)^4 + 2*a*d*cos(d*x + c)^2*sin(d*x + c) + 2*a*d*sin(d*x + c)^3 + a*d*cos(d*x + c)^2 + (a*d*cos(d*x + c)^2 + a*d*sin(d*x + c)^2 + 2*a*d*sin(d*x + c) + a*d)*cos(2*d*x + 2*c)^2 + (a*d*cos(d*x + c)^2 + a*d*sin(d*x + c)^2 + 2*a*d*sin(d*x + c) + a*d)*sin(2*d*x + 2*c)^2 + (2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c)^2 - 2*(a*d*sin(d*x + c)^3 + 2*a*d*sin(d*x + c)^2 + (a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))*cos(2*d*x + 2*c) + 2*(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)*sin(d*x + c)^2 + 2*a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))*sin(2*d*x + 2*c)))/d","B",0
188,1,129,0,0.936885," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 2}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)}}{d}"," ",0,"-2*((sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2)/(a + a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
189,-1,0,0,0.000000," ","integrate(sin(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(sin(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-2,0,0,0.000000," ","integrate((f*x+e)^3*sin(d*x+c)^3/(a+a*sin(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
192,-2,0,0,0.000000," ","integrate((f*x+e)^2*sin(d*x+c)^3/(a+a*sin(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
193,-2,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)^3/(a+a*sin(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
194,1,212,0,0.666748," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 4}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{d}"," ",0,"((sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4)/(a + a*sin(d*x + c)/(cos(d*x + c) + 1) + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
195,-2,0,0,0.000000," ","integrate(sin(d*x+c)^3/(f*x+e)/(a+a*sin(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
196,-2,0,0,0.000000," ","integrate(sin(d*x+c)^3/(f*x+e)^2/(a+a*sin(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
197,1,2778,0,2.482851," ","integrate((f*x+e)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, c e^{2} f {\left(\frac{2}{a d + \frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - e^{3} {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{2}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right)} + \frac{12 i \, c^{2} d e f^{2} - 4 i \, c^{3} f^{3} + {\left(12 i \, d^{2} e^{2} f - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3} + 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(12 i \, d^{2} e^{2} f - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)} - 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(6 i \, c^{2} d e f^{2} + 2 i \, {\left(d x + c\right)}^{3} f^{3} - 2 i \, c^{3} f^{3} + {\left(6 i \, d e f^{2} - 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)} + 2 \, {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(6 i \, c^{2} d e f^{2} + 2 i \, {\left(d x + c\right)}^{3} f^{3} - 2 i \, c^{3} f^{3} + {\left(6 i \, d e f^{2} - 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + {\left(-6 i \, c^{2} d e f^{2} + 2 i \, c^{3} f^{3} - 2 \, {\left(3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \cos\left(d x + c\right) + {\left(-6 i \, c^{2} d e f^{2} + 2 i \, c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(6 i \, d e f^{2} - 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(6 i \, d e f^{2} - 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - 4 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-24 i \, d e f^{2} - 24 i \, {\left(d x + c\right)} f^{3} + 24 i \, c f^{3} - 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) + {\left(-24 i \, d e f^{2} - 24 i \, {\left(d x + c\right)} f^{3} + 24 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} - 6 i \, c^{2} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} - 6 i \, c^{2} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + 6 i \, c^{2} f^{3} + {\left(12 i \, d e f^{2} - 12 i \, c f^{3}\right)} {\left(d x + c\right)} + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + 6 i \, c^{2} f^{3} + {\left(12 i \, d e f^{2} - 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) + {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)} + {\left(-3 i \, c^{2} d e f^{2} - i \, {\left(d x + c\right)}^{3} f^{3} + i \, c^{3} f^{3} + {\left(-3 i \, d e f^{2} + 3 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-3 i \, d^{2} e^{2} f + 6 i \, c d e f^{2} - 3 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) - {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)} - {\left(3 i \, c^{2} d e f^{2} + i \, {\left(d x + c\right)}^{3} f^{3} - i \, c^{3} f^{3} + {\left(3 i \, d e f^{2} - 3 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 i \, d^{2} e^{2} f - 6 i \, c d e f^{2} + 3 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) + {\left(6 \, d^{2} e^{2} f - 12 \, c d e f^{2} + 6 \, {\left(d x + c\right)}^{2} f^{3} + 6 \, c^{2} f^{3} + 12 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} - 6 i \, c^{2} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(12 \, f^{3} \cos\left(d x + c\right) + 12 i \, f^{3} \sin\left(d x + c\right) + 12 i \, f^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, d x + i \, c\right)}) - {\left(12 \, f^{3} \cos\left(d x + c\right) + 12 i \, f^{3} \sin\left(d x + c\right) + 12 i \, f^{3}\right)} {\rm Li}_{4}(e^{\left(i \, d x + i \, c\right)}) - 24 \, {\left(i \, f^{3} \cos\left(d x + c\right) - f^{3} \sin\left(d x + c\right) - f^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left(12 \, d e f^{2} + 12 \, {\left(d x + c\right)} f^{3} - 12 \, c f^{3} + {\left(-12 i \, d e f^{2} - 12 i \, {\left(d x + c\right)} f^{3} + 12 i \, c f^{3}\right)} \cos\left(d x + c\right) + 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(-e^{\left(i \, d x + i \, c\right)}) - {\left(12 \, d e f^{2} + 12 \, {\left(d x + c\right)} f^{3} - 12 \, c f^{3} - {\left(12 i \, d e f^{2} + 12 i \, {\left(d x + c\right)} f^{3} - 12 i \, c f^{3}\right)} \cos\left(d x + c\right) + 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(e^{\left(i \, d x + i \, c\right)}) + {\left(-4 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)}{-2 i \, a d^{3} \cos\left(d x + c\right) + 2 \, a d^{3} \sin\left(d x + c\right) + 2 \, a d^{3}}}{d}"," ",0,"-(3*c*e^2*f*(2/(a*d + a*d*sin(d*x + c)/(cos(d*x + c) + 1)) + log(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - e^3*(log(sin(d*x + c)/(cos(d*x + c) + 1))/a + 2/(a + a*sin(d*x + c)/(cos(d*x + c) + 1))) + (12*I*c^2*d*e*f^2 - 4*I*c^3*f^3 + (12*I*d^2*e^2*f - 24*I*c*d*e*f^2 + 12*I*c^2*f^3 + 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (12*I*d^2*e^2*f - 24*I*c*d*e*f^2 + 12*I*c^2*f^3)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (-12*I*(d*x + c)^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c) - 12*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + (-12*I*(d*x + c)^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (6*I*c^2*d*e*f^2 + 2*I*(d*x + c)^3*f^3 - 2*I*c^3*f^3 + (6*I*d*e*f^2 - 6*I*c*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*(d*x + c) + 2*(3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(d*x + c) + (6*I*c^2*d*e*f^2 + 2*I*(d*x + c)^3*f^3 - 2*I*c^3*f^3 + (6*I*d*e*f^2 - 6*I*c*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) + 1) + (-6*I*c^2*d*e*f^2 + 2*I*c^3*f^3 - 2*(3*c^2*d*e*f^2 - c^3*f^3)*cos(d*x + c) + (-6*I*c^2*d*e*f^2 + 2*I*c^3*f^3)*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) - 1) + (2*I*(d*x + c)^3*f^3 + (6*I*d*e*f^2 - 6*I*c*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*(d*x + c) + 2*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^3*f^3 + (6*I*d*e*f^2 - 6*I*c*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - 4*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(d*x + c) + (-24*I*d*e*f^2 - 24*I*(d*x + c)*f^3 + 24*I*c*f^3 - 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) + (-24*I*d*e*f^2 - 24*I*(d*x + c)*f^3 + 24*I*c*f^3)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*(d*x + c)^2*f^3 - 6*I*c^2*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*(d*x + c)^2*f^3 - 6*I*c^2*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c))*sin(d*x + c))*dilog(-e^(I*d*x + I*c)) + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + 6*I*c^2*f^3 + (12*I*d*e*f^2 - 12*I*c*f^3)*(d*x + c) + 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + 6*I*c^2*f^3 + (12*I*d*e*f^2 - 12*I*c*f^3)*(d*x + c))*sin(d*x + c))*dilog(e^(I*d*x + I*c)) + (3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c) + (-3*I*c^2*d*e*f^2 - I*(d*x + c)^3*f^3 + I*c^3*f^3 + (-3*I*d*e*f^2 + 3*I*c*f^3)*(d*x + c)^2 + (-3*I*d^2*e^2*f + 6*I*c*d*e*f^2 - 3*I*c^2*f^3)*(d*x + c))*cos(d*x + c) + (3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) - (3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c) - (3*I*c^2*d*e*f^2 + I*(d*x + c)^3*f^3 - I*c^3*f^3 + (3*I*d*e*f^2 - 3*I*c*f^3)*(d*x + c)^2 + (3*I*d^2*e^2*f - 6*I*c*d*e*f^2 + 3*I*c^2*f^3)*(d*x + c))*cos(d*x + c) + (3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) + (6*d^2*e^2*f - 12*c*d*e*f^2 + 6*(d*x + c)^2*f^3 + 6*c^2*f^3 + 12*(d*e*f^2 - c*f^3)*(d*x + c) + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*(d*x + c)^2*f^3 - 6*I*c^2*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c))*cos(d*x + c) + 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (12*f^3*cos(d*x + c) + 12*I*f^3*sin(d*x + c) + 12*I*f^3)*polylog(4, -e^(I*d*x + I*c)) - (12*f^3*cos(d*x + c) + 12*I*f^3*sin(d*x + c) + 12*I*f^3)*polylog(4, e^(I*d*x + I*c)) - 24*(I*f^3*cos(d*x + c) - f^3*sin(d*x + c) - f^3)*polylog(3, I*e^(I*d*x + I*c)) + (12*d*e*f^2 + 12*(d*x + c)*f^3 - 12*c*f^3 + (-12*I*d*e*f^2 - 12*I*(d*x + c)*f^3 + 12*I*c*f^3)*cos(d*x + c) + 12*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(d*x + c))*polylog(3, -e^(I*d*x + I*c)) - (12*d*e*f^2 + 12*(d*x + c)*f^3 - 12*c*f^3 - (12*I*d*e*f^2 + 12*I*(d*x + c)*f^3 - 12*I*c*f^3)*cos(d*x + c) + 12*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(d*x + c))*polylog(3, e^(I*d*x + I*c)) + (-4*I*(d*x + c)^3*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c)^2 + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3)*(d*x + c))*sin(d*x + c))/(-2*I*a*d^3*cos(d*x + c) + 2*a*d^3*sin(d*x + c) + 2*a*d^3))/d","B",0
198,1,1410,0,1.385890," ","integrate((f*x+e)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, c e f {\left(\frac{2}{a d + \frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - e^{2} {\left(\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{2}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}\right)} + \frac{4 i \, c^{2} f^{2} + {\left(8 i \, d e f - 8 i \, c f^{2} + 8 \, {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(8 i \, d e f - 8 i \, c f^{2}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(8 \, {\left(d x + c\right)} f^{2} \cos\left(d x + c\right) + 8 i \, {\left(d x + c\right)} f^{2} \sin\left(d x + c\right) + 8 i \, {\left(d x + c\right)} f^{2}\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + 2 i \, c^{2} f^{2} + {\left(4 i \, d e f - 4 i \, c f^{2}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + 2 i \, c^{2} f^{2} + {\left(4 i \, d e f - 4 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - {\left(2 \, c^{2} f^{2} \cos\left(d x + c\right) + 2 i \, c^{2} f^{2} \sin\left(d x + c\right) + 2 i \, c^{2} f^{2}\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(4 i \, d e f - 4 i \, c f^{2}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(4 i \, d e f - 4 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - 4 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(8 \, f^{2} \cos\left(d x + c\right) + 8 i \, f^{2} \sin\left(d x + c\right) + 8 i \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + 4 i \, c f^{2} - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(d x + c\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + 4 i \, c f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) + {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} - 4 i \, c f^{2} + 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(d x + c\right) + {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} - 4 i \, c f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) + {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)} + {\left(-i \, {\left(d x + c\right)}^{2} f^{2} - i \, c^{2} f^{2} + {\left(-2 i \, d e f + 2 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) - {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)} - {\left(i \, {\left(d x + c\right)}^{2} f^{2} + i \, c^{2} f^{2} + {\left(2 i \, d e f - 2 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) + {\left(4 \, d e f + 4 \, {\left(d x + c\right)} f^{2} - 4 \, c f^{2} + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + 4 i \, c f^{2}\right)} \cos\left(d x + c\right) + 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(i \, f^{2} \cos\left(d x + c\right) - f^{2} \sin\left(d x + c\right) - f^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, d x + i \, c\right)}) - 4 \, {\left(-i \, f^{2} \cos\left(d x + c\right) + f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm Li}_{3}(e^{\left(i \, d x + i \, c\right)}) + {\left(-4 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)}{-2 i \, a d^{2} \cos\left(d x + c\right) + 2 \, a d^{2} \sin\left(d x + c\right) + 2 \, a d^{2}}}{d}"," ",0,"-(2*c*e*f*(2/(a*d + a*d*sin(d*x + c)/(cos(d*x + c) + 1)) + log(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - e^2*(log(sin(d*x + c)/(cos(d*x + c) + 1))/a + 2/(a + a*sin(d*x + c)/(cos(d*x + c) + 1))) + (4*I*c^2*f^2 + (8*I*d*e*f - 8*I*c*f^2 + 8*(d*e*f - c*f^2)*cos(d*x + c) + (8*I*d*e*f - 8*I*c*f^2)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (8*(d*x + c)*f^2*cos(d*x + c) + 8*I*(d*x + c)*f^2*sin(d*x + c) + 8*I*(d*x + c)*f^2)*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (2*I*(d*x + c)^2*f^2 + 2*I*c^2*f^2 + (4*I*d*e*f - 4*I*c*f^2)*(d*x + c) + 2*((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^2*f^2 + 2*I*c^2*f^2 + (4*I*d*e*f - 4*I*c*f^2)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) + 1) - (2*c^2*f^2*cos(d*x + c) + 2*I*c^2*f^2*sin(d*x + c) + 2*I*c^2*f^2)*arctan2(sin(d*x + c), cos(d*x + c) - 1) + (2*I*(d*x + c)^2*f^2 + (4*I*d*e*f - 4*I*c*f^2)*(d*x + c) + 2*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^2*f^2 + (4*I*d*e*f - 4*I*c*f^2)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - 4*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) - (8*f^2*cos(d*x + c) + 8*I*f^2*sin(d*x + c) + 8*I*f^2)*dilog(I*e^(I*d*x + I*c)) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + 4*I*c*f^2 - 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(d*x + c) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + 4*I*c*f^2)*sin(d*x + c))*dilog(-e^(I*d*x + I*c)) + (4*I*d*e*f + 4*I*(d*x + c)*f^2 - 4*I*c*f^2 + 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(d*x + c) + (4*I*d*e*f + 4*I*(d*x + c)*f^2 - 4*I*c*f^2)*sin(d*x + c))*dilog(e^(I*d*x + I*c)) + ((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c) + (-I*(d*x + c)^2*f^2 - I*c^2*f^2 + (-2*I*d*e*f + 2*I*c*f^2)*(d*x + c))*cos(d*x + c) + ((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) - ((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c) - (I*(d*x + c)^2*f^2 + I*c^2*f^2 + (2*I*d*e*f - 2*I*c*f^2)*(d*x + c))*cos(d*x + c) + ((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) + (4*d*e*f + 4*(d*x + c)*f^2 - 4*c*f^2 + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + 4*I*c*f^2)*cos(d*x + c) + 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - 4*(I*f^2*cos(d*x + c) - f^2*sin(d*x + c) - f^2)*polylog(3, -e^(I*d*x + I*c)) - 4*(-I*f^2*cos(d*x + c) + f^2*sin(d*x + c) + f^2)*polylog(3, e^(I*d*x + I*c)) + (-4*I*(d*x + c)^2*f^2 + (-8*I*d*e*f + 8*I*c*f^2)*(d*x + c))*sin(d*x + c))/(-2*I*a*d^2*cos(d*x + c) + 2*a*d^2*sin(d*x + c) + 2*a*d^2))/d","B",0
199,1,517,0,0.909588," ","integrate((f*x+e)*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, d f x \cos\left(d x + c\right) + 4 i \, d f x \sin\left(d x + c\right) - 4 i \, d e - {\left(4 \, f \cos\left(d x + c\right) + 4 i \, f \sin\left(d x + c\right) + 4 i \, f\right)} \arctan\left(\cos\left(c\right) + \sin\left(d x\right), \cos\left(d x\right) + \sin\left(c\right)\right) - {\left(2 i \, d f x + 2 i \, d e + 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(2 i \, d f x + 2 i \, d e\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + {\left(2 \, d e \cos\left(d x + c\right) + 2 i \, d e \sin\left(d x + c\right) + 2 i \, d e\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) - {\left(2 \, d f x \cos\left(d x + c\right) + 2 i \, d f x \sin\left(d x + c\right) + 2 i \, d f x\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) + {\left(2 \, f \cos\left(d x + c\right) + 2 i \, f \sin\left(d x + c\right) + 2 i \, f\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) - {\left(2 \, f \cos\left(d x + c\right) + 2 i \, f \sin\left(d x + c\right) + 2 i \, f\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) - {\left(d f x + d e + {\left(-i \, d f x - i \, d e\right)} \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) + {\left(d f x + d e - {\left(i \, d f x + i \, d e\right)} \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) + 2 \, {\left(i \, f \cos\left(d x + c\right) - f \sin\left(d x + c\right) - f\right)} \log\left(\cos\left(d x\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(d x\right) + \sin\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right)}{-2 i \, a d^{2} \cos\left(d x + c\right) + 2 \, a d^{2} \sin\left(d x + c\right) + 2 \, a d^{2}}"," ",0,"(4*d*f*x*cos(d*x + c) + 4*I*d*f*x*sin(d*x + c) - 4*I*d*e - (4*f*cos(d*x + c) + 4*I*f*sin(d*x + c) + 4*I*f)*arctan2(cos(c) + sin(d*x), cos(d*x) + sin(c)) - (2*I*d*f*x + 2*I*d*e + 2*(d*f*x + d*e)*cos(d*x + c) + (2*I*d*f*x + 2*I*d*e)*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) + 1) + (2*d*e*cos(d*x + c) + 2*I*d*e*sin(d*x + c) + 2*I*d*e)*arctan2(sin(d*x + c), cos(d*x + c) - 1) - (2*d*f*x*cos(d*x + c) + 2*I*d*f*x*sin(d*x + c) + 2*I*d*f*x)*arctan2(sin(d*x + c), -cos(d*x + c) + 1) + (2*f*cos(d*x + c) + 2*I*f*sin(d*x + c) + 2*I*f)*dilog(-e^(I*d*x + I*c)) - (2*f*cos(d*x + c) + 2*I*f*sin(d*x + c) + 2*I*f)*dilog(e^(I*d*x + I*c)) - (d*f*x + d*e + (-I*d*f*x - I*d*e)*cos(d*x + c) + (d*f*x + d*e)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) + (d*f*x + d*e - (I*d*f*x + I*d*e)*cos(d*x + c) + (d*f*x + d*e)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) + 2*(I*f*cos(d*x + c) - f*sin(d*x + c) - f)*log(cos(d*x)^2 + cos(c)^2 + 2*cos(c)*sin(d*x) + sin(d*x)^2 + 2*cos(d*x)*sin(c) + sin(c)^2))/(-2*I*a*d^2*cos(d*x + c) + 2*a*d^2*sin(d*x + c) + 2*a*d^2)","B",0
200,1,51,0,0.625951," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{2}{a + \frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}}}{d}"," ",0,"(log(sin(d*x + c)/(cos(d*x + c) + 1))/a + 2/(a + a*sin(d*x + c)/(cos(d*x + c) + 1)))/d","A",0
201,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(csc(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,1,7587,0,9.052782," ","integrate((f*x+e)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, c e^{2} f {\left(\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d} - \frac{\sin\left(d x + c\right)}{a d {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - e^{3} {\left(\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{2 \, {\left(-24 i \, c^{2} d e f^{2} + 8 i \, c^{3} f^{3} + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3} + 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(12 i \, d^{2} e^{2} f - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(12 i \, d^{2} e^{2} f - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(24 i \, d e f^{2} - 24 i \, c f^{3}\right)} {\left(d x + c\right)} - 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(24 i \, d e f^{2} - 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(-2 i \, {\left(d x + c\right)}^{3} f^{3} - 6 i \, d^{2} e^{2} f + {\left(-6 i \, c^{2} + 12 i \, c\right)} d e f^{2} + {\left(2 i \, c^{3} - 6 i \, c^{2}\right)} f^{3} + {\left(-6 i \, d e f^{2} + {\left(6 i \, c - 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c - 12 i\right)} d e f^{2} + {\left(-6 i \, c^{2} + 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + 6 i \, d^{2} e^{2} f + {\left(6 i \, c^{2} - 12 i \, c\right)} d e f^{2} + {\left(-2 i \, c^{3} + 6 i \, c^{2}\right)} f^{3} + {\left(6 i \, d e f^{2} + {\left(-6 i \, c + 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c + 12 i\right)} d e f^{2} + {\left(6 i \, c^{2} - 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + 6 i \, d^{2} e^{2} f + {\left(6 i \, c^{2} - 12 i \, c\right)} d e f^{2} + {\left(-2 i \, c^{3} + 6 i \, c^{2}\right)} f^{3} + {\left(6 i \, d e f^{2} + {\left(-6 i \, c + 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c + 12 i\right)} d e f^{2} + {\left(6 i \, c^{2} - 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, {\left(d x + c\right)}^{3} f^{3} - 6 i \, d^{2} e^{2} f + {\left(-6 i \, c^{2} + 12 i \, c\right)} d e f^{2} + {\left(2 i \, c^{3} - 6 i \, c^{2}\right)} f^{3} + {\left(-6 i \, d e f^{2} + {\left(6 i \, c - 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c - 12 i\right)} d e f^{2} + {\left(-6 i \, c^{2} + 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + {\left(-6 i \, d^{2} e^{2} f + {\left(6 i \, c^{2} + 12 i \, c\right)} d e f^{2} + {\left(-2 i \, c^{3} - 6 i \, c^{2}\right)} f^{3} + 2 \, {\left(3 \, d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(6 i \, d^{2} e^{2} f + {\left(-6 i \, c^{2} - 12 i \, c\right)} d e f^{2} + {\left(2 i \, c^{3} + 6 i \, c^{2}\right)} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(3 \, d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \cos\left(d x + c\right) + {\left(6 i \, d^{2} e^{2} f + {\left(-6 i \, c^{2} - 12 i \, c\right)} d e f^{2} + {\left(2 i \, c^{3} + 6 i \, c^{2}\right)} f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left(3 \, d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-6 i \, d^{2} e^{2} f + {\left(6 i \, c^{2} + 12 i \, c\right)} d e f^{2} + {\left(-2 i \, c^{3} - 6 i \, c^{2}\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) + {\left(-2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-6 i \, d e f^{2} + {\left(6 i \, c + 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c + 12 i\right)} d e f^{2} + {\left(-6 i \, c^{2} - 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(6 i \, d e f^{2} + {\left(-6 i \, c - 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c - 12 i\right)} d e f^{2} + {\left(6 i \, c^{2} + 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(6 i \, d e f^{2} + {\left(-6 i \, c - 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c - 12 i\right)} d e f^{2} + {\left(6 i \, c^{2} + 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-6 i \, d e f^{2} + {\left(6 i \, c + 6 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c + 12 i\right)} d e f^{2} + {\left(-6 i \, c^{2} - 12 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - 8 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(12 i \, c^{2} d e f^{2} - 4 i \, {\left(d x + c\right)}^{3} f^{3} - 4 i \, c^{3} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, c^{2} d e f^{2} - {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} - 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} - 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(24 i \, d e f^{2} + 24 i \, {\left(d x + c\right)} f^{3} - 24 i \, c f^{3} - 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-24 i \, d e f^{2} - 24 i \, {\left(d x + c\right)} f^{3} + 24 i \, c f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) + {\left(-24 i \, d e f^{2} - 24 i \, {\left(d x + c\right)} f^{3} + 24 i \, c f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(24 i \, d e f^{2} + 24 i \, {\left(d x + c\right)} f^{3} - 24 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c + 12 i\right)} d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(6 i \, c^{2} - 12 i \, c\right)} f^{3} + {\left(12 i \, d e f^{2} + {\left(-12 i \, c + 12 i\right)} f^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} - 2 \, c\right)} f^{3} + 2 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c - 12 i\right)} d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-6 i \, c^{2} + 12 i \, c\right)} f^{3} + {\left(-12 i \, d e f^{2} + {\left(12 i \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 6 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} - 2 \, c\right)} f^{3} + 2 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c - 12 i\right)} d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-6 i \, c^{2} + 12 i \, c\right)} f^{3} + {\left(-12 i \, d e f^{2} + {\left(12 i \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 6 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} - 2 \, c\right)} f^{3} + 2 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c + 12 i\right)} d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(6 i \, c^{2} - 12 i \, c\right)} f^{3} + {\left(12 i \, d e f^{2} + {\left(-12 i \, c + 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c + 12 i\right)} d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-6 i \, c^{2} - 12 i \, c\right)} f^{3} + {\left(-12 i \, d e f^{2} + {\left(12 i \, c + 12 i\right)} f^{3}\right)} {\left(d x + c\right)} + 6 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} + 2 \, c\right)} f^{3} + 2 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c - 12 i\right)} d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(6 i \, c^{2} + 12 i \, c\right)} f^{3} + {\left(12 i \, d e f^{2} + {\left(-12 i \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 6 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} + 2 \, c\right)} f^{3} + 2 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(6 i \, d^{2} e^{2} f + {\left(-12 i \, c - 12 i\right)} d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(6 i \, c^{2} + 12 i \, c\right)} f^{3} + {\left(12 i \, d e f^{2} + {\left(-12 i \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - 6 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} + 2 \, c\right)} f^{3} + 2 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-6 i \, d^{2} e^{2} f + {\left(12 i \, c + 12 i\right)} d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-6 i \, c^{2} - 12 i \, c\right)} f^{3} + {\left(-12 i \, d e f^{2} + {\left(12 i \, c + 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) - {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)} - {\left(-i \, {\left(d x + c\right)}^{3} f^{3} - 3 i \, d^{2} e^{2} f + {\left(-3 i \, c^{2} + 6 i \, c\right)} d e f^{2} + {\left(i \, c^{3} - 3 i \, c^{2}\right)} f^{3} + {\left(-3 i \, d e f^{2} + {\left(3 i \, c - 3 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-3 i \, d^{2} e^{2} f + {\left(6 i \, c - 6 i\right)} d e f^{2} + {\left(-3 i \, c^{2} + 6 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(i \, {\left(d x + c\right)}^{3} f^{3} + 3 i \, d^{2} e^{2} f + {\left(3 i \, c^{2} - 6 i \, c\right)} d e f^{2} + {\left(-i \, c^{3} + 3 i \, c^{2}\right)} f^{3} + {\left(3 i \, d e f^{2} + {\left(-3 i \, c + 3 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 i \, d^{2} e^{2} f + {\left(-6 i \, c + 6 i\right)} d e f^{2} + {\left(3 i \, c^{2} - 6 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(i \, {\left(d x + c\right)}^{3} f^{3} + 3 i \, d^{2} e^{2} f + {\left(3 i \, c^{2} - 6 i \, c\right)} d e f^{2} + {\left(-i \, c^{3} + 3 i \, c^{2}\right)} f^{3} + {\left(3 i \, d e f^{2} + {\left(-3 i \, c + 3 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 i \, d^{2} e^{2} f + {\left(-6 i \, c + 6 i\right)} d e f^{2} + {\left(3 i \, c^{2} - 6 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 \, c\right)} d e f^{2} - {\left(c^{3} - 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c - 1\right)} d e f^{2} + {\left(c^{2} - 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) + {\left({\left(d x + c\right)}^{3} f^{3} - 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)} + {\left(i \, {\left(d x + c\right)}^{3} f^{3} - 3 i \, d^{2} e^{2} f + {\left(3 i \, c^{2} + 6 i \, c\right)} d e f^{2} + {\left(-i \, c^{3} - 3 i \, c^{2}\right)} f^{3} + {\left(3 i \, d e f^{2} + {\left(-3 i \, c - 3 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 i \, d^{2} e^{2} f + {\left(-6 i \, c - 6 i\right)} d e f^{2} + {\left(3 i \, c^{2} + 6 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(d x + c\right)}^{3} f^{3} - 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-i \, {\left(d x + c\right)}^{3} f^{3} + 3 i \, d^{2} e^{2} f + {\left(-3 i \, c^{2} - 6 i \, c\right)} d e f^{2} + {\left(i \, c^{3} + 3 i \, c^{2}\right)} f^{3} + {\left(-3 i \, d e f^{2} + {\left(3 i \, c + 3 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-3 i \, d^{2} e^{2} f + {\left(6 i \, c + 6 i\right)} d e f^{2} + {\left(-3 i \, c^{2} - 6 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left({\left(d x + c\right)}^{3} f^{3} - 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-i \, {\left(d x + c\right)}^{3} f^{3} + 3 i \, d^{2} e^{2} f + {\left(-3 i \, c^{2} - 6 i \, c\right)} d e f^{2} + {\left(i \, c^{3} + 3 i \, c^{2}\right)} f^{3} + {\left(-3 i \, d e f^{2} + {\left(3 i \, c + 3 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-3 i \, d^{2} e^{2} f + {\left(6 i \, c + 6 i\right)} d e f^{2} + {\left(-3 i \, c^{2} - 6 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(d x + c\right)}^{3} f^{3} - 3 \, d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d e f^{2} - {\left(c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, {\left(c + 1\right)} d e f^{2} + {\left(c^{2} + 2 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) - {\left(6 \, d^{2} e^{2} f - 12 \, c d e f^{2} + 6 \, {\left(d x + c\right)}^{2} f^{3} + 6 \, c^{2} f^{3} + 12 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} - 6 i \, c^{2} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + 6 i \, c^{2} f^{3} + {\left(12 i \, d e f^{2} - 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + 6 i \, c^{2} f^{3} + {\left(12 i \, d e f^{2} - 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(12 \, f^{3} \cos\left(3 \, d x + 3 \, c\right) + 12 i \, f^{3} \cos\left(2 \, d x + 2 \, c\right) - 12 \, f^{3} \cos\left(d x + c\right) + 12 i \, f^{3} \sin\left(3 \, d x + 3 \, c\right) - 12 \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 12 i \, f^{3} \sin\left(d x + c\right) - 12 i \, f^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, d x + i \, c\right)}) - {\left(12 \, f^{3} \cos\left(3 \, d x + 3 \, c\right) + 12 i \, f^{3} \cos\left(2 \, d x + 2 \, c\right) - 12 \, f^{3} \cos\left(d x + c\right) + 12 i \, f^{3} \sin\left(3 \, d x + 3 \, c\right) - 12 \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 12 i \, f^{3} \sin\left(d x + c\right) - 12 i \, f^{3}\right)} {\rm Li}_{4}(e^{\left(i \, d x + i \, c\right)}) + {\left(-24 i \, f^{3} \cos\left(3 \, d x + 3 \, c\right) + 24 \, f^{3} \cos\left(2 \, d x + 2 \, c\right) + 24 i \, f^{3} \cos\left(d x + c\right) + 24 \, f^{3} \sin\left(3 \, d x + 3 \, c\right) + 24 i \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 24 \, f^{3} \sin\left(d x + c\right) - 24 \, f^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) - {\left(12 \, d e f^{2} + 12 \, {\left(d x + c\right)} f^{3} - 12 \, {\left(c - 1\right)} f^{3} - {\left(-12 i \, d e f^{2} - 12 i \, {\left(d x + c\right)} f^{3} + {\left(12 i \, c - 12 i\right)} f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - {\left(c - 1\right)} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(12 i \, d e f^{2} + 12 i \, {\left(d x + c\right)} f^{3} + {\left(-12 i \, c + 12 i\right)} f^{3}\right)} \cos\left(d x + c\right) - 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - {\left(c - 1\right)} f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(12 i \, d e f^{2} + 12 i \, {\left(d x + c\right)} f^{3} + {\left(-12 i \, c + 12 i\right)} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - {\left(c - 1\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(-e^{\left(i \, d x + i \, c\right)}) + {\left(12 \, d e f^{2} + 12 \, {\left(d x + c\right)} f^{3} - 12 \, {\left(c + 1\right)} f^{3} + {\left(12 i \, d e f^{2} + 12 i \, {\left(d x + c\right)} f^{3} + {\left(-12 i \, c - 12 i\right)} f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) - 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - {\left(c + 1\right)} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, d e f^{2} - 12 i \, {\left(d x + c\right)} f^{3} + {\left(12 i \, c + 12 i\right)} f^{3}\right)} \cos\left(d x + c\right) - 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - {\left(c + 1\right)} f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-12 i \, d e f^{2} - 12 i \, {\left(d x + c\right)} f^{3} + {\left(12 i \, c + 12 i\right)} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - {\left(c + 1\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(e^{\left(i \, d x + i \, c\right)}) + {\left(-8 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-24 i \, d^{2} e^{2} f + 48 i \, c d e f^{2} - 24 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, {\left(3 \, c^{2} d e f^{2} - {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} - 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} - 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, c^{2} d e f^{2} + 4 i \, {\left(d x + c\right)}^{3} f^{3} + 4 i \, c^{3} f^{3} + {\left(12 i \, d e f^{2} - 12 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(12 i \, d^{2} e^{2} f - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-2 i \, a d^{3} \cos\left(3 \, d x + 3 \, c\right) + 2 \, a d^{3} \cos\left(2 \, d x + 2 \, c\right) + 2 i \, a d^{3} \cos\left(d x + c\right) + 2 \, a d^{3} \sin\left(3 \, d x + 3 \, c\right) + 2 i \, a d^{3} \sin\left(2 \, d x + 2 \, c\right) - 2 \, a d^{3} \sin\left(d x + c\right) - 2 \, a d^{3}}}{2 \, d}"," ",0,"1/2*(3*c*e^2*f*((5*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a*d*sin(d*x + c)/(cos(d*x + c) + 1) + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 2*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d) - sin(d*x + c)/(a*d*(cos(d*x + c) + 1))) - e^3*((5*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 2*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 2*(-24*I*c^2*d*e*f^2 + 8*I*c^3*f^3 + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3 + 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(3*d*x + 3*c) + (12*I*d^2*e^2*f - 24*I*c*d*e*f^2 + 12*I*c^2*f^3)*cos(2*d*x + 2*c) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (12*I*d^2*e^2*f - 24*I*c*d*e*f^2 + 12*I*c^2*f^3)*sin(3*d*x + 3*c) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(2*d*x + 2*c) + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (12*I*(d*x + c)^2*f^3 + (24*I*d*e*f^2 - 24*I*c*f^3)*(d*x + c) - 12*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (-12*I*(d*x + c)^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*cos(2*d*x + 2*c) + 12*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + (-12*I*(d*x + c)^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*sin(3*d*x + 3*c) + 12*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (12*I*(d*x + c)^2*f^3 + (24*I*d*e*f^2 - 24*I*c*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (-2*I*(d*x + c)^3*f^3 - 6*I*d^2*e^2*f + (-6*I*c^2 + 12*I*c)*d*e*f^2 + (2*I*c^3 - 6*I*c^2)*f^3 + (-6*I*d*e*f^2 + (6*I*c - 6*I)*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + (12*I*c - 12*I)*d*e*f^2 + (-6*I*c^2 + 12*I*c)*f^3)*(d*x + c) + 2*((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (2*I*(d*x + c)^3*f^3 + 6*I*d^2*e^2*f + (6*I*c^2 - 12*I*c)*d*e*f^2 + (-2*I*c^3 + 6*I*c^2)*f^3 + (6*I*d*e*f^2 + (-6*I*c + 6*I)*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f + (-12*I*c + 12*I)*d*e*f^2 + (6*I*c^2 - 12*I*c)*f^3)*(d*x + c))*cos(2*d*x + 2*c) - 2*((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^3*f^3 + 6*I*d^2*e^2*f + (6*I*c^2 - 12*I*c)*d*e*f^2 + (-2*I*c^3 + 6*I*c^2)*f^3 + (6*I*d*e*f^2 + (-6*I*c + 6*I)*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f + (-12*I*c + 12*I)*d*e*f^2 + (6*I*c^2 - 12*I*c)*f^3)*(d*x + c))*sin(3*d*x + 3*c) - 2*((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (-2*I*(d*x + c)^3*f^3 - 6*I*d^2*e^2*f + (-6*I*c^2 + 12*I*c)*d*e*f^2 + (2*I*c^3 - 6*I*c^2)*f^3 + (-6*I*d*e*f^2 + (6*I*c - 6*I)*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + (12*I*c - 12*I)*d*e*f^2 + (-6*I*c^2 + 12*I*c)*f^3)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) + 1) + (-6*I*d^2*e^2*f + (6*I*c^2 + 12*I*c)*d*e*f^2 + (-2*I*c^3 - 6*I*c^2)*f^3 + 2*(3*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3)*cos(3*d*x + 3*c) + (6*I*d^2*e^2*f + (-6*I*c^2 - 12*I*c)*d*e*f^2 + (2*I*c^3 + 6*I*c^2)*f^3)*cos(2*d*x + 2*c) - 2*(3*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3)*cos(d*x + c) + (6*I*d^2*e^2*f + (-6*I*c^2 - 12*I*c)*d*e*f^2 + (2*I*c^3 + 6*I*c^2)*f^3)*sin(3*d*x + 3*c) - 2*(3*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3)*sin(2*d*x + 2*c) + (-6*I*d^2*e^2*f + (6*I*c^2 + 12*I*c)*d*e*f^2 + (-2*I*c^3 - 6*I*c^2)*f^3)*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) - 1) + (-2*I*(d*x + c)^3*f^3 + (-6*I*d*e*f^2 + (6*I*c + 6*I)*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + (12*I*c + 12*I)*d*e*f^2 + (-6*I*c^2 - 12*I*c)*f^3)*(d*x + c) + 2*((d*x + c)^3*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (2*I*(d*x + c)^3*f^3 + (6*I*d*e*f^2 + (-6*I*c - 6*I)*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f + (-12*I*c - 12*I)*d*e*f^2 + (6*I*c^2 + 12*I*c)*f^3)*(d*x + c))*cos(2*d*x + 2*c) - 2*((d*x + c)^3*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^3*f^3 + (6*I*d*e*f^2 + (-6*I*c - 6*I)*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f + (-12*I*c - 12*I)*d*e*f^2 + (6*I*c^2 + 12*I*c)*f^3)*(d*x + c))*sin(3*d*x + 3*c) - 2*((d*x + c)^3*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (-2*I*(d*x + c)^3*f^3 + (-6*I*d*e*f^2 + (6*I*c + 6*I)*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + (12*I*c + 12*I)*d*e*f^2 + (-6*I*c^2 - 12*I*c)*f^3)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - 8*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (12*I*c^2*d*e*f^2 - 4*I*(d*x + c)^3*f^3 - 4*I*c^3*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c)^2 + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3)*(d*x + c))*cos(2*d*x + 2*c) - 4*(3*c^2*d*e*f^2 - (d*x + c)^3*f^3 - c^3*f^3 - 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 - 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(d*x + c) + (24*I*d*e*f^2 + 24*I*(d*x + c)*f^3 - 24*I*c*f^3 - 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(3*d*x + 3*c) + (-24*I*d*e*f^2 - 24*I*(d*x + c)*f^3 + 24*I*c*f^3)*cos(2*d*x + 2*c) + 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) + (-24*I*d*e*f^2 - 24*I*(d*x + c)*f^3 + 24*I*c*f^3)*sin(3*d*x + 3*c) + 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(2*d*x + 2*c) + (24*I*d*e*f^2 + 24*I*(d*x + c)*f^3 - 24*I*c*f^3)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) + (6*I*d^2*e^2*f + (-12*I*c + 12*I)*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + (6*I*c^2 - 12*I*c)*f^3 + (12*I*d*e*f^2 + (-12*I*c + 12*I)*f^3)*(d*x + c) - 6*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 - 2*c)*f^3 + 2*(d*e*f^2 - (c - 1)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (-6*I*d^2*e^2*f + (12*I*c - 12*I)*d*e*f^2 - 6*I*(d*x + c)^2*f^3 + (-6*I*c^2 + 12*I*c)*f^3 + (-12*I*d*e*f^2 + (12*I*c - 12*I)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + 6*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 - 2*c)*f^3 + 2*(d*e*f^2 - (c - 1)*f^3)*(d*x + c))*cos(d*x + c) + (-6*I*d^2*e^2*f + (12*I*c - 12*I)*d*e*f^2 - 6*I*(d*x + c)^2*f^3 + (-6*I*c^2 + 12*I*c)*f^3 + (-12*I*d*e*f^2 + (12*I*c - 12*I)*f^3)*(d*x + c))*sin(3*d*x + 3*c) + 6*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 - 2*c)*f^3 + 2*(d*e*f^2 - (c - 1)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (6*I*d^2*e^2*f + (-12*I*c + 12*I)*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + (6*I*c^2 - 12*I*c)*f^3 + (12*I*d*e*f^2 + (-12*I*c + 12*I)*f^3)*(d*x + c))*sin(d*x + c))*dilog(-e^(I*d*x + I*c)) + (-6*I*d^2*e^2*f + (12*I*c + 12*I)*d*e*f^2 - 6*I*(d*x + c)^2*f^3 + (-6*I*c^2 - 12*I*c)*f^3 + (-12*I*d*e*f^2 + (12*I*c + 12*I)*f^3)*(d*x + c) + 6*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 + 2*c)*f^3 + 2*(d*e*f^2 - (c + 1)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (6*I*d^2*e^2*f + (-12*I*c - 12*I)*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + (6*I*c^2 + 12*I*c)*f^3 + (12*I*d*e*f^2 + (-12*I*c - 12*I)*f^3)*(d*x + c))*cos(2*d*x + 2*c) - 6*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 + 2*c)*f^3 + 2*(d*e*f^2 - (c + 1)*f^3)*(d*x + c))*cos(d*x + c) + (6*I*d^2*e^2*f + (-12*I*c - 12*I)*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + (6*I*c^2 + 12*I*c)*f^3 + (12*I*d*e*f^2 + (-12*I*c - 12*I)*f^3)*(d*x + c))*sin(3*d*x + 3*c) - 6*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 + 2*c)*f^3 + 2*(d*e*f^2 - (c + 1)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (-6*I*d^2*e^2*f + (12*I*c + 12*I)*d*e*f^2 - 6*I*(d*x + c)^2*f^3 + (-6*I*c^2 - 12*I*c)*f^3 + (-12*I*d*e*f^2 + (12*I*c + 12*I)*f^3)*(d*x + c))*sin(d*x + c))*dilog(e^(I*d*x + I*c)) - ((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c) - (-I*(d*x + c)^3*f^3 - 3*I*d^2*e^2*f + (-3*I*c^2 + 6*I*c)*d*e*f^2 + (I*c^3 - 3*I*c^2)*f^3 + (-3*I*d*e*f^2 + (3*I*c - 3*I)*f^3)*(d*x + c)^2 + (-3*I*d^2*e^2*f + (6*I*c - 6*I)*d*e*f^2 + (-3*I*c^2 + 6*I*c)*f^3)*(d*x + c))*cos(3*d*x + 3*c) - ((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c))*cos(2*d*x + 2*c) - (I*(d*x + c)^3*f^3 + 3*I*d^2*e^2*f + (3*I*c^2 - 6*I*c)*d*e*f^2 + (-I*c^3 + 3*I*c^2)*f^3 + (3*I*d*e*f^2 + (-3*I*c + 3*I)*f^3)*(d*x + c)^2 + (3*I*d^2*e^2*f + (-6*I*c + 6*I)*d*e*f^2 + (3*I*c^2 - 6*I*c)*f^3)*(d*x + c))*cos(d*x + c) - ((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c))*sin(3*d*x + 3*c) - (I*(d*x + c)^3*f^3 + 3*I*d^2*e^2*f + (3*I*c^2 - 6*I*c)*d*e*f^2 + (-I*c^3 + 3*I*c^2)*f^3 + (3*I*d*e*f^2 + (-3*I*c + 3*I)*f^3)*(d*x + c)^2 + (3*I*d^2*e^2*f + (-6*I*c + 6*I)*d*e*f^2 + (3*I*c^2 - 6*I*c)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + ((d*x + c)^3*f^3 + 3*d^2*e^2*f + 3*(c^2 - 2*c)*d*e*f^2 - (c^3 - 3*c^2)*f^3 + 3*(d*e*f^2 - (c - 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c - 1)*d*e*f^2 + (c^2 - 2*c)*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) + ((d*x + c)^3*f^3 - 3*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c) + (I*(d*x + c)^3*f^3 - 3*I*d^2*e^2*f + (3*I*c^2 + 6*I*c)*d*e*f^2 + (-I*c^3 - 3*I*c^2)*f^3 + (3*I*d*e*f^2 + (-3*I*c - 3*I)*f^3)*(d*x + c)^2 + (3*I*d^2*e^2*f + (-6*I*c - 6*I)*d*e*f^2 + (3*I*c^2 + 6*I*c)*f^3)*(d*x + c))*cos(3*d*x + 3*c) - ((d*x + c)^3*f^3 - 3*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-I*(d*x + c)^3*f^3 + 3*I*d^2*e^2*f + (-3*I*c^2 - 6*I*c)*d*e*f^2 + (I*c^3 + 3*I*c^2)*f^3 + (-3*I*d*e*f^2 + (3*I*c + 3*I)*f^3)*(d*x + c)^2 + (-3*I*d^2*e^2*f + (6*I*c + 6*I)*d*e*f^2 + (-3*I*c^2 - 6*I*c)*f^3)*(d*x + c))*cos(d*x + c) - ((d*x + c)^3*f^3 - 3*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (-I*(d*x + c)^3*f^3 + 3*I*d^2*e^2*f + (-3*I*c^2 - 6*I*c)*d*e*f^2 + (I*c^3 + 3*I*c^2)*f^3 + (-3*I*d*e*f^2 + (3*I*c + 3*I)*f^3)*(d*x + c)^2 + (-3*I*d^2*e^2*f + (6*I*c + 6*I)*d*e*f^2 + (-3*I*c^2 - 6*I*c)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + ((d*x + c)^3*f^3 - 3*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 + 3*(d*e*f^2 - (c + 1)*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*(c + 1)*d*e*f^2 + (c^2 + 2*c)*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) - (6*d^2*e^2*f - 12*c*d*e*f^2 + 6*(d*x + c)^2*f^3 + 6*c^2*f^3 + 12*(d*e*f^2 - c*f^3)*(d*x + c) - (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*(d*x + c)^2*f^3 - 6*I*c^2*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c))*cos(3*d*x + 3*c) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(2*d*x + 2*c) - (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + 6*I*c^2*f^3 + (12*I*d*e*f^2 - 12*I*c*f^3)*(d*x + c))*cos(d*x + c) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(3*d*x + 3*c) - (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + 6*I*c^2*f^3 + (12*I*d*e*f^2 - 12*I*c*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (12*f^3*cos(3*d*x + 3*c) + 12*I*f^3*cos(2*d*x + 2*c) - 12*f^3*cos(d*x + c) + 12*I*f^3*sin(3*d*x + 3*c) - 12*f^3*sin(2*d*x + 2*c) - 12*I*f^3*sin(d*x + c) - 12*I*f^3)*polylog(4, -e^(I*d*x + I*c)) - (12*f^3*cos(3*d*x + 3*c) + 12*I*f^3*cos(2*d*x + 2*c) - 12*f^3*cos(d*x + c) + 12*I*f^3*sin(3*d*x + 3*c) - 12*f^3*sin(2*d*x + 2*c) - 12*I*f^3*sin(d*x + c) - 12*I*f^3)*polylog(4, e^(I*d*x + I*c)) + (-24*I*f^3*cos(3*d*x + 3*c) + 24*f^3*cos(2*d*x + 2*c) + 24*I*f^3*cos(d*x + c) + 24*f^3*sin(3*d*x + 3*c) + 24*I*f^3*sin(2*d*x + 2*c) - 24*f^3*sin(d*x + c) - 24*f^3)*polylog(3, I*e^(I*d*x + I*c)) - (12*d*e*f^2 + 12*(d*x + c)*f^3 - 12*(c - 1)*f^3 - (-12*I*d*e*f^2 - 12*I*(d*x + c)*f^3 + (12*I*c - 12*I)*f^3)*cos(3*d*x + 3*c) - 12*(d*e*f^2 + (d*x + c)*f^3 - (c - 1)*f^3)*cos(2*d*x + 2*c) - (12*I*d*e*f^2 + 12*I*(d*x + c)*f^3 + (-12*I*c + 12*I)*f^3)*cos(d*x + c) - 12*(d*e*f^2 + (d*x + c)*f^3 - (c - 1)*f^3)*sin(3*d*x + 3*c) - (12*I*d*e*f^2 + 12*I*(d*x + c)*f^3 + (-12*I*c + 12*I)*f^3)*sin(2*d*x + 2*c) + 12*(d*e*f^2 + (d*x + c)*f^3 - (c - 1)*f^3)*sin(d*x + c))*polylog(3, -e^(I*d*x + I*c)) + (12*d*e*f^2 + 12*(d*x + c)*f^3 - 12*(c + 1)*f^3 + (12*I*d*e*f^2 + 12*I*(d*x + c)*f^3 + (-12*I*c - 12*I)*f^3)*cos(3*d*x + 3*c) - 12*(d*e*f^2 + (d*x + c)*f^3 - (c + 1)*f^3)*cos(2*d*x + 2*c) + (-12*I*d*e*f^2 - 12*I*(d*x + c)*f^3 + (12*I*c + 12*I)*f^3)*cos(d*x + c) - 12*(d*e*f^2 + (d*x + c)*f^3 - (c + 1)*f^3)*sin(3*d*x + 3*c) + (-12*I*d*e*f^2 - 12*I*(d*x + c)*f^3 + (12*I*c + 12*I)*f^3)*sin(2*d*x + 2*c) + 12*(d*e*f^2 + (d*x + c)*f^3 - (c + 1)*f^3)*sin(d*x + c))*polylog(3, e^(I*d*x + I*c)) + (-8*I*(d*x + c)^3*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c)^2 + (-24*I*d^2*e^2*f + 48*I*c*d*e*f^2 - 24*I*c^2*f^3)*(d*x + c))*sin(3*d*x + 3*c) - 4*(3*c^2*d*e*f^2 - (d*x + c)^3*f^3 - c^3*f^3 - 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 - 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (-12*I*c^2*d*e*f^2 + 4*I*(d*x + c)^3*f^3 + 4*I*c^3*f^3 + (12*I*d*e*f^2 - 12*I*c*f^3)*(d*x + c)^2 + (12*I*d^2*e^2*f - 24*I*c*d*e*f^2 + 12*I*c^2*f^3)*(d*x + c))*sin(d*x + c))/(-2*I*a*d^3*cos(3*d*x + 3*c) + 2*a*d^3*cos(2*d*x + 2*c) + 2*I*a*d^3*cos(d*x + c) + 2*a*d^3*sin(3*d*x + 3*c) + 2*I*a*d^3*sin(2*d*x + 2*c) - 2*a*d^3*sin(d*x + c) - 2*a*d^3))/d","B",0
204,1,3706,0,3.431197," ","integrate((f*x+e)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, c e f {\left(\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d} - \frac{\sin\left(d x + c\right)}{a d {\left(\cos\left(d x + c\right) + 1\right)}}\right)} - e^{2} {\left(\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}\right)} + \frac{2 \, {\left(-8 i \, c^{2} f^{2} + {\left(-8 i \, d e f + 8 i \, c f^{2} + 8 \, {\left(d e f - c f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(8 i \, d e f - 8 i \, c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 8 \, {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(8 i \, d e f - 8 i \, c f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - 8 \, {\left(d e f - c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(8 \, {\left(d x + c\right)} f^{2} \cos\left(3 \, d x + 3 \, c\right) + 8 i \, {\left(d x + c\right)} f^{2} \cos\left(2 \, d x + 2 \, c\right) - 8 \, {\left(d x + c\right)} f^{2} \cos\left(d x + c\right) + 8 i \, {\left(d x + c\right)} f^{2} \sin\left(3 \, d x + 3 \, c\right) - 8 \, {\left(d x + c\right)} f^{2} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, {\left(d x + c\right)} f^{2} \sin\left(d x + c\right) - 8 i \, {\left(d x + c\right)} f^{2}\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, d e f + {\left(-2 i \, c^{2} + 4 i \, c\right)} f^{2} + {\left(-4 i \, d e f + {\left(4 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + 4 i \, d e f + {\left(2 i \, c^{2} - 4 i \, c\right)} f^{2} + {\left(4 i \, d e f + {\left(-4 i \, c + 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + 4 i \, d e f + {\left(2 i \, c^{2} - 4 i \, c\right)} f^{2} + {\left(4 i \, d e f + {\left(-4 i \, c + 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, d e f + {\left(-2 i \, c^{2} + 4 i \, c\right)} f^{2} + {\left(-4 i \, d e f + {\left(4 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + {\left(-4 i \, d e f + {\left(2 i \, c^{2} + 4 i \, c\right)} f^{2} + 2 \, {\left(2 \, d e f - {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(4 i \, d e f + {\left(-2 i \, c^{2} - 4 i \, c\right)} f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(2 \, d e f - {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(4 i \, d e f + {\left(-2 i \, c^{2} - 4 i \, c\right)} f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left(2 \, d e f - {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-4 i \, d e f + {\left(2 i \, c^{2} + 4 i \, c\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-4 i \, d e f + {\left(4 i \, c + 4 i\right)} f^{2}\right)} {\left(d x + c\right)} + 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(4 i \, d e f + {\left(-4 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(4 i \, d e f + {\left(-4 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-4 i \, d e f + {\left(4 i \, c + 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - 8 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-4 i \, {\left(d x + c\right)}^{2} f^{2} + 4 i \, c^{2} f^{2} + {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left({\left(d x + c\right)}^{2} f^{2} - c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(8 \, f^{2} \cos\left(3 \, d x + 3 \, c\right) + 8 i \, f^{2} \cos\left(2 \, d x + 2 \, c\right) - 8 \, f^{2} \cos\left(d x + c\right) + 8 i \, f^{2} \sin\left(3 \, d x + 3 \, c\right) - 8 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, f^{2} \sin\left(d x + c\right) - 8 i \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} + {\left(-4 i \, c + 4 i\right)} f^{2} - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - {\left(c - 1\right)} f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + {\left(4 i \, c - 4 i\right)} f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - {\left(c - 1\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + {\left(4 i \, c - 4 i\right)} f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - {\left(c - 1\right)} f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} + {\left(-4 i \, c + 4 i\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + {\left(4 i \, c + 4 i\right)} f^{2} + 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - {\left(c + 1\right)} f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} + {\left(-4 i \, c - 4 i\right)} f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - {\left(c + 1\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} + {\left(-4 i \, c - 4 i\right)} f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - {\left(c + 1\right)} f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + {\left(4 i \, c + 4 i\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) - {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)} - {\left(-i \, {\left(d x + c\right)}^{2} f^{2} - 2 i \, d e f + {\left(-i \, c^{2} + 2 i \, c\right)} f^{2} + {\left(-2 i \, d e f + {\left(2 i \, c - 2 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(i \, {\left(d x + c\right)}^{2} f^{2} + 2 i \, d e f + {\left(i \, c^{2} - 2 i \, c\right)} f^{2} + {\left(2 i \, d e f + {\left(-2 i \, c + 2 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(i \, {\left(d x + c\right)}^{2} f^{2} + 2 i \, d e f + {\left(i \, c^{2} - 2 i \, c\right)} f^{2} + {\left(2 i \, d e f + {\left(-2 i \, c + 2 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, d e f + {\left(c^{2} - 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) + {\left({\left(d x + c\right)}^{2} f^{2} - 2 \, d e f + {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)} + {\left(i \, {\left(d x + c\right)}^{2} f^{2} - 2 i \, d e f + {\left(i \, c^{2} + 2 i \, c\right)} f^{2} + {\left(2 i \, d e f + {\left(-2 i \, c - 2 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left({\left(d x + c\right)}^{2} f^{2} - 2 \, d e f + {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-i \, {\left(d x + c\right)}^{2} f^{2} + 2 i \, d e f + {\left(-i \, c^{2} - 2 i \, c\right)} f^{2} + {\left(-2 i \, d e f + {\left(2 i \, c + 2 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left({\left(d x + c\right)}^{2} f^{2} - 2 \, d e f + {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-i \, {\left(d x + c\right)}^{2} f^{2} + 2 i \, d e f + {\left(-i \, c^{2} - 2 i \, c\right)} f^{2} + {\left(-2 i \, d e f + {\left(2 i \, c + 2 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left({\left(d x + c\right)}^{2} f^{2} - 2 \, d e f + {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d e f - {\left(c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) - {\left(4 \, d e f + 4 \, {\left(d x + c\right)} f^{2} - 4 \, c f^{2} - {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + 4 i \, c f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} - 4 i \, c f^{2}\right)} \cos\left(d x + c\right) - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} - 4 i \, c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(-4 i \, f^{2} \cos\left(3 \, d x + 3 \, c\right) + 4 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 i \, f^{2} \cos\left(d x + c\right) + 4 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) + 4 i \, f^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, f^{2} \sin\left(d x + c\right) - 4 \, f^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, d x + i \, c\right)}) + {\left(4 i \, f^{2} \cos\left(3 \, d x + 3 \, c\right) - 4 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) - 4 i \, f^{2} \cos\left(d x + c\right) - 4 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) - 4 i \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, f^{2} \sin\left(d x + c\right) + 4 \, f^{2}\right)} {\rm Li}_{3}(e^{\left(i \, d x + i \, c\right)}) + {\left(-8 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-16 i \, d e f + 16 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left({\left(d x + c\right)}^{2} f^{2} - c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(4 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, c^{2} f^{2} + {\left(8 i \, d e f - 8 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-2 i \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) + 2 \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 i \, a d^{2} \cos\left(d x + c\right) + 2 \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) + 2 i \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) - 2 \, a d^{2} \sin\left(d x + c\right) - 2 \, a d^{2}}}{2 \, d}"," ",0,"1/2*(2*c*e*f*((5*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a*d*sin(d*x + c)/(cos(d*x + c) + 1) + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 2*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d) - sin(d*x + c)/(a*d*(cos(d*x + c) + 1))) - e^2*((5*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 2*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1))) + 2*(-8*I*c^2*f^2 + (-8*I*d*e*f + 8*I*c*f^2 + 8*(d*e*f - c*f^2)*cos(3*d*x + 3*c) + (8*I*d*e*f - 8*I*c*f^2)*cos(2*d*x + 2*c) - 8*(d*e*f - c*f^2)*cos(d*x + c) + (8*I*d*e*f - 8*I*c*f^2)*sin(3*d*x + 3*c) - 8*(d*e*f - c*f^2)*sin(2*d*x + 2*c) + (-8*I*d*e*f + 8*I*c*f^2)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (8*(d*x + c)*f^2*cos(3*d*x + 3*c) + 8*I*(d*x + c)*f^2*cos(2*d*x + 2*c) - 8*(d*x + c)*f^2*cos(d*x + c) + 8*I*(d*x + c)*f^2*sin(3*d*x + 3*c) - 8*(d*x + c)*f^2*sin(2*d*x + 2*c) - 8*I*(d*x + c)*f^2*sin(d*x + c) - 8*I*(d*x + c)*f^2)*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (-2*I*(d*x + c)^2*f^2 - 4*I*d*e*f + (-2*I*c^2 + 4*I*c)*f^2 + (-4*I*d*e*f + (4*I*c - 4*I)*f^2)*(d*x + c) + 2*((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (2*I*(d*x + c)^2*f^2 + 4*I*d*e*f + (2*I*c^2 - 4*I*c)*f^2 + (4*I*d*e*f + (-4*I*c + 4*I)*f^2)*(d*x + c))*cos(2*d*x + 2*c) - 2*((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^2*f^2 + 4*I*d*e*f + (2*I*c^2 - 4*I*c)*f^2 + (4*I*d*e*f + (-4*I*c + 4*I)*f^2)*(d*x + c))*sin(3*d*x + 3*c) - 2*((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (-2*I*(d*x + c)^2*f^2 - 4*I*d*e*f + (-2*I*c^2 + 4*I*c)*f^2 + (-4*I*d*e*f + (4*I*c - 4*I)*f^2)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) + 1) + (-4*I*d*e*f + (2*I*c^2 + 4*I*c)*f^2 + 2*(2*d*e*f - (c^2 + 2*c)*f^2)*cos(3*d*x + 3*c) + (4*I*d*e*f + (-2*I*c^2 - 4*I*c)*f^2)*cos(2*d*x + 2*c) - 2*(2*d*e*f - (c^2 + 2*c)*f^2)*cos(d*x + c) + (4*I*d*e*f + (-2*I*c^2 - 4*I*c)*f^2)*sin(3*d*x + 3*c) - 2*(2*d*e*f - (c^2 + 2*c)*f^2)*sin(2*d*x + 2*c) + (-4*I*d*e*f + (2*I*c^2 + 4*I*c)*f^2)*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) - 1) + (-2*I*(d*x + c)^2*f^2 + (-4*I*d*e*f + (4*I*c + 4*I)*f^2)*(d*x + c) + 2*((d*x + c)^2*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (2*I*(d*x + c)^2*f^2 + (4*I*d*e*f + (-4*I*c - 4*I)*f^2)*(d*x + c))*cos(2*d*x + 2*c) - 2*((d*x + c)^2*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c))*cos(d*x + c) + (2*I*(d*x + c)^2*f^2 + (4*I*d*e*f + (-4*I*c - 4*I)*f^2)*(d*x + c))*sin(3*d*x + 3*c) - 2*((d*x + c)^2*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (-2*I*(d*x + c)^2*f^2 + (-4*I*d*e*f + (4*I*c + 4*I)*f^2)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - 8*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (-4*I*(d*x + c)^2*f^2 + 4*I*c^2*f^2 + (-8*I*d*e*f + 8*I*c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + 4*((d*x + c)^2*f^2 - c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) - (8*f^2*cos(3*d*x + 3*c) + 8*I*f^2*cos(2*d*x + 2*c) - 8*f^2*cos(d*x + c) + 8*I*f^2*sin(3*d*x + 3*c) - 8*f^2*sin(2*d*x + 2*c) - 8*I*f^2*sin(d*x + c) - 8*I*f^2)*dilog(I*e^(I*d*x + I*c)) + (4*I*d*e*f + 4*I*(d*x + c)*f^2 + (-4*I*c + 4*I)*f^2 - 4*(d*e*f + (d*x + c)*f^2 - (c - 1)*f^2)*cos(3*d*x + 3*c) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + (4*I*c - 4*I)*f^2)*cos(2*d*x + 2*c) + 4*(d*e*f + (d*x + c)*f^2 - (c - 1)*f^2)*cos(d*x + c) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + (4*I*c - 4*I)*f^2)*sin(3*d*x + 3*c) + 4*(d*e*f + (d*x + c)*f^2 - (c - 1)*f^2)*sin(2*d*x + 2*c) + (4*I*d*e*f + 4*I*(d*x + c)*f^2 + (-4*I*c + 4*I)*f^2)*sin(d*x + c))*dilog(-e^(I*d*x + I*c)) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + (4*I*c + 4*I)*f^2 + 4*(d*e*f + (d*x + c)*f^2 - (c + 1)*f^2)*cos(3*d*x + 3*c) + (4*I*d*e*f + 4*I*(d*x + c)*f^2 + (-4*I*c - 4*I)*f^2)*cos(2*d*x + 2*c) - 4*(d*e*f + (d*x + c)*f^2 - (c + 1)*f^2)*cos(d*x + c) + (4*I*d*e*f + 4*I*(d*x + c)*f^2 + (-4*I*c - 4*I)*f^2)*sin(3*d*x + 3*c) - 4*(d*e*f + (d*x + c)*f^2 - (c + 1)*f^2)*sin(2*d*x + 2*c) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + (4*I*c + 4*I)*f^2)*sin(d*x + c))*dilog(e^(I*d*x + I*c)) - ((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c) - (-I*(d*x + c)^2*f^2 - 2*I*d*e*f + (-I*c^2 + 2*I*c)*f^2 + (-2*I*d*e*f + (2*I*c - 2*I)*f^2)*(d*x + c))*cos(3*d*x + 3*c) - ((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c))*cos(2*d*x + 2*c) - (I*(d*x + c)^2*f^2 + 2*I*d*e*f + (I*c^2 - 2*I*c)*f^2 + (2*I*d*e*f + (-2*I*c + 2*I)*f^2)*(d*x + c))*cos(d*x + c) - ((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c))*sin(3*d*x + 3*c) - (I*(d*x + c)^2*f^2 + 2*I*d*e*f + (I*c^2 - 2*I*c)*f^2 + (2*I*d*e*f + (-2*I*c + 2*I)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + ((d*x + c)^2*f^2 + 2*d*e*f + (c^2 - 2*c)*f^2 + 2*(d*e*f - (c - 1)*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) + ((d*x + c)^2*f^2 - 2*d*e*f + (c^2 + 2*c)*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c) + (I*(d*x + c)^2*f^2 - 2*I*d*e*f + (I*c^2 + 2*I*c)*f^2 + (2*I*d*e*f + (-2*I*c - 2*I)*f^2)*(d*x + c))*cos(3*d*x + 3*c) - ((d*x + c)^2*f^2 - 2*d*e*f + (c^2 + 2*c)*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (-I*(d*x + c)^2*f^2 + 2*I*d*e*f + (-I*c^2 - 2*I*c)*f^2 + (-2*I*d*e*f + (2*I*c + 2*I)*f^2)*(d*x + c))*cos(d*x + c) - ((d*x + c)^2*f^2 - 2*d*e*f + (c^2 + 2*c)*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c))*sin(3*d*x + 3*c) + (-I*(d*x + c)^2*f^2 + 2*I*d*e*f + (-I*c^2 - 2*I*c)*f^2 + (-2*I*d*e*f + (2*I*c + 2*I)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + ((d*x + c)^2*f^2 - 2*d*e*f + (c^2 + 2*c)*f^2 + 2*(d*e*f - (c + 1)*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) - (4*d*e*f + 4*(d*x + c)*f^2 - 4*c*f^2 - (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + 4*I*c*f^2)*cos(3*d*x + 3*c) - 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(2*d*x + 2*c) - (4*I*d*e*f + 4*I*(d*x + c)*f^2 - 4*I*c*f^2)*cos(d*x + c) - 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(3*d*x + 3*c) - (4*I*d*e*f + 4*I*(d*x + c)*f^2 - 4*I*c*f^2)*sin(2*d*x + 2*c) + 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (-4*I*f^2*cos(3*d*x + 3*c) + 4*f^2*cos(2*d*x + 2*c) + 4*I*f^2*cos(d*x + c) + 4*f^2*sin(3*d*x + 3*c) + 4*I*f^2*sin(2*d*x + 2*c) - 4*f^2*sin(d*x + c) - 4*f^2)*polylog(3, -e^(I*d*x + I*c)) + (4*I*f^2*cos(3*d*x + 3*c) - 4*f^2*cos(2*d*x + 2*c) - 4*I*f^2*cos(d*x + c) - 4*f^2*sin(3*d*x + 3*c) - 4*I*f^2*sin(2*d*x + 2*c) + 4*f^2*sin(d*x + c) + 4*f^2)*polylog(3, e^(I*d*x + I*c)) + (-8*I*(d*x + c)^2*f^2 + (-16*I*d*e*f + 16*I*c*f^2)*(d*x + c))*sin(3*d*x + 3*c) + 4*((d*x + c)^2*f^2 - c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (4*I*(d*x + c)^2*f^2 - 4*I*c^2*f^2 + (8*I*d*e*f - 8*I*c*f^2)*(d*x + c))*sin(d*x + c))/(-2*I*a*d^2*cos(3*d*x + 3*c) + 2*a*d^2*cos(2*d*x + 2*c) + 2*I*a*d^2*cos(d*x + c) + 2*a*d^2*sin(3*d*x + 3*c) + 2*I*a*d^2*sin(2*d*x + 2*c) - 2*a*d^2*sin(d*x + c) - 2*a*d^2))/d","B",0
205,1,1279,0,0.901794," ","integrate((f*x+e)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, d f x \cos\left(3 \, d x + 3 \, c\right) + 8 i \, d f x \sin\left(3 \, d x + 3 \, c\right) + 8 i \, d e - {\left(4 \, f \cos\left(3 \, d x + 3 \, c\right) + 4 i \, f \cos\left(2 \, d x + 2 \, c\right) - 4 \, f \cos\left(d x + c\right) + 4 i \, f \sin\left(3 \, d x + 3 \, c\right) - 4 \, f \sin\left(2 \, d x + 2 \, c\right) - 4 i \, f \sin\left(d x + c\right) - 4 i \, f\right)} \arctan\left(\cos\left(c\right) + \sin\left(d x\right), \cos\left(d x\right) + \sin\left(c\right)\right) - {\left(-2 i \, d f x - 2 i \, d e + 2 \, {\left(d f x + d e + f\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(2 i \, d f x + 2 i \, d e + 2 i \, f\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(d f x + d e + f\right)} \cos\left(d x + c\right) + {\left(2 i \, d f x + 2 i \, d e + 2 i \, f\right)} \sin\left(3 \, d x + 3 \, c\right) - 2 \, {\left(d f x + d e + f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, d f x - 2 i \, d e - 2 i \, f\right)} \sin\left(d x + c\right) - 2 i \, f\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - {\left(2 i \, d e - 2 \, {\left(d e - f\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-2 i \, d e + 2 i \, f\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(d e - f\right)} \cos\left(d x + c\right) + {\left(-2 i \, d e + 2 i \, f\right)} \sin\left(3 \, d x + 3 \, c\right) + 2 \, {\left(d e - f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(2 i \, d e - 2 i \, f\right)} \sin\left(d x + c\right) - 2 i \, f\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) - {\left(2 \, d f x \cos\left(3 \, d x + 3 \, c\right) + 2 i \, d f x \cos\left(2 \, d x + 2 \, c\right) - 2 \, d f x \cos\left(d x + c\right) + 2 i \, d f x \sin\left(3 \, d x + 3 \, c\right) - 2 \, d f x \sin\left(2 \, d x + 2 \, c\right) - 2 i \, d f x \sin\left(d x + c\right) - 2 i \, d f x\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - {\left(-4 i \, d f x + 4 i \, d e\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(d f x - d e\right)} \cos\left(d x + c\right) + {\left(2 \, f \cos\left(3 \, d x + 3 \, c\right) + 2 i \, f \cos\left(2 \, d x + 2 \, c\right) - 2 \, f \cos\left(d x + c\right) + 2 i \, f \sin\left(3 \, d x + 3 \, c\right) - 2 \, f \sin\left(2 \, d x + 2 \, c\right) - 2 i \, f \sin\left(d x + c\right) - 2 i \, f\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) - {\left(2 \, f \cos\left(3 \, d x + 3 \, c\right) + 2 i \, f \cos\left(2 \, d x + 2 \, c\right) - 2 \, f \cos\left(d x + c\right) + 2 i \, f \sin\left(3 \, d x + 3 \, c\right) - 2 \, f \sin\left(2 \, d x + 2 \, c\right) - 2 i \, f \sin\left(d x + c\right) - 2 i \, f\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) + {\left(d f x + d e - {\left(-i \, d f x - i \, d e - i \, f\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(d f x + d e + f\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(i \, d f x + i \, d e + i \, f\right)} \cos\left(d x + c\right) - {\left(d f x + d e + f\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(i \, d f x + i \, d e + i \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(d f x + d e + f\right)} \sin\left(d x + c\right) + f\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) - {\left(d f x + d e + {\left(i \, d f x + i \, d e - i \, f\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(d f x + d e - f\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-i \, d f x - i \, d e + i \, f\right)} \cos\left(d x + c\right) - {\left(d f x + d e - f\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-i \, d f x - i \, d e + i \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(d f x + d e - f\right)} \sin\left(d x + c\right) - f\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) - {\left(-2 i \, f \cos\left(3 \, d x + 3 \, c\right) + 2 \, f \cos\left(2 \, d x + 2 \, c\right) + 2 i \, f \cos\left(d x + c\right) + 2 \, f \sin\left(3 \, d x + 3 \, c\right) + 2 i \, f \sin\left(2 \, d x + 2 \, c\right) - 2 \, f \sin\left(d x + c\right) - 2 \, f\right)} \log\left(\cos\left(d x\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(d x\right) + \sin\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - 4 \, {\left(d f x - d e\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(4 i \, d f x - 4 i \, d e\right)} \sin\left(d x + c\right)}{-2 i \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) + 2 \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 i \, a d^{2} \cos\left(d x + c\right) + 2 \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) + 2 i \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) - 2 \, a d^{2} \sin\left(d x + c\right) - 2 \, a d^{2}}"," ",0,"-(8*d*f*x*cos(3*d*x + 3*c) + 8*I*d*f*x*sin(3*d*x + 3*c) + 8*I*d*e - (4*f*cos(3*d*x + 3*c) + 4*I*f*cos(2*d*x + 2*c) - 4*f*cos(d*x + c) + 4*I*f*sin(3*d*x + 3*c) - 4*f*sin(2*d*x + 2*c) - 4*I*f*sin(d*x + c) - 4*I*f)*arctan2(cos(c) + sin(d*x), cos(d*x) + sin(c)) - (-2*I*d*f*x - 2*I*d*e + 2*(d*f*x + d*e + f)*cos(3*d*x + 3*c) + (2*I*d*f*x + 2*I*d*e + 2*I*f)*cos(2*d*x + 2*c) - 2*(d*f*x + d*e + f)*cos(d*x + c) + (2*I*d*f*x + 2*I*d*e + 2*I*f)*sin(3*d*x + 3*c) - 2*(d*f*x + d*e + f)*sin(2*d*x + 2*c) + (-2*I*d*f*x - 2*I*d*e - 2*I*f)*sin(d*x + c) - 2*I*f)*arctan2(sin(d*x + c), cos(d*x + c) + 1) - (2*I*d*e - 2*(d*e - f)*cos(3*d*x + 3*c) + (-2*I*d*e + 2*I*f)*cos(2*d*x + 2*c) + 2*(d*e - f)*cos(d*x + c) + (-2*I*d*e + 2*I*f)*sin(3*d*x + 3*c) + 2*(d*e - f)*sin(2*d*x + 2*c) + (2*I*d*e - 2*I*f)*sin(d*x + c) - 2*I*f)*arctan2(sin(d*x + c), cos(d*x + c) - 1) - (2*d*f*x*cos(3*d*x + 3*c) + 2*I*d*f*x*cos(2*d*x + 2*c) - 2*d*f*x*cos(d*x + c) + 2*I*d*f*x*sin(3*d*x + 3*c) - 2*d*f*x*sin(2*d*x + 2*c) - 2*I*d*f*x*sin(d*x + c) - 2*I*d*f*x)*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - (-4*I*d*f*x + 4*I*d*e)*cos(2*d*x + 2*c) - 4*(d*f*x - d*e)*cos(d*x + c) + (2*f*cos(3*d*x + 3*c) + 2*I*f*cos(2*d*x + 2*c) - 2*f*cos(d*x + c) + 2*I*f*sin(3*d*x + 3*c) - 2*f*sin(2*d*x + 2*c) - 2*I*f*sin(d*x + c) - 2*I*f)*dilog(-e^(I*d*x + I*c)) - (2*f*cos(3*d*x + 3*c) + 2*I*f*cos(2*d*x + 2*c) - 2*f*cos(d*x + c) + 2*I*f*sin(3*d*x + 3*c) - 2*f*sin(2*d*x + 2*c) - 2*I*f*sin(d*x + c) - 2*I*f)*dilog(e^(I*d*x + I*c)) + (d*f*x + d*e - (-I*d*f*x - I*d*e - I*f)*cos(3*d*x + 3*c) - (d*f*x + d*e + f)*cos(2*d*x + 2*c) - (I*d*f*x + I*d*e + I*f)*cos(d*x + c) - (d*f*x + d*e + f)*sin(3*d*x + 3*c) - (I*d*f*x + I*d*e + I*f)*sin(2*d*x + 2*c) + (d*f*x + d*e + f)*sin(d*x + c) + f)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) - (d*f*x + d*e + (I*d*f*x + I*d*e - I*f)*cos(3*d*x + 3*c) - (d*f*x + d*e - f)*cos(2*d*x + 2*c) + (-I*d*f*x - I*d*e + I*f)*cos(d*x + c) - (d*f*x + d*e - f)*sin(3*d*x + 3*c) + (-I*d*f*x - I*d*e + I*f)*sin(2*d*x + 2*c) + (d*f*x + d*e - f)*sin(d*x + c) - f)*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) - (-2*I*f*cos(3*d*x + 3*c) + 2*f*cos(2*d*x + 2*c) + 2*I*f*cos(d*x + c) + 2*f*sin(3*d*x + 3*c) + 2*I*f*sin(2*d*x + 2*c) - 2*f*sin(d*x + c) - 2*f)*log(cos(d*x)^2 + cos(c)^2 + 2*cos(c)*sin(d*x) + sin(d*x)^2 + 2*cos(d*x)*sin(c) + sin(c)^2) - 4*(d*f*x - d*e)*sin(2*d*x + 2*c) - (4*I*d*f*x - 4*I*d*e)*sin(d*x + c))/(-2*I*a*d^2*cos(3*d*x + 3*c) + 2*a*d^2*cos(2*d*x + 2*c) + 2*I*a*d^2*cos(d*x + c) + 2*a*d^2*sin(3*d*x + 3*c) + 2*I*a*d^2*sin(2*d*x + 2*c) - 2*a*d^2*sin(d*x + c) - 2*a*d^2)","B",0
206,1,112,0,0.361994," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*((5*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 2*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
207,-1,0,0,0.000000," ","integrate(csc(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
208,-1,0,0,0.000000," ","integrate(csc(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate((f*x+e)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,1,6123,0,7.595291," ","integrate((f*x+e)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, c e f {\left(\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}{\frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a d \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} - \frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a d} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} + e^{2} {\left(\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a} - \frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}{\frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)} + \frac{8 \, {\left(16 i \, c^{2} f^{2} + {\left(16 i \, d e f - 16 i \, c f^{2} + 16 \, {\left(d e f - c f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(16 i \, d e f - 16 i \, c f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(d e f - c f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-32 i \, d e f + 32 i \, c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 16 \, {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(16 i \, d e f - 16 i \, c f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - 16 \, {\left(d e f - c f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-32 i \, d e f + 32 i \, c f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + 32 \, {\left(d e f - c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(16 i \, d e f - 16 i \, c f^{2}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(16 \, {\left(d x + c\right)} f^{2} \cos\left(5 \, d x + 5 \, c\right) + 16 i \, {\left(d x + c\right)} f^{2} \cos\left(4 \, d x + 4 \, c\right) - 32 \, {\left(d x + c\right)} f^{2} \cos\left(3 \, d x + 3 \, c\right) - 32 i \, {\left(d x + c\right)} f^{2} \cos\left(2 \, d x + 2 \, c\right) + 16 \, {\left(d x + c\right)} f^{2} \cos\left(d x + c\right) + 16 i \, {\left(d x + c\right)} f^{2} \sin\left(5 \, d x + 5 \, c\right) - 16 \, {\left(d x + c\right)} f^{2} \sin\left(4 \, d x + 4 \, c\right) - 32 i \, {\left(d x + c\right)} f^{2} \sin\left(3 \, d x + 3 \, c\right) + 32 \, {\left(d x + c\right)} f^{2} \sin\left(2 \, d x + 2 \, c\right) + 16 i \, {\left(d x + c\right)} f^{2} \sin\left(d x + c\right) + 16 i \, {\left(d x + c\right)} f^{2}\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + {\left(6 i \, c^{2} - 8 i \, c + 4 i\right)} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)} + 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + {\left(6 i \, c^{2} - 8 i \, c + 4 i\right)} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{2} - 16 i \, d e f + {\left(-12 i \, c^{2} + 16 i \, c - 8 i\right)} f^{2} + {\left(-24 i \, d e f + {\left(24 i \, c - 16 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + {\left(6 i \, c^{2} - 8 i \, c + 4 i\right)} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{2} - 16 i \, d e f + {\left(-12 i \, c^{2} + 16 i \, c - 8 i\right)} f^{2} + {\left(-24 i \, d e f + {\left(24 i \, c - 16 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + {\left(6 i \, c^{2} - 8 i \, c + 4 i\right)} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) + {\left(8 i \, d e f + {\left(-6 i \, c^{2} - 8 i \, c - 4 i\right)} f^{2} + 2 \, {\left(4 \, d e f - {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(8 i \, d e f + {\left(-6 i \, c^{2} - 8 i \, c - 4 i\right)} f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(4 \, d e f - {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-16 i \, d e f + {\left(12 i \, c^{2} + 16 i \, c + 8 i\right)} f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(4 \, d e f - {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(8 i \, d e f + {\left(-6 i \, c^{2} - 8 i \, c - 4 i\right)} f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left(4 \, d e f - {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-16 i \, d e f + {\left(12 i \, c^{2} + 16 i \, c + 8 i\right)} f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(4 \, d e f - {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(8 i \, d e f + {\left(-6 i \, c^{2} - 8 i \, c - 4 i\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)} + 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-24 i \, d e f + {\left(24 i \, c + 16 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-24 i \, d e f + {\left(24 i \, c + 16 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - 16 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-4 i \, {\left(d x + c\right)}^{2} f^{2} + 8 \, d e f + {\left(12 i \, c^{2} - 8 \, c\right)} f^{2} + {\left(-8 i \, d e f - 8 \, {\left(-i \, c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(20 \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f - 4 \, {\left(3 \, c^{2} + 2 i \, c\right)} f^{2} + {\left(40 \, d e f - {\left(40 \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(12 i \, {\left(d x + c\right)}^{2} f^{2} - 8 \, d e f + {\left(-20 i \, c^{2} + 8 \, c\right)} f^{2} - 8 \, {\left(-3 i \, d e f + {\left(3 i \, c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(12 \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f - 4 \, {\left(c^{2} + 2 i \, c\right)} f^{2} + {\left(24 \, d e f - {\left(24 \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(16 \, f^{2} \cos\left(5 \, d x + 5 \, c\right) + 16 i \, f^{2} \cos\left(4 \, d x + 4 \, c\right) - 32 \, f^{2} \cos\left(3 \, d x + 3 \, c\right) - 32 i \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 16 \, f^{2} \cos\left(d x + c\right) + 16 i \, f^{2} \sin\left(5 \, d x + 5 \, c\right) - 16 \, f^{2} \sin\left(4 \, d x + 4 \, c\right) - 32 i \, f^{2} \sin\left(3 \, d x + 3 \, c\right) + 32 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 16 i \, f^{2} \sin\left(d x + c\right) + 16 i \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(-12 i \, d e f - 12 i \, {\left(d x + c\right)} f^{2} + {\left(12 i \, c - 8 i\right)} f^{2} - 4 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c - 2\right)} f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-12 i \, d e f - 12 i \, {\left(d x + c\right)} f^{2} + {\left(12 i \, c - 8 i\right)} f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 8 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c - 2\right)} f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(24 i \, d e f + 24 i \, {\left(d x + c\right)} f^{2} + {\left(-24 i \, c + 16 i\right)} f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - 4 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c - 2\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(-12 i \, d e f - 12 i \, {\left(d x + c\right)} f^{2} + {\left(12 i \, c - 8 i\right)} f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + 4 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c - 2\right)} f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(24 i \, d e f + 24 i \, {\left(d x + c\right)} f^{2} + {\left(-24 i \, c + 16 i\right)} f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - 8 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c - 2\right)} f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, d e f - 12 i \, {\left(d x + c\right)} f^{2} + {\left(12 i \, c - 8 i\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) + {\left(12 i \, d e f + 12 i \, {\left(d x + c\right)} f^{2} + {\left(-12 i \, c - 8 i\right)} f^{2} + 4 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c + 2\right)} f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(12 i \, d e f + 12 i \, {\left(d x + c\right)} f^{2} + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - 8 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c + 2\right)} f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-24 i \, d e f - 24 i \, {\left(d x + c\right)} f^{2} + {\left(24 i \, c + 16 i\right)} f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(12 i \, d e f + 12 i \, {\left(d x + c\right)} f^{2} + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - 4 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c + 2\right)} f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-24 i \, d e f - 24 i \, {\left(d x + c\right)} f^{2} + {\left(24 i \, c + 16 i\right)} f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + 8 \, {\left(3 \, d e f + 3 \, {\left(d x + c\right)} f^{2} - {\left(3 \, c + 2\right)} f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(12 i \, d e f + 12 i \, {\left(d x + c\right)} f^{2} + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)} + {\left(-3 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, d e f + {\left(-3 i \, c^{2} + 4 i \, c - 2 i\right)} f^{2} + {\left(-6 i \, d e f + {\left(6 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + {\left(6 i \, c^{2} - 8 i \, c + 4 i\right)} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-3 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, d e f + {\left(-3 i \, c^{2} + 4 i \, c - 2 i\right)} f^{2} + {\left(-6 i \, d e f + {\left(6 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(3 i \, {\left(d x + c\right)}^{2} f^{2} + 4 i \, d e f + {\left(3 i \, c^{2} - 4 i \, c + 2 i\right)} f^{2} + {\left(6 i \, d e f + {\left(-6 i \, c + 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-6 i \, {\left(d x + c\right)}^{2} f^{2} - 8 i \, d e f + {\left(-6 i \, c^{2} + 8 i \, c - 4 i\right)} f^{2} + {\left(-12 i \, d e f + {\left(12 i \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, d e f + {\left(3 \, c^{2} - 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c - 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) - {\left(3 \, {\left(d x + c\right)}^{2} f^{2} - 4 \, d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)} - {\left(3 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, d e f + {\left(3 i \, c^{2} + 4 i \, c + 2 i\right)} f^{2} + {\left(6 i \, d e f + {\left(-6 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} - 4 \, d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(-6 i \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + {\left(-6 i \, c^{2} - 8 i \, c - 4 i\right)} f^{2} + {\left(-12 i \, d e f + {\left(12 i \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} - 4 \, d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(3 i \, {\left(d x + c\right)}^{2} f^{2} - 4 i \, d e f + {\left(3 i \, c^{2} + 4 i \, c + 2 i\right)} f^{2} + {\left(6 i \, d e f + {\left(-6 i \, c - 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} - 4 \, d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(-3 i \, {\left(d x + c\right)}^{2} f^{2} + 4 i \, d e f + {\left(-3 i \, c^{2} - 4 i \, c - 2 i\right)} f^{2} + {\left(-6 i \, d e f + {\left(6 i \, c + 4 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} - 4 \, d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(6 i \, {\left(d x + c\right)}^{2} f^{2} - 8 i \, d e f + {\left(6 i \, c^{2} + 8 i \, c + 4 i\right)} f^{2} + {\left(12 i \, d e f + {\left(-12 i \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, {\left(d x + c\right)}^{2} f^{2} - 4 \, d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} + 2 \, {\left(3 \, d e f - {\left(3 \, c + 2\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) + {\left(8 \, d e f + 8 \, {\left(d x + c\right)} f^{2} - 8 \, c f^{2} + {\left(-8 i \, d e f - 8 i \, {\left(d x + c\right)} f^{2} + 8 i \, c f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) + 8 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(16 i \, d e f + 16 i \, {\left(d x + c\right)} f^{2} - 16 i \, c f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) - 16 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-8 i \, d e f - 8 i \, {\left(d x + c\right)} f^{2} + 8 i \, c f^{2}\right)} \cos\left(d x + c\right) + 8 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(8 i \, d e f + 8 i \, {\left(d x + c\right)} f^{2} - 8 i \, c f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - 16 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-16 i \, d e f - 16 i \, {\left(d x + c\right)} f^{2} + 16 i \, c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(-12 i \, f^{2} \cos\left(5 \, d x + 5 \, c\right) + 12 \, f^{2} \cos\left(4 \, d x + 4 \, c\right) + 24 i \, f^{2} \cos\left(3 \, d x + 3 \, c\right) - 24 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) - 12 i \, f^{2} \cos\left(d x + c\right) + 12 \, f^{2} \sin\left(5 \, d x + 5 \, c\right) + 12 i \, f^{2} \sin\left(4 \, d x + 4 \, c\right) - 24 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) - 24 i \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 12 \, f^{2} \sin\left(d x + c\right) + 12 \, f^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, d x + i \, c\right)}) + {\left(12 i \, f^{2} \cos\left(5 \, d x + 5 \, c\right) - 12 \, f^{2} \cos\left(4 \, d x + 4 \, c\right) - 24 i \, f^{2} \cos\left(3 \, d x + 3 \, c\right) + 24 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 12 i \, f^{2} \cos\left(d x + c\right) - 12 \, f^{2} \sin\left(5 \, d x + 5 \, c\right) - 12 i \, f^{2} \sin\left(4 \, d x + 4 \, c\right) + 24 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) + 24 i \, f^{2} \sin\left(2 \, d x + 2 \, c\right) - 12 \, f^{2} \sin\left(d x + c\right) - 12 \, f^{2}\right)} {\rm Li}_{3}(e^{\left(i \, d x + i \, c\right)}) + {\left(-16 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-32 i \, d e f + 32 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(4 \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f - 4 \, {\left(3 \, c^{2} + 2 i \, c\right)} f^{2} + {\left(8 \, d e f - {\left(8 \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(20 i \, {\left(d x + c\right)}^{2} f^{2} - 8 \, d e f + {\left(-12 i \, c^{2} + 8 \, c\right)} f^{2} - 8 \, {\left(-5 i \, d e f + {\left(5 i \, c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(12 \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f - 4 \, {\left(5 \, c^{2} + 2 i \, c\right)} f^{2} + {\left(24 \, d e f - {\left(24 \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{2} f^{2} + 8 \, d e f + {\left(4 i \, c^{2} - 8 \, c\right)} f^{2} - 8 \, {\left(3 i \, d e f + {\left(-3 i \, c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-4 i \, a d^{2} \cos\left(5 \, d x + 5 \, c\right) + 4 \, a d^{2} \cos\left(4 \, d x + 4 \, c\right) + 8 i \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) - 8 \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) - 4 i \, a d^{2} \cos\left(d x + c\right) + 4 \, a d^{2} \sin\left(5 \, d x + 5 \, c\right) + 4 i \, a d^{2} \sin\left(4 \, d x + 4 \, c\right) - 8 \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) - 8 i \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, a d^{2} \sin\left(d x + c\right) + 4 \, a d^{2}}}{8 \, d}"," ",0,"-1/8*(2*c*e*f*((3*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*d*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) - (4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/(a*d) + 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) + e^2*((4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a) + 8*(16*I*c^2*f^2 + (16*I*d*e*f - 16*I*c*f^2 + 16*(d*e*f - c*f^2)*cos(5*d*x + 5*c) + (16*I*d*e*f - 16*I*c*f^2)*cos(4*d*x + 4*c) - 32*(d*e*f - c*f^2)*cos(3*d*x + 3*c) + (-32*I*d*e*f + 32*I*c*f^2)*cos(2*d*x + 2*c) + 16*(d*e*f - c*f^2)*cos(d*x + c) + (16*I*d*e*f - 16*I*c*f^2)*sin(5*d*x + 5*c) - 16*(d*e*f - c*f^2)*sin(4*d*x + 4*c) + (-32*I*d*e*f + 32*I*c*f^2)*sin(3*d*x + 3*c) + 32*(d*e*f - c*f^2)*sin(2*d*x + 2*c) + (16*I*d*e*f - 16*I*c*f^2)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (16*(d*x + c)*f^2*cos(5*d*x + 5*c) + 16*I*(d*x + c)*f^2*cos(4*d*x + 4*c) - 32*(d*x + c)*f^2*cos(3*d*x + 3*c) - 32*I*(d*x + c)*f^2*cos(2*d*x + 2*c) + 16*(d*x + c)*f^2*cos(d*x + c) + 16*I*(d*x + c)*f^2*sin(5*d*x + 5*c) - 16*(d*x + c)*f^2*sin(4*d*x + 4*c) - 32*I*(d*x + c)*f^2*sin(3*d*x + 3*c) + 32*(d*x + c)*f^2*sin(2*d*x + 2*c) + 16*I*(d*x + c)*f^2*sin(d*x + c) + 16*I*(d*x + c)*f^2)*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (6*I*(d*x + c)^2*f^2 + 8*I*d*e*f + (6*I*c^2 - 8*I*c + 4*I)*f^2 + (12*I*d*e*f + (-12*I*c + 8*I)*f^2)*(d*x + c) + 2*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (6*I*(d*x + c)^2*f^2 + 8*I*d*e*f + (6*I*c^2 - 8*I*c + 4*I)*f^2 + (12*I*d*e*f + (-12*I*c + 8*I)*f^2)*(d*x + c))*cos(4*d*x + 4*c) - 4*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (-12*I*(d*x + c)^2*f^2 - 16*I*d*e*f + (-12*I*c^2 + 16*I*c - 8*I)*f^2 + (-24*I*d*e*f + (24*I*c - 16*I)*f^2)*(d*x + c))*cos(2*d*x + 2*c) + 2*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*cos(d*x + c) + (6*I*(d*x + c)^2*f^2 + 8*I*d*e*f + (6*I*c^2 - 8*I*c + 4*I)*f^2 + (12*I*d*e*f + (-12*I*c + 8*I)*f^2)*(d*x + c))*sin(5*d*x + 5*c) - 2*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*sin(4*d*x + 4*c) + (-12*I*(d*x + c)^2*f^2 - 16*I*d*e*f + (-12*I*c^2 + 16*I*c - 8*I)*f^2 + (-24*I*d*e*f + (24*I*c - 16*I)*f^2)*(d*x + c))*sin(3*d*x + 3*c) + 4*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (6*I*(d*x + c)^2*f^2 + 8*I*d*e*f + (6*I*c^2 - 8*I*c + 4*I)*f^2 + (12*I*d*e*f + (-12*I*c + 8*I)*f^2)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) + 1) + (8*I*d*e*f + (-6*I*c^2 - 8*I*c - 4*I)*f^2 + 2*(4*d*e*f - (3*c^2 + 4*c + 2)*f^2)*cos(5*d*x + 5*c) + (8*I*d*e*f + (-6*I*c^2 - 8*I*c - 4*I)*f^2)*cos(4*d*x + 4*c) - 4*(4*d*e*f - (3*c^2 + 4*c + 2)*f^2)*cos(3*d*x + 3*c) + (-16*I*d*e*f + (12*I*c^2 + 16*I*c + 8*I)*f^2)*cos(2*d*x + 2*c) + 2*(4*d*e*f - (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c) + (8*I*d*e*f + (-6*I*c^2 - 8*I*c - 4*I)*f^2)*sin(5*d*x + 5*c) - 2*(4*d*e*f - (3*c^2 + 4*c + 2)*f^2)*sin(4*d*x + 4*c) + (-16*I*d*e*f + (12*I*c^2 + 16*I*c + 8*I)*f^2)*sin(3*d*x + 3*c) + 4*(4*d*e*f - (3*c^2 + 4*c + 2)*f^2)*sin(2*d*x + 2*c) + (8*I*d*e*f + (-6*I*c^2 - 8*I*c - 4*I)*f^2)*sin(d*x + c))*arctan2(sin(d*x + c), cos(d*x + c) - 1) + (6*I*(d*x + c)^2*f^2 + (12*I*d*e*f + (-12*I*c - 8*I)*f^2)*(d*x + c) + 2*(3*(d*x + c)^2*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (6*I*(d*x + c)^2*f^2 + (12*I*d*e*f + (-12*I*c - 8*I)*f^2)*(d*x + c))*cos(4*d*x + 4*c) - 4*(3*(d*x + c)^2*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (-12*I*(d*x + c)^2*f^2 + (-24*I*d*e*f + (24*I*c + 16*I)*f^2)*(d*x + c))*cos(2*d*x + 2*c) + 2*(3*(d*x + c)^2*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*cos(d*x + c) + (6*I*(d*x + c)^2*f^2 + (12*I*d*e*f + (-12*I*c - 8*I)*f^2)*(d*x + c))*sin(5*d*x + 5*c) - 2*(3*(d*x + c)^2*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*sin(4*d*x + 4*c) + (-12*I*(d*x + c)^2*f^2 + (-24*I*d*e*f + (24*I*c + 16*I)*f^2)*(d*x + c))*sin(3*d*x + 3*c) + 4*(3*(d*x + c)^2*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (6*I*(d*x + c)^2*f^2 + (12*I*d*e*f + (-12*I*c - 8*I)*f^2)*(d*x + c))*sin(d*x + c))*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - 16*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (-4*I*(d*x + c)^2*f^2 + 8*d*e*f + (12*I*c^2 - 8*c)*f^2 + (-8*I*d*e*f - 8*(-I*c - 1)*f^2)*(d*x + c))*cos(4*d*x + 4*c) + (20*(d*x + c)^2*f^2 + 8*I*d*e*f - 4*(3*c^2 + 2*I*c)*f^2 + (40*d*e*f - (40*c - 8*I)*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (12*I*(d*x + c)^2*f^2 - 8*d*e*f + (-20*I*c^2 + 8*c)*f^2 - 8*(-3*I*d*e*f + (3*I*c + 1)*f^2)*(d*x + c))*cos(2*d*x + 2*c) - (12*(d*x + c)^2*f^2 + 8*I*d*e*f - 4*(c^2 + 2*I*c)*f^2 + (24*d*e*f - (24*c - 8*I)*f^2)*(d*x + c))*cos(d*x + c) - (16*f^2*cos(5*d*x + 5*c) + 16*I*f^2*cos(4*d*x + 4*c) - 32*f^2*cos(3*d*x + 3*c) - 32*I*f^2*cos(2*d*x + 2*c) + 16*f^2*cos(d*x + c) + 16*I*f^2*sin(5*d*x + 5*c) - 16*f^2*sin(4*d*x + 4*c) - 32*I*f^2*sin(3*d*x + 3*c) + 32*f^2*sin(2*d*x + 2*c) + 16*I*f^2*sin(d*x + c) + 16*I*f^2)*dilog(I*e^(I*d*x + I*c)) + (-12*I*d*e*f - 12*I*(d*x + c)*f^2 + (12*I*c - 8*I)*f^2 - 4*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c - 2)*f^2)*cos(5*d*x + 5*c) + (-12*I*d*e*f - 12*I*(d*x + c)*f^2 + (12*I*c - 8*I)*f^2)*cos(4*d*x + 4*c) + 8*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c - 2)*f^2)*cos(3*d*x + 3*c) + (24*I*d*e*f + 24*I*(d*x + c)*f^2 + (-24*I*c + 16*I)*f^2)*cos(2*d*x + 2*c) - 4*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c - 2)*f^2)*cos(d*x + c) + (-12*I*d*e*f - 12*I*(d*x + c)*f^2 + (12*I*c - 8*I)*f^2)*sin(5*d*x + 5*c) + 4*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c - 2)*f^2)*sin(4*d*x + 4*c) + (24*I*d*e*f + 24*I*(d*x + c)*f^2 + (-24*I*c + 16*I)*f^2)*sin(3*d*x + 3*c) - 8*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c - 2)*f^2)*sin(2*d*x + 2*c) + (-12*I*d*e*f - 12*I*(d*x + c)*f^2 + (12*I*c - 8*I)*f^2)*sin(d*x + c))*dilog(-e^(I*d*x + I*c)) + (12*I*d*e*f + 12*I*(d*x + c)*f^2 + (-12*I*c - 8*I)*f^2 + 4*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c + 2)*f^2)*cos(5*d*x + 5*c) + (12*I*d*e*f + 12*I*(d*x + c)*f^2 + (-12*I*c - 8*I)*f^2)*cos(4*d*x + 4*c) - 8*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c + 2)*f^2)*cos(3*d*x + 3*c) + (-24*I*d*e*f - 24*I*(d*x + c)*f^2 + (24*I*c + 16*I)*f^2)*cos(2*d*x + 2*c) + 4*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c + 2)*f^2)*cos(d*x + c) + (12*I*d*e*f + 12*I*(d*x + c)*f^2 + (-12*I*c - 8*I)*f^2)*sin(5*d*x + 5*c) - 4*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c + 2)*f^2)*sin(4*d*x + 4*c) + (-24*I*d*e*f - 24*I*(d*x + c)*f^2 + (24*I*c + 16*I)*f^2)*sin(3*d*x + 3*c) + 8*(3*d*e*f + 3*(d*x + c)*f^2 - (3*c + 2)*f^2)*sin(2*d*x + 2*c) + (12*I*d*e*f + 12*I*(d*x + c)*f^2 + (-12*I*c - 8*I)*f^2)*sin(d*x + c))*dilog(e^(I*d*x + I*c)) + (3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c) + (-3*I*(d*x + c)^2*f^2 - 4*I*d*e*f + (-3*I*c^2 + 4*I*c - 2*I)*f^2 + (-6*I*d*e*f + (6*I*c - 4*I)*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*cos(4*d*x + 4*c) + (6*I*(d*x + c)^2*f^2 + 8*I*d*e*f + (6*I*c^2 - 8*I*c + 4*I)*f^2 + (12*I*d*e*f + (-12*I*c + 8*I)*f^2)*(d*x + c))*cos(3*d*x + 3*c) - 2*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (-3*I*(d*x + c)^2*f^2 - 4*I*d*e*f + (-3*I*c^2 + 4*I*c - 2*I)*f^2 + (-6*I*d*e*f + (6*I*c - 4*I)*f^2)*(d*x + c))*cos(d*x + c) + (3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*sin(5*d*x + 5*c) + (3*I*(d*x + c)^2*f^2 + 4*I*d*e*f + (3*I*c^2 - 4*I*c + 2*I)*f^2 + (6*I*d*e*f + (-6*I*c + 4*I)*f^2)*(d*x + c))*sin(4*d*x + 4*c) - 2*(3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*sin(3*d*x + 3*c) + (-6*I*(d*x + c)^2*f^2 - 8*I*d*e*f + (-6*I*c^2 + 8*I*c - 4*I)*f^2 + (-12*I*d*e*f + (12*I*c - 8*I)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (3*(d*x + c)^2*f^2 + 4*d*e*f + (3*c^2 - 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c - 2)*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) - (3*(d*x + c)^2*f^2 - 4*d*e*f + (3*c^2 + 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c) - (3*I*(d*x + c)^2*f^2 - 4*I*d*e*f + (3*I*c^2 + 4*I*c + 2*I)*f^2 + (6*I*d*e*f + (-6*I*c - 4*I)*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (3*(d*x + c)^2*f^2 - 4*d*e*f + (3*c^2 + 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*cos(4*d*x + 4*c) - (-6*I*(d*x + c)^2*f^2 + 8*I*d*e*f + (-6*I*c^2 - 8*I*c - 4*I)*f^2 + (-12*I*d*e*f + (12*I*c + 8*I)*f^2)*(d*x + c))*cos(3*d*x + 3*c) - 2*(3*(d*x + c)^2*f^2 - 4*d*e*f + (3*c^2 + 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*cos(2*d*x + 2*c) - (3*I*(d*x + c)^2*f^2 - 4*I*d*e*f + (3*I*c^2 + 4*I*c + 2*I)*f^2 + (6*I*d*e*f + (-6*I*c - 4*I)*f^2)*(d*x + c))*cos(d*x + c) + (3*(d*x + c)^2*f^2 - 4*d*e*f + (3*c^2 + 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*sin(5*d*x + 5*c) - (-3*I*(d*x + c)^2*f^2 + 4*I*d*e*f + (-3*I*c^2 - 4*I*c - 2*I)*f^2 + (-6*I*d*e*f + (6*I*c + 4*I)*f^2)*(d*x + c))*sin(4*d*x + 4*c) - 2*(3*(d*x + c)^2*f^2 - 4*d*e*f + (3*c^2 + 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*sin(3*d*x + 3*c) - (6*I*(d*x + c)^2*f^2 - 8*I*d*e*f + (6*I*c^2 + 8*I*c + 4*I)*f^2 + (12*I*d*e*f + (-12*I*c - 8*I)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (3*(d*x + c)^2*f^2 - 4*d*e*f + (3*c^2 + 4*c + 2)*f^2 + 2*(3*d*e*f - (3*c + 2)*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) + (8*d*e*f + 8*(d*x + c)*f^2 - 8*c*f^2 + (-8*I*d*e*f - 8*I*(d*x + c)*f^2 + 8*I*c*f^2)*cos(5*d*x + 5*c) + 8*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(4*d*x + 4*c) + (16*I*d*e*f + 16*I*(d*x + c)*f^2 - 16*I*c*f^2)*cos(3*d*x + 3*c) - 16*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(2*d*x + 2*c) + (-8*I*d*e*f - 8*I*(d*x + c)*f^2 + 8*I*c*f^2)*cos(d*x + c) + 8*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(5*d*x + 5*c) + (8*I*d*e*f + 8*I*(d*x + c)*f^2 - 8*I*c*f^2)*sin(4*d*x + 4*c) - 16*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(3*d*x + 3*c) + (-16*I*d*e*f - 16*I*(d*x + c)*f^2 + 16*I*c*f^2)*sin(2*d*x + 2*c) + 8*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (-12*I*f^2*cos(5*d*x + 5*c) + 12*f^2*cos(4*d*x + 4*c) + 24*I*f^2*cos(3*d*x + 3*c) - 24*f^2*cos(2*d*x + 2*c) - 12*I*f^2*cos(d*x + c) + 12*f^2*sin(5*d*x + 5*c) + 12*I*f^2*sin(4*d*x + 4*c) - 24*f^2*sin(3*d*x + 3*c) - 24*I*f^2*sin(2*d*x + 2*c) + 12*f^2*sin(d*x + c) + 12*f^2)*polylog(3, -e^(I*d*x + I*c)) + (12*I*f^2*cos(5*d*x + 5*c) - 12*f^2*cos(4*d*x + 4*c) - 24*I*f^2*cos(3*d*x + 3*c) + 24*f^2*cos(2*d*x + 2*c) + 12*I*f^2*cos(d*x + c) - 12*f^2*sin(5*d*x + 5*c) - 12*I*f^2*sin(4*d*x + 4*c) + 24*f^2*sin(3*d*x + 3*c) + 24*I*f^2*sin(2*d*x + 2*c) - 12*f^2*sin(d*x + c) - 12*f^2)*polylog(3, e^(I*d*x + I*c)) + (-16*I*(d*x + c)^2*f^2 + (-32*I*d*e*f + 32*I*c*f^2)*(d*x + c))*sin(5*d*x + 5*c) + (4*(d*x + c)^2*f^2 + 8*I*d*e*f - 4*(3*c^2 + 2*I*c)*f^2 + (8*d*e*f - (8*c - 8*I)*f^2)*(d*x + c))*sin(4*d*x + 4*c) + (20*I*(d*x + c)^2*f^2 - 8*d*e*f + (-12*I*c^2 + 8*c)*f^2 - 8*(-5*I*d*e*f + (5*I*c + 1)*f^2)*(d*x + c))*sin(3*d*x + 3*c) - (12*(d*x + c)^2*f^2 + 8*I*d*e*f - 4*(5*c^2 + 2*I*c)*f^2 + (24*d*e*f - (24*c - 8*I)*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (-12*I*(d*x + c)^2*f^2 + 8*d*e*f + (4*I*c^2 - 8*c)*f^2 - 8*(3*I*d*e*f + (-3*I*c - 1)*f^2)*(d*x + c))*sin(d*x + c))/(-4*I*a*d^2*cos(5*d*x + 5*c) + 4*a*d^2*cos(4*d*x + 4*c) + 8*I*a*d^2*cos(3*d*x + 3*c) - 8*a*d^2*cos(2*d*x + 2*c) - 4*I*a*d^2*cos(d*x + c) + 4*a*d^2*sin(5*d*x + 5*c) + 4*I*a*d^2*sin(4*d*x + 4*c) - 8*a*d^2*sin(3*d*x + 3*c) - 8*I*a*d^2*sin(2*d*x + 2*c) + 4*a*d^2*sin(d*x + c) + 4*a*d^2))/d","B",0
211,1,2087,0,2.511154," ","integrate((f*x+e)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, d f x \cos\left(5 \, d x + 5 \, c\right) + 16 i \, d f x \sin\left(5 \, d x + 5 \, c\right) - 16 i \, d e - {\left(8 \, f \cos\left(5 \, d x + 5 \, c\right) + 8 i \, f \cos\left(4 \, d x + 4 \, c\right) - 16 \, f \cos\left(3 \, d x + 3 \, c\right) - 16 i \, f \cos\left(2 \, d x + 2 \, c\right) + 8 \, f \cos\left(d x + c\right) + 8 i \, f \sin\left(5 \, d x + 5 \, c\right) - 8 \, f \sin\left(4 \, d x + 4 \, c\right) - 16 i \, f \sin\left(3 \, d x + 3 \, c\right) + 16 \, f \sin\left(2 \, d x + 2 \, c\right) + 8 i \, f \sin\left(d x + c\right) + 8 i \, f\right)} \arctan\left(\cos\left(c\right) + \sin\left(d x\right), \cos\left(d x\right) + \sin\left(c\right)\right) - {\left(6 i \, d f x + 6 i \, d e + 2 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(6 i \, d f x + 6 i \, d e + 4 i \, f\right)} \cos\left(4 \, d x + 4 \, c\right) - 4 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-12 i \, d f x - 12 i \, d e - 8 i \, f\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right) + {\left(6 i \, d f x + 6 i \, d e + 4 i \, f\right)} \sin\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-12 i \, d f x - 12 i \, d e - 8 i \, f\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(6 i \, d f x + 6 i \, d e + 4 i \, f\right)} \sin\left(d x + c\right) + 4 i \, f\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) + 1\right) - {\left(-6 i \, d e - 2 \, {\left(3 \, d e - 2 \, f\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-6 i \, d e + 4 i \, f\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(3 \, d e - 2 \, f\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(12 i \, d e - 8 i \, f\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(3 \, d e - 2 \, f\right)} \cos\left(d x + c\right) + {\left(-6 i \, d e + 4 i \, f\right)} \sin\left(5 \, d x + 5 \, c\right) + 2 \, {\left(3 \, d e - 2 \, f\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(12 i \, d e - 8 i \, f\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, {\left(3 \, d e - 2 \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-6 i \, d e + 4 i \, f\right)} \sin\left(d x + c\right) + 4 i \, f\right)} \arctan\left(\sin\left(d x + c\right), \cos\left(d x + c\right) - 1\right) - {\left(6 \, d f x \cos\left(5 \, d x + 5 \, c\right) + 6 i \, d f x \cos\left(4 \, d x + 4 \, c\right) - 12 \, d f x \cos\left(3 \, d x + 3 \, c\right) - 12 i \, d f x \cos\left(2 \, d x + 2 \, c\right) + 6 \, d f x \cos\left(d x + c\right) + 6 i \, d f x \sin\left(5 \, d x + 5 \, c\right) - 6 \, d f x \sin\left(4 \, d x + 4 \, c\right) - 12 i \, d f x \sin\left(3 \, d x + 3 \, c\right) + 12 \, d f x \sin\left(2 \, d x + 2 \, c\right) + 6 i \, d f x \sin\left(d x + c\right) + 6 i \, d f x\right)} \arctan\left(\sin\left(d x + c\right), -\cos\left(d x + c\right) + 1\right) - {\left(-4 i \, d f x + 12 i \, d e + 4 \, f\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(20 \, d f x - 12 \, d e + 4 i \, f\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(12 i \, d f x - 20 i \, d e - 4 \, f\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(12 \, d f x - 4 \, d e + 4 i \, f\right)} \cos\left(d x + c\right) + {\left(6 \, f \cos\left(5 \, d x + 5 \, c\right) + 6 i \, f \cos\left(4 \, d x + 4 \, c\right) - 12 \, f \cos\left(3 \, d x + 3 \, c\right) - 12 i \, f \cos\left(2 \, d x + 2 \, c\right) + 6 \, f \cos\left(d x + c\right) + 6 i \, f \sin\left(5 \, d x + 5 \, c\right) - 6 \, f \sin\left(4 \, d x + 4 \, c\right) - 12 i \, f \sin\left(3 \, d x + 3 \, c\right) + 12 \, f \sin\left(2 \, d x + 2 \, c\right) + 6 i \, f \sin\left(d x + c\right) + 6 i \, f\right)} {\rm Li}_2\left(-e^{\left(i \, d x + i \, c\right)}\right) - {\left(6 \, f \cos\left(5 \, d x + 5 \, c\right) + 6 i \, f \cos\left(4 \, d x + 4 \, c\right) - 12 \, f \cos\left(3 \, d x + 3 \, c\right) - 12 i \, f \cos\left(2 \, d x + 2 \, c\right) + 6 \, f \cos\left(d x + c\right) + 6 i \, f \sin\left(5 \, d x + 5 \, c\right) - 6 \, f \sin\left(4 \, d x + 4 \, c\right) - 12 i \, f \sin\left(3 \, d x + 3 \, c\right) + 12 \, f \sin\left(2 \, d x + 2 \, c\right) + 6 i \, f \sin\left(d x + c\right) + 6 i \, f\right)} {\rm Li}_2\left(e^{\left(i \, d x + i \, c\right)}\right) - {\left(3 \, d f x + 3 \, d e + {\left(-3 i \, d f x - 3 i \, d e - 2 i \, f\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(6 i \, d f x + 6 i \, d e + 4 i \, f\right)} \cos\left(3 \, d x + 3 \, c\right) - 2 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-3 i \, d f x - 3 i \, d e - 2 i \, f\right)} \cos\left(d x + c\right) + {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(3 i \, d f x + 3 i \, d e + 2 i \, f\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(-6 i \, d f x - 6 i \, d e - 4 i \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \sin\left(d x + c\right) + 2 \, f\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1\right) + {\left(3 \, d f x + 3 \, d e - {\left(3 i \, d f x + 3 i \, d e - 2 i \, f\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(3 \, d f x + 3 \, d e - 2 \, f\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(-6 i \, d f x - 6 i \, d e + 4 i \, f\right)} \cos\left(3 \, d x + 3 \, c\right) - 2 \, {\left(3 \, d f x + 3 \, d e - 2 \, f\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(3 i \, d f x + 3 i \, d e - 2 i \, f\right)} \cos\left(d x + c\right) + {\left(3 \, d f x + 3 \, d e - 2 \, f\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(-3 i \, d f x - 3 i \, d e + 2 i \, f\right)} \sin\left(4 \, d x + 4 \, c\right) - 2 \, {\left(3 \, d f x + 3 \, d e - 2 \, f\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(6 i \, d f x + 6 i \, d e - 4 i \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(3 \, d f x + 3 \, d e - 2 \, f\right)} \sin\left(d x + c\right) - 2 \, f\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) + 1\right) - {\left(-4 i \, f \cos\left(5 \, d x + 5 \, c\right) + 4 \, f \cos\left(4 \, d x + 4 \, c\right) + 8 i \, f \cos\left(3 \, d x + 3 \, c\right) - 8 \, f \cos\left(2 \, d x + 2 \, c\right) - 4 i \, f \cos\left(d x + c\right) + 4 \, f \sin\left(5 \, d x + 5 \, c\right) + 4 i \, f \sin\left(4 \, d x + 4 \, c\right) - 8 \, f \sin\left(3 \, d x + 3 \, c\right) - 8 i \, f \sin\left(2 \, d x + 2 \, c\right) + 4 \, f \sin\left(d x + c\right) + 4 \, f\right)} \log\left(\cos\left(d x\right)^{2} + \cos\left(c\right)^{2} + 2 \, \cos\left(c\right) \sin\left(d x\right) + \sin\left(d x\right)^{2} + 2 \, \cos\left(d x\right) \sin\left(c\right) + \sin\left(c\right)^{2}\right) - {\left(4 \, d f x - 12 \, d e + 4 i \, f\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(20 i \, d f x - 12 i \, d e - 4 \, f\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(12 \, d f x - 20 \, d e + 4 i \, f\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(-12 i \, d f x + 4 i \, d e + 4 \, f\right)} \sin\left(d x + c\right)}{-4 i \, a d^{2} \cos\left(5 \, d x + 5 \, c\right) + 4 \, a d^{2} \cos\left(4 \, d x + 4 \, c\right) + 8 i \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) - 8 \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) - 4 i \, a d^{2} \cos\left(d x + c\right) + 4 \, a d^{2} \sin\left(5 \, d x + 5 \, c\right) + 4 i \, a d^{2} \sin\left(4 \, d x + 4 \, c\right) - 8 \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) - 8 i \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, a d^{2} \sin\left(d x + c\right) + 4 \, a d^{2}}"," ",0,"(16*d*f*x*cos(5*d*x + 5*c) + 16*I*d*f*x*sin(5*d*x + 5*c) - 16*I*d*e - (8*f*cos(5*d*x + 5*c) + 8*I*f*cos(4*d*x + 4*c) - 16*f*cos(3*d*x + 3*c) - 16*I*f*cos(2*d*x + 2*c) + 8*f*cos(d*x + c) + 8*I*f*sin(5*d*x + 5*c) - 8*f*sin(4*d*x + 4*c) - 16*I*f*sin(3*d*x + 3*c) + 16*f*sin(2*d*x + 2*c) + 8*I*f*sin(d*x + c) + 8*I*f)*arctan2(cos(c) + sin(d*x), cos(d*x) + sin(c)) - (6*I*d*f*x + 6*I*d*e + 2*(3*d*f*x + 3*d*e + 2*f)*cos(5*d*x + 5*c) + (6*I*d*f*x + 6*I*d*e + 4*I*f)*cos(4*d*x + 4*c) - 4*(3*d*f*x + 3*d*e + 2*f)*cos(3*d*x + 3*c) + (-12*I*d*f*x - 12*I*d*e - 8*I*f)*cos(2*d*x + 2*c) + 2*(3*d*f*x + 3*d*e + 2*f)*cos(d*x + c) + (6*I*d*f*x + 6*I*d*e + 4*I*f)*sin(5*d*x + 5*c) - 2*(3*d*f*x + 3*d*e + 2*f)*sin(4*d*x + 4*c) + (-12*I*d*f*x - 12*I*d*e - 8*I*f)*sin(3*d*x + 3*c) + 4*(3*d*f*x + 3*d*e + 2*f)*sin(2*d*x + 2*c) + (6*I*d*f*x + 6*I*d*e + 4*I*f)*sin(d*x + c) + 4*I*f)*arctan2(sin(d*x + c), cos(d*x + c) + 1) - (-6*I*d*e - 2*(3*d*e - 2*f)*cos(5*d*x + 5*c) + (-6*I*d*e + 4*I*f)*cos(4*d*x + 4*c) + 4*(3*d*e - 2*f)*cos(3*d*x + 3*c) + (12*I*d*e - 8*I*f)*cos(2*d*x + 2*c) - 2*(3*d*e - 2*f)*cos(d*x + c) + (-6*I*d*e + 4*I*f)*sin(5*d*x + 5*c) + 2*(3*d*e - 2*f)*sin(4*d*x + 4*c) + (12*I*d*e - 8*I*f)*sin(3*d*x + 3*c) - 4*(3*d*e - 2*f)*sin(2*d*x + 2*c) + (-6*I*d*e + 4*I*f)*sin(d*x + c) + 4*I*f)*arctan2(sin(d*x + c), cos(d*x + c) - 1) - (6*d*f*x*cos(5*d*x + 5*c) + 6*I*d*f*x*cos(4*d*x + 4*c) - 12*d*f*x*cos(3*d*x + 3*c) - 12*I*d*f*x*cos(2*d*x + 2*c) + 6*d*f*x*cos(d*x + c) + 6*I*d*f*x*sin(5*d*x + 5*c) - 6*d*f*x*sin(4*d*x + 4*c) - 12*I*d*f*x*sin(3*d*x + 3*c) + 12*d*f*x*sin(2*d*x + 2*c) + 6*I*d*f*x*sin(d*x + c) + 6*I*d*f*x)*arctan2(sin(d*x + c), -cos(d*x + c) + 1) - (-4*I*d*f*x + 12*I*d*e + 4*f)*cos(4*d*x + 4*c) - (20*d*f*x - 12*d*e + 4*I*f)*cos(3*d*x + 3*c) - (12*I*d*f*x - 20*I*d*e - 4*f)*cos(2*d*x + 2*c) + (12*d*f*x - 4*d*e + 4*I*f)*cos(d*x + c) + (6*f*cos(5*d*x + 5*c) + 6*I*f*cos(4*d*x + 4*c) - 12*f*cos(3*d*x + 3*c) - 12*I*f*cos(2*d*x + 2*c) + 6*f*cos(d*x + c) + 6*I*f*sin(5*d*x + 5*c) - 6*f*sin(4*d*x + 4*c) - 12*I*f*sin(3*d*x + 3*c) + 12*f*sin(2*d*x + 2*c) + 6*I*f*sin(d*x + c) + 6*I*f)*dilog(-e^(I*d*x + I*c)) - (6*f*cos(5*d*x + 5*c) + 6*I*f*cos(4*d*x + 4*c) - 12*f*cos(3*d*x + 3*c) - 12*I*f*cos(2*d*x + 2*c) + 6*f*cos(d*x + c) + 6*I*f*sin(5*d*x + 5*c) - 6*f*sin(4*d*x + 4*c) - 12*I*f*sin(3*d*x + 3*c) + 12*f*sin(2*d*x + 2*c) + 6*I*f*sin(d*x + c) + 6*I*f)*dilog(e^(I*d*x + I*c)) - (3*d*f*x + 3*d*e + (-3*I*d*f*x - 3*I*d*e - 2*I*f)*cos(5*d*x + 5*c) + (3*d*f*x + 3*d*e + 2*f)*cos(4*d*x + 4*c) + (6*I*d*f*x + 6*I*d*e + 4*I*f)*cos(3*d*x + 3*c) - 2*(3*d*f*x + 3*d*e + 2*f)*cos(2*d*x + 2*c) + (-3*I*d*f*x - 3*I*d*e - 2*I*f)*cos(d*x + c) + (3*d*f*x + 3*d*e + 2*f)*sin(5*d*x + 5*c) + (3*I*d*f*x + 3*I*d*e + 2*I*f)*sin(4*d*x + 4*c) - 2*(3*d*f*x + 3*d*e + 2*f)*sin(3*d*x + 3*c) + (-6*I*d*f*x - 6*I*d*e - 4*I*f)*sin(2*d*x + 2*c) + (3*d*f*x + 3*d*e + 2*f)*sin(d*x + c) + 2*f)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*cos(d*x + c) + 1) + (3*d*f*x + 3*d*e - (3*I*d*f*x + 3*I*d*e - 2*I*f)*cos(5*d*x + 5*c) + (3*d*f*x + 3*d*e - 2*f)*cos(4*d*x + 4*c) - (-6*I*d*f*x - 6*I*d*e + 4*I*f)*cos(3*d*x + 3*c) - 2*(3*d*f*x + 3*d*e - 2*f)*cos(2*d*x + 2*c) - (3*I*d*f*x + 3*I*d*e - 2*I*f)*cos(d*x + c) + (3*d*f*x + 3*d*e - 2*f)*sin(5*d*x + 5*c) - (-3*I*d*f*x - 3*I*d*e + 2*I*f)*sin(4*d*x + 4*c) - 2*(3*d*f*x + 3*d*e - 2*f)*sin(3*d*x + 3*c) - (6*I*d*f*x + 6*I*d*e - 4*I*f)*sin(2*d*x + 2*c) + (3*d*f*x + 3*d*e - 2*f)*sin(d*x + c) - 2*f)*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*cos(d*x + c) + 1) - (-4*I*f*cos(5*d*x + 5*c) + 4*f*cos(4*d*x + 4*c) + 8*I*f*cos(3*d*x + 3*c) - 8*f*cos(2*d*x + 2*c) - 4*I*f*cos(d*x + c) + 4*f*sin(5*d*x + 5*c) + 4*I*f*sin(4*d*x + 4*c) - 8*f*sin(3*d*x + 3*c) - 8*I*f*sin(2*d*x + 2*c) + 4*f*sin(d*x + c) + 4*f)*log(cos(d*x)^2 + cos(c)^2 + 2*cos(c)*sin(d*x) + sin(d*x)^2 + 2*cos(d*x)*sin(c) + sin(c)^2) - (4*d*f*x - 12*d*e + 4*I*f)*sin(4*d*x + 4*c) - (20*I*d*f*x - 12*I*d*e - 4*f)*sin(3*d*x + 3*c) + (12*d*f*x - 20*d*e + 4*I*f)*sin(2*d*x + 2*c) - (-12*I*d*f*x + 4*I*d*e + 4*f)*sin(d*x + c))/(-4*I*a*d^2*cos(5*d*x + 5*c) + 4*a*d^2*cos(4*d*x + 4*c) + 8*I*a*d^2*cos(3*d*x + 3*c) - 8*a*d^2*cos(2*d*x + 2*c) - 4*I*a*d^2*cos(d*x + c) + 4*a*d^2*sin(5*d*x + 5*c) + 4*I*a*d^2*sin(4*d*x + 4*c) - 8*a*d^2*sin(3*d*x + 3*c) - 8*I*a*d^2*sin(2*d*x + 2*c) + 4*a*d^2*sin(d*x + c) + 4*a*d^2)","B",0
212,1,157,0,0.568290," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a} - \frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}{\frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{8 \, d}"," ",0,"-1/8*((4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
213,-1,0,0,0.000000," ","integrate(csc(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(csc(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,0,0,0,0.000000," ","integrate((f*x+e)^m*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \sin\left(d x + c\right)^{2}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*sin(d*x + c)^2/(a*sin(d*x + c) + a), x)","F",0
216,0,0,0,0.000000," ","integrate((f*x+e)^m*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \sin\left(d x + c\right)}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*sin(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
217,0,0,0,0.000000," ","integrate((f*x+e)^m/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m/(a*sin(d*x + c) + a), x)","F",0
218,0,0,0,0.000000," ","integrate((f*x+e)^m*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*csc(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
219,0,0,0,0.000000," ","integrate((f*x+e)^m*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)^{2}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*csc(d*x + c)^2/(a*sin(d*x + c) + a), x)","F",0
220,-2,0,0,0.000000," ","integrate((f*x+e)^3*sin(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
221,-2,0,0,0.000000," ","integrate((f*x+e)^2*sin(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
222,-2,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
223,-2,0,0,0.000000," ","integrate(sin(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
224,-2,0,0,0.000000," ","integrate((f*x+e)^3*sin(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
225,-2,0,0,0.000000," ","integrate((f*x+e)^2*sin(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
226,-2,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
227,-2,0,0,0.000000," ","integrate(sin(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
228,-2,0,0,0.000000," ","integrate((f*x+e)^3*sin(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
229,-2,0,0,0.000000," ","integrate((f*x+e)^2*sin(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
230,-2,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
231,-2,0,0,0.000000," ","integrate(sin(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
232,-2,0,0,0.000000," ","integrate((f*x+e)^3*csc(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
233,-2,0,0,0.000000," ","integrate((f*x+e)^2*csc(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
234,-2,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
235,-2,0,0,0.000000," ","integrate(csc(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
236,-2,0,0,0.000000," ","integrate((f*x+e)^3*csc(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
237,-2,0,0,0.000000," ","integrate((f*x+e)^2*csc(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
238,-2,0,0,0.000000," ","integrate((f*x+e)*csc(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
239,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
240,0,0,0,0.000000," ","integrate((f*x+e)^m*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \sin\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*sin(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
241,0,0,0,0.000000," ","integrate((f*x+e)^m*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \sin\left(d x + c\right)}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*sin(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
242,0,0,0,0.000000," ","integrate((f*x+e)^m/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m/(b*sin(d*x + c) + a), x)","F",0
243,0,0,0,0.000000," ","integrate((f*x+e)^m*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*csc(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
244,0,0,0,0.000000," ","integrate((f*x+e)^m*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*csc(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
245,-2,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))^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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
246,-2,0,0,0.000000," ","integrate((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
247,-2,0,0,0.000000," ","integrate((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
248,-2,0,0,0.000000," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
249,-2,0,0,0.000000," ","integrate((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
250,-2,0,0,0.000000," ","integrate((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
251,1,510,0,1.234475," ","integrate((f*x+e)^3*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{12 \, c e^{2} f \log\left(a d \sin\left(d x + c\right) + a d\right)}{a d} - \frac{4 \, e^{3} \log\left(a \sin\left(d x + c\right) + a\right)}{a} - \frac{-i \, {\left(d x + c\right)}^{4} f^{3} + {\left(-4 i \, d e f^{2} + 4 i \, c f^{3}\right)} {\left(d x + c\right)}^{3} + 48 i \, f^{3} {\rm Li}_{4}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, c^{2} d e f^{2} + 4 i \, c^{3} f^{3}\right)} {\left(d x + c\right)} + {\left(24 i \, c^{2} d e f^{2} - 8 i \, c^{3} f^{3}\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(-8 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-24 i \, d^{2} e^{2} f + 48 i \, c d e f^{2} - 24 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(-24 i \, d^{2} e^{2} f + 48 i \, c d e f^{2} - 24 i \, {\left(d x + c\right)}^{2} f^{3} - 24 i \, c^{2} f^{3} + {\left(-48 i \, d e f^{2} + 48 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + 4 \, {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + 48 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)})}{a d^{3}}}{4 \, d}"," ",0,"-1/4*(12*c*e^2*f*log(a*d*sin(d*x + c) + a*d)/(a*d) - 4*e^3*log(a*sin(d*x + c) + a)/a - (-I*(d*x + c)^4*f^3 + (-4*I*d*e*f^2 + 4*I*c*f^3)*(d*x + c)^3 + 48*I*f^3*polylog(4, I*e^(I*d*x + I*c)) + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*c^2*f^3)*(d*x + c)^2 + (-12*I*c^2*d*e*f^2 + 4*I*c^3*f^3)*(d*x + c) + (24*I*c^2*d*e*f^2 - 8*I*c^3*f^3)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (-8*I*(d*x + c)^3*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c)^2 + (-24*I*d^2*e^2*f + 48*I*c*d*e*f^2 - 24*I*c^2*f^3)*(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (-24*I*d^2*e^2*f + 48*I*c*d*e*f^2 - 24*I*(d*x + c)^2*f^3 - 24*I*c^2*f^3 + (-48*I*d*e*f^2 + 48*I*c*f^3)*(d*x + c))*dilog(I*e^(I*d*x + I*c)) + 4*(3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + 48*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*polylog(3, I*e^(I*d*x + I*c)))/(a*d^3))/d","B",0
252,1,293,0,0.872831," ","integrate((f*x+e)^2*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{6 \, c e f \log\left(a d \sin\left(d x + c\right) + a d\right)}{a d} - \frac{3 \, e^{2} \log\left(a \sin\left(d x + c\right) + a\right)}{a} - \frac{-i \, {\left(d x + c\right)}^{3} f^{2} - 3 i \, {\left(d x + c\right)} c^{2} f^{2} + 6 i \, c^{2} f^{2} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(-3 i \, d e f + 3 i \, c f^{2}\right)} {\left(d x + c\right)}^{2} + 12 \, f^{2} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left(-6 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-12 i \, d e f + 12 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(-12 i \, d e f - 12 i \, {\left(d x + c\right)} f^{2} + 12 i \, c f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + 3 \, {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)}{a d^{2}}}{3 \, d}"," ",0,"-1/3*(6*c*e*f*log(a*d*sin(d*x + c) + a*d)/(a*d) - 3*e^2*log(a*sin(d*x + c) + a)/a - (-I*(d*x + c)^3*f^2 - 3*I*(d*x + c)*c^2*f^2 + 6*I*c^2*f^2*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (-3*I*d*e*f + 3*I*c*f^2)*(d*x + c)^2 + 12*f^2*polylog(3, I*e^(I*d*x + I*c)) + (-6*I*(d*x + c)^2*f^2 + (-12*I*d*e*f + 12*I*c*f^2)*(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (-12*I*d*e*f - 12*I*(d*x + c)*f^2 + 12*I*c*f^2)*dilog(I*e^(I*d*x + I*c)) + 3*((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1))/(a*d^2))/d","B",0
253,1,116,0,0.946048," ","integrate((f*x+e)*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{-i \, d^{2} f x^{2} - 2 i \, d^{2} e x - 4 i \, d f x \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + 4 i \, d e \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - 4 i \, f {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + 2 \, {\left(d f x + d e\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right)}{2 \, a d^{2}}"," ",0,"1/2*(-I*d^2*f*x^2 - 2*I*d^2*e*x - 4*I*d*f*x*arctan2(cos(d*x + c), sin(d*x + c) + 1) + 4*I*d*e*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - 4*I*f*dilog(I*e^(I*d*x + I*c)) + 2*(d*f*x + d*e)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1))/(a*d^2)","A",0
254,1,18,0,0.297061," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(a \sin\left(d x + c\right) + a\right)}{a d}"," ",0,"log(a*sin(d*x + c) + a)/(a*d)","A",0
255,0,0,0,0.000000," ","integrate(cos(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(f x + e\right)} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)/((f*x + e)*(a*sin(d*x + c) + a)), x)","F",0
256,0,0,0,0.000000," ","integrate(cos(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)}{{\left(f x + e\right)}^{2} {\left(a \sin\left(d x + c\right) + a\right)}}\,{d x}"," ",0,"integrate(cos(d*x + c)/((f*x + e)^2*(a*sin(d*x + c) + a)), x)","F",0
257,1,534,0,0.731117," ","integrate((f*x+e)^3*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, c^{3} f^{3} {\left(\frac{1}{a d^{3} + \frac{a d^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d^{3}}\right)} - 24 \, c^{2} e f^{2} {\left(\frac{1}{a d^{2} + \frac{a d^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d^{2}}\right)} + 24 \, c e^{2} f {\left(\frac{1}{a d + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - 8 \, e^{3} {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}\right)} - \frac{6 \, {\left({\left(d x + c\right)}^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right)\right)} e^{2} f}{a d} + \frac{12 \, {\left({\left(d x + c\right)}^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right)\right)} c e f^{2}}{a d^{2}} - \frac{6 \, {\left({\left(d x + c\right)}^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right)\right)} c^{2} f^{3}}{a d^{3}} - \frac{4 \, {\left({\left(d x + c\right)}^{3} + 3 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \cos\left(d x + c\right) - 6 \, {\left(d x + c\right)} \sin\left(d x + c\right)\right)} e f^{2}}{a d^{2}} + \frac{4 \, {\left({\left(d x + c\right)}^{3} + 3 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \cos\left(d x + c\right) - 6 \, {\left(d x + c\right)} \sin\left(d x + c\right)\right)} c f^{3}}{a d^{3}} - \frac{{\left({\left(d x + c\right)}^{4} + 4 \, {\left({\left(d x + c\right)}^{3} - 6 \, d x - 6 \, c\right)} \cos\left(d x + c\right) - 12 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \sin\left(d x + c\right)\right)} f^{3}}{a d^{3}}}{4 \, d}"," ",0,"-1/4*(8*c^3*f^3*(1/(a*d^3 + a*d^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d^3)) - 24*c^2*e*f^2*(1/(a*d^2 + a*d^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d^2)) + 24*c*e^2*f*(1/(a*d + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - 8*e^3*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)) - 6*((d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 2*sin(d*x + c))*e^2*f/(a*d) + 12*((d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 2*sin(d*x + c))*c*e*f^2/(a*d^2) - 6*((d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 2*sin(d*x + c))*c^2*f^3/(a*d^3) - 4*((d*x + c)^3 + 3*((d*x + c)^2 - 2)*cos(d*x + c) - 6*(d*x + c)*sin(d*x + c))*e*f^2/(a*d^2) + 4*((d*x + c)^3 + 3*((d*x + c)^2 - 2)*cos(d*x + c) - 6*(d*x + c)*sin(d*x + c))*c*f^3/(a*d^3) - ((d*x + c)^4 + 4*((d*x + c)^3 - 6*d*x - 6*c)*cos(d*x + c) - 12*((d*x + c)^2 - 2)*sin(d*x + c))*f^3/(a*d^3))/d","B",0
258,1,309,0,0.725513," ","integrate((f*x+e)^2*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{6 \, c^{2} f^{2} {\left(\frac{1}{a d^{2} + \frac{a d^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d^{2}}\right)} - 12 \, c e f {\left(\frac{1}{a d + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} + 6 \, e^{2} {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}\right)} + \frac{3 \, {\left({\left(d x + c\right)}^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right)\right)} e f}{a d} - \frac{3 \, {\left({\left(d x + c\right)}^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right)\right)} c f^{2}}{a d^{2}} + \frac{{\left({\left(d x + c\right)}^{3} + 3 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \cos\left(d x + c\right) - 6 \, {\left(d x + c\right)} \sin\left(d x + c\right)\right)} f^{2}}{a d^{2}}}{3 \, d}"," ",0,"1/3*(6*c^2*f^2*(1/(a*d^2 + a*d^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d^2)) - 12*c*e*f*(1/(a*d + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) + 6*e^2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)) + 3*((d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 2*sin(d*x + c))*e*f/(a*d) - 3*((d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 2*sin(d*x + c))*c*f^2/(a*d^2) + ((d*x + c)^3 + 3*((d*x + c)^2 - 2)*cos(d*x + c) - 6*(d*x + c)*sin(d*x + c))*f^2/(a*d^2))/d","B",0
259,1,151,0,0.945903," ","integrate((f*x+e)*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, c f {\left(\frac{1}{a d + \frac{a d \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a d}\right)} - 4 \, e {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}\right)} - \frac{{\left({\left(d x + c\right)}^{2} + 2 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, \sin\left(d x + c\right)\right)} f}{a d}}{2 \, d}"," ",0,"-1/2*(4*c*f*(1/(a*d + a*d*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/(a*d)) - 4*e*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2)) - ((d*x + c)^2 + 2*(d*x + c)*cos(d*x + c) - 2*sin(d*x + c))*f/(a*d))/d","B",0
260,1,52,0,0.738473," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{1}{a + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}\right)}}{d}"," ",0,"2*(arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 1/(a + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2))/d","B",0
261,1,163,0,0.408262," ","integrate(cos(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{d {\left(i \, E_{1}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) - i \, E_{1}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \cos\left(-\frac{d e - c f}{f}\right) + d {\left(E_{1}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) + E_{1}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \sin\left(-\frac{d e - c f}{f}\right) + 2 \, d \log\left(d e + {\left(d x + c\right)} f - c f\right)}{2 \, a d f}"," ",0,"1/2*(d*(I*exp_integral_e(1, (I*d*e + I*(d*x + c)*f - I*c*f)/f) - I*exp_integral_e(1, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*cos(-(d*e - c*f)/f) + d*(exp_integral_e(1, (I*d*e + I*(d*x + c)*f - I*c*f)/f) + exp_integral_e(1, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*sin(-(d*e - c*f)/f) + 2*d*log(d*e + (d*x + c)*f - c*f))/(a*d*f)","C",0
262,1,172,0,1.042971," ","integrate(cos(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{d^{2} {\left(i \, E_{2}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) - i \, E_{2}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \cos\left(-\frac{d e - c f}{f}\right) + d^{2} {\left(E_{2}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) + E_{2}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \sin\left(-\frac{d e - c f}{f}\right) - 2 \, d^{2}}{2 \, {\left(a d e f + {\left(d x + c\right)} a f^{2} - a c f^{2}\right)} d}"," ",0,"1/2*(d^2*(I*exp_integral_e(2, (I*d*e + I*(d*x + c)*f - I*c*f)/f) - I*exp_integral_e(2, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*cos(-(d*e - c*f)/f) + d^2*(exp_integral_e(2, (I*d*e + I*(d*x + c)*f - I*c*f)/f) + exp_integral_e(2, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*sin(-(d*e - c*f)/f) - 2*d^2)/((a*d*e*f + (d*x + c)*a*f^2 - a*c*f^2)*d)","C",0
263,1,572,0,0.787148," ","integrate((f*x+e)^3*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} e^{3}}{a} - \frac{24 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} c e^{2} f}{a d} + \frac{24 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} c^{2} e f^{2}}{a d^{2}} - \frac{8 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} c^{3} f^{3}}{a d^{3}} - \frac{6 \, {\left(2 \, {\left(d x + c\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, \cos\left(d x + c\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} e^{2} f}{a d} + \frac{12 \, {\left(2 \, {\left(d x + c\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, \cos\left(d x + c\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} c e f^{2}}{a d^{2}} - \frac{6 \, {\left(2 \, {\left(d x + c\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, \cos\left(d x + c\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} c^{2} f^{3}}{a d^{3}} - \frac{6 \, {\left({\left(2 \, {\left(d x + c\right)}^{2} - 1\right)} \cos\left(2 \, d x + 2 \, c\right) + 16 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(d x + c\right)} \sin\left(2 \, d x + 2 \, c\right) + 8 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \sin\left(d x + c\right)\right)} e f^{2}}{a d^{2}} + \frac{6 \, {\left({\left(2 \, {\left(d x + c\right)}^{2} - 1\right)} \cos\left(2 \, d x + 2 \, c\right) + 16 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(d x + c\right)} \sin\left(2 \, d x + 2 \, c\right) + 8 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \sin\left(d x + c\right)\right)} c f^{3}}{a d^{3}} - \frac{{\left(2 \, {\left(2 \, {\left(d x + c\right)}^{3} - 3 \, d x - 3 \, c\right)} \cos\left(2 \, d x + 2 \, c\right) + 48 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \cos\left(d x + c\right) - 3 \, {\left(2 \, {\left(d x + c\right)}^{2} - 1\right)} \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left({\left(d x + c\right)}^{3} - 6 \, d x - 6 \, c\right)} \sin\left(d x + c\right)\right)} f^{3}}{a d^{3}}}{16 \, d}"," ",0,"-1/16*(8*(sin(d*x + c)^2 - 2*sin(d*x + c))*e^3/a - 24*(sin(d*x + c)^2 - 2*sin(d*x + c))*c*e^2*f/(a*d) + 24*(sin(d*x + c)^2 - 2*sin(d*x + c))*c^2*e*f^2/(a*d^2) - 8*(sin(d*x + c)^2 - 2*sin(d*x + c))*c^3*f^3/(a*d^3) - 6*(2*(d*x + c)*cos(2*d*x + 2*c) + 8*(d*x + c)*sin(d*x + c) + 8*cos(d*x + c) - sin(2*d*x + 2*c))*e^2*f/(a*d) + 12*(2*(d*x + c)*cos(2*d*x + 2*c) + 8*(d*x + c)*sin(d*x + c) + 8*cos(d*x + c) - sin(2*d*x + 2*c))*c*e*f^2/(a*d^2) - 6*(2*(d*x + c)*cos(2*d*x + 2*c) + 8*(d*x + c)*sin(d*x + c) + 8*cos(d*x + c) - sin(2*d*x + 2*c))*c^2*f^3/(a*d^3) - 6*((2*(d*x + c)^2 - 1)*cos(2*d*x + 2*c) + 16*(d*x + c)*cos(d*x + c) - 2*(d*x + c)*sin(2*d*x + 2*c) + 8*((d*x + c)^2 - 2)*sin(d*x + c))*e*f^2/(a*d^2) + 6*((2*(d*x + c)^2 - 1)*cos(2*d*x + 2*c) + 16*(d*x + c)*cos(d*x + c) - 2*(d*x + c)*sin(2*d*x + 2*c) + 8*((d*x + c)^2 - 2)*sin(d*x + c))*c*f^3/(a*d^3) - (2*(2*(d*x + c)^3 - 3*d*x - 3*c)*cos(2*d*x + 2*c) + 48*((d*x + c)^2 - 2)*cos(d*x + c) - 3*(2*(d*x + c)^2 - 1)*sin(2*d*x + 2*c) + 16*((d*x + c)^3 - 6*d*x - 6*c)*sin(d*x + c))*f^3/(a*d^3))/d","B",0
264,1,289,0,0.916810," ","integrate((f*x+e)^2*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} e^{2}}{a} - \frac{8 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} c e f}{a d} + \frac{4 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} c^{2} f^{2}}{a d^{2}} - \frac{2 \, {\left(2 \, {\left(d x + c\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, \cos\left(d x + c\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} e f}{a d} + \frac{2 \, {\left(2 \, {\left(d x + c\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, \cos\left(d x + c\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} c f^{2}}{a d^{2}} - \frac{{\left({\left(2 \, {\left(d x + c\right)}^{2} - 1\right)} \cos\left(2 \, d x + 2 \, c\right) + 16 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 2 \, {\left(d x + c\right)} \sin\left(2 \, d x + 2 \, c\right) + 8 \, {\left({\left(d x + c\right)}^{2} - 2\right)} \sin\left(d x + c\right)\right)} f^{2}}{a d^{2}}}{8 \, d}"," ",0,"-1/8*(4*(sin(d*x + c)^2 - 2*sin(d*x + c))*e^2/a - 8*(sin(d*x + c)^2 - 2*sin(d*x + c))*c*e*f/(a*d) + 4*(sin(d*x + c)^2 - 2*sin(d*x + c))*c^2*f^2/(a*d^2) - 2*(2*(d*x + c)*cos(2*d*x + 2*c) + 8*(d*x + c)*sin(d*x + c) + 8*cos(d*x + c) - sin(2*d*x + 2*c))*e*f/(a*d) + 2*(2*(d*x + c)*cos(2*d*x + 2*c) + 8*(d*x + c)*sin(d*x + c) + 8*cos(d*x + c) - sin(2*d*x + 2*c))*c*f^2/(a*d^2) - ((2*(d*x + c)^2 - 1)*cos(2*d*x + 2*c) + 16*(d*x + c)*cos(d*x + c) - 2*(d*x + c)*sin(2*d*x + 2*c) + 8*((d*x + c)^2 - 2)*sin(d*x + c))*f^2/(a*d^2))/d","A",0
265,1,114,0,0.658966," ","integrate((f*x+e)*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} e}{a} - \frac{4 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)} c f}{a d} - \frac{{\left(2 \, {\left(d x + c\right)} \cos\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 8 \, \cos\left(d x + c\right) - \sin\left(2 \, d x + 2 \, c\right)\right)} f}{a d}}{8 \, d}"," ",0,"-1/8*(4*(sin(d*x + c)^2 - 2*sin(d*x + c))*e/a - 4*(sin(d*x + c)^2 - 2*sin(d*x + c))*c*f/(a*d) - (2*(d*x + c)*cos(2*d*x + 2*c) + 8*(d*x + c)*sin(d*x + c) + 8*cos(d*x + c) - sin(2*d*x + 2*c))*f/(a*d))/d","A",0
266,1,25,0,0.431889," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(sin(d*x + c)^2 - 2*sin(d*x + c))/(a*d)","A",0
267,1,280,0,0.820464," ","integrate(cos(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, d {\left(E_{1}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) + E_{1}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \cos\left(-\frac{d e - c f}{f}\right) - d {\left(i \, E_{1}\left(\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right) - i \, E_{1}\left(-\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right) - d {\left(2 i \, E_{1}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) - 2 i \, E_{1}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \sin\left(-\frac{d e - c f}{f}\right) - d {\left(E_{1}\left(\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right) + E_{1}\left(-\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right)}{4 \, a d f}"," ",0,"-1/4*(2*d*(exp_integral_e(1, (I*d*e + I*(d*x + c)*f - I*c*f)/f) + exp_integral_e(1, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*cos(-(d*e - c*f)/f) - d*(I*exp_integral_e(1, (2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f) - I*exp_integral_e(1, -(2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f))*cos(-2*(d*e - c*f)/f) - d*(2*I*exp_integral_e(1, (I*d*e + I*(d*x + c)*f - I*c*f)/f) - 2*I*exp_integral_e(1, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*sin(-(d*e - c*f)/f) - d*(exp_integral_e(1, (2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f) + exp_integral_e(1, -(2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f))*sin(-2*(d*e - c*f)/f))/(a*d*f)","C",0
268,1,307,0,0.506500," ","integrate(cos(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, d^{2} {\left(E_{2}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) + E_{2}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \cos\left(-\frac{d e - c f}{f}\right) - d^{2} {\left(i \, E_{2}\left(\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right) - i \, E_{2}\left(-\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right) - d^{2} {\left(2 i \, E_{2}\left(\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right) - 2 i \, E_{2}\left(-\frac{i \, d e + i \, {\left(d x + c\right)} f - i \, c f}{f}\right)\right)} \sin\left(-\frac{d e - c f}{f}\right) - d^{2} {\left(E_{2}\left(\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right) + E_{2}\left(-\frac{2 i \, d e + 2 i \, {\left(d x + c\right)} f - 2 i \, c f}{f}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right)}{4 \, {\left(a d e f + {\left(d x + c\right)} a f^{2} - a c f^{2}\right)} d}"," ",0,"-1/4*(2*d^2*(exp_integral_e(2, (I*d*e + I*(d*x + c)*f - I*c*f)/f) + exp_integral_e(2, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*cos(-(d*e - c*f)/f) - d^2*(I*exp_integral_e(2, (2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f) - I*exp_integral_e(2, -(2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f))*cos(-2*(d*e - c*f)/f) - d^2*(2*I*exp_integral_e(2, (I*d*e + I*(d*x + c)*f - I*c*f)/f) - 2*I*exp_integral_e(2, -(I*d*e + I*(d*x + c)*f - I*c*f)/f))*sin(-(d*e - c*f)/f) - d^2*(exp_integral_e(2, (2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f) + exp_integral_e(2, -(2*I*d*e + 2*I*(d*x + c)*f - 2*I*c*f)/f))*sin(-2*(d*e - c*f)/f))/((a*d*e*f + (d*x + c)*a*f^2 - a*c*f^2)*d)","C",0
269,1,3825,0,1.795914," ","integrate((f*x+e)^3*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, c e^{2} f {\left(\frac{2}{a d \sin\left(d x + c\right) + a d} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a d} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a d}\right)} + e^{3} {\left(\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2}{a \sin\left(d x + c\right) + a}\right)} - \frac{4 \, {\left(12 \, d^{2} e^{2} f - 24 \, c d e f^{2} + 12 \, c^{2} f^{3} + {\left(6 \, {\left(c^{2} + 4\right)} d e f^{2} - 2 \, {\left(c^{3} + 12 \, c\right)} f^{3} - 2 \, {\left(3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(12 i \, c^{2} + 48 i\right)} d e f^{2} + {\left(-4 i \, c^{3} - 48 i \, c\right)} f^{3}\right)} \cos\left(d x + c\right) - {\left({\left(6 i \, c^{2} + 24 i\right)} d e f^{2} + {\left(-2 i \, c^{3} - 24 i \, c\right)} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(6 \, c^{2} d e f^{2} - 2 \, c^{3} f^{3} - 2 \, {\left(3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, c^{2} d e f^{2} + 4 i \, c^{3} f^{3}\right)} \cos\left(d x + c\right) + {\left(-6 i \, c^{2} d e f^{2} + 2 i \, c^{3} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(2 \, {\left(d x + c\right)}^{3} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)} - 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-4 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} + {\left(-12 i \, c^{2} - 48 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-6 i \, d e f^{2} + 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} + {\left(-6 i \, c^{2} - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(2 \, {\left(d x + c\right)}^{3} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)} - 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-4 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-6 i \, d e f^{2} + 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + 12 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(4 \, {\left(d x + c\right)}^{3} f^{3} - 12 i \, d^{2} e^{2} f + 12 \, {\left(c^{2} + 2 i \, c\right)} d e f^{2} - 4 \, {\left(c^{3} + 3 i \, c^{2}\right)} f^{3} + {\left(12 \, d e f^{2} - {\left(12 \, c - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(12 \, d^{2} e^{2} f - {\left(24 \, c - 24 i\right)} d e f^{2} + 12 \, {\left(c^{2} - 2 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(6 \, d^{2} e^{2} f - 12 \, c d e f^{2} + 6 \, {\left(d x + c\right)}^{2} f^{3} + 6 \, {\left(c^{2} + 4\right)} f^{3} + 12 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} + 4\right)} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-12 i \, c^{2} - 48 i\right)} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-6 i \, c^{2} - 24 i\right)} f^{3} + {\left(-12 i \, d e f^{2} + 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + {\left(c^{2} + 4\right)} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(6 \, d^{2} e^{2} f - 12 \, c d e f^{2} + 6 \, {\left(d x + c\right)}^{2} f^{3} + 6 \, c^{2} f^{3} + 12 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(12 i \, d^{2} e^{2} f - 24 i \, c d e f^{2} + 12 i \, {\left(d x + c\right)}^{2} f^{3} + 12 i \, c^{2} f^{3} + {\left(24 i \, d e f^{2} - 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, {\left(d x + c\right)}^{2} f^{3} + 6 i \, c^{2} f^{3} + {\left(12 i \, d e f^{2} - 12 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(i \, {\left(d x + c\right)}^{3} f^{3} + {\left(3 i \, c^{2} + 12 i\right)} d e f^{2} + {\left(-i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(3 i \, d e f^{2} - 3 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 i \, d^{2} e^{2} f - 6 i \, c d e f^{2} + {\left(3 i \, c^{2} + 12 i\right)} f^{3}\right)} {\left(d x + c\right)} + {\left(-i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-3 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-3 i \, d e f^{2} + 3 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-3 i \, d^{2} e^{2} f + 6 i \, c d e f^{2} + {\left(-3 i \, c^{2} - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + {\left(c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(2 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(6 i \, c^{2} + 24 i\right)} d e f^{2} + {\left(-2 i \, c^{3} - 24 i \, c\right)} f^{3} + {\left(6 i \, d e f^{2} - 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + {\left(6 i \, c^{2} + 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-3 i \, c^{2} d e f^{2} - i \, {\left(d x + c\right)}^{3} f^{3} + i \, c^{3} f^{3} + {\left(-3 i \, d e f^{2} + 3 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-3 i \, d^{2} e^{2} f + 6 i \, c d e f^{2} - 3 i \, c^{2} f^{3}\right)} {\left(d x + c\right)} + {\left(3 i \, c^{2} d e f^{2} + i \, {\left(d x + c\right)}^{3} f^{3} - i \, c^{3} f^{3} + {\left(3 i \, d e f^{2} - 3 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 i \, d^{2} e^{2} f - 6 i \, c d e f^{2} + 3 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(3 \, c^{2} d e f^{2} + {\left(d x + c\right)}^{3} f^{3} - c^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 3 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-6 i \, c^{2} d e f^{2} - 2 i \, {\left(d x + c\right)}^{3} f^{3} + 2 i \, c^{3} f^{3} + {\left(-6 i \, d e f^{2} + 6 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - {\left(12 \, f^{3} \cos\left(2 \, d x + 2 \, c\right) + 24 i \, f^{3} \cos\left(d x + c\right) + 12 i \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 24 \, f^{3} \sin\left(d x + c\right) - 12 \, f^{3}\right)} {\rm Li}_{4}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left(12 \, f^{3} \cos\left(2 \, d x + 2 \, c\right) + 24 i \, f^{3} \cos\left(d x + c\right) + 12 i \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 24 \, f^{3} \sin\left(d x + c\right) - 12 \, f^{3}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(12 i \, d e f^{2} + 12 i \, {\left(d x + c\right)} f^{3} - 12 i \, c f^{3} + {\left(-12 i \, d e f^{2} - 12 i \, {\left(d x + c\right)} f^{3} + 12 i \, c f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) + 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(24 i \, d e f^{2} + 24 i \, {\left(d x + c\right)} f^{3} - 24 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-12 i \, d e f^{2} - 12 i \, {\left(d x + c\right)} f^{3} + 12 i \, c f^{3} + {\left(12 i \, d e f^{2} + 12 i \, {\left(d x + c\right)} f^{3} - 12 i \, c f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) - 12 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-24 i \, d e f^{2} - 24 i \, {\left(d x + c\right)} f^{3} + 24 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-24 i \, d e f^{2} + 24 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(-4 i \, {\left(d x + c\right)}^{3} f^{3} - 12 \, d^{2} e^{2} f + {\left(-12 i \, c^{2} + 24 \, c\right)} d e f^{2} + {\left(4 i \, c^{3} - 12 \, c^{2}\right)} f^{3} + {\left(-12 i \, d e f^{2} - 12 \, {\left(-i \, c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-12 i \, d^{2} e^{2} f - 24 \, {\left(-i \, c - 1\right)} d e f^{2} + {\left(-12 i \, c^{2} - 24 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-4 i \, a d^{3} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a d^{3} \cos\left(d x + c\right) + 4 \, a d^{3} \sin\left(2 \, d x + 2 \, c\right) + 8 i \, a d^{3} \sin\left(d x + c\right) + 4 i \, a d^{3}}}{4 \, d}"," ",0,"1/4*(3*c*e^2*f*(2/(a*d*sin(d*x + c) + a*d) - log(sin(d*x + c) + 1)/(a*d) + log(sin(d*x + c) - 1)/(a*d)) + e^3*(log(sin(d*x + c) + 1)/a - log(sin(d*x + c) - 1)/a - 2/(a*sin(d*x + c) + a)) - 4*(12*d^2*e^2*f - 24*c*d*e*f^2 + 12*c^2*f^3 + (6*(c^2 + 4)*d*e*f^2 - 2*(c^3 + 12*c)*f^3 - 2*(3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3)*cos(2*d*x + 2*c) - ((12*I*c^2 + 48*I)*d*e*f^2 + (-4*I*c^3 - 48*I*c)*f^3)*cos(d*x + c) - ((6*I*c^2 + 24*I)*d*e*f^2 + (-2*I*c^3 - 24*I*c)*f^3)*sin(2*d*x + 2*c) + 4*(3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (6*c^2*d*e*f^2 - 2*c^3*f^3 - 2*(3*c^2*d*e*f^2 - c^3*f^3)*cos(2*d*x + 2*c) + (-12*I*c^2*d*e*f^2 + 4*I*c^3*f^3)*cos(d*x + c) + (-6*I*c^2*d*e*f^2 + 2*I*c^3*f^3)*sin(2*d*x + 2*c) + 4*(3*c^2*d*e*f^2 - c^3*f^3)*sin(d*x + c))*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (2*(d*x + c)^3*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 6*(d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 4)*f^3)*(d*x + c) - 2*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 4)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-4*I*(d*x + c)^3*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c)^2 + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 + (-12*I*c^2 - 48*I)*f^3)*(d*x + c))*cos(d*x + c) + (-2*I*(d*x + c)^3*f^3 + (-6*I*d*e*f^2 + 6*I*c*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 + (-6*I*c^2 - 24*I)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 4*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 4)*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (2*(d*x + c)^3*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c) - 2*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-4*I*(d*x + c)^3*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c)^2 + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3)*(d*x + c))*cos(d*x + c) + (-2*I*(d*x + c)^3*f^3 + (-6*I*d*e*f^2 + 6*I*c*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*c^2*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 4*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + 12*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (4*(d*x + c)^3*f^3 - 12*I*d^2*e^2*f + 12*(c^2 + 2*I*c)*d*e*f^2 - 4*(c^3 + 3*I*c^2)*f^3 + (12*d*e*f^2 - (12*c - 12*I)*f^3)*(d*x + c)^2 + (12*d^2*e^2*f - (24*c - 24*I)*d*e*f^2 + 12*(c^2 - 2*I*c)*f^3)*(d*x + c))*cos(d*x + c) - (6*d^2*e^2*f - 12*c*d*e*f^2 + 6*(d*x + c)^2*f^3 + 6*(c^2 + 4)*f^3 + 12*(d*e*f^2 - c*f^3)*(d*x + c) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 + 4)*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*(d*x + c)^2*f^3 + (-12*I*c^2 - 48*I)*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*cos(d*x + c) + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*(d*x + c)^2*f^3 + (-6*I*c^2 - 24*I)*f^3 + (-12*I*d*e*f^2 + 12*I*c*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 12*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + (c^2 + 4)*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) + (6*d^2*e^2*f - 12*c*d*e*f^2 + 6*(d*x + c)^2*f^3 + 6*c^2*f^3 + 12*(d*e*f^2 - c*f^3)*(d*x + c) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(2*d*x + 2*c) - (12*I*d^2*e^2*f - 24*I*c*d*e*f^2 + 12*I*(d*x + c)^2*f^3 + 12*I*c^2*f^3 + (24*I*d*e*f^2 - 24*I*c*f^3)*(d*x + c))*cos(d*x + c) - (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*(d*x + c)^2*f^3 + 6*I*c^2*f^3 + (12*I*d*e*f^2 - 12*I*c*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 12*(d^2*e^2*f - 2*c*d*e*f^2 + (d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*dilog(-I*e^(I*d*x + I*c)) - (I*(d*x + c)^3*f^3 + (3*I*c^2 + 12*I)*d*e*f^2 + (-I*c^3 - 12*I*c)*f^3 + (3*I*d*e*f^2 - 3*I*c*f^3)*(d*x + c)^2 + (3*I*d^2*e^2*f - 6*I*c*d*e*f^2 + (3*I*c^2 + 12*I)*f^3)*(d*x + c) + (-I*(d*x + c)^3*f^3 + (-3*I*c^2 - 12*I)*d*e*f^2 + (I*c^3 + 12*I*c)*f^3 + (-3*I*d*e*f^2 + 3*I*c*f^3)*(d*x + c)^2 + (-3*I*d^2*e^2*f + 6*I*c*d*e*f^2 + (-3*I*c^2 - 12*I)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + 2*((d*x + c)^3*f^3 + 3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 4)*f^3)*(d*x + c))*cos(d*x + c) + ((d*x + c)^3*f^3 + 3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + (c^2 + 4)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (2*I*(d*x + c)^3*f^3 + (6*I*c^2 + 24*I)*d*e*f^2 + (-2*I*c^3 - 24*I*c)*f^3 + (6*I*d*e*f^2 - 6*I*c*f^3)*(d*x + c)^2 + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + (6*I*c^2 + 24*I)*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (-3*I*c^2*d*e*f^2 - I*(d*x + c)^3*f^3 + I*c^3*f^3 + (-3*I*d*e*f^2 + 3*I*c*f^3)*(d*x + c)^2 + (-3*I*d^2*e^2*f + 6*I*c*d*e*f^2 - 3*I*c^2*f^3)*(d*x + c) + (3*I*c^2*d*e*f^2 + I*(d*x + c)^3*f^3 - I*c^3*f^3 + (3*I*d*e*f^2 - 3*I*c*f^3)*(d*x + c)^2 + (3*I*d^2*e^2*f - 6*I*c*d*e*f^2 + 3*I*c^2*f^3)*(d*x + c))*cos(2*d*x + 2*c) - 2*(3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*cos(d*x + c) - (3*c^2*d*e*f^2 + (d*x + c)^3*f^3 - c^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 3*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (-6*I*c^2*d*e*f^2 - 2*I*(d*x + c)^3*f^3 + 2*I*c^3*f^3 + (-6*I*d*e*f^2 + 6*I*c*f^3)*(d*x + c)^2 + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*c^2*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - (12*f^3*cos(2*d*x + 2*c) + 24*I*f^3*cos(d*x + c) + 12*I*f^3*sin(2*d*x + 2*c) - 24*f^3*sin(d*x + c) - 12*f^3)*polylog(4, I*e^(I*d*x + I*c)) + (12*f^3*cos(2*d*x + 2*c) + 24*I*f^3*cos(d*x + c) + 12*I*f^3*sin(2*d*x + 2*c) - 24*f^3*sin(d*x + c) - 12*f^3)*polylog(4, -I*e^(I*d*x + I*c)) - (12*I*d*e*f^2 + 12*I*(d*x + c)*f^3 - 12*I*c*f^3 + (-12*I*d*e*f^2 - 12*I*(d*x + c)*f^3 + 12*I*c*f^3)*cos(2*d*x + 2*c) + 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) + 12*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(2*d*x + 2*c) + (24*I*d*e*f^2 + 24*I*(d*x + c)*f^3 - 24*I*c*f^3)*sin(d*x + c))*polylog(3, I*e^(I*d*x + I*c)) - (-12*I*d*e*f^2 - 12*I*(d*x + c)*f^3 + 12*I*c*f^3 + (12*I*d*e*f^2 + 12*I*(d*x + c)*f^3 - 12*I*c*f^3)*cos(2*d*x + 2*c) - 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) - 12*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(2*d*x + 2*c) + (-24*I*d*e*f^2 - 24*I*(d*x + c)*f^3 + 24*I*c*f^3)*sin(d*x + c))*polylog(3, -I*e^(I*d*x + I*c)) - (-12*I*(d*x + c)^2*f^3 + (-24*I*d*e*f^2 + 24*I*c*f^3)*(d*x + c))*sin(2*d*x + 2*c) - (-4*I*(d*x + c)^3*f^3 - 12*d^2*e^2*f + (-12*I*c^2 + 24*c)*d*e*f^2 + (4*I*c^3 - 12*c^2)*f^3 + (-12*I*d*e*f^2 - 12*(-I*c - 1)*f^3)*(d*x + c)^2 + (-12*I*d^2*e^2*f - 24*(-I*c - 1)*d*e*f^2 + (-12*I*c^2 - 24*c)*f^3)*(d*x + c))*sin(d*x + c))/(-4*I*a*d^3*cos(2*d*x + 2*c) + 8*a*d^3*cos(d*x + c) + 4*a*d^3*sin(2*d*x + 2*c) + 8*I*a*d^3*sin(d*x + c) + 4*I*a*d^3))/d","B",0
270,1,1923,0,0.835882," ","integrate((f*x+e)^2*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, c e f {\left(\frac{2}{a d \sin\left(d x + c\right) + a d} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a d} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a d}\right)} + e^{2} {\left(\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2}{a \sin\left(d x + c\right) + a}\right)} - \frac{4 \, {\left(8 \, {\left(d x + c\right)} f^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 i \, {\left(d x + c\right)} f^{2} \sin\left(2 \, d x + 2 \, c\right) + 8 \, d e f - 8 \, c f^{2} - {\left(2 \, {\left(c^{2} + 4\right)} f^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(4 i \, c^{2} + 16 i\right)} f^{2} \cos\left(d x + c\right) + {\left(2 i \, c^{2} + 8 i\right)} f^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(c^{2} + 4\right)} f^{2} \sin\left(d x + c\right) - 2 \, {\left(c^{2} + 4\right)} f^{2}\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(2 \, c^{2} f^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 i \, c^{2} f^{2} \cos\left(d x + c\right) + 2 i \, c^{2} f^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, c^{2} f^{2} \sin\left(d x + c\right) - 2 \, c^{2} f^{2}\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(2 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)} - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-4 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-4 i \, d e f + 4 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(2 \, {\left(d x + c\right)}^{2} f^{2} + 4 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)} - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-4 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-4 i \, d e f + 4 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + {\left(4 \, {\left(d x + c\right)}^{2} f^{2} - 8 i \, d e f + 4 \, {\left(c^{2} + 2 i \, c\right)} f^{2} + {\left(8 \, d e f - {\left(8 \, c - 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(4 \, d e f + 4 \, {\left(d x + c\right)} f^{2} - 4 \, c f^{2} - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-8 i \, d e f - 8 i \, {\left(d x + c\right)} f^{2} + 8 i \, c f^{2}\right)} \cos\left(d x + c\right) + {\left(-4 i \, d e f - 4 i \, {\left(d x + c\right)} f^{2} + 4 i \, c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(4 \, d e f + 4 \, {\left(d x + c\right)} f^{2} - 4 \, c f^{2} - 4 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(8 i \, d e f + 8 i \, {\left(d x + c\right)} f^{2} - 8 i \, c f^{2}\right)} \cos\left(d x + c\right) - {\left(4 i \, d e f + 4 i \, {\left(d x + c\right)} f^{2} - 4 i \, c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + 8 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(i \, {\left(d x + c\right)}^{2} f^{2} + {\left(i \, c^{2} + 4 i\right)} f^{2} + {\left(2 i \, d e f - 2 i \, c f^{2}\right)} {\left(d x + c\right)} + {\left(-i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-i \, c^{2} - 4 i\right)} f^{2} + {\left(-2 i \, d e f + 2 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + {\left(c^{2} + 4\right)} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left({\left(d x + c\right)}^{2} f^{2} + {\left(c^{2} + 4\right)} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(2 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(2 i \, c^{2} + 8 i\right)} f^{2} + {\left(4 i \, d e f - 4 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-i \, {\left(d x + c\right)}^{2} f^{2} - i \, c^{2} f^{2} + {\left(-2 i \, d e f + 2 i \, c f^{2}\right)} {\left(d x + c\right)} + {\left(i \, {\left(d x + c\right)}^{2} f^{2} + i \, c^{2} f^{2} + {\left(2 i \, d e f - 2 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left({\left(d x + c\right)}^{2} f^{2} + c^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, {\left(d x + c\right)}^{2} f^{2} - 2 i \, c^{2} f^{2} + {\left(-4 i \, d e f + 4 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-4 i \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, f^{2} \cos\left(d x + c\right) + 4 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 8 i \, f^{2} \sin\left(d x + c\right) + 4 i \, f^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) - {\left(4 i \, f^{2} \cos\left(2 \, d x + 2 \, c\right) - 8 \, f^{2} \cos\left(d x + c\right) - 4 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) - 8 i \, f^{2} \sin\left(d x + c\right) - 4 i \, f^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-4 i \, {\left(d x + c\right)}^{2} f^{2} - 8 \, d e f + {\left(-4 i \, c^{2} + 8 \, c\right)} f^{2} + {\left(-8 i \, d e f - 8 \, {\left(-i \, c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-4 i \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a d^{2} \cos\left(d x + c\right) + 4 \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) + 8 i \, a d^{2} \sin\left(d x + c\right) + 4 i \, a d^{2}}}{4 \, d}"," ",0,"1/4*(2*c*e*f*(2/(a*d*sin(d*x + c) + a*d) - log(sin(d*x + c) + 1)/(a*d) + log(sin(d*x + c) - 1)/(a*d)) + e^2*(log(sin(d*x + c) + 1)/a - log(sin(d*x + c) - 1)/a - 2/(a*sin(d*x + c) + a)) - 4*(8*(d*x + c)*f^2*cos(2*d*x + 2*c) + 8*I*(d*x + c)*f^2*sin(2*d*x + 2*c) + 8*d*e*f - 8*c*f^2 - (2*(c^2 + 4)*f^2*cos(2*d*x + 2*c) + (4*I*c^2 + 16*I)*f^2*cos(d*x + c) + (2*I*c^2 + 8*I)*f^2*sin(2*d*x + 2*c) - 4*(c^2 + 4)*f^2*sin(d*x + c) - 2*(c^2 + 4)*f^2)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (2*c^2*f^2*cos(2*d*x + 2*c) + 4*I*c^2*f^2*cos(d*x + c) + 2*I*c^2*f^2*sin(2*d*x + 2*c) - 4*c^2*f^2*sin(d*x + c) - 2*c^2*f^2)*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (2*(d*x + c)^2*f^2 + 4*(d*e*f - c*f^2)*(d*x + c) - 2*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (-4*I*(d*x + c)^2*f^2 + (-8*I*d*e*f + 8*I*c*f^2)*(d*x + c))*cos(d*x + c) + (-2*I*(d*x + c)^2*f^2 + (-4*I*d*e*f + 4*I*c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + 4*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (2*(d*x + c)^2*f^2 + 4*(d*e*f - c*f^2)*(d*x + c) - 2*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (-4*I*(d*x + c)^2*f^2 + (-8*I*d*e*f + 8*I*c*f^2)*(d*x + c))*cos(d*x + c) + (-2*I*(d*x + c)^2*f^2 + (-4*I*d*e*f + 4*I*c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + 4*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + (4*(d*x + c)^2*f^2 - 8*I*d*e*f + 4*(c^2 + 2*I*c)*f^2 + (8*d*e*f - (8*c - 8*I)*f^2)*(d*x + c))*cos(d*x + c) - (4*d*e*f + 4*(d*x + c)*f^2 - 4*c*f^2 - 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(2*d*x + 2*c) + (-8*I*d*e*f - 8*I*(d*x + c)*f^2 + 8*I*c*f^2)*cos(d*x + c) + (-4*I*d*e*f - 4*I*(d*x + c)*f^2 + 4*I*c*f^2)*sin(2*d*x + 2*c) + 8*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) + (4*d*e*f + 4*(d*x + c)*f^2 - 4*c*f^2 - 4*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(2*d*x + 2*c) - (8*I*d*e*f + 8*I*(d*x + c)*f^2 - 8*I*c*f^2)*cos(d*x + c) - (4*I*d*e*f + 4*I*(d*x + c)*f^2 - 4*I*c*f^2)*sin(2*d*x + 2*c) + 8*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*dilog(-I*e^(I*d*x + I*c)) - (I*(d*x + c)^2*f^2 + (I*c^2 + 4*I)*f^2 + (2*I*d*e*f - 2*I*c*f^2)*(d*x + c) + (-I*(d*x + c)^2*f^2 + (-I*c^2 - 4*I)*f^2 + (-2*I*d*e*f + 2*I*c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + 2*((d*x + c)^2*f^2 + (c^2 + 4)*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) + ((d*x + c)^2*f^2 + (c^2 + 4)*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (2*I*(d*x + c)^2*f^2 + (2*I*c^2 + 8*I)*f^2 + (4*I*d*e*f - 4*I*c*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (-I*(d*x + c)^2*f^2 - I*c^2*f^2 + (-2*I*d*e*f + 2*I*c*f^2)*(d*x + c) + (I*(d*x + c)^2*f^2 + I*c^2*f^2 + (2*I*d*e*f - 2*I*c*f^2)*(d*x + c))*cos(2*d*x + 2*c) - 2*((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) - ((d*x + c)^2*f^2 + c^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (-2*I*(d*x + c)^2*f^2 - 2*I*c^2*f^2 + (-4*I*d*e*f + 4*I*c*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - (-4*I*f^2*cos(2*d*x + 2*c) + 8*f^2*cos(d*x + c) + 4*f^2*sin(2*d*x + 2*c) + 8*I*f^2*sin(d*x + c) + 4*I*f^2)*polylog(3, I*e^(I*d*x + I*c)) - (4*I*f^2*cos(2*d*x + 2*c) - 8*f^2*cos(d*x + c) - 4*f^2*sin(2*d*x + 2*c) - 8*I*f^2*sin(d*x + c) - 4*I*f^2)*polylog(3, -I*e^(I*d*x + I*c)) - (-4*I*(d*x + c)^2*f^2 - 8*d*e*f + (-4*I*c^2 + 8*c)*f^2 + (-8*I*d*e*f - 8*(-I*c - 1)*f^2)*(d*x + c))*sin(d*x + c))/(-4*I*a*d^2*cos(2*d*x + 2*c) + 8*a*d^2*cos(d*x + c) + 4*a*d^2*sin(2*d*x + 2*c) + 8*I*a*d^2*sin(d*x + c) + 4*I*a*d^2))/d","B",0
271,1,730,0,1.393477," ","integrate((f*x+e)*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d e \cos\left(2 \, d x + 2 \, c\right) + 4 i \, d e \cos\left(d x + c\right) + 2 i \, d e \sin\left(2 \, d x + 2 \, c\right) - 4 \, d e \sin\left(d x + c\right) - 2 \, d e\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(2 \, d e \cos\left(2 \, d x + 2 \, c\right) + 4 i \, d e \cos\left(d x + c\right) + 2 i \, d e \sin\left(2 \, d x + 2 \, c\right) - 4 \, d e \sin\left(d x + c\right) - 2 \, d e\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(2 \, d f x \cos\left(2 \, d x + 2 \, c\right) + 4 i \, d f x \cos\left(d x + c\right) + 2 i \, d f x \sin\left(2 \, d x + 2 \, c\right) - 4 \, d f x \sin\left(d x + c\right) - 2 \, d f x\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(2 \, d f x \cos\left(2 \, d x + 2 \, c\right) + 4 i \, d f x \cos\left(d x + c\right) + 2 i \, d f x \sin\left(2 \, d x + 2 \, c\right) - 4 \, d f x \sin\left(d x + c\right) - 2 \, d f x\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(4 \, d f x + 4 \, d e - 4 i \, f\right)} \cos\left(d x + c\right) - {\left(2 \, f \cos\left(2 \, d x + 2 \, c\right) + 4 i \, f \cos\left(d x + c\right) + 2 i \, f \sin\left(2 \, d x + 2 \, c\right) - 4 \, f \sin\left(d x + c\right) - 2 \, f\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(2 \, f \cos\left(2 \, d x + 2 \, c\right) + 4 i \, f \cos\left(d x + c\right) + 2 i \, f \sin\left(2 \, d x + 2 \, c\right) - 4 \, f \sin\left(d x + c\right) - 2 \, f\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(i \, d f x + i \, d e + {\left(-i \, d f x - i \, d e\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(2 i \, d f x + 2 i \, d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(-i \, d f x - i \, d e + {\left(i \, d f x + i \, d e\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) - {\left(d f x + d e\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-2 i \, d f x - 2 i \, d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + {\left(-4 i \, d f x - 4 i \, d e - 4 \, f\right)} \sin\left(d x + c\right) - 4 \, f}{-4 i \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) + 8 \, a d^{2} \cos\left(d x + c\right) + 4 \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) + 8 i \, a d^{2} \sin\left(d x + c\right) + 4 i \, a d^{2}}"," ",0,"((2*d*e*cos(2*d*x + 2*c) + 4*I*d*e*cos(d*x + c) + 2*I*d*e*sin(2*d*x + 2*c) - 4*d*e*sin(d*x + c) - 2*d*e)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (2*d*e*cos(2*d*x + 2*c) + 4*I*d*e*cos(d*x + c) + 2*I*d*e*sin(2*d*x + 2*c) - 4*d*e*sin(d*x + c) - 2*d*e)*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (2*d*f*x*cos(2*d*x + 2*c) + 4*I*d*f*x*cos(d*x + c) + 2*I*d*f*x*sin(2*d*x + 2*c) - 4*d*f*x*sin(d*x + c) - 2*d*f*x)*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (2*d*f*x*cos(2*d*x + 2*c) + 4*I*d*f*x*cos(d*x + c) + 2*I*d*f*x*sin(2*d*x + 2*c) - 4*d*f*x*sin(d*x + c) - 2*d*f*x)*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (4*d*f*x + 4*d*e - 4*I*f)*cos(d*x + c) - (2*f*cos(2*d*x + 2*c) + 4*I*f*cos(d*x + c) + 2*I*f*sin(2*d*x + 2*c) - 4*f*sin(d*x + c) - 2*f)*dilog(I*e^(I*d*x + I*c)) + (2*f*cos(2*d*x + 2*c) + 4*I*f*cos(d*x + c) + 2*I*f*sin(2*d*x + 2*c) - 4*f*sin(d*x + c) - 2*f)*dilog(-I*e^(I*d*x + I*c)) + (I*d*f*x + I*d*e + (-I*d*f*x - I*d*e)*cos(2*d*x + 2*c) + 2*(d*f*x + d*e)*cos(d*x + c) + (d*f*x + d*e)*sin(2*d*x + 2*c) + (2*I*d*f*x + 2*I*d*e)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (-I*d*f*x - I*d*e + (I*d*f*x + I*d*e)*cos(2*d*x + 2*c) - 2*(d*f*x + d*e)*cos(d*x + c) - (d*f*x + d*e)*sin(2*d*x + 2*c) + (-2*I*d*f*x - 2*I*d*e)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + (-4*I*d*f*x - 4*I*d*e - 4*f)*sin(d*x + c) - 4*f)/(-4*I*a*d^2*cos(2*d*x + 2*c) + 8*a*d^2*cos(d*x + c) + 4*a*d^2*sin(2*d*x + 2*c) + 8*I*a*d^2*sin(d*x + c) + 4*I*a*d^2)","B",0
272,1,47,0,0.486872," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2}{a \sin\left(d x + c\right) + a}}{4 \, d}"," ",0,"1/4*(log(sin(d*x + c) + 1)/a - log(sin(d*x + c) - 1)/a - 2/(a*sin(d*x + c) + a))/d","A",0
273,0,0,0,0.000000," ","integrate(sec(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d f x + d e\right)} \sin\left(d x + c\right)^{2} - {\left(f \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - f \cos\left(d x + c\right) - \frac{1}{2} \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \int \frac{{\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} + 4 \, f^{2}\right)} \cos\left(d x + c\right)}{a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)}\,{d x} - \frac{1}{2} \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \int \frac{\cos\left(d x + c\right)}{a f x + {\left(a f x + a e\right)} \cos\left(d x + c\right)^{2} + {\left(a f x + a e\right)} \sin\left(d x + c\right)^{2} + a e - 2 \, {\left(a f x + a e\right)} \sin\left(d x + c\right)}\,{d x} + {\left({\left(d f x + d e\right)} \cos\left(d x + c\right) - f \sin\left(d x + c\right) - f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)}{a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sin\left(d x + c\right)}"," ",0,"-(2*(d*f*x + d*e)*cos(d*x + c)^2 + 2*(d*f*x + d*e)*sin(d*x + c)^2 - (f*cos(d*x + c) + (d*f*x + d*e)*sin(d*x + c))*cos(2*d*x + 2*c) - f*cos(d*x + c) - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(2*d*x + 2*c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(d*x + c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(d*x + c)*sin(2*d*x + 2*c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(2*d*x + 2*c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c)^2 - 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 + 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c))*cos(2*d*x + 2*c) + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c))*integrate(1/2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 + 4*f^2)*cos(d*x + c)/(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)^2 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c)^2 + 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c)), x) - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(2*d*x + 2*c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(d*x + c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(d*x + c)*sin(2*d*x + 2*c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(2*d*x + 2*c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c)^2 - 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 + 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c))*cos(2*d*x + 2*c) + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c))*integrate(1/2*cos(d*x + c)/(a*f*x + (a*f*x + a*e)*cos(d*x + c)^2 + (a*f*x + a*e)*sin(d*x + c)^2 + a*e - 2*(a*f*x + a*e)*sin(d*x + c)), x) + ((d*f*x + d*e)*cos(d*x + c) - f*sin(d*x + c) - f)*sin(2*d*x + 2*c) + (d*f*x + d*e)*sin(d*x + c))/(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(2*d*x + 2*c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(d*x + c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cos(d*x + c)*sin(2*d*x + 2*c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(2*d*x + 2*c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c)^2 - 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 + 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c))*cos(2*d*x + 2*c) + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sin(d*x + c))","F",0
274,0,0,0,0.000000," ","integrate(sec(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d f x + d e\right)} \sin\left(d x + c\right)^{2} - {\left(2 \, f \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) - 2 \, f \cos\left(d x + c\right) - \frac{1}{2} \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)\right)} \int \frac{{\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} + 12 \, f^{2}\right)} \cos\left(d x + c\right)}{a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4} + {\left(a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4}\right)} \sin\left(d x + c\right)}\,{d x} - \frac{1}{2} \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)\right)} \int \frac{\cos\left(d x + c\right)}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}\,{d x} + {\left({\left(d f x + d e\right)} \cos\left(d x + c\right) - 2 \, f \sin\left(d x + c\right) - 2 \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)}{a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \cos\left(d x + c\right) \sin\left(2 \, d x + 2 \, c\right) + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(2 \, d x + 2 \, c\right)^{2} + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(2 \, d x + 2 \, c\right) + 4 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} \sin\left(d x + c\right)}"," ",0,"-(2*(d*f*x + d*e)*cos(d*x + c)^2 + 2*(d*f*x + d*e)*sin(d*x + c)^2 - (2*f*cos(d*x + c) + (d*f*x + d*e)*sin(d*x + c))*cos(2*d*x + 2*c) - 2*f*cos(d*x + c) - (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(2*d*x + 2*c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)*sin(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(2*d*x + 2*c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c)^2 - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c))*cos(2*d*x + 2*c) + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c))*integrate(1/2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 + 12*f^2)*cos(d*x + c)/(a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4 + (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4)*cos(d*x + c)^2 + (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4)*sin(d*x + c)^2 + 2*(a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4)*sin(d*x + c)), x) - (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(2*d*x + 2*c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)*sin(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(2*d*x + 2*c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c)^2 - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c))*cos(2*d*x + 2*c) + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c))*integrate(1/2*cos(d*x + c)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*cos(d*x + c)^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)^2 - 2*(a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x) + ((d*f*x + d*e)*cos(d*x + c) - 2*f*sin(d*x + c) - 2*f)*sin(2*d*x + 2*c) + (d*f*x + d*e)*sin(d*x + c))/(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(2*d*x + 2*c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*cos(d*x + c)*sin(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(2*d*x + 2*c)^2 + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c)^2 - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c))*cos(2*d*x + 2*c) + 4*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*sin(d*x + c))","F",0
275,1,5107,0,2.182507," ","integrate((f*x+e)^3*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{24 \, c^{2} e f^{2} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{a d^{2} + \frac{2 \, a d^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a d^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a d^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{6 \, {\left(4 \, {\left(8 \, {\left(d x + c\right)} \cos\left(d x + c\right) - \sin\left(3 \, d x + 3 \, c\right) - \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 16 \, {\left(2 \, d x + 4 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 2 \, c + \cos\left(d x + c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 8 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(2 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, \sin\left(3 \, d x + 3 \, c\right)^{2} - 4 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, \sin\left(3 \, d x + 3 \, c\right)^{2} - 4 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(4 \, d x + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 4 \, c + \cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 4 \, \sin\left(d x + c\right) - 1\right)} \sin\left(3 \, d x + 3 \, c\right) + 8 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 8 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)\right)} c e f^{2}}{a d^{2} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d^{2} \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + 4 \, a d^{2} \cos\left(d x + c\right)^{2} + a d^{2} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d^{2} \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, a d^{2} \sin\left(d x + c\right)^{2} + 4 \, a d^{2} \sin\left(d x + c\right) + a d^{2} - 2 \, {\left(2 \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) + 2 \, a d^{2} \sin\left(d x + c\right) + a d^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a d^{2} \cos\left(3 \, d x + 3 \, c\right) + a d^{2} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a d^{2} \sin\left(d x + c\right) + a d^{2}\right)} \sin\left(3 \, d x + 3 \, c\right)} - \frac{24 \, c e^{2} f {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{a d + \frac{2 \, a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a d \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a d \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{3 \, {\left(4 \, {\left(8 \, {\left(d x + c\right)} \cos\left(d x + c\right) - \sin\left(3 \, d x + 3 \, c\right) - \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 16 \, {\left(2 \, d x + 4 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 2 \, c + \cos\left(d x + c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 8 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(2 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, \sin\left(3 \, d x + 3 \, c\right)^{2} - 4 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, \sin\left(3 \, d x + 3 \, c\right)^{2} - 4 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(4 \, d x + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 4 \, c + \cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 4 \, \sin\left(d x + c\right) - 1\right)} \sin\left(3 \, d x + 3 \, c\right) + 8 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 8 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)\right)} e^{2} f}{a d \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, a d \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + 4 \, a d \cos\left(d x + c\right)^{2} + a d \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, a d \sin\left(d x + c\right)^{2} + 4 \, a d \sin\left(d x + c\right) + a d - 2 \, {\left(2 \, a d \sin\left(3 \, d x + 3 \, c\right) + 2 \, a d \sin\left(d x + c\right) + a d\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a d \cos\left(3 \, d x + 3 \, c\right) + a d \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a d \sin\left(d x + c\right) + a d\right)} \sin\left(3 \, d x + 3 \, c\right)} + \frac{8 \, e^{3} {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{12 \, {\left(24 \, d e f^{2} - 8 \, {\left(2 \, c^{3} + 3 \, c\right)} f^{3} - {\left(6 \, {\left(5 \, c^{2} + 4\right)} f^{3} \cos\left(4 \, d x + 4 \, c\right) + {\left(60 i \, c^{2} + 48 i\right)} f^{3} \cos\left(3 \, d x + 3 \, c\right) + {\left(60 i \, c^{2} + 48 i\right)} f^{3} \cos\left(d x + c\right) + {\left(30 i \, c^{2} + 24 i\right)} f^{3} \sin\left(4 \, d x + 4 \, c\right) - 12 \, {\left(5 \, c^{2} + 4\right)} f^{3} \sin\left(3 \, d x + 3 \, c\right) - 12 \, {\left(5 \, c^{2} + 4\right)} f^{3} \sin\left(d x + c\right) - 6 \, {\left(5 \, c^{2} + 4\right)} f^{3}\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(18 \, c^{2} f^{3} \cos\left(4 \, d x + 4 \, c\right) + 36 i \, c^{2} f^{3} \cos\left(3 \, d x + 3 \, c\right) + 36 i \, c^{2} f^{3} \cos\left(d x + c\right) + 18 i \, c^{2} f^{3} \sin\left(4 \, d x + 4 \, c\right) - 36 \, c^{2} f^{3} \sin\left(3 \, d x + 3 \, c\right) - 36 \, c^{2} f^{3} \sin\left(d x + c\right) - 18 \, c^{2} f^{3}\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(30 \, {\left(d x + c\right)}^{2} f^{3} + 60 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - 30 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-60 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-120 i \, d e f^{2} + 120 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-60 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-120 i \, d e f^{2} + 120 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-30 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-60 i \, d e f^{2} + 60 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 60 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 60 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) + {\left(18 \, {\left(d x + c\right)}^{2} f^{3} + 36 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - 18 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(36 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(72 i \, d e f^{2} - 72 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(36 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(72 i \, d e f^{2} - 72 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 36 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 36 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + 8 \, {\left(2 \, {\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(2 \, c^{2} + 1\right)} {\left(d x + c\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(-32 i \, {\left(d x + c\right)}^{3} f^{3} + 24 i \, d e f^{2} - 12 \, {\left(c^{2} + 2 i \, c\right)} f^{3} - 12 \, {\left(8 i \, d e f^{2} + {\left(-8 i \, c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} - {\left(24 \, d e f^{2} - {\left(-96 i \, c^{2} + 24 \, c - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 24 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(12 \, {\left(d x + c\right)}^{2} f^{3} - 24 i \, d e f^{2} - {\left(-32 i \, c^{3} - 12 \, c^{2} - 24 i \, c\right)} f^{3} + {\left(24 \, d e f^{2} - {\left(24 \, c - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(60 \, d e f^{2} + 60 \, {\left(d x + c\right)} f^{3} - 60 \, c f^{3} - 60 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-120 i \, d e f^{2} - 120 i \, {\left(d x + c\right)} f^{3} + 120 i \, c f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-120 i \, d e f^{2} - 120 i \, {\left(d x + c\right)} f^{3} + 120 i \, c f^{3}\right)} \cos\left(d x + c\right) + {\left(-60 i \, d e f^{2} - 60 i \, {\left(d x + c\right)} f^{3} + 60 i \, c f^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 120 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + 120 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(36 \, d e f^{2} + 36 \, {\left(d x + c\right)} f^{3} - 36 \, c f^{3} - 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-72 i \, d e f^{2} - 72 i \, {\left(d x + c\right)} f^{3} + 72 i \, c f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-72 i \, d e f^{2} - 72 i \, {\left(d x + c\right)} f^{3} + 72 i \, c f^{3}\right)} \cos\left(d x + c\right) + {\left(-36 i \, d e f^{2} - 36 i \, {\left(d x + c\right)} f^{3} + 36 i \, c f^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 72 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + 72 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(15 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(15 i \, c^{2} + 12 i\right)} f^{3} + {\left(30 i \, d e f^{2} - 30 i \, c f^{3}\right)} {\left(d x + c\right)} + {\left(-15 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-15 i \, c^{2} - 12 i\right)} f^{3} + {\left(-30 i \, d e f^{2} + 30 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(5 \, {\left(d x + c\right)}^{2} f^{3} + {\left(5 \, c^{2} + 4\right)} f^{3} + 10 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 6 \, {\left(5 \, {\left(d x + c\right)}^{2} f^{3} + {\left(5 \, c^{2} + 4\right)} f^{3} + 10 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + 3 \, {\left(5 \, {\left(d x + c\right)}^{2} f^{3} + {\left(5 \, c^{2} + 4\right)} f^{3} + 10 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(30 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(30 i \, c^{2} + 24 i\right)} f^{3} + {\left(60 i \, d e f^{2} - 60 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(30 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(30 i \, c^{2} + 24 i\right)} f^{3} + {\left(60 i \, d e f^{2} - 60 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(9 i \, {\left(d x + c\right)}^{2} f^{3} + 9 i \, c^{2} f^{3} + {\left(18 i \, d e f^{2} - 18 i \, c f^{3}\right)} {\left(d x + c\right)} + {\left(-9 i \, {\left(d x + c\right)}^{2} f^{3} - 9 i \, c^{2} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + 18 \, {\left({\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 18 \, {\left({\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + 9 \, {\left({\left(d x + c\right)}^{2} f^{3} + c^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(18 i \, {\left(d x + c\right)}^{2} f^{3} + 18 i \, c^{2} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(18 i \, {\left(d x + c\right)}^{2} f^{3} + 18 i \, c^{2} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-60 i \, f^{3} \cos\left(4 \, d x + 4 \, c\right) + 120 \, f^{3} \cos\left(3 \, d x + 3 \, c\right) + 120 \, f^{3} \cos\left(d x + c\right) + 60 \, f^{3} \sin\left(4 \, d x + 4 \, c\right) + 120 i \, f^{3} \sin\left(3 \, d x + 3 \, c\right) + 120 i \, f^{3} \sin\left(d x + c\right) + 60 i \, f^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-36 i \, f^{3} \cos\left(4 \, d x + 4 \, c\right) + 72 \, f^{3} \cos\left(3 \, d x + 3 \, c\right) + 72 \, f^{3} \cos\left(d x + c\right) + 36 \, f^{3} \sin\left(4 \, d x + 4 \, c\right) + 72 i \, f^{3} \sin\left(3 \, d x + 3 \, c\right) + 72 i \, f^{3} \sin\left(d x + c\right) + 36 i \, f^{3}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-16 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-48 i \, c^{2} - 24 i\right)} {\left(d x + c\right)} f^{3} + {\left(-48 i \, d e f^{2} + 48 i \, c f^{3}\right)} {\left(d x + c\right)}^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(32 \, {\left(d x + c\right)}^{3} f^{3} - 24 \, d e f^{2} + {\left(-12 i \, c^{2} + 24 \, c\right)} f^{3} + {\left(96 \, d e f^{2} - {\left(96 \, c + 12 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} - 24 \, {\left(i \, d e f^{2} - {\left(4 \, c^{2} + i \, c + 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(-24 i \, d e f^{2} - 24 i \, {\left(d x + c\right)} f^{3} + 24 i \, c f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(-12 i \, {\left(d x + c\right)}^{2} f^{3} - 24 \, d e f^{2} + {\left(32 \, c^{3} - 12 i \, c^{2} + 24 \, c\right)} f^{3} + {\left(-24 i \, d e f^{2} - 24 \, {\left(-i \, c - 1\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-12 i \, a d^{3} \cos\left(4 \, d x + 4 \, c\right) + 24 \, a d^{3} \cos\left(3 \, d x + 3 \, c\right) + 24 \, a d^{3} \cos\left(d x + c\right) + 12 \, a d^{3} \sin\left(4 \, d x + 4 \, c\right) + 24 i \, a d^{3} \sin\left(3 \, d x + 3 \, c\right) + 24 i \, a d^{3} \sin\left(d x + c\right) + 12 i \, a d^{3}}}{12 \, d}"," ",0,"1/12*(24*c^2*e*f^2*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a*d^2 + 2*a*d^2*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*d^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*d^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + 6*(4*(8*(d*x + c)*cos(d*x + c) - sin(3*d*x + 3*c) - sin(d*x + c))*cos(4*d*x + 4*c) + 16*(2*d*x + 4*(d*x + c)*sin(d*x + c) + 2*c + cos(d*x + c))*cos(3*d*x + 3*c) + 8*cos(3*d*x + 3*c)^2 + 8*cos(d*x + c)^2 + 5*(2*(2*sin(3*d*x + 3*c) + 2*sin(d*x + c) + 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(3*d*x + 3*c)^2 - 8*cos(3*d*x + 3*c)*cos(d*x + c) - 4*cos(d*x + c)^2 - 4*(cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - sin(4*d*x + 4*c)^2 - 4*(2*sin(d*x + c) + 1)*sin(3*d*x + 3*c) - 4*sin(3*d*x + 3*c)^2 - 4*sin(d*x + c)^2 - 4*sin(d*x + c) - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + 3*(2*(2*sin(3*d*x + 3*c) + 2*sin(d*x + c) + 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(3*d*x + 3*c)^2 - 8*cos(3*d*x + 3*c)*cos(d*x + c) - 4*cos(d*x + c)^2 - 4*(cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - sin(4*d*x + 4*c)^2 - 4*(2*sin(d*x + c) + 1)*sin(3*d*x + 3*c) - 4*sin(3*d*x + 3*c)^2 - 4*sin(d*x + c)^2 - 4*sin(d*x + c) - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 4*(4*d*x + 8*(d*x + c)*sin(d*x + c) + 4*c + cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - 4*(16*(d*x + c)*cos(d*x + c) - 4*sin(d*x + c) - 1)*sin(3*d*x + 3*c) + 8*sin(3*d*x + 3*c)^2 + 8*sin(d*x + c)^2 + 4*sin(d*x + c))*c*e*f^2/(a*d^2*cos(4*d*x + 4*c)^2 + 4*a*d^2*cos(3*d*x + 3*c)^2 + 8*a*d^2*cos(3*d*x + 3*c)*cos(d*x + c) + 4*a*d^2*cos(d*x + c)^2 + a*d^2*sin(4*d*x + 4*c)^2 + 4*a*d^2*sin(3*d*x + 3*c)^2 + 4*a*d^2*sin(d*x + c)^2 + 4*a*d^2*sin(d*x + c) + a*d^2 - 2*(2*a*d^2*sin(3*d*x + 3*c) + 2*a*d^2*sin(d*x + c) + a*d^2)*cos(4*d*x + 4*c) + 4*(a*d^2*cos(3*d*x + 3*c) + a*d^2*cos(d*x + c))*sin(4*d*x + 4*c) + 4*(2*a*d^2*sin(d*x + c) + a*d^2)*sin(3*d*x + 3*c)) - 24*c*e^2*f*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a*d + 2*a*d*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*d*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*d*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 3*(4*(8*(d*x + c)*cos(d*x + c) - sin(3*d*x + 3*c) - sin(d*x + c))*cos(4*d*x + 4*c) + 16*(2*d*x + 4*(d*x + c)*sin(d*x + c) + 2*c + cos(d*x + c))*cos(3*d*x + 3*c) + 8*cos(3*d*x + 3*c)^2 + 8*cos(d*x + c)^2 + 5*(2*(2*sin(3*d*x + 3*c) + 2*sin(d*x + c) + 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(3*d*x + 3*c)^2 - 8*cos(3*d*x + 3*c)*cos(d*x + c) - 4*cos(d*x + c)^2 - 4*(cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - sin(4*d*x + 4*c)^2 - 4*(2*sin(d*x + c) + 1)*sin(3*d*x + 3*c) - 4*sin(3*d*x + 3*c)^2 - 4*sin(d*x + c)^2 - 4*sin(d*x + c) - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + 3*(2*(2*sin(3*d*x + 3*c) + 2*sin(d*x + c) + 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(3*d*x + 3*c)^2 - 8*cos(3*d*x + 3*c)*cos(d*x + c) - 4*cos(d*x + c)^2 - 4*(cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - sin(4*d*x + 4*c)^2 - 4*(2*sin(d*x + c) + 1)*sin(3*d*x + 3*c) - 4*sin(3*d*x + 3*c)^2 - 4*sin(d*x + c)^2 - 4*sin(d*x + c) - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 4*(4*d*x + 8*(d*x + c)*sin(d*x + c) + 4*c + cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - 4*(16*(d*x + c)*cos(d*x + c) - 4*sin(d*x + c) - 1)*sin(3*d*x + 3*c) + 8*sin(3*d*x + 3*c)^2 + 8*sin(d*x + c)^2 + 4*sin(d*x + c))*e^2*f/(a*d*cos(4*d*x + 4*c)^2 + 4*a*d*cos(3*d*x + 3*c)^2 + 8*a*d*cos(3*d*x + 3*c)*cos(d*x + c) + 4*a*d*cos(d*x + c)^2 + a*d*sin(4*d*x + 4*c)^2 + 4*a*d*sin(3*d*x + 3*c)^2 + 4*a*d*sin(d*x + c)^2 + 4*a*d*sin(d*x + c) + a*d - 2*(2*a*d*sin(3*d*x + 3*c) + 2*a*d*sin(d*x + c) + a*d)*cos(4*d*x + 4*c) + 4*(a*d*cos(3*d*x + 3*c) + a*d*cos(d*x + c))*sin(4*d*x + 4*c) + 4*(2*a*d*sin(d*x + c) + a*d)*sin(3*d*x + 3*c)) + 8*e^3*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 12*(24*d*e*f^2 - 8*(2*c^3 + 3*c)*f^3 - (6*(5*c^2 + 4)*f^3*cos(4*d*x + 4*c) + (60*I*c^2 + 48*I)*f^3*cos(3*d*x + 3*c) + (60*I*c^2 + 48*I)*f^3*cos(d*x + c) + (30*I*c^2 + 24*I)*f^3*sin(4*d*x + 4*c) - 12*(5*c^2 + 4)*f^3*sin(3*d*x + 3*c) - 12*(5*c^2 + 4)*f^3*sin(d*x + c) - 6*(5*c^2 + 4)*f^3)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (18*c^2*f^3*cos(4*d*x + 4*c) + 36*I*c^2*f^3*cos(3*d*x + 3*c) + 36*I*c^2*f^3*cos(d*x + c) + 18*I*c^2*f^3*sin(4*d*x + 4*c) - 36*c^2*f^3*sin(3*d*x + 3*c) - 36*c^2*f^3*sin(d*x + c) - 18*c^2*f^3)*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (30*(d*x + c)^2*f^3 + 60*(d*e*f^2 - c*f^3)*(d*x + c) - 30*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(4*d*x + 4*c) + (-60*I*(d*x + c)^2*f^3 + (-120*I*d*e*f^2 + 120*I*c*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (-60*I*(d*x + c)^2*f^3 + (-120*I*d*e*f^2 + 120*I*c*f^3)*(d*x + c))*cos(d*x + c) + (-30*I*(d*x + c)^2*f^3 + (-60*I*d*e*f^2 + 60*I*c*f^3)*(d*x + c))*sin(4*d*x + 4*c) + 60*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(3*d*x + 3*c) + 60*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) + (18*(d*x + c)^2*f^3 + 36*(d*e*f^2 - c*f^3)*(d*x + c) - 18*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(4*d*x + 4*c) - (36*I*(d*x + c)^2*f^3 + (72*I*d*e*f^2 - 72*I*c*f^3)*(d*x + c))*cos(3*d*x + 3*c) - (36*I*(d*x + c)^2*f^3 + (72*I*d*e*f^2 - 72*I*c*f^3)*(d*x + c))*cos(d*x + c) - (18*I*(d*x + c)^2*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c))*sin(4*d*x + 4*c) + 36*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(3*d*x + 3*c) + 36*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + 8*(2*(d*x + c)^3*f^3 + 3*(2*c^2 + 1)*(d*x + c)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c)^2)*cos(4*d*x + 4*c) - (-32*I*(d*x + c)^3*f^3 + 24*I*d*e*f^2 - 12*(c^2 + 2*I*c)*f^3 - 12*(8*I*d*e*f^2 + (-8*I*c + 1)*f^3)*(d*x + c)^2 - (24*d*e*f^2 - (-96*I*c^2 + 24*c - 24*I)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 24*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(2*d*x + 2*c) + (12*(d*x + c)^2*f^3 - 24*I*d*e*f^2 - (-32*I*c^3 - 12*c^2 - 24*I*c)*f^3 + (24*d*e*f^2 - (24*c - 24*I)*f^3)*(d*x + c))*cos(d*x + c) - (60*d*e*f^2 + 60*(d*x + c)*f^3 - 60*c*f^3 - 60*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(4*d*x + 4*c) + (-120*I*d*e*f^2 - 120*I*(d*x + c)*f^3 + 120*I*c*f^3)*cos(3*d*x + 3*c) + (-120*I*d*e*f^2 - 120*I*(d*x + c)*f^3 + 120*I*c*f^3)*cos(d*x + c) + (-60*I*d*e*f^2 - 60*I*(d*x + c)*f^3 + 60*I*c*f^3)*sin(4*d*x + 4*c) + 120*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(3*d*x + 3*c) + 120*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) - (36*d*e*f^2 + 36*(d*x + c)*f^3 - 36*c*f^3 - 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(4*d*x + 4*c) + (-72*I*d*e*f^2 - 72*I*(d*x + c)*f^3 + 72*I*c*f^3)*cos(3*d*x + 3*c) + (-72*I*d*e*f^2 - 72*I*(d*x + c)*f^3 + 72*I*c*f^3)*cos(d*x + c) + (-36*I*d*e*f^2 - 36*I*(d*x + c)*f^3 + 36*I*c*f^3)*sin(4*d*x + 4*c) + 72*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(3*d*x + 3*c) + 72*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(d*x + c))*dilog(-I*e^(I*d*x + I*c)) - (15*I*(d*x + c)^2*f^3 + (15*I*c^2 + 12*I)*f^3 + (30*I*d*e*f^2 - 30*I*c*f^3)*(d*x + c) + (-15*I*(d*x + c)^2*f^3 + (-15*I*c^2 - 12*I)*f^3 + (-30*I*d*e*f^2 + 30*I*c*f^3)*(d*x + c))*cos(4*d*x + 4*c) + 6*(5*(d*x + c)^2*f^3 + (5*c^2 + 4)*f^3 + 10*(d*e*f^2 - c*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 6*(5*(d*x + c)^2*f^3 + (5*c^2 + 4)*f^3 + 10*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + 3*(5*(d*x + c)^2*f^3 + (5*c^2 + 4)*f^3 + 10*(d*e*f^2 - c*f^3)*(d*x + c))*sin(4*d*x + 4*c) + (30*I*(d*x + c)^2*f^3 + (30*I*c^2 + 24*I)*f^3 + (60*I*d*e*f^2 - 60*I*c*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (30*I*(d*x + c)^2*f^3 + (30*I*c^2 + 24*I)*f^3 + (60*I*d*e*f^2 - 60*I*c*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (9*I*(d*x + c)^2*f^3 + 9*I*c^2*f^3 + (18*I*d*e*f^2 - 18*I*c*f^3)*(d*x + c) + (-9*I*(d*x + c)^2*f^3 - 9*I*c^2*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c))*cos(4*d*x + 4*c) + 18*((d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 18*((d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(d*x + c) + 9*((d*x + c)^2*f^3 + c^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*sin(4*d*x + 4*c) + (18*I*(d*x + c)^2*f^3 + 18*I*c^2*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (18*I*(d*x + c)^2*f^3 + 18*I*c^2*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - (-60*I*f^3*cos(4*d*x + 4*c) + 120*f^3*cos(3*d*x + 3*c) + 120*f^3*cos(d*x + c) + 60*f^3*sin(4*d*x + 4*c) + 120*I*f^3*sin(3*d*x + 3*c) + 120*I*f^3*sin(d*x + c) + 60*I*f^3)*polylog(3, I*e^(I*d*x + I*c)) - (-36*I*f^3*cos(4*d*x + 4*c) + 72*f^3*cos(3*d*x + 3*c) + 72*f^3*cos(d*x + c) + 36*f^3*sin(4*d*x + 4*c) + 72*I*f^3*sin(3*d*x + 3*c) + 72*I*f^3*sin(d*x + c) + 36*I*f^3)*polylog(3, -I*e^(I*d*x + I*c)) - (-16*I*(d*x + c)^3*f^3 + (-48*I*c^2 - 24*I)*(d*x + c)*f^3 + (-48*I*d*e*f^2 + 48*I*c*f^3)*(d*x + c)^2)*sin(4*d*x + 4*c) - (32*(d*x + c)^3*f^3 - 24*d*e*f^2 + (-12*I*c^2 + 24*c)*f^3 + (96*d*e*f^2 - (96*c + 12*I)*f^3)*(d*x + c)^2 - 24*(I*d*e*f^2 - (4*c^2 + I*c + 1)*f^3)*(d*x + c))*sin(3*d*x + 3*c) - (-24*I*d*e*f^2 - 24*I*(d*x + c)*f^3 + 24*I*c*f^3)*sin(2*d*x + 2*c) - (-12*I*(d*x + c)^2*f^3 - 24*d*e*f^2 + (32*c^3 - 12*I*c^2 + 24*c)*f^3 + (-24*I*d*e*f^2 - 24*(-I*c - 1)*f^3)*(d*x + c))*sin(d*x + c))/(-12*I*a*d^3*cos(4*d*x + 4*c) + 24*a*d^3*cos(3*d*x + 3*c) + 24*a*d^3*cos(d*x + c) + 12*a*d^3*sin(4*d*x + 4*c) + 24*I*a*d^3*sin(3*d*x + 3*c) + 24*I*a*d^3*sin(d*x + c) + 12*I*a*d^3))/d","B",0
276,1,1332,0,0.869289," ","integrate((f*x+e)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, d^{2} e^{2} + 4 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 4 i \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 4 \, f^{2} - {\left(10 \, d e f \cos\left(4 \, d x + 4 \, c\right) + 20 i \, d e f \cos\left(3 \, d x + 3 \, c\right) + 20 i \, d e f \cos\left(d x + c\right) + 10 i \, d e f \sin\left(4 \, d x + 4 \, c\right) - 20 \, d e f \sin\left(3 \, d x + 3 \, c\right) - 20 \, d e f \sin\left(d x + c\right) - 10 \, d e f\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(6 \, d e f \cos\left(4 \, d x + 4 \, c\right) + 12 i \, d e f \cos\left(3 \, d x + 3 \, c\right) + 12 i \, d e f \cos\left(d x + c\right) + 6 i \, d e f \sin\left(4 \, d x + 4 \, c\right) - 12 \, d e f \sin\left(3 \, d x + 3 \, c\right) - 12 \, d e f \sin\left(d x + c\right) - 6 \, d e f\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) + {\left(10 \, d f^{2} x \cos\left(4 \, d x + 4 \, c\right) + 20 i \, d f^{2} x \cos\left(3 \, d x + 3 \, c\right) + 20 i \, d f^{2} x \cos\left(d x + c\right) + 10 i \, d f^{2} x \sin\left(4 \, d x + 4 \, c\right) - 20 \, d f^{2} x \sin\left(3 \, d x + 3 \, c\right) - 20 \, d f^{2} x \sin\left(d x + c\right) - 10 \, d f^{2} x\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(6 \, d f^{2} x \cos\left(4 \, d x + 4 \, c\right) + 12 i \, d f^{2} x \cos\left(3 \, d x + 3 \, c\right) + 12 i \, d f^{2} x \cos\left(d x + c\right) + 6 i \, d f^{2} x \sin\left(4 \, d x + 4 \, c\right) - 12 \, d f^{2} x \sin\left(3 \, d x + 3 \, c\right) - 12 \, d f^{2} x \sin\left(d x + c\right) - 6 \, d f^{2} x\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + 8 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(-16 i \, d^{2} f^{2} x^{2} - 4 \, d e f + 4 i \, f^{2} - 4 \, {\left(8 i \, d^{2} e f + d f^{2}\right)} x\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(16 i \, d^{2} e^{2} - 4 \, d f^{2} x - 4 \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right) + {\left(10 \, f^{2} \cos\left(4 \, d x + 4 \, c\right) + 20 i \, f^{2} \cos\left(3 \, d x + 3 \, c\right) + 20 i \, f^{2} \cos\left(d x + c\right) + 10 i \, f^{2} \sin\left(4 \, d x + 4 \, c\right) - 20 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) - 20 \, f^{2} \sin\left(d x + c\right) - 10 \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(6 \, f^{2} \cos\left(4 \, d x + 4 \, c\right) + 12 i \, f^{2} \cos\left(3 \, d x + 3 \, c\right) + 12 i \, f^{2} \cos\left(d x + c\right) + 6 i \, f^{2} \sin\left(4 \, d x + 4 \, c\right) - 12 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) - 12 \, f^{2} \sin\left(d x + c\right) - 6 \, f^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(5 i \, d f^{2} x + 5 i \, d e f + {\left(-5 i \, d f^{2} x - 5 i \, d e f\right)} \cos\left(4 \, d x + 4 \, c\right) + 10 \, {\left(d f^{2} x + d e f\right)} \cos\left(3 \, d x + 3 \, c\right) + 10 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) + 5 \, {\left(d f^{2} x + d e f\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(10 i \, d f^{2} x + 10 i \, d e f\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(10 i \, d f^{2} x + 10 i \, d e f\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(3 i \, d f^{2} x + 3 i \, d e f + {\left(-3 i \, d f^{2} x - 3 i \, d e f\right)} \cos\left(4 \, d x + 4 \, c\right) + 6 \, {\left(d f^{2} x + d e f\right)} \cos\left(3 \, d x + 3 \, c\right) + 6 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) + 3 \, {\left(d f^{2} x + d e f\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(6 i \, d f^{2} x + 6 i \, d e f\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(6 i \, d f^{2} x + 6 i \, d e f\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-8 i \, d^{2} f^{2} x^{2} - 16 i \, d^{2} e f x\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(16 \, d^{2} f^{2} x^{2} - 4 i \, d e f - 4 \, f^{2} + {\left(32 \, d^{2} e f - 4 i \, d f^{2}\right)} x\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(16 \, d^{2} e^{2} + 4 i \, d f^{2} x + 4 i \, d e f + 4 \, f^{2}\right)} \sin\left(d x + c\right)}{-6 i \, a d^{3} \cos\left(4 \, d x + 4 \, c\right) + 12 \, a d^{3} \cos\left(3 \, d x + 3 \, c\right) + 12 \, a d^{3} \cos\left(d x + c\right) + 6 \, a d^{3} \sin\left(4 \, d x + 4 \, c\right) + 12 i \, a d^{3} \sin\left(3 \, d x + 3 \, c\right) + 12 i \, a d^{3} \sin\left(d x + c\right) + 6 i \, a d^{3}}"," ",0,"-(8*d^2*e^2 + 4*f^2*cos(2*d*x + 2*c) + 4*I*f^2*sin(2*d*x + 2*c) + 4*f^2 - (10*d*e*f*cos(4*d*x + 4*c) + 20*I*d*e*f*cos(3*d*x + 3*c) + 20*I*d*e*f*cos(d*x + c) + 10*I*d*e*f*sin(4*d*x + 4*c) - 20*d*e*f*sin(3*d*x + 3*c) - 20*d*e*f*sin(d*x + c) - 10*d*e*f)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (6*d*e*f*cos(4*d*x + 4*c) + 12*I*d*e*f*cos(3*d*x + 3*c) + 12*I*d*e*f*cos(d*x + c) + 6*I*d*e*f*sin(4*d*x + 4*c) - 12*d*e*f*sin(3*d*x + 3*c) - 12*d*e*f*sin(d*x + c) - 6*d*e*f)*arctan2(sin(d*x + c) - 1, cos(d*x + c)) + (10*d*f^2*x*cos(4*d*x + 4*c) + 20*I*d*f^2*x*cos(3*d*x + 3*c) + 20*I*d*f^2*x*cos(d*x + c) + 10*I*d*f^2*x*sin(4*d*x + 4*c) - 20*d*f^2*x*sin(3*d*x + 3*c) - 20*d*f^2*x*sin(d*x + c) - 10*d*f^2*x)*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (6*d*f^2*x*cos(4*d*x + 4*c) + 12*I*d*f^2*x*cos(3*d*x + 3*c) + 12*I*d*f^2*x*cos(d*x + c) + 6*I*d*f^2*x*sin(4*d*x + 4*c) - 12*d*f^2*x*sin(3*d*x + 3*c) - 12*d*f^2*x*sin(d*x + c) - 6*d*f^2*x)*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + 8*(d^2*f^2*x^2 + 2*d^2*e*f*x)*cos(4*d*x + 4*c) - (-16*I*d^2*f^2*x^2 - 4*d*e*f + 4*I*f^2 - 4*(8*I*d^2*e*f + d*f^2)*x)*cos(3*d*x + 3*c) - (16*I*d^2*e^2 - 4*d*f^2*x - 4*d*e*f + 4*I*f^2)*cos(d*x + c) + (10*f^2*cos(4*d*x + 4*c) + 20*I*f^2*cos(3*d*x + 3*c) + 20*I*f^2*cos(d*x + c) + 10*I*f^2*sin(4*d*x + 4*c) - 20*f^2*sin(3*d*x + 3*c) - 20*f^2*sin(d*x + c) - 10*f^2)*dilog(I*e^(I*d*x + I*c)) + (6*f^2*cos(4*d*x + 4*c) + 12*I*f^2*cos(3*d*x + 3*c) + 12*I*f^2*cos(d*x + c) + 6*I*f^2*sin(4*d*x + 4*c) - 12*f^2*sin(3*d*x + 3*c) - 12*f^2*sin(d*x + c) - 6*f^2)*dilog(-I*e^(I*d*x + I*c)) - (5*I*d*f^2*x + 5*I*d*e*f + (-5*I*d*f^2*x - 5*I*d*e*f)*cos(4*d*x + 4*c) + 10*(d*f^2*x + d*e*f)*cos(3*d*x + 3*c) + 10*(d*f^2*x + d*e*f)*cos(d*x + c) + 5*(d*f^2*x + d*e*f)*sin(4*d*x + 4*c) + (10*I*d*f^2*x + 10*I*d*e*f)*sin(3*d*x + 3*c) + (10*I*d*f^2*x + 10*I*d*e*f)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (3*I*d*f^2*x + 3*I*d*e*f + (-3*I*d*f^2*x - 3*I*d*e*f)*cos(4*d*x + 4*c) + 6*(d*f^2*x + d*e*f)*cos(3*d*x + 3*c) + 6*(d*f^2*x + d*e*f)*cos(d*x + c) + 3*(d*f^2*x + d*e*f)*sin(4*d*x + 4*c) + (6*I*d*f^2*x + 6*I*d*e*f)*sin(3*d*x + 3*c) + (6*I*d*f^2*x + 6*I*d*e*f)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - (-8*I*d^2*f^2*x^2 - 16*I*d^2*e*f*x)*sin(4*d*x + 4*c) - (16*d^2*f^2*x^2 - 4*I*d*e*f - 4*f^2 + (32*d^2*e*f - 4*I*d*f^2)*x)*sin(3*d*x + 3*c) + (16*d^2*e^2 + 4*I*d*f^2*x + 4*I*d*e*f + 4*f^2)*sin(d*x + c))/(-6*I*a*d^3*cos(4*d*x + 4*c) + 12*a*d^3*cos(3*d*x + 3*c) + 12*a*d^3*cos(d*x + c) + 6*a*d^3*sin(4*d*x + 4*c) + 12*I*a*d^3*sin(3*d*x + 3*c) + 12*I*a*d^3*sin(d*x + c) + 6*I*a*d^3)","B",0
277,1,1115,0,0.387517," ","integrate((f*x+e)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{8 \, c f {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{a d + \frac{2 \, a d \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a d \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a d \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{{\left(4 \, {\left(8 \, {\left(d x + c\right)} \cos\left(d x + c\right) - \sin\left(3 \, d x + 3 \, c\right) - \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 16 \, {\left(2 \, d x + 4 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 2 \, c + \cos\left(d x + c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + 8 \, \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, \cos\left(d x + c\right)^{2} + 5 \, {\left(2 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, \sin\left(3 \, d x + 3 \, c\right)^{2} - 4 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + 3 \, {\left(2 \, {\left(2 \, \sin\left(3 \, d x + 3 \, c\right) + 2 \, \sin\left(d x + c\right) + 1\right)} \cos\left(4 \, d x + 4 \, c\right) - \cos\left(4 \, d x + 4 \, c\right)^{2} - 4 \, \cos\left(3 \, d x + 3 \, c\right)^{2} - 8 \, \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) - 4 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - \sin\left(4 \, d x + 4 \, c\right)^{2} - 4 \, {\left(2 \, \sin\left(d x + c\right) + 1\right)} \sin\left(3 \, d x + 3 \, c\right) - 4 \, \sin\left(3 \, d x + 3 \, c\right)^{2} - 4 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) - 1\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(4 \, d x + 8 \, {\left(d x + c\right)} \sin\left(d x + c\right) + 4 \, c + \cos\left(3 \, d x + 3 \, c\right) + \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - 4 \, {\left(16 \, {\left(d x + c\right)} \cos\left(d x + c\right) - 4 \, \sin\left(d x + c\right) - 1\right)} \sin\left(3 \, d x + 3 \, c\right) + 8 \, \sin\left(3 \, d x + 3 \, c\right)^{2} + 8 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right)\right)} f}{a d \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, a d \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + 4 \, a d \cos\left(d x + c\right)^{2} + a d \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, a d \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, a d \sin\left(d x + c\right)^{2} + 4 \, a d \sin\left(d x + c\right) + a d - 2 \, {\left(2 \, a d \sin\left(3 \, d x + 3 \, c\right) + 2 \, a d \sin\left(d x + c\right) + a d\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a d \cos\left(3 \, d x + 3 \, c\right) + a d \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(2 \, a d \sin\left(d x + c\right) + a d\right)} \sin\left(3 \, d x + 3 \, c\right)} - \frac{8 \, e {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}}{12 \, d}"," ",0,"-1/12*(8*c*f*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a*d + 2*a*d*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*d*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*d*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (4*(8*(d*x + c)*cos(d*x + c) - sin(3*d*x + 3*c) - sin(d*x + c))*cos(4*d*x + 4*c) + 16*(2*d*x + 4*(d*x + c)*sin(d*x + c) + 2*c + cos(d*x + c))*cos(3*d*x + 3*c) + 8*cos(3*d*x + 3*c)^2 + 8*cos(d*x + c)^2 + 5*(2*(2*sin(3*d*x + 3*c) + 2*sin(d*x + c) + 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(3*d*x + 3*c)^2 - 8*cos(3*d*x + 3*c)*cos(d*x + c) - 4*cos(d*x + c)^2 - 4*(cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - sin(4*d*x + 4*c)^2 - 4*(2*sin(d*x + c) + 1)*sin(3*d*x + 3*c) - 4*sin(3*d*x + 3*c)^2 - 4*sin(d*x + c)^2 - 4*sin(d*x + c) - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + 3*(2*(2*sin(3*d*x + 3*c) + 2*sin(d*x + c) + 1)*cos(4*d*x + 4*c) - cos(4*d*x + 4*c)^2 - 4*cos(3*d*x + 3*c)^2 - 8*cos(3*d*x + 3*c)*cos(d*x + c) - 4*cos(d*x + c)^2 - 4*(cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - sin(4*d*x + 4*c)^2 - 4*(2*sin(d*x + c) + 1)*sin(3*d*x + 3*c) - 4*sin(3*d*x + 3*c)^2 - 4*sin(d*x + c)^2 - 4*sin(d*x + c) - 1)*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + 4*(4*d*x + 8*(d*x + c)*sin(d*x + c) + 4*c + cos(3*d*x + 3*c) + cos(d*x + c))*sin(4*d*x + 4*c) - 4*(16*(d*x + c)*cos(d*x + c) - 4*sin(d*x + c) - 1)*sin(3*d*x + 3*c) + 8*sin(3*d*x + 3*c)^2 + 8*sin(d*x + c)^2 + 4*sin(d*x + c))*f/(a*d*cos(4*d*x + 4*c)^2 + 4*a*d*cos(3*d*x + 3*c)^2 + 8*a*d*cos(3*d*x + 3*c)*cos(d*x + c) + 4*a*d*cos(d*x + c)^2 + a*d*sin(4*d*x + 4*c)^2 + 4*a*d*sin(3*d*x + 3*c)^2 + 4*a*d*sin(d*x + c)^2 + 4*a*d*sin(d*x + c) + a*d - 2*(2*a*d*sin(3*d*x + 3*c) + 2*a*d*sin(d*x + c) + a*d)*cos(4*d*x + 4*c) + 4*(a*d*cos(3*d*x + 3*c) + a*d*cos(d*x + c))*sin(4*d*x + 4*c) + 4*(2*a*d*sin(d*x + c) + a*d)*sin(3*d*x + 3*c)) - 8*e*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4))/d","B",0
278,1,129,0,0.324686," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)}}{3 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d}"," ",0,"2/3*(sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d)","B",0
279,0,0,0,0.000000," ","integrate(sec(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) \cos\left(d x + c\right) - 2 \, {\left(d f^{2} x + d e f\right)} \cos\left(3 \, d x + 3 \, c\right)^{2} + 2 \, f^{2} \cos\left(d x + c\right) - 2 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(d f^{2} x + d e f\right)} \sin\left(3 \, d x + 3 \, c\right)^{2} - 2 \, {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)^{2} + {\left(2 \, f^{2} \cos\left(3 \, d x + 3 \, c\right) - 2 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 2 \, {\left(4 \, d^{2} f^{2} x^{2} + 8 \, d^{2} e f x + 4 \, d^{2} e^{2} + f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + d e f\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 2 \, {\left(4 \, d^{2} f^{2} x^{2} + 8 \, d^{2} e f x + 4 \, d^{2} e^{2} + 2 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + f^{2} - 2 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) + 8 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \cos\left(3 \, d x + 3 \, c\right) + \frac{1}{2} \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3} + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3} + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left({\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3} + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \int \frac{{\left(5 \, d^{2} f^{3} x^{2} + 10 \, d^{2} e f^{2} x + 5 \, d^{2} e^{2} f + 12 \, f^{3}\right)} \cos\left(d x + c\right)}{a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4} + {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4}\right)} \sin\left(d x + c\right)}\,{d x} - \frac{3}{2} \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f + {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + 4 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \cos\left(d x + c\right)^{2} + {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f + 2 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(3 \, d x + 3 \, c\right) + 2 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left({\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f + 2 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(d x + c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(a d^{3} f^{4} x^{3} + 3 \, a d^{3} e f^{3} x^{2} + 3 \, a d^{3} e^{2} f^{2} x + a d^{3} e^{3} f\right)} \sin\left(d x + c\right)\right)} \int \frac{\cos\left(d x + c\right)}{a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} \sin\left(d x + c\right)}\,{d x} + {\left(4 \, d^{2} f^{2} x^{2} + 8 \, d^{2} e f x + 4 \, d^{2} e^{2} + 2 \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 2 \, f^{2} \sin\left(3 \, d x + 3 \, c\right) + 2 \, f^{2} - {\left(d f^{2} x + d e f\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) + 2 \, {\left(4 \, d^{2} f^{2} x^{2} + 8 \, d^{2} e f x + 4 \, d^{2} e^{2} + f^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(d f^{2} x + d e f - 4 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 16 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right) + 4 \, {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) + 2 \, {\left(2 \, f^{2} \sin\left(d x + c\right) + f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)}{3 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3} + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(3 \, d x + 3 \, c\right)^{2} + 8 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) \cos\left(d x + c\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(4 \, d x + 4 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(3 \, d x + 3 \, c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3} + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left({\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(4 \, d x + 4 \, c\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3} + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \sin\left(3 \, d x + 3 \, c\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(4*f^2*cos(2*d*x + 2*c)*cos(d*x + c) - 2*(d*f^2*x + d*e*f)*cos(3*d*x + 3*c)^2 + 2*f^2*cos(d*x + c) - 2*(d*f^2*x + d*e*f)*cos(d*x + c)^2 - 2*(d*f^2*x + d*e*f)*sin(3*d*x + 3*c)^2 - 2*(d*f^2*x + d*e*f)*sin(d*x + c)^2 + (2*f^2*cos(3*d*x + 3*c) - 2*f^2*sin(2*d*x + 2*c) + 2*(4*d^2*f^2*x^2 + 8*d^2*e*f*x + 4*d^2*e^2 + f^2)*cos(d*x + c) + (d*f^2*x + d*e*f)*sin(3*d*x + 3*c) + (d*f^2*x + d*e*f)*sin(d*x + c))*cos(4*d*x + 4*c) + 2*(4*d^2*f^2*x^2 + 8*d^2*e*f*x + 4*d^2*e^2 + 2*f^2*cos(2*d*x + 2*c) + f^2 - 2*(d*f^2*x + d*e*f)*cos(d*x + c) + 8*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*sin(d*x + c))*cos(3*d*x + 3*c) + 3*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3 + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(4*d*x + 4*c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(3*d*x + 3*c)^2 + 8*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(3*d*x + 3*c)*cos(d*x + c) + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(d*x + c)^2 + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(4*d*x + 4*c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(3*d*x + 3*c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c)^2 - 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3 + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(3*d*x + 3*c) + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c))*cos(4*d*x + 4*c) + 4*((a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(3*d*x + 3*c) + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(d*x + c))*sin(4*d*x + 4*c) + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3 + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c))*sin(3*d*x + 3*c) + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c))*integrate(1/6*(5*d^2*f^3*x^2 + 10*d^2*e*f^2*x + 5*d^2*e^2*f + 12*f^3)*cos(d*x + c)/(a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4 + (a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4)*cos(d*x + c)^2 + (a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4)*sin(d*x + c)^2 + 2*(a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4)*sin(d*x + c)), x) - 3*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f + (a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*cos(4*d*x + 4*c)^2 + 4*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*cos(3*d*x + 3*c)^2 + 8*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*cos(3*d*x + 3*c)*cos(d*x + c) + 4*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*cos(d*x + c)^2 + (a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(4*d*x + 4*c)^2 + 4*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(3*d*x + 3*c)^2 + 4*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(d*x + c)^2 - 2*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f + 2*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(3*d*x + 3*c) + 2*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(d*x + c))*cos(4*d*x + 4*c) + 4*((a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*cos(3*d*x + 3*c) + (a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*cos(d*x + c))*sin(4*d*x + 4*c) + 4*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f + 2*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(d*x + c))*sin(3*d*x + 3*c) + 4*(a*d^3*f^4*x^3 + 3*a*d^3*e*f^3*x^2 + 3*a*d^3*e^2*f^2*x + a*d^3*e^3*f)*sin(d*x + c))*integrate(1/2*cos(d*x + c)/(a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*cos(d*x + c)^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*sin(d*x + c)^2 - 2*(a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*sin(d*x + c)), x) + (4*d^2*f^2*x^2 + 8*d^2*e*f*x + 4*d^2*e^2 + 2*f^2*cos(2*d*x + 2*c) + 2*f^2*sin(3*d*x + 3*c) + 2*f^2 - (d*f^2*x + d*e*f)*cos(3*d*x + 3*c) - (d*f^2*x + d*e*f)*cos(d*x + c) + 2*(4*d^2*f^2*x^2 + 8*d^2*e*f*x + 4*d^2*e^2 + f^2)*sin(d*x + c))*sin(4*d*x + 4*c) - (d*f^2*x + d*e*f - 4*f^2*sin(2*d*x + 2*c) + 16*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c) + 4*(d*f^2*x + d*e*f)*sin(d*x + c))*sin(3*d*x + 3*c) + 2*(2*f^2*sin(d*x + c) + f^2)*sin(2*d*x + 2*c) - (d*f^2*x + d*e*f)*sin(d*x + c))/(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3 + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(4*d*x + 4*c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(3*d*x + 3*c)^2 + 8*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(3*d*x + 3*c)*cos(d*x + c) + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(d*x + c)^2 + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(4*d*x + 4*c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(3*d*x + 3*c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c)^2 - 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3 + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(3*d*x + 3*c) + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c))*cos(4*d*x + 4*c) + 4*((a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(3*d*x + 3*c) + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cos(d*x + c))*sin(4*d*x + 4*c) + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3 + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c))*sin(3*d*x + 3*c) + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sin(d*x + c))","F",0
280,-1,0,0,0.000000," ","integrate(sec(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,1,10800,0,79.655180," ","integrate((f*x+e)^3*sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, c e^{2} f {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2\right)}}{a d \sin\left(d x + c\right)^{3} + a d \sin\left(d x + c\right)^{2} - a d \sin\left(d x + c\right) - a d} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a d} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a d}\right)} - e^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2\right)}}{a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}\right)} - \frac{16 \, {\left(16 \, d^{2} e^{2} f - 32 \, c d e f^{2} + 8 \, {\left(2 \, c^{2} + 1\right)} f^{3} + {\left(2 \, {\left(9 \, c^{2} + 28\right)} d e f^{2} - 2 \, {\left(3 \, c^{3} + 28 \, c\right)} f^{3} - 2 \, {\left({\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left({\left(36 i \, c^{2} + 112 i\right)} d e f^{2} + {\left(-12 i \, c^{3} - 112 i \, c\right)} f^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left({\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left({\left(72 i \, c^{2} + 224 i\right)} d e f^{2} + {\left(-24 i \, c^{3} - 224 i \, c\right)} f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + 2 \, {\left({\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left({\left(36 i \, c^{2} + 112 i\right)} d e f^{2} + {\left(-12 i \, c^{3} - 112 i \, c\right)} f^{3}\right)} \cos\left(d x + c\right) - {\left({\left(18 i \, c^{2} + 56 i\right)} d e f^{2} + {\left(-6 i \, c^{3} - 56 i \, c\right)} f^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left({\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left({\left(18 i \, c^{2} + 56 i\right)} d e f^{2} + {\left(-6 i \, c^{3} - 56 i \, c\right)} f^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left({\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left({\left(-18 i \, c^{2} - 56 i\right)} d e f^{2} + {\left(6 i \, c^{3} + 56 i \, c\right)} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left({\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(6 \, {\left(3 \, c^{2} + 4\right)} d e f^{2} - 6 \, {\left(c^{3} + 4 \, c\right)} f^{3} - 6 \, {\left({\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left({\left(-36 i \, c^{2} - 48 i\right)} d e f^{2} + {\left(12 i \, c^{3} + 48 i \, c\right)} f^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) - 6 \, {\left({\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left({\left(-72 i \, c^{2} - 96 i\right)} d e f^{2} + {\left(24 i \, c^{3} + 96 i \, c\right)} f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + 6 \, {\left({\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left({\left(-36 i \, c^{2} - 48 i\right)} d e f^{2} + {\left(12 i \, c^{3} + 48 i \, c\right)} f^{3}\right)} \cos\left(d x + c\right) + {\left({\left(-18 i \, c^{2} - 24 i\right)} d e f^{2} + {\left(6 i \, c^{3} + 24 i \, c\right)} f^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + 12 \, {\left({\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left({\left(-18 i \, c^{2} - 24 i\right)} d e f^{2} + {\left(6 i \, c^{3} + 24 i \, c\right)} f^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + 24 \, {\left({\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left({\left(18 i \, c^{2} + 24 i\right)} d e f^{2} + {\left(-6 i \, c^{3} - 24 i \, c\right)} f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left({\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(6 \, {\left(d x + c\right)}^{3} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 2 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} + {\left(-36 i \, c^{2} - 112 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-24 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-72 i \, d e f^{2} + 72 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-72 i \, d^{2} e^{2} f + 144 i \, c d e f^{2} + {\left(-72 i \, c^{2} - 224 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 2 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} + {\left(-36 i \, c^{2} - 112 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} + {\left(-18 i \, c^{2} - 56 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} + {\left(-18 i \, c^{2} - 56 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(18 i \, d e f^{2} - 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + {\left(18 i \, c^{2} + 56 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(6 \, {\left(d x + c\right)}^{3} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + 6 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)} - 6 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} + {\left(-36 i \, c^{2} - 48 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - 6 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-24 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-72 i \, d e f^{2} + 72 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-72 i \, d^{2} e^{2} f + 144 i \, c d e f^{2} + {\left(-72 i \, c^{2} - 96 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 6 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} + {\left(-36 i \, c^{2} - 48 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} + {\left(-18 i \, c^{2} - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + 12 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} + {\left(-18 i \, c^{2} - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 24 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(18 i \, d e f^{2} - 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + {\left(18 i \, c^{2} + 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left({\left(d x + c\right)}^{3} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + 16 \, {\left({\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(12 \, {\left(d x + c\right)}^{3} f^{3} - 36 i \, d^{2} e^{2} f + 4 \, {\left(9 \, c^{2} + 18 i \, c + 2\right)} d e f^{2} - {\left(12 \, c^{3} + 36 i \, c^{2} + 8 \, c + 8 i\right)} f^{3} + {\left(36 \, d e f^{2} - {\left(36 \, c + 4 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(36 \, d^{2} e^{2} f - {\left(72 \, c + 8 i\right)} d e f^{2} + 4 \, {\left(9 \, c^{2} + 2 i \, c + 2\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(-24 i \, {\left(d x + c\right)}^{3} f^{3} - 72 \, d^{2} e^{2} f + {\left(-72 i \, c^{2} + 144 \, c\right)} d e f^{2} + {\left(24 i \, c^{3} - 72 \, c^{2} - 8\right)} f^{3} - 8 \, {\left(9 i \, d e f^{2} + {\left(-9 i \, c + 11\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-72 i \, d^{2} e^{2} f - 16 \, {\left(-9 i \, c + 11\right)} d e f^{2} + {\left(-72 i \, c^{2} + 176 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(8 \, {\left(d x + c\right)}^{3} f^{3} - 32 i \, d^{2} e^{2} f + 8 \, {\left(3 \, c^{2} + 8 i \, c + 2\right)} d e f^{2} - {\left(8 \, c^{3} + 32 i \, c^{2} + 16 \, c + 16 i\right)} f^{3} + {\left(24 \, d e f^{2} - {\left(24 \, c - 32 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(24 \, d^{2} e^{2} f - {\left(48 \, c - 64 i\right)} d e f^{2} + 8 \, {\left(3 \, c^{2} - 8 i \, c + 2\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(24 i \, {\left(d x + c\right)}^{3} f^{3} - 88 \, d^{2} e^{2} f + {\left(72 i \, c^{2} + 176 \, c\right)} d e f^{2} + {\left(-24 i \, c^{3} - 88 \, c^{2} - 16\right)} f^{3} + {\left(72 i \, d e f^{2} - 72 \, {\left(i \, c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(72 i \, d^{2} e^{2} f - 144 \, {\left(i \, c + 1\right)} d e f^{2} + {\left(72 i \, c^{2} + 144 \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(12 \, {\left(d x + c\right)}^{3} f^{3} + 4 i \, d^{2} e^{2} f + 4 \, {\left(9 \, c^{2} - 2 i \, c + 2\right)} d e f^{2} - {\left(12 \, c^{3} - 4 i \, c^{2} + 8 \, c + 8 i\right)} f^{3} + {\left(36 \, d e f^{2} - {\left(36 \, c - 36 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(36 \, d^{2} e^{2} f - {\left(72 \, c - 72 i\right)} d e f^{2} + 4 \, {\left(9 \, c^{2} - 18 i \, c + 2\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(18 \, d^{2} e^{2} f - 36 \, c d e f^{2} + 18 \, {\left(d x + c\right)}^{2} f^{3} + 2 \, {\left(9 \, c^{2} + 28\right)} f^{3} + 36 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - 2 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, {\left(d x + c\right)}^{2} f^{3} + {\left(9 \, c^{2} + 28\right)} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} - 36 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-36 i \, c^{2} - 112 i\right)} f^{3} + {\left(-72 i \, d e f^{2} + 72 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - 2 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, {\left(d x + c\right)}^{2} f^{3} + {\left(9 \, c^{2} + 28\right)} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-72 i \, d^{2} e^{2} f + 144 i \, c d e f^{2} - 72 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-72 i \, c^{2} - 224 i\right)} f^{3} + {\left(-144 i \, d e f^{2} + 144 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 2 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, {\left(d x + c\right)}^{2} f^{3} + {\left(9 \, c^{2} + 28\right)} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} - 36 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-36 i \, c^{2} - 112 i\right)} f^{3} + {\left(-72 i \, d e f^{2} + 72 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} - 18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-18 i \, c^{2} - 56 i\right)} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + 4 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, {\left(d x + c\right)}^{2} f^{3} + {\left(9 \, c^{2} + 28\right)} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} - 18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-18 i \, c^{2} - 56 i\right)} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 8 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, {\left(d x + c\right)}^{2} f^{3} + {\left(9 \, c^{2} + 28\right)} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + 18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(18 i \, c^{2} + 56 i\right)} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 4 \, {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, {\left(d x + c\right)}^{2} f^{3} + {\left(9 \, c^{2} + 28\right)} f^{3} + 18 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(18 \, d^{2} e^{2} f - 36 \, c d e f^{2} + 18 \, {\left(d x + c\right)}^{2} f^{3} + 6 \, {\left(3 \, c^{2} + 4\right)} f^{3} + 36 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)} - 6 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + 3 \, {\left(d x + c\right)}^{2} f^{3} + {\left(3 \, c^{2} + 4\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(36 i \, d^{2} e^{2} f - 72 i \, c d e f^{2} + 36 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(36 i \, c^{2} + 48 i\right)} f^{3} + {\left(72 i \, d e f^{2} - 72 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - 6 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + 3 \, {\left(d x + c\right)}^{2} f^{3} + {\left(3 \, c^{2} + 4\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(72 i \, d^{2} e^{2} f - 144 i \, c d e f^{2} + 72 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(72 i \, c^{2} + 96 i\right)} f^{3} + {\left(144 i \, d e f^{2} - 144 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 6 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + 3 \, {\left(d x + c\right)}^{2} f^{3} + {\left(3 \, c^{2} + 4\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(36 i \, d^{2} e^{2} f - 72 i \, c d e f^{2} + 36 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(36 i \, c^{2} + 48 i\right)} f^{3} + {\left(72 i \, d e f^{2} - 72 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + 18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(18 i \, c^{2} + 24 i\right)} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + 12 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + 3 \, {\left(d x + c\right)}^{2} f^{3} + {\left(3 \, c^{2} + 4\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + 18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(18 i \, c^{2} + 24 i\right)} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 24 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + 3 \, {\left(d x + c\right)}^{2} f^{3} + {\left(3 \, c^{2} + 4\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} - 18 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-18 i \, c^{2} - 24 i\right)} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 12 \, {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + 3 \, {\left(d x + c\right)}^{2} f^{3} + {\left(3 \, c^{2} + 4\right)} f^{3} + 6 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 i \, c^{2} + 28 i\right)} d e f^{2} + {\left(-3 i \, c^{3} - 28 i \, c\right)} f^{3} + {\left(9 i \, d e f^{2} - 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 i \, d^{2} e^{2} f - 18 i \, c d e f^{2} + {\left(9 i \, c^{2} + 28 i\right)} f^{3}\right)} {\left(d x + c\right)} + {\left(-3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-9 i \, c^{2} - 28 i\right)} d e f^{2} + {\left(3 i \, c^{3} + 28 i \, c\right)} f^{3} + {\left(-9 i \, d e f^{2} + 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-9 i \, d^{2} e^{2} f + 18 i \, c d e f^{2} + {\left(-9 i \, c^{2} - 28 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-9 i \, c^{2} - 28 i\right)} d e f^{2} + {\left(3 i \, c^{3} + 28 i \, c\right)} f^{3} + {\left(-9 i \, d e f^{2} + 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-9 i \, d^{2} e^{2} f + 18 i \, c d e f^{2} + {\left(-9 i \, c^{2} - 28 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 i \, c^{2} + 28 i\right)} d e f^{2} + {\left(-3 i \, c^{3} - 28 i \, c\right)} f^{3} + {\left(9 i \, d e f^{2} - 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 i \, d^{2} e^{2} f - 18 i \, c d e f^{2} + {\left(9 i \, c^{2} + 28 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(18 i \, c^{2} + 56 i\right)} d e f^{2} + {\left(-6 i \, c^{3} - 56 i \, c\right)} f^{3} + {\left(18 i \, d e f^{2} - 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + {\left(18 i \, c^{2} + 56 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(12 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(36 i \, c^{2} + 112 i\right)} d e f^{2} + {\left(-12 i \, c^{3} - 112 i \, c\right)} f^{3} + {\left(36 i \, d e f^{2} - 36 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(36 i \, d^{2} e^{2} f - 72 i \, c d e f^{2} + {\left(36 i \, c^{2} + 112 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(3 \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + 9 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + {\left(9 \, c^{2} + 28\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(18 i \, c^{2} + 56 i\right)} d e f^{2} + {\left(-6 i \, c^{3} - 56 i \, c\right)} f^{3} + {\left(18 i \, d e f^{2} - 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + {\left(18 i \, c^{2} + 56 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-9 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(3 i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-9 i \, d e f^{2} + 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-9 i \, d^{2} e^{2} f + 18 i \, c d e f^{2} + {\left(-9 i \, c^{2} - 12 i\right)} f^{3}\right)} {\left(d x + c\right)} + {\left(3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 i \, c^{2} + 12 i\right)} d e f^{2} + {\left(-3 i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(9 i \, d e f^{2} - 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 i \, d^{2} e^{2} f - 18 i \, c d e f^{2} + {\left(9 i \, c^{2} + 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left({\left(d x + c\right)}^{3} f^{3} + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(9 i \, c^{2} + 12 i\right)} d e f^{2} + {\left(-3 i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(9 i \, d e f^{2} - 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(9 i \, d^{2} e^{2} f - 18 i \, c d e f^{2} + {\left(9 i \, c^{2} + 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - 12 \, {\left({\left(d x + c\right)}^{3} f^{3} + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-3 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-9 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(3 i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-9 i \, d e f^{2} + 9 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-9 i \, d^{2} e^{2} f + 18 i \, c d e f^{2} + {\left(-9 i \, c^{2} - 12 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 6 \, {\left({\left(d x + c\right)}^{3} f^{3} + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - 3 \, {\left({\left(d x + c\right)}^{3} f^{3} + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(-6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-18 i \, c^{2} - 24 i\right)} d e f^{2} + {\left(6 i \, c^{3} + 24 i \, c\right)} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} + {\left(-18 i \, c^{2} - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - 3 \, {\left({\left(d x + c\right)}^{3} f^{3} + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-36 i \, c^{2} - 48 i\right)} d e f^{2} + {\left(12 i \, c^{3} + 48 i \, c\right)} f^{3} + {\left(-36 i \, d e f^{2} + 36 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f + 72 i \, c d e f^{2} + {\left(-36 i \, c^{2} - 48 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 3 \, {\left({\left(d x + c\right)}^{3} f^{3} + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3} + 3 \, {\left(d e f^{2} - c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(3 \, d^{2} e^{2} f - 6 \, c d e f^{2} + {\left(3 \, c^{2} + 4\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-6 i \, {\left(d x + c\right)}^{3} f^{3} + {\left(-18 i \, c^{2} - 24 i\right)} d e f^{2} + {\left(6 i \, c^{3} + 24 i \, c\right)} f^{3} + {\left(-18 i \, d e f^{2} + 18 i \, c f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-18 i \, d^{2} e^{2} f + 36 i \, c d e f^{2} + {\left(-18 i \, c^{2} - 24 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - {\left(36 \, f^{3} \cos\left(6 \, d x + 6 \, c\right) + 72 i \, f^{3} \cos\left(5 \, d x + 5 \, c\right) + 36 \, f^{3} \cos\left(4 \, d x + 4 \, c\right) + 144 i \, f^{3} \cos\left(3 \, d x + 3 \, c\right) - 36 \, f^{3} \cos\left(2 \, d x + 2 \, c\right) + 72 i \, f^{3} \cos\left(d x + c\right) + 36 i \, f^{3} \sin\left(6 \, d x + 6 \, c\right) - 72 \, f^{3} \sin\left(5 \, d x + 5 \, c\right) + 36 i \, f^{3} \sin\left(4 \, d x + 4 \, c\right) - 144 \, f^{3} \sin\left(3 \, d x + 3 \, c\right) - 36 i \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 72 \, f^{3} \sin\left(d x + c\right) - 36 \, f^{3}\right)} {\rm Li}_{4}(i \, e^{\left(i \, d x + i \, c\right)}) + {\left(36 \, f^{3} \cos\left(6 \, d x + 6 \, c\right) + 72 i \, f^{3} \cos\left(5 \, d x + 5 \, c\right) + 36 \, f^{3} \cos\left(4 \, d x + 4 \, c\right) + 144 i \, f^{3} \cos\left(3 \, d x + 3 \, c\right) - 36 \, f^{3} \cos\left(2 \, d x + 2 \, c\right) + 72 i \, f^{3} \cos\left(d x + c\right) + 36 i \, f^{3} \sin\left(6 \, d x + 6 \, c\right) - 72 \, f^{3} \sin\left(5 \, d x + 5 \, c\right) + 36 i \, f^{3} \sin\left(4 \, d x + 4 \, c\right) - 144 \, f^{3} \sin\left(3 \, d x + 3 \, c\right) - 36 i \, f^{3} \sin\left(2 \, d x + 2 \, c\right) - 72 \, f^{3} \sin\left(d x + c\right) - 36 \, f^{3}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(36 i \, d e f^{2} + 36 i \, {\left(d x + c\right)} f^{3} - 36 i \, c f^{3} + {\left(-36 i \, d e f^{2} - 36 i \, {\left(d x + c\right)} f^{3} + 36 i \, c f^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) + 72 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-36 i \, d e f^{2} - 36 i \, {\left(d x + c\right)} f^{3} + 36 i \, c f^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) + 144 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(36 i \, d e f^{2} + 36 i \, {\left(d x + c\right)} f^{3} - 36 i \, c f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) + 72 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) + 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(72 i \, d e f^{2} + 72 i \, {\left(d x + c\right)} f^{3} - 72 i \, c f^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) + 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(144 i \, d e f^{2} + 144 i \, {\left(d x + c\right)} f^{3} - 144 i \, c f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) - 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(72 i \, d e f^{2} + 72 i \, {\left(d x + c\right)} f^{3} - 72 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-36 i \, d e f^{2} - 36 i \, {\left(d x + c\right)} f^{3} + 36 i \, c f^{3} + {\left(36 i \, d e f^{2} + 36 i \, {\left(d x + c\right)} f^{3} - 36 i \, c f^{3}\right)} \cos\left(6 \, d x + 6 \, c\right) - 72 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(36 i \, d e f^{2} + 36 i \, {\left(d x + c\right)} f^{3} - 36 i \, c f^{3}\right)} \cos\left(4 \, d x + 4 \, c\right) - 144 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-36 i \, d e f^{2} - 36 i \, {\left(d x + c\right)} f^{3} + 36 i \, c f^{3}\right)} \cos\left(2 \, d x + 2 \, c\right) - 72 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \cos\left(d x + c\right) - 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(-72 i \, d e f^{2} - 72 i \, {\left(d x + c\right)} f^{3} + 72 i \, c f^{3}\right)} \sin\left(5 \, d x + 5 \, c\right) - 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-144 i \, d e f^{2} - 144 i \, {\left(d x + c\right)} f^{3} + 144 i \, c f^{3}\right)} \sin\left(3 \, d x + 3 \, c\right) + 36 \, {\left(d e f^{2} + {\left(d x + c\right)} f^{3} - c f^{3}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-72 i \, d e f^{2} - 72 i \, {\left(d x + c\right)} f^{3} + 72 i \, c f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-16 i \, {\left(d x + c\right)}^{2} f^{3} + {\left(-32 i \, d e f^{2} + 32 i \, c f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) - {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} - 36 \, d^{2} e^{2} f + {\left(-36 i \, c^{2} + 72 \, c - 8 i\right)} d e f^{2} + {\left(12 i \, c^{3} - 36 \, c^{2} + 8 i \, c - 8\right)} f^{3} - 4 \, {\left(9 i \, d e f^{2} + {\left(-9 i \, c + 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f - 8 \, {\left(-9 i \, c + 1\right)} d e f^{2} + {\left(-36 i \, c^{2} + 8 \, c - 8 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(24 \, {\left(d x + c\right)}^{3} f^{3} - 72 i \, d^{2} e^{2} f + 72 \, {\left(c^{2} + 2 i \, c\right)} d e f^{2} - {\left(24 \, c^{3} + 72 i \, c^{2} + 8 i\right)} f^{3} + {\left(72 \, d e f^{2} - {\left(72 \, c + 88 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(72 \, d^{2} e^{2} f - {\left(144 \, c + 176 i\right)} d e f^{2} + 8 \, {\left(9 \, c^{2} + 22 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(-8 i \, {\left(d x + c\right)}^{3} f^{3} - 32 \, d^{2} e^{2} f + {\left(-24 i \, c^{2} + 64 \, c - 16 i\right)} d e f^{2} + {\left(8 i \, c^{3} - 32 \, c^{2} + 16 i \, c - 16\right)} f^{3} - 8 \, {\left(3 i \, d e f^{2} + {\left(-3 i \, c - 4\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-24 i \, d^{2} e^{2} f - 16 \, {\left(-3 i \, c - 4\right)} d e f^{2} + {\left(-24 i \, c^{2} - 64 \, c - 16 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(24 \, {\left(d x + c\right)}^{3} f^{3} + 88 i \, d^{2} e^{2} f + 8 \, {\left(9 \, c^{2} - 22 i \, c\right)} d e f^{2} - {\left(24 \, c^{3} - 88 i \, c^{2} - 16 i\right)} f^{3} + {\left(72 \, d e f^{2} - {\left(72 \, c - 72 i\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(72 \, d^{2} e^{2} f - {\left(144 \, c - 144 i\right)} d e f^{2} + 72 \, {\left(c^{2} - 2 i \, c\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(-12 i \, {\left(d x + c\right)}^{3} f^{3} + 4 \, d^{2} e^{2} f + {\left(-36 i \, c^{2} - 8 \, c - 8 i\right)} d e f^{2} + {\left(12 i \, c^{3} + 4 \, c^{2} + 8 i \, c - 8\right)} f^{3} + {\left(-36 i \, d e f^{2} - 36 \, {\left(-i \, c - 1\right)} f^{3}\right)} {\left(d x + c\right)}^{2} + {\left(-36 i \, d^{2} e^{2} f - 72 \, {\left(-i \, c - 1\right)} d e f^{2} + {\left(-36 i \, c^{2} - 72 \, c - 8 i\right)} f^{3}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-16 i \, a d^{3} \cos\left(6 \, d x + 6 \, c\right) + 32 \, a d^{3} \cos\left(5 \, d x + 5 \, c\right) - 16 i \, a d^{3} \cos\left(4 \, d x + 4 \, c\right) + 64 \, a d^{3} \cos\left(3 \, d x + 3 \, c\right) + 16 i \, a d^{3} \cos\left(2 \, d x + 2 \, c\right) + 32 \, a d^{3} \cos\left(d x + c\right) + 16 \, a d^{3} \sin\left(6 \, d x + 6 \, c\right) + 32 i \, a d^{3} \sin\left(5 \, d x + 5 \, c\right) + 16 \, a d^{3} \sin\left(4 \, d x + 4 \, c\right) + 64 i \, a d^{3} \sin\left(3 \, d x + 3 \, c\right) - 16 \, a d^{3} \sin\left(2 \, d x + 2 \, c\right) + 32 i \, a d^{3} \sin\left(d x + c\right) + 16 i \, a d^{3}}}{16 \, d}"," ",0,"1/16*(3*c*e^2*f*(2*(3*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*d*sin(d*x + c)^3 + a*d*sin(d*x + c)^2 - a*d*sin(d*x + c) - a*d) - 3*log(sin(d*x + c) + 1)/(a*d) + 3*log(sin(d*x + c) - 1)/(a*d)) - e^3*(2*(3*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*sin(d*x + c)^3 + a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 3*log(sin(d*x + c) + 1)/a + 3*log(sin(d*x + c) - 1)/a) - 16*(16*d^2*e^2*f - 32*c*d*e*f^2 + 8*(2*c^2 + 1)*f^3 + (2*(9*c^2 + 28)*d*e*f^2 - 2*(3*c^3 + 28*c)*f^3 - 2*((9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(6*d*x + 6*c) - ((36*I*c^2 + 112*I)*d*e*f^2 + (-12*I*c^3 - 112*I*c)*f^3)*cos(5*d*x + 5*c) - 2*((9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(4*d*x + 4*c) - ((72*I*c^2 + 224*I)*d*e*f^2 + (-24*I*c^3 - 224*I*c)*f^3)*cos(3*d*x + 3*c) + 2*((9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(2*d*x + 2*c) - ((36*I*c^2 + 112*I)*d*e*f^2 + (-12*I*c^3 - 112*I*c)*f^3)*cos(d*x + c) - ((18*I*c^2 + 56*I)*d*e*f^2 + (-6*I*c^3 - 56*I*c)*f^3)*sin(6*d*x + 6*c) + 4*((9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*sin(5*d*x + 5*c) - ((18*I*c^2 + 56*I)*d*e*f^2 + (-6*I*c^3 - 56*I*c)*f^3)*sin(4*d*x + 4*c) + 8*((9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*sin(3*d*x + 3*c) - ((-18*I*c^2 - 56*I)*d*e*f^2 + (6*I*c^3 + 56*I*c)*f^3)*sin(2*d*x + 2*c) + 4*((9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*sin(d*x + c))*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (6*(3*c^2 + 4)*d*e*f^2 - 6*(c^3 + 4*c)*f^3 - 6*((3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(6*d*x + 6*c) + ((-36*I*c^2 - 48*I)*d*e*f^2 + (12*I*c^3 + 48*I*c)*f^3)*cos(5*d*x + 5*c) - 6*((3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(4*d*x + 4*c) + ((-72*I*c^2 - 96*I)*d*e*f^2 + (24*I*c^3 + 96*I*c)*f^3)*cos(3*d*x + 3*c) + 6*((3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(2*d*x + 2*c) + ((-36*I*c^2 - 48*I)*d*e*f^2 + (12*I*c^3 + 48*I*c)*f^3)*cos(d*x + c) + ((-18*I*c^2 - 24*I)*d*e*f^2 + (6*I*c^3 + 24*I*c)*f^3)*sin(6*d*x + 6*c) + 12*((3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*sin(5*d*x + 5*c) + ((-18*I*c^2 - 24*I)*d*e*f^2 + (6*I*c^3 + 24*I*c)*f^3)*sin(4*d*x + 4*c) + 24*((3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*sin(3*d*x + 3*c) + ((18*I*c^2 + 24*I)*d*e*f^2 + (-6*I*c^3 - 24*I*c)*f^3)*sin(2*d*x + 2*c) + 12*((3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*sin(d*x + c))*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (6*(d*x + c)^3*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 2*(9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c) - 2*(3*(d*x + c)^3*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*cos(6*d*x + 6*c) + (-12*I*(d*x + c)^3*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 + (-36*I*c^2 - 112*I)*f^3)*(d*x + c))*cos(5*d*x + 5*c) - 2*(3*(d*x + c)^3*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*cos(4*d*x + 4*c) + (-24*I*(d*x + c)^3*f^3 + (-72*I*d*e*f^2 + 72*I*c*f^3)*(d*x + c)^2 + (-72*I*d^2*e^2*f + 144*I*c*d*e*f^2 + (-72*I*c^2 - 224*I)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 2*(3*(d*x + c)^3*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-12*I*(d*x + c)^3*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 + (-36*I*c^2 - 112*I)*f^3)*(d*x + c))*cos(d*x + c) + (-6*I*(d*x + c)^3*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c)^2 + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 + (-18*I*c^2 - 56*I)*f^3)*(d*x + c))*sin(6*d*x + 6*c) + 4*(3*(d*x + c)^3*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*sin(5*d*x + 5*c) + (-6*I*(d*x + c)^3*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c)^2 + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 + (-18*I*c^2 - 56*I)*f^3)*(d*x + c))*sin(4*d*x + 4*c) + 8*(3*(d*x + c)^3*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (6*I*(d*x + c)^3*f^3 + (18*I*d*e*f^2 - 18*I*c*f^3)*(d*x + c)^2 + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + (18*I*c^2 + 56*I)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 4*(3*(d*x + c)^3*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (6*(d*x + c)^3*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c)^2 + 6*(3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c) - 6*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*cos(6*d*x + 6*c) + (-12*I*(d*x + c)^3*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 + (-36*I*c^2 - 48*I)*f^3)*(d*x + c))*cos(5*d*x + 5*c) - 6*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*cos(4*d*x + 4*c) + (-24*I*(d*x + c)^3*f^3 + (-72*I*d*e*f^2 + 72*I*c*f^3)*(d*x + c)^2 + (-72*I*d^2*e^2*f + 144*I*c*d*e*f^2 + (-72*I*c^2 - 96*I)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 6*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-12*I*(d*x + c)^3*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 + (-36*I*c^2 - 48*I)*f^3)*(d*x + c))*cos(d*x + c) + (-6*I*(d*x + c)^3*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c)^2 + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 + (-18*I*c^2 - 24*I)*f^3)*(d*x + c))*sin(6*d*x + 6*c) + 12*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*sin(5*d*x + 5*c) + (-6*I*(d*x + c)^3*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c)^2 + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 + (-18*I*c^2 - 24*I)*f^3)*(d*x + c))*sin(4*d*x + 4*c) + 24*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (6*I*(d*x + c)^3*f^3 + (18*I*d*e*f^2 - 18*I*c*f^3)*(d*x + c)^2 + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + (18*I*c^2 + 24*I)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 12*((d*x + c)^3*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + 16*((d*x + c)^2*f^3 + 2*(d*e*f^2 - c*f^3)*(d*x + c))*cos(6*d*x + 6*c) + (12*(d*x + c)^3*f^3 - 36*I*d^2*e^2*f + 4*(9*c^2 + 18*I*c + 2)*d*e*f^2 - (12*c^3 + 36*I*c^2 + 8*c + 8*I)*f^3 + (36*d*e*f^2 - (36*c + 4*I)*f^3)*(d*x + c)^2 + (36*d^2*e^2*f - (72*c + 8*I)*d*e*f^2 + 4*(9*c^2 + 2*I*c + 2)*f^3)*(d*x + c))*cos(5*d*x + 5*c) - (-24*I*(d*x + c)^3*f^3 - 72*d^2*e^2*f + (-72*I*c^2 + 144*c)*d*e*f^2 + (24*I*c^3 - 72*c^2 - 8)*f^3 - 8*(9*I*d*e*f^2 + (-9*I*c + 11)*f^3)*(d*x + c)^2 + (-72*I*d^2*e^2*f - 16*(-9*I*c + 11)*d*e*f^2 + (-72*I*c^2 + 176*c)*f^3)*(d*x + c))*cos(4*d*x + 4*c) + (8*(d*x + c)^3*f^3 - 32*I*d^2*e^2*f + 8*(3*c^2 + 8*I*c + 2)*d*e*f^2 - (8*c^3 + 32*I*c^2 + 16*c + 16*I)*f^3 + (24*d*e*f^2 - (24*c - 32*I)*f^3)*(d*x + c)^2 + (24*d^2*e^2*f - (48*c - 64*I)*d*e*f^2 + 8*(3*c^2 - 8*I*c + 2)*f^3)*(d*x + c))*cos(3*d*x + 3*c) - (24*I*(d*x + c)^3*f^3 - 88*d^2*e^2*f + (72*I*c^2 + 176*c)*d*e*f^2 + (-24*I*c^3 - 88*c^2 - 16)*f^3 + (72*I*d*e*f^2 - 72*(I*c + 1)*f^3)*(d*x + c)^2 + (72*I*d^2*e^2*f - 144*(I*c + 1)*d*e*f^2 + (72*I*c^2 + 144*c)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (12*(d*x + c)^3*f^3 + 4*I*d^2*e^2*f + 4*(9*c^2 - 2*I*c + 2)*d*e*f^2 - (12*c^3 - 4*I*c^2 + 8*c + 8*I)*f^3 + (36*d*e*f^2 - (36*c - 36*I)*f^3)*(d*x + c)^2 + (36*d^2*e^2*f - (72*c - 72*I)*d*e*f^2 + 4*(9*c^2 - 18*I*c + 2)*f^3)*(d*x + c))*cos(d*x + c) - (18*d^2*e^2*f - 36*c*d*e*f^2 + 18*(d*x + c)^2*f^3 + 2*(9*c^2 + 28)*f^3 + 36*(d*e*f^2 - c*f^3)*(d*x + c) - 2*(9*d^2*e^2*f - 18*c*d*e*f^2 + 9*(d*x + c)^2*f^3 + (9*c^2 + 28)*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c))*cos(6*d*x + 6*c) + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 - 36*I*(d*x + c)^2*f^3 + (-36*I*c^2 - 112*I)*f^3 + (-72*I*d*e*f^2 + 72*I*c*f^3)*(d*x + c))*cos(5*d*x + 5*c) - 2*(9*d^2*e^2*f - 18*c*d*e*f^2 + 9*(d*x + c)^2*f^3 + (9*c^2 + 28)*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c))*cos(4*d*x + 4*c) + (-72*I*d^2*e^2*f + 144*I*c*d*e*f^2 - 72*I*(d*x + c)^2*f^3 + (-72*I*c^2 - 224*I)*f^3 + (-144*I*d*e*f^2 + 144*I*c*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 2*(9*d^2*e^2*f - 18*c*d*e*f^2 + 9*(d*x + c)^2*f^3 + (9*c^2 + 28)*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c))*cos(2*d*x + 2*c) + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 - 36*I*(d*x + c)^2*f^3 + (-36*I*c^2 - 112*I)*f^3 + (-72*I*d*e*f^2 + 72*I*c*f^3)*(d*x + c))*cos(d*x + c) + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 - 18*I*(d*x + c)^2*f^3 + (-18*I*c^2 - 56*I)*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c))*sin(6*d*x + 6*c) + 4*(9*d^2*e^2*f - 18*c*d*e*f^2 + 9*(d*x + c)^2*f^3 + (9*c^2 + 28)*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c))*sin(5*d*x + 5*c) + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 - 18*I*(d*x + c)^2*f^3 + (-18*I*c^2 - 56*I)*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c))*sin(4*d*x + 4*c) + 8*(9*d^2*e^2*f - 18*c*d*e*f^2 + 9*(d*x + c)^2*f^3 + (9*c^2 + 28)*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + 18*I*(d*x + c)^2*f^3 + (18*I*c^2 + 56*I)*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 4*(9*d^2*e^2*f - 18*c*d*e*f^2 + 9*(d*x + c)^2*f^3 + (9*c^2 + 28)*f^3 + 18*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) + (18*d^2*e^2*f - 36*c*d*e*f^2 + 18*(d*x + c)^2*f^3 + 6*(3*c^2 + 4)*f^3 + 36*(d*e*f^2 - c*f^3)*(d*x + c) - 6*(3*d^2*e^2*f - 6*c*d*e*f^2 + 3*(d*x + c)^2*f^3 + (3*c^2 + 4)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c))*cos(6*d*x + 6*c) - (36*I*d^2*e^2*f - 72*I*c*d*e*f^2 + 36*I*(d*x + c)^2*f^3 + (36*I*c^2 + 48*I)*f^3 + (72*I*d*e*f^2 - 72*I*c*f^3)*(d*x + c))*cos(5*d*x + 5*c) - 6*(3*d^2*e^2*f - 6*c*d*e*f^2 + 3*(d*x + c)^2*f^3 + (3*c^2 + 4)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c))*cos(4*d*x + 4*c) - (72*I*d^2*e^2*f - 144*I*c*d*e*f^2 + 72*I*(d*x + c)^2*f^3 + (72*I*c^2 + 96*I)*f^3 + (144*I*d*e*f^2 - 144*I*c*f^3)*(d*x + c))*cos(3*d*x + 3*c) + 6*(3*d^2*e^2*f - 6*c*d*e*f^2 + 3*(d*x + c)^2*f^3 + (3*c^2 + 4)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c))*cos(2*d*x + 2*c) - (36*I*d^2*e^2*f - 72*I*c*d*e*f^2 + 36*I*(d*x + c)^2*f^3 + (36*I*c^2 + 48*I)*f^3 + (72*I*d*e*f^2 - 72*I*c*f^3)*(d*x + c))*cos(d*x + c) - (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + 18*I*(d*x + c)^2*f^3 + (18*I*c^2 + 24*I)*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c))*sin(6*d*x + 6*c) + 12*(3*d^2*e^2*f - 6*c*d*e*f^2 + 3*(d*x + c)^2*f^3 + (3*c^2 + 4)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c))*sin(5*d*x + 5*c) - (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + 18*I*(d*x + c)^2*f^3 + (18*I*c^2 + 24*I)*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c))*sin(4*d*x + 4*c) + 24*(3*d^2*e^2*f - 6*c*d*e*f^2 + 3*(d*x + c)^2*f^3 + (3*c^2 + 4)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c))*sin(3*d*x + 3*c) - (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 - 18*I*(d*x + c)^2*f^3 + (-18*I*c^2 - 24*I)*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c))*sin(2*d*x + 2*c) + 12*(3*d^2*e^2*f - 6*c*d*e*f^2 + 3*(d*x + c)^2*f^3 + (3*c^2 + 4)*f^3 + 6*(d*e*f^2 - c*f^3)*(d*x + c))*sin(d*x + c))*dilog(-I*e^(I*d*x + I*c)) - (3*I*(d*x + c)^3*f^3 + (9*I*c^2 + 28*I)*d*e*f^2 + (-3*I*c^3 - 28*I*c)*f^3 + (9*I*d*e*f^2 - 9*I*c*f^3)*(d*x + c)^2 + (9*I*d^2*e^2*f - 18*I*c*d*e*f^2 + (9*I*c^2 + 28*I)*f^3)*(d*x + c) + (-3*I*(d*x + c)^3*f^3 + (-9*I*c^2 - 28*I)*d*e*f^2 + (3*I*c^3 + 28*I*c)*f^3 + (-9*I*d*e*f^2 + 9*I*c*f^3)*(d*x + c)^2 + (-9*I*d^2*e^2*f + 18*I*c*d*e*f^2 + (-9*I*c^2 - 28*I)*f^3)*(d*x + c))*cos(6*d*x + 6*c) + 2*(3*(d*x + c)^3*f^3 + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*cos(5*d*x + 5*c) + (-3*I*(d*x + c)^3*f^3 + (-9*I*c^2 - 28*I)*d*e*f^2 + (3*I*c^3 + 28*I*c)*f^3 + (-9*I*d*e*f^2 + 9*I*c*f^3)*(d*x + c)^2 + (-9*I*d^2*e^2*f + 18*I*c*d*e*f^2 + (-9*I*c^2 - 28*I)*f^3)*(d*x + c))*cos(4*d*x + 4*c) + 4*(3*(d*x + c)^3*f^3 + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (3*I*(d*x + c)^3*f^3 + (9*I*c^2 + 28*I)*d*e*f^2 + (-3*I*c^3 - 28*I*c)*f^3 + (9*I*d*e*f^2 - 9*I*c*f^3)*(d*x + c)^2 + (9*I*d^2*e^2*f - 18*I*c*d*e*f^2 + (9*I*c^2 + 28*I)*f^3)*(d*x + c))*cos(2*d*x + 2*c) + 2*(3*(d*x + c)^3*f^3 + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*cos(d*x + c) + (3*(d*x + c)^3*f^3 + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*sin(6*d*x + 6*c) + (6*I*(d*x + c)^3*f^3 + (18*I*c^2 + 56*I)*d*e*f^2 + (-6*I*c^3 - 56*I*c)*f^3 + (18*I*d*e*f^2 - 18*I*c*f^3)*(d*x + c)^2 + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + (18*I*c^2 + 56*I)*f^3)*(d*x + c))*sin(5*d*x + 5*c) + (3*(d*x + c)^3*f^3 + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*sin(4*d*x + 4*c) + (12*I*(d*x + c)^3*f^3 + (36*I*c^2 + 112*I)*d*e*f^2 + (-12*I*c^3 - 112*I*c)*f^3 + (36*I*d*e*f^2 - 36*I*c*f^3)*(d*x + c)^2 + (36*I*d^2*e^2*f - 72*I*c*d*e*f^2 + (36*I*c^2 + 112*I)*f^3)*(d*x + c))*sin(3*d*x + 3*c) - (3*(d*x + c)^3*f^3 + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3 + 9*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (9*d^2*e^2*f - 18*c*d*e*f^2 + (9*c^2 + 28)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (6*I*(d*x + c)^3*f^3 + (18*I*c^2 + 56*I)*d*e*f^2 + (-6*I*c^3 - 56*I*c)*f^3 + (18*I*d*e*f^2 - 18*I*c*f^3)*(d*x + c)^2 + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + (18*I*c^2 + 56*I)*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (-3*I*(d*x + c)^3*f^3 + (-9*I*c^2 - 12*I)*d*e*f^2 + (3*I*c^3 + 12*I*c)*f^3 + (-9*I*d*e*f^2 + 9*I*c*f^3)*(d*x + c)^2 + (-9*I*d^2*e^2*f + 18*I*c*d*e*f^2 + (-9*I*c^2 - 12*I)*f^3)*(d*x + c) + (3*I*(d*x + c)^3*f^3 + (9*I*c^2 + 12*I)*d*e*f^2 + (-3*I*c^3 - 12*I*c)*f^3 + (9*I*d*e*f^2 - 9*I*c*f^3)*(d*x + c)^2 + (9*I*d^2*e^2*f - 18*I*c*d*e*f^2 + (9*I*c^2 + 12*I)*f^3)*(d*x + c))*cos(6*d*x + 6*c) - 6*((d*x + c)^3*f^3 + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*cos(5*d*x + 5*c) + (3*I*(d*x + c)^3*f^3 + (9*I*c^2 + 12*I)*d*e*f^2 + (-3*I*c^3 - 12*I*c)*f^3 + (9*I*d*e*f^2 - 9*I*c*f^3)*(d*x + c)^2 + (9*I*d^2*e^2*f - 18*I*c*d*e*f^2 + (9*I*c^2 + 12*I)*f^3)*(d*x + c))*cos(4*d*x + 4*c) - 12*((d*x + c)^3*f^3 + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*cos(3*d*x + 3*c) + (-3*I*(d*x + c)^3*f^3 + (-9*I*c^2 - 12*I)*d*e*f^2 + (3*I*c^3 + 12*I*c)*f^3 + (-9*I*d*e*f^2 + 9*I*c*f^3)*(d*x + c)^2 + (-9*I*d^2*e^2*f + 18*I*c*d*e*f^2 + (-9*I*c^2 - 12*I)*f^3)*(d*x + c))*cos(2*d*x + 2*c) - 6*((d*x + c)^3*f^3 + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*cos(d*x + c) - 3*((d*x + c)^3*f^3 + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*sin(6*d*x + 6*c) + (-6*I*(d*x + c)^3*f^3 + (-18*I*c^2 - 24*I)*d*e*f^2 + (6*I*c^3 + 24*I*c)*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c)^2 + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 + (-18*I*c^2 - 24*I)*f^3)*(d*x + c))*sin(5*d*x + 5*c) - 3*((d*x + c)^3*f^3 + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*sin(4*d*x + 4*c) + (-12*I*(d*x + c)^3*f^3 + (-36*I*c^2 - 48*I)*d*e*f^2 + (12*I*c^3 + 48*I*c)*f^3 + (-36*I*d*e*f^2 + 36*I*c*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f + 72*I*c*d*e*f^2 + (-36*I*c^2 - 48*I)*f^3)*(d*x + c))*sin(3*d*x + 3*c) + 3*((d*x + c)^3*f^3 + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3 + 3*(d*e*f^2 - c*f^3)*(d*x + c)^2 + (3*d^2*e^2*f - 6*c*d*e*f^2 + (3*c^2 + 4)*f^3)*(d*x + c))*sin(2*d*x + 2*c) + (-6*I*(d*x + c)^3*f^3 + (-18*I*c^2 - 24*I)*d*e*f^2 + (6*I*c^3 + 24*I*c)*f^3 + (-18*I*d*e*f^2 + 18*I*c*f^3)*(d*x + c)^2 + (-18*I*d^2*e^2*f + 36*I*c*d*e*f^2 + (-18*I*c^2 - 24*I)*f^3)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - (36*f^3*cos(6*d*x + 6*c) + 72*I*f^3*cos(5*d*x + 5*c) + 36*f^3*cos(4*d*x + 4*c) + 144*I*f^3*cos(3*d*x + 3*c) - 36*f^3*cos(2*d*x + 2*c) + 72*I*f^3*cos(d*x + c) + 36*I*f^3*sin(6*d*x + 6*c) - 72*f^3*sin(5*d*x + 5*c) + 36*I*f^3*sin(4*d*x + 4*c) - 144*f^3*sin(3*d*x + 3*c) - 36*I*f^3*sin(2*d*x + 2*c) - 72*f^3*sin(d*x + c) - 36*f^3)*polylog(4, I*e^(I*d*x + I*c)) + (36*f^3*cos(6*d*x + 6*c) + 72*I*f^3*cos(5*d*x + 5*c) + 36*f^3*cos(4*d*x + 4*c) + 144*I*f^3*cos(3*d*x + 3*c) - 36*f^3*cos(2*d*x + 2*c) + 72*I*f^3*cos(d*x + c) + 36*I*f^3*sin(6*d*x + 6*c) - 72*f^3*sin(5*d*x + 5*c) + 36*I*f^3*sin(4*d*x + 4*c) - 144*f^3*sin(3*d*x + 3*c) - 36*I*f^3*sin(2*d*x + 2*c) - 72*f^3*sin(d*x + c) - 36*f^3)*polylog(4, -I*e^(I*d*x + I*c)) - (36*I*d*e*f^2 + 36*I*(d*x + c)*f^3 - 36*I*c*f^3 + (-36*I*d*e*f^2 - 36*I*(d*x + c)*f^3 + 36*I*c*f^3)*cos(6*d*x + 6*c) + 72*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(5*d*x + 5*c) + (-36*I*d*e*f^2 - 36*I*(d*x + c)*f^3 + 36*I*c*f^3)*cos(4*d*x + 4*c) + 144*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(3*d*x + 3*c) + (36*I*d*e*f^2 + 36*I*(d*x + c)*f^3 - 36*I*c*f^3)*cos(2*d*x + 2*c) + 72*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) + 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(6*d*x + 6*c) + (72*I*d*e*f^2 + 72*I*(d*x + c)*f^3 - 72*I*c*f^3)*sin(5*d*x + 5*c) + 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(4*d*x + 4*c) + (144*I*d*e*f^2 + 144*I*(d*x + c)*f^3 - 144*I*c*f^3)*sin(3*d*x + 3*c) - 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(2*d*x + 2*c) + (72*I*d*e*f^2 + 72*I*(d*x + c)*f^3 - 72*I*c*f^3)*sin(d*x + c))*polylog(3, I*e^(I*d*x + I*c)) - (-36*I*d*e*f^2 - 36*I*(d*x + c)*f^3 + 36*I*c*f^3 + (36*I*d*e*f^2 + 36*I*(d*x + c)*f^3 - 36*I*c*f^3)*cos(6*d*x + 6*c) - 72*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(5*d*x + 5*c) + (36*I*d*e*f^2 + 36*I*(d*x + c)*f^3 - 36*I*c*f^3)*cos(4*d*x + 4*c) - 144*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(3*d*x + 3*c) + (-36*I*d*e*f^2 - 36*I*(d*x + c)*f^3 + 36*I*c*f^3)*cos(2*d*x + 2*c) - 72*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*cos(d*x + c) - 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(6*d*x + 6*c) + (-72*I*d*e*f^2 - 72*I*(d*x + c)*f^3 + 72*I*c*f^3)*sin(5*d*x + 5*c) - 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(4*d*x + 4*c) + (-144*I*d*e*f^2 - 144*I*(d*x + c)*f^3 + 144*I*c*f^3)*sin(3*d*x + 3*c) + 36*(d*e*f^2 + (d*x + c)*f^3 - c*f^3)*sin(2*d*x + 2*c) + (-72*I*d*e*f^2 - 72*I*(d*x + c)*f^3 + 72*I*c*f^3)*sin(d*x + c))*polylog(3, -I*e^(I*d*x + I*c)) - (-16*I*(d*x + c)^2*f^3 + (-32*I*d*e*f^2 + 32*I*c*f^3)*(d*x + c))*sin(6*d*x + 6*c) - (-12*I*(d*x + c)^3*f^3 - 36*d^2*e^2*f + (-36*I*c^2 + 72*c - 8*I)*d*e*f^2 + (12*I*c^3 - 36*c^2 + 8*I*c - 8)*f^3 - 4*(9*I*d*e*f^2 + (-9*I*c + 1)*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f - 8*(-9*I*c + 1)*d*e*f^2 + (-36*I*c^2 + 8*c - 8*I)*f^3)*(d*x + c))*sin(5*d*x + 5*c) - (24*(d*x + c)^3*f^3 - 72*I*d^2*e^2*f + 72*(c^2 + 2*I*c)*d*e*f^2 - (24*c^3 + 72*I*c^2 + 8*I)*f^3 + (72*d*e*f^2 - (72*c + 88*I)*f^3)*(d*x + c)^2 + (72*d^2*e^2*f - (144*c + 176*I)*d*e*f^2 + 8*(9*c^2 + 22*I*c)*f^3)*(d*x + c))*sin(4*d*x + 4*c) - (-8*I*(d*x + c)^3*f^3 - 32*d^2*e^2*f + (-24*I*c^2 + 64*c - 16*I)*d*e*f^2 + (8*I*c^3 - 32*c^2 + 16*I*c - 16)*f^3 - 8*(3*I*d*e*f^2 + (-3*I*c - 4)*f^3)*(d*x + c)^2 + (-24*I*d^2*e^2*f - 16*(-3*I*c - 4)*d*e*f^2 + (-24*I*c^2 - 64*c - 16*I)*f^3)*(d*x + c))*sin(3*d*x + 3*c) + (24*(d*x + c)^3*f^3 + 88*I*d^2*e^2*f + 8*(9*c^2 - 22*I*c)*d*e*f^2 - (24*c^3 - 88*I*c^2 - 16*I)*f^3 + (72*d*e*f^2 - (72*c - 72*I)*f^3)*(d*x + c)^2 + (72*d^2*e^2*f - (144*c - 144*I)*d*e*f^2 + 72*(c^2 - 2*I*c)*f^3)*(d*x + c))*sin(2*d*x + 2*c) - (-12*I*(d*x + c)^3*f^3 + 4*d^2*e^2*f + (-36*I*c^2 - 8*c - 8*I)*d*e*f^2 + (12*I*c^3 + 4*c^2 + 8*I*c - 8)*f^3 + (-36*I*d*e*f^2 - 36*(-I*c - 1)*f^3)*(d*x + c)^2 + (-36*I*d^2*e^2*f - 72*(-I*c - 1)*d*e*f^2 + (-36*I*c^2 - 72*c - 8*I)*f^3)*(d*x + c))*sin(d*x + c))/(-16*I*a*d^3*cos(6*d*x + 6*c) + 32*a*d^3*cos(5*d*x + 5*c) - 16*I*a*d^3*cos(4*d*x + 4*c) + 64*a*d^3*cos(3*d*x + 3*c) + 16*I*a*d^3*cos(2*d*x + 2*c) + 32*a*d^3*cos(d*x + c) + 16*a*d^3*sin(6*d*x + 6*c) + 32*I*a*d^3*sin(5*d*x + 5*c) + 16*a*d^3*sin(4*d*x + 4*c) + 64*I*a*d^3*sin(3*d*x + 3*c) - 16*a*d^3*sin(2*d*x + 2*c) + 32*I*a*d^3*sin(d*x + c) + 16*I*a*d^3))/d","B",0
282,1,5262,0,17.696671," ","integrate((f*x+e)^2*sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, c e f {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2\right)}}{a d \sin\left(d x + c\right)^{3} + a d \sin\left(d x + c\right)^{2} - a d \sin\left(d x + c\right) - a d} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a d} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a d}\right)} - e^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2\right)}}{a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}\right)} - \frac{16 \, {\left(32 \, {\left(d x + c\right)} f^{2} \cos\left(6 \, d x + 6 \, c\right) + 32 i \, {\left(d x + c\right)} f^{2} \sin\left(6 \, d x + 6 \, c\right) + 32 \, d e f - 32 \, c f^{2} - {\left(2 \, {\left(9 \, c^{2} + 28\right)} f^{2} \cos\left(6 \, d x + 6 \, c\right) + {\left(36 i \, c^{2} + 112 i\right)} f^{2} \cos\left(5 \, d x + 5 \, c\right) + 2 \, {\left(9 \, c^{2} + 28\right)} f^{2} \cos\left(4 \, d x + 4 \, c\right) + {\left(72 i \, c^{2} + 224 i\right)} f^{2} \cos\left(3 \, d x + 3 \, c\right) - 2 \, {\left(9 \, c^{2} + 28\right)} f^{2} \cos\left(2 \, d x + 2 \, c\right) + {\left(36 i \, c^{2} + 112 i\right)} f^{2} \cos\left(d x + c\right) + {\left(18 i \, c^{2} + 56 i\right)} f^{2} \sin\left(6 \, d x + 6 \, c\right) - 4 \, {\left(9 \, c^{2} + 28\right)} f^{2} \sin\left(5 \, d x + 5 \, c\right) + {\left(18 i \, c^{2} + 56 i\right)} f^{2} \sin\left(4 \, d x + 4 \, c\right) - 8 \, {\left(9 \, c^{2} + 28\right)} f^{2} \sin\left(3 \, d x + 3 \, c\right) + {\left(-18 i \, c^{2} - 56 i\right)} f^{2} \sin\left(2 \, d x + 2 \, c\right) - 4 \, {\left(9 \, c^{2} + 28\right)} f^{2} \sin\left(d x + c\right) - 2 \, {\left(9 \, c^{2} + 28\right)} f^{2}\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) + {\left(6 \, {\left(3 \, c^{2} + 4\right)} f^{2} \cos\left(6 \, d x + 6 \, c\right) - {\left(-36 i \, c^{2} - 48 i\right)} f^{2} \cos\left(5 \, d x + 5 \, c\right) + 6 \, {\left(3 \, c^{2} + 4\right)} f^{2} \cos\left(4 \, d x + 4 \, c\right) - {\left(-72 i \, c^{2} - 96 i\right)} f^{2} \cos\left(3 \, d x + 3 \, c\right) - 6 \, {\left(3 \, c^{2} + 4\right)} f^{2} \cos\left(2 \, d x + 2 \, c\right) - {\left(-36 i \, c^{2} - 48 i\right)} f^{2} \cos\left(d x + c\right) - {\left(-18 i \, c^{2} - 24 i\right)} f^{2} \sin\left(6 \, d x + 6 \, c\right) - 12 \, {\left(3 \, c^{2} + 4\right)} f^{2} \sin\left(5 \, d x + 5 \, c\right) - {\left(-18 i \, c^{2} - 24 i\right)} f^{2} \sin\left(4 \, d x + 4 \, c\right) - 24 \, {\left(3 \, c^{2} + 4\right)} f^{2} \sin\left(3 \, d x + 3 \, c\right) - {\left(18 i \, c^{2} + 24 i\right)} f^{2} \sin\left(2 \, d x + 2 \, c\right) - 12 \, {\left(3 \, c^{2} + 4\right)} f^{2} \sin\left(d x + c\right) - 6 \, {\left(3 \, c^{2} + 4\right)} f^{2}\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(18 \, {\left(d x + c\right)}^{2} f^{2} + 36 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)} - 18 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-72 i \, d e f + 72 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - 18 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-72 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-144 i \, d e f + 144 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 18 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-72 i \, d e f + 72 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-36 i \, d e f + 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + 36 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-36 i \, d e f + 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 72 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(36 i \, d e f - 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 36 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(18 \, {\left(d x + c\right)}^{2} f^{2} + 36 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)} - 18 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-72 i \, d e f + 72 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - 18 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-72 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-144 i \, d e f + 144 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + 18 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-72 i \, d e f + 72 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(-18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-36 i \, d e f + 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + 36 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-36 i \, d e f + 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + 72 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(36 i \, d e f - 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + 36 \, {\left({\left(d x + c\right)}^{2} f^{2} + 2 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) + {\left(36 \, {\left(d x + c\right)}^{2} f^{2} - 72 i \, d e f + 4 \, {\left(9 \, c^{2} + 18 i \, c + 2\right)} f^{2} + {\left(72 \, d e f - {\left(72 \, c + 8 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) - {\left(-72 i \, {\left(d x + c\right)}^{2} f^{2} - 144 \, d e f + {\left(-72 i \, c^{2} + 144 \, c\right)} f^{2} - 16 \, {\left(9 i \, d e f + {\left(-9 i \, c + 11\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(24 \, {\left(d x + c\right)}^{2} f^{2} - 64 i \, d e f + 8 \, {\left(3 \, c^{2} + 8 i \, c + 2\right)} f^{2} + {\left(48 \, d e f - {\left(48 \, c - 64 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) - {\left(72 i \, {\left(d x + c\right)}^{2} f^{2} - 176 \, d e f + {\left(72 i \, c^{2} + 176 \, c\right)} f^{2} + {\left(144 i \, d e f - 144 \, {\left(i \, c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(36 \, {\left(d x + c\right)}^{2} f^{2} + 8 i \, d e f + 4 \, {\left(9 \, c^{2} - 2 i \, c + 2\right)} f^{2} + {\left(72 \, d e f - {\left(72 \, c - 72 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - {\left(36 \, d e f + 36 \, {\left(d x + c\right)} f^{2} - 36 \, c f^{2} - 36 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) + {\left(-72 i \, d e f - 72 i \, {\left(d x + c\right)} f^{2} + 72 i \, c f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - 36 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) + {\left(-144 i \, d e f - 144 i \, {\left(d x + c\right)} f^{2} + 144 i \, c f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + 36 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) + {\left(-72 i \, d e f - 72 i \, {\left(d x + c\right)} f^{2} + 72 i \, c f^{2}\right)} \cos\left(d x + c\right) + {\left(-36 i \, d e f - 36 i \, {\left(d x + c\right)} f^{2} + 36 i \, c f^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) + 72 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(-36 i \, d e f - 36 i \, {\left(d x + c\right)} f^{2} + 36 i \, c f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 144 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(36 i \, d e f + 36 i \, {\left(d x + c\right)} f^{2} - 36 i \, c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + 72 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(36 \, d e f + 36 \, {\left(d x + c\right)} f^{2} - 36 \, c f^{2} - 36 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(6 \, d x + 6 \, c\right) - {\left(72 i \, d e f + 72 i \, {\left(d x + c\right)} f^{2} - 72 i \, c f^{2}\right)} \cos\left(5 \, d x + 5 \, c\right) - 36 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(144 i \, d e f + 144 i \, {\left(d x + c\right)} f^{2} - 144 i \, c f^{2}\right)} \cos\left(3 \, d x + 3 \, c\right) + 36 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(72 i \, d e f + 72 i \, {\left(d x + c\right)} f^{2} - 72 i \, c f^{2}\right)} \cos\left(d x + c\right) - {\left(36 i \, d e f + 36 i \, {\left(d x + c\right)} f^{2} - 36 i \, c f^{2}\right)} \sin\left(6 \, d x + 6 \, c\right) + 72 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(36 i \, d e f + 36 i \, {\left(d x + c\right)} f^{2} - 36 i \, c f^{2}\right)} \sin\left(4 \, d x + 4 \, c\right) + 144 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(-36 i \, d e f - 36 i \, {\left(d x + c\right)} f^{2} + 36 i \, c f^{2}\right)} \sin\left(2 \, d x + 2 \, c\right) + 72 \, {\left(d e f + {\left(d x + c\right)} f^{2} - c f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) - {\left(9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 i \, c^{2} + 28 i\right)} f^{2} + {\left(18 i \, d e f - 18 i \, c f^{2}\right)} {\left(d x + c\right)} + {\left(-9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-9 i \, c^{2} - 28 i\right)} f^{2} + {\left(-18 i \, d e f + 18 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) + 2 \, {\left(9 \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 \, c^{2} + 28\right)} f^{2} + 18 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-9 i \, c^{2} - 28 i\right)} f^{2} + {\left(-18 i \, d e f + 18 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) + 4 \, {\left(9 \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 \, c^{2} + 28\right)} f^{2} + 18 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 i \, c^{2} + 28 i\right)} f^{2} + {\left(18 i \, d e f - 18 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) + 2 \, {\left(9 \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 \, c^{2} + 28\right)} f^{2} + 18 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) + {\left(9 \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 \, c^{2} + 28\right)} f^{2} + 18 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(18 i \, c^{2} + 56 i\right)} f^{2} + {\left(36 i \, d e f - 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(9 \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 \, c^{2} + 28\right)} f^{2} + 18 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(36 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(36 i \, c^{2} + 112 i\right)} f^{2} + {\left(72 i \, d e f - 72 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(9 \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 \, c^{2} + 28\right)} f^{2} + 18 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(18 i \, c^{2} + 56 i\right)} f^{2} + {\left(36 i \, d e f - 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-9 i \, c^{2} - 12 i\right)} f^{2} + {\left(-18 i \, d e f + 18 i \, c f^{2}\right)} {\left(d x + c\right)} + {\left(9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 i \, c^{2} + 12 i\right)} f^{2} + {\left(18 i \, d e f - 18 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(6 \, d x + 6 \, c\right) - 6 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + {\left(3 \, c^{2} + 4\right)} f^{2} + 6 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(9 i \, c^{2} + 12 i\right)} f^{2} + {\left(18 i \, d e f - 18 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(4 \, d x + 4 \, c\right) - 12 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + {\left(3 \, c^{2} + 4\right)} f^{2} + 6 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-9 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-9 i \, c^{2} - 12 i\right)} f^{2} + {\left(-18 i \, d e f + 18 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(2 \, d x + 2 \, c\right) - 6 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + {\left(3 \, c^{2} + 4\right)} f^{2} + 6 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \cos\left(d x + c\right) - 3 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + {\left(3 \, c^{2} + 4\right)} f^{2} + 6 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(-18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-18 i \, c^{2} - 24 i\right)} f^{2} + {\left(-36 i \, d e f + 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - 3 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + {\left(3 \, c^{2} + 4\right)} f^{2} + 6 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-36 i \, c^{2} - 48 i\right)} f^{2} + {\left(-72 i \, d e f + 72 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + 3 \, {\left(3 \, {\left(d x + c\right)}^{2} f^{2} + {\left(3 \, c^{2} + 4\right)} f^{2} + 6 \, {\left(d e f - c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-18 i \, {\left(d x + c\right)}^{2} f^{2} + {\left(-18 i \, c^{2} - 24 i\right)} f^{2} + {\left(-36 i \, d e f + 36 i \, c f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) - {\left(-36 i \, f^{2} \cos\left(6 \, d x + 6 \, c\right) + 72 \, f^{2} \cos\left(5 \, d x + 5 \, c\right) - 36 i \, f^{2} \cos\left(4 \, d x + 4 \, c\right) + 144 \, f^{2} \cos\left(3 \, d x + 3 \, c\right) + 36 i \, f^{2} \cos\left(2 \, d x + 2 \, c\right) + 72 \, f^{2} \cos\left(d x + c\right) + 36 \, f^{2} \sin\left(6 \, d x + 6 \, c\right) + 72 i \, f^{2} \sin\left(5 \, d x + 5 \, c\right) + 36 \, f^{2} \sin\left(4 \, d x + 4 \, c\right) + 144 i \, f^{2} \sin\left(3 \, d x + 3 \, c\right) - 36 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) + 72 i \, f^{2} \sin\left(d x + c\right) + 36 i \, f^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, d x + i \, c\right)}) - {\left(36 i \, f^{2} \cos\left(6 \, d x + 6 \, c\right) - 72 \, f^{2} \cos\left(5 \, d x + 5 \, c\right) + 36 i \, f^{2} \cos\left(4 \, d x + 4 \, c\right) - 144 \, f^{2} \cos\left(3 \, d x + 3 \, c\right) - 36 i \, f^{2} \cos\left(2 \, d x + 2 \, c\right) - 72 \, f^{2} \cos\left(d x + c\right) - 36 \, f^{2} \sin\left(6 \, d x + 6 \, c\right) - 72 i \, f^{2} \sin\left(5 \, d x + 5 \, c\right) - 36 \, f^{2} \sin\left(4 \, d x + 4 \, c\right) - 144 i \, f^{2} \sin\left(3 \, d x + 3 \, c\right) + 36 \, f^{2} \sin\left(2 \, d x + 2 \, c\right) - 72 i \, f^{2} \sin\left(d x + c\right) - 36 i \, f^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, d x + i \, c\right)}) - {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} - 72 \, d e f + {\left(-36 i \, c^{2} + 72 \, c - 8 i\right)} f^{2} - 8 \, {\left(9 i \, d e f + {\left(-9 i \, c + 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(5 \, d x + 5 \, c\right) - {\left(72 \, {\left(d x + c\right)}^{2} f^{2} - 144 i \, d e f + 72 \, {\left(c^{2} + 2 i \, c\right)} f^{2} + {\left(144 \, d e f - {\left(144 \, c + 176 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(4 \, d x + 4 \, c\right) - {\left(-24 i \, {\left(d x + c\right)}^{2} f^{2} - 64 \, d e f + {\left(-24 i \, c^{2} + 64 \, c - 16 i\right)} f^{2} - 16 \, {\left(3 i \, d e f + {\left(-3 i \, c - 4\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(3 \, d x + 3 \, c\right) + {\left(72 \, {\left(d x + c\right)}^{2} f^{2} + 176 i \, d e f + 8 \, {\left(9 \, c^{2} - 22 i \, c\right)} f^{2} + {\left(144 \, d e f - {\left(144 \, c - 144 i\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(2 \, d x + 2 \, c\right) - {\left(-36 i \, {\left(d x + c\right)}^{2} f^{2} + 8 \, d e f + {\left(-36 i \, c^{2} - 8 \, c - 8 i\right)} f^{2} + {\left(-72 i \, d e f - 72 \, {\left(-i \, c - 1\right)} f^{2}\right)} {\left(d x + c\right)}\right)} \sin\left(d x + c\right)\right)}}{-48 i \, a d^{2} \cos\left(6 \, d x + 6 \, c\right) + 96 \, a d^{2} \cos\left(5 \, d x + 5 \, c\right) - 48 i \, a d^{2} \cos\left(4 \, d x + 4 \, c\right) + 192 \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) + 48 i \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) + 96 \, a d^{2} \cos\left(d x + c\right) + 48 \, a d^{2} \sin\left(6 \, d x + 6 \, c\right) + 96 i \, a d^{2} \sin\left(5 \, d x + 5 \, c\right) + 48 \, a d^{2} \sin\left(4 \, d x + 4 \, c\right) + 192 i \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) - 48 \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) + 96 i \, a d^{2} \sin\left(d x + c\right) + 48 i \, a d^{2}}}{16 \, d}"," ",0,"1/16*(2*c*e*f*(2*(3*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*d*sin(d*x + c)^3 + a*d*sin(d*x + c)^2 - a*d*sin(d*x + c) - a*d) - 3*log(sin(d*x + c) + 1)/(a*d) + 3*log(sin(d*x + c) - 1)/(a*d)) - e^2*(2*(3*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*sin(d*x + c)^3 + a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 3*log(sin(d*x + c) + 1)/a + 3*log(sin(d*x + c) - 1)/a) - 16*(32*(d*x + c)*f^2*cos(6*d*x + 6*c) + 32*I*(d*x + c)*f^2*sin(6*d*x + 6*c) + 32*d*e*f - 32*c*f^2 - (2*(9*c^2 + 28)*f^2*cos(6*d*x + 6*c) + (36*I*c^2 + 112*I)*f^2*cos(5*d*x + 5*c) + 2*(9*c^2 + 28)*f^2*cos(4*d*x + 4*c) + (72*I*c^2 + 224*I)*f^2*cos(3*d*x + 3*c) - 2*(9*c^2 + 28)*f^2*cos(2*d*x + 2*c) + (36*I*c^2 + 112*I)*f^2*cos(d*x + c) + (18*I*c^2 + 56*I)*f^2*sin(6*d*x + 6*c) - 4*(9*c^2 + 28)*f^2*sin(5*d*x + 5*c) + (18*I*c^2 + 56*I)*f^2*sin(4*d*x + 4*c) - 8*(9*c^2 + 28)*f^2*sin(3*d*x + 3*c) + (-18*I*c^2 - 56*I)*f^2*sin(2*d*x + 2*c) - 4*(9*c^2 + 28)*f^2*sin(d*x + c) - 2*(9*c^2 + 28)*f^2)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) + (6*(3*c^2 + 4)*f^2*cos(6*d*x + 6*c) - (-36*I*c^2 - 48*I)*f^2*cos(5*d*x + 5*c) + 6*(3*c^2 + 4)*f^2*cos(4*d*x + 4*c) - (-72*I*c^2 - 96*I)*f^2*cos(3*d*x + 3*c) - 6*(3*c^2 + 4)*f^2*cos(2*d*x + 2*c) - (-36*I*c^2 - 48*I)*f^2*cos(d*x + c) - (-18*I*c^2 - 24*I)*f^2*sin(6*d*x + 6*c) - 12*(3*c^2 + 4)*f^2*sin(5*d*x + 5*c) - (-18*I*c^2 - 24*I)*f^2*sin(4*d*x + 4*c) - 24*(3*c^2 + 4)*f^2*sin(3*d*x + 3*c) - (18*I*c^2 + 24*I)*f^2*sin(2*d*x + 2*c) - 12*(3*c^2 + 4)*f^2*sin(d*x + c) - 6*(3*c^2 + 4)*f^2)*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (18*(d*x + c)^2*f^2 + 36*(d*e*f - c*f^2)*(d*x + c) - 18*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(6*d*x + 6*c) + (-36*I*(d*x + c)^2*f^2 + (-72*I*d*e*f + 72*I*c*f^2)*(d*x + c))*cos(5*d*x + 5*c) - 18*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(4*d*x + 4*c) + (-72*I*(d*x + c)^2*f^2 + (-144*I*d*e*f + 144*I*c*f^2)*(d*x + c))*cos(3*d*x + 3*c) + 18*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (-36*I*(d*x + c)^2*f^2 + (-72*I*d*e*f + 72*I*c*f^2)*(d*x + c))*cos(d*x + c) + (-18*I*(d*x + c)^2*f^2 + (-36*I*d*e*f + 36*I*c*f^2)*(d*x + c))*sin(6*d*x + 6*c) + 36*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(5*d*x + 5*c) + (-18*I*(d*x + c)^2*f^2 + (-36*I*d*e*f + 36*I*c*f^2)*(d*x + c))*sin(4*d*x + 4*c) + 72*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(3*d*x + 3*c) + (18*I*(d*x + c)^2*f^2 + (36*I*d*e*f - 36*I*c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + 36*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (18*(d*x + c)^2*f^2 + 36*(d*e*f - c*f^2)*(d*x + c) - 18*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(6*d*x + 6*c) + (-36*I*(d*x + c)^2*f^2 + (-72*I*d*e*f + 72*I*c*f^2)*(d*x + c))*cos(5*d*x + 5*c) - 18*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(4*d*x + 4*c) + (-72*I*(d*x + c)^2*f^2 + (-144*I*d*e*f + 144*I*c*f^2)*(d*x + c))*cos(3*d*x + 3*c) + 18*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (-36*I*(d*x + c)^2*f^2 + (-72*I*d*e*f + 72*I*c*f^2)*(d*x + c))*cos(d*x + c) + (-18*I*(d*x + c)^2*f^2 + (-36*I*d*e*f + 36*I*c*f^2)*(d*x + c))*sin(6*d*x + 6*c) + 36*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(5*d*x + 5*c) + (-18*I*(d*x + c)^2*f^2 + (-36*I*d*e*f + 36*I*c*f^2)*(d*x + c))*sin(4*d*x + 4*c) + 72*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(3*d*x + 3*c) + (18*I*(d*x + c)^2*f^2 + (36*I*d*e*f - 36*I*c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + 36*((d*x + c)^2*f^2 + 2*(d*e*f - c*f^2)*(d*x + c))*sin(d*x + c))*arctan2(cos(d*x + c), -sin(d*x + c) + 1) + (36*(d*x + c)^2*f^2 - 72*I*d*e*f + 4*(9*c^2 + 18*I*c + 2)*f^2 + (72*d*e*f - (72*c + 8*I)*f^2)*(d*x + c))*cos(5*d*x + 5*c) - (-72*I*(d*x + c)^2*f^2 - 144*d*e*f + (-72*I*c^2 + 144*c)*f^2 - 16*(9*I*d*e*f + (-9*I*c + 11)*f^2)*(d*x + c))*cos(4*d*x + 4*c) + (24*(d*x + c)^2*f^2 - 64*I*d*e*f + 8*(3*c^2 + 8*I*c + 2)*f^2 + (48*d*e*f - (48*c - 64*I)*f^2)*(d*x + c))*cos(3*d*x + 3*c) - (72*I*(d*x + c)^2*f^2 - 176*d*e*f + (72*I*c^2 + 176*c)*f^2 + (144*I*d*e*f - 144*(I*c + 1)*f^2)*(d*x + c))*cos(2*d*x + 2*c) + (36*(d*x + c)^2*f^2 + 8*I*d*e*f + 4*(9*c^2 - 2*I*c + 2)*f^2 + (72*d*e*f - (72*c - 72*I)*f^2)*(d*x + c))*cos(d*x + c) - (36*d*e*f + 36*(d*x + c)*f^2 - 36*c*f^2 - 36*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(6*d*x + 6*c) + (-72*I*d*e*f - 72*I*(d*x + c)*f^2 + 72*I*c*f^2)*cos(5*d*x + 5*c) - 36*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(4*d*x + 4*c) + (-144*I*d*e*f - 144*I*(d*x + c)*f^2 + 144*I*c*f^2)*cos(3*d*x + 3*c) + 36*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(2*d*x + 2*c) + (-72*I*d*e*f - 72*I*(d*x + c)*f^2 + 72*I*c*f^2)*cos(d*x + c) + (-36*I*d*e*f - 36*I*(d*x + c)*f^2 + 36*I*c*f^2)*sin(6*d*x + 6*c) + 72*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(5*d*x + 5*c) + (-36*I*d*e*f - 36*I*(d*x + c)*f^2 + 36*I*c*f^2)*sin(4*d*x + 4*c) + 144*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(3*d*x + 3*c) + (36*I*d*e*f + 36*I*(d*x + c)*f^2 - 36*I*c*f^2)*sin(2*d*x + 2*c) + 72*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*dilog(I*e^(I*d*x + I*c)) + (36*d*e*f + 36*(d*x + c)*f^2 - 36*c*f^2 - 36*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(6*d*x + 6*c) - (72*I*d*e*f + 72*I*(d*x + c)*f^2 - 72*I*c*f^2)*cos(5*d*x + 5*c) - 36*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(4*d*x + 4*c) - (144*I*d*e*f + 144*I*(d*x + c)*f^2 - 144*I*c*f^2)*cos(3*d*x + 3*c) + 36*(d*e*f + (d*x + c)*f^2 - c*f^2)*cos(2*d*x + 2*c) - (72*I*d*e*f + 72*I*(d*x + c)*f^2 - 72*I*c*f^2)*cos(d*x + c) - (36*I*d*e*f + 36*I*(d*x + c)*f^2 - 36*I*c*f^2)*sin(6*d*x + 6*c) + 72*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(5*d*x + 5*c) - (36*I*d*e*f + 36*I*(d*x + c)*f^2 - 36*I*c*f^2)*sin(4*d*x + 4*c) + 144*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(3*d*x + 3*c) - (-36*I*d*e*f - 36*I*(d*x + c)*f^2 + 36*I*c*f^2)*sin(2*d*x + 2*c) + 72*(d*e*f + (d*x + c)*f^2 - c*f^2)*sin(d*x + c))*dilog(-I*e^(I*d*x + I*c)) - (9*I*(d*x + c)^2*f^2 + (9*I*c^2 + 28*I)*f^2 + (18*I*d*e*f - 18*I*c*f^2)*(d*x + c) + (-9*I*(d*x + c)^2*f^2 + (-9*I*c^2 - 28*I)*f^2 + (-18*I*d*e*f + 18*I*c*f^2)*(d*x + c))*cos(6*d*x + 6*c) + 2*(9*(d*x + c)^2*f^2 + (9*c^2 + 28)*f^2 + 18*(d*e*f - c*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (-9*I*(d*x + c)^2*f^2 + (-9*I*c^2 - 28*I)*f^2 + (-18*I*d*e*f + 18*I*c*f^2)*(d*x + c))*cos(4*d*x + 4*c) + 4*(9*(d*x + c)^2*f^2 + (9*c^2 + 28)*f^2 + 18*(d*e*f - c*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (9*I*(d*x + c)^2*f^2 + (9*I*c^2 + 28*I)*f^2 + (18*I*d*e*f - 18*I*c*f^2)*(d*x + c))*cos(2*d*x + 2*c) + 2*(9*(d*x + c)^2*f^2 + (9*c^2 + 28)*f^2 + 18*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) + (9*(d*x + c)^2*f^2 + (9*c^2 + 28)*f^2 + 18*(d*e*f - c*f^2)*(d*x + c))*sin(6*d*x + 6*c) + (18*I*(d*x + c)^2*f^2 + (18*I*c^2 + 56*I)*f^2 + (36*I*d*e*f - 36*I*c*f^2)*(d*x + c))*sin(5*d*x + 5*c) + (9*(d*x + c)^2*f^2 + (9*c^2 + 28)*f^2 + 18*(d*e*f - c*f^2)*(d*x + c))*sin(4*d*x + 4*c) + (36*I*(d*x + c)^2*f^2 + (36*I*c^2 + 112*I)*f^2 + (72*I*d*e*f - 72*I*c*f^2)*(d*x + c))*sin(3*d*x + 3*c) - (9*(d*x + c)^2*f^2 + (9*c^2 + 28)*f^2 + 18*(d*e*f - c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (18*I*(d*x + c)^2*f^2 + (18*I*c^2 + 56*I)*f^2 + (36*I*d*e*f - 36*I*c*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) - (-9*I*(d*x + c)^2*f^2 + (-9*I*c^2 - 12*I)*f^2 + (-18*I*d*e*f + 18*I*c*f^2)*(d*x + c) + (9*I*(d*x + c)^2*f^2 + (9*I*c^2 + 12*I)*f^2 + (18*I*d*e*f - 18*I*c*f^2)*(d*x + c))*cos(6*d*x + 6*c) - 6*(3*(d*x + c)^2*f^2 + (3*c^2 + 4)*f^2 + 6*(d*e*f - c*f^2)*(d*x + c))*cos(5*d*x + 5*c) + (9*I*(d*x + c)^2*f^2 + (9*I*c^2 + 12*I)*f^2 + (18*I*d*e*f - 18*I*c*f^2)*(d*x + c))*cos(4*d*x + 4*c) - 12*(3*(d*x + c)^2*f^2 + (3*c^2 + 4)*f^2 + 6*(d*e*f - c*f^2)*(d*x + c))*cos(3*d*x + 3*c) + (-9*I*(d*x + c)^2*f^2 + (-9*I*c^2 - 12*I)*f^2 + (-18*I*d*e*f + 18*I*c*f^2)*(d*x + c))*cos(2*d*x + 2*c) - 6*(3*(d*x + c)^2*f^2 + (3*c^2 + 4)*f^2 + 6*(d*e*f - c*f^2)*(d*x + c))*cos(d*x + c) - 3*(3*(d*x + c)^2*f^2 + (3*c^2 + 4)*f^2 + 6*(d*e*f - c*f^2)*(d*x + c))*sin(6*d*x + 6*c) + (-18*I*(d*x + c)^2*f^2 + (-18*I*c^2 - 24*I)*f^2 + (-36*I*d*e*f + 36*I*c*f^2)*(d*x + c))*sin(5*d*x + 5*c) - 3*(3*(d*x + c)^2*f^2 + (3*c^2 + 4)*f^2 + 6*(d*e*f - c*f^2)*(d*x + c))*sin(4*d*x + 4*c) + (-36*I*(d*x + c)^2*f^2 + (-36*I*c^2 - 48*I)*f^2 + (-72*I*d*e*f + 72*I*c*f^2)*(d*x + c))*sin(3*d*x + 3*c) + 3*(3*(d*x + c)^2*f^2 + (3*c^2 + 4)*f^2 + 6*(d*e*f - c*f^2)*(d*x + c))*sin(2*d*x + 2*c) + (-18*I*(d*x + c)^2*f^2 + (-18*I*c^2 - 24*I)*f^2 + (-36*I*d*e*f + 36*I*c*f^2)*(d*x + c))*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) - (-36*I*f^2*cos(6*d*x + 6*c) + 72*f^2*cos(5*d*x + 5*c) - 36*I*f^2*cos(4*d*x + 4*c) + 144*f^2*cos(3*d*x + 3*c) + 36*I*f^2*cos(2*d*x + 2*c) + 72*f^2*cos(d*x + c) + 36*f^2*sin(6*d*x + 6*c) + 72*I*f^2*sin(5*d*x + 5*c) + 36*f^2*sin(4*d*x + 4*c) + 144*I*f^2*sin(3*d*x + 3*c) - 36*f^2*sin(2*d*x + 2*c) + 72*I*f^2*sin(d*x + c) + 36*I*f^2)*polylog(3, I*e^(I*d*x + I*c)) - (36*I*f^2*cos(6*d*x + 6*c) - 72*f^2*cos(5*d*x + 5*c) + 36*I*f^2*cos(4*d*x + 4*c) - 144*f^2*cos(3*d*x + 3*c) - 36*I*f^2*cos(2*d*x + 2*c) - 72*f^2*cos(d*x + c) - 36*f^2*sin(6*d*x + 6*c) - 72*I*f^2*sin(5*d*x + 5*c) - 36*f^2*sin(4*d*x + 4*c) - 144*I*f^2*sin(3*d*x + 3*c) + 36*f^2*sin(2*d*x + 2*c) - 72*I*f^2*sin(d*x + c) - 36*I*f^2)*polylog(3, -I*e^(I*d*x + I*c)) - (-36*I*(d*x + c)^2*f^2 - 72*d*e*f + (-36*I*c^2 + 72*c - 8*I)*f^2 - 8*(9*I*d*e*f + (-9*I*c + 1)*f^2)*(d*x + c))*sin(5*d*x + 5*c) - (72*(d*x + c)^2*f^2 - 144*I*d*e*f + 72*(c^2 + 2*I*c)*f^2 + (144*d*e*f - (144*c + 176*I)*f^2)*(d*x + c))*sin(4*d*x + 4*c) - (-24*I*(d*x + c)^2*f^2 - 64*d*e*f + (-24*I*c^2 + 64*c - 16*I)*f^2 - 16*(3*I*d*e*f + (-3*I*c - 4)*f^2)*(d*x + c))*sin(3*d*x + 3*c) + (72*(d*x + c)^2*f^2 + 176*I*d*e*f + 8*(9*c^2 - 22*I*c)*f^2 + (144*d*e*f - (144*c - 144*I)*f^2)*(d*x + c))*sin(2*d*x + 2*c) - (-36*I*(d*x + c)^2*f^2 + 8*d*e*f + (-36*I*c^2 - 8*c - 8*I)*f^2 + (-72*I*d*e*f - 72*(-I*c - 1)*f^2)*(d*x + c))*sin(d*x + c))/(-48*I*a*d^2*cos(6*d*x + 6*c) + 96*a*d^2*cos(5*d*x + 5*c) - 48*I*a*d^2*cos(4*d*x + 4*c) + 192*a*d^2*cos(3*d*x + 3*c) + 48*I*a*d^2*cos(2*d*x + 2*c) + 96*a*d^2*cos(d*x + c) + 48*a*d^2*sin(6*d*x + 6*c) + 96*I*a*d^2*sin(5*d*x + 5*c) + 48*a*d^2*sin(4*d*x + 4*c) + 192*I*a*d^2*sin(3*d*x + 3*c) - 48*a*d^2*sin(2*d*x + 2*c) + 96*I*a*d^2*sin(d*x + c) + 48*I*a*d^2))/d","B",0
283,1,1974,0,2.944967," ","integrate((f*x+e)*sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(18 \, d e \cos\left(6 \, d x + 6 \, c\right) + 36 i \, d e \cos\left(5 \, d x + 5 \, c\right) + 18 \, d e \cos\left(4 \, d x + 4 \, c\right) + 72 i \, d e \cos\left(3 \, d x + 3 \, c\right) - 18 \, d e \cos\left(2 \, d x + 2 \, c\right) + 36 i \, d e \cos\left(d x + c\right) + 18 i \, d e \sin\left(6 \, d x + 6 \, c\right) - 36 \, d e \sin\left(5 \, d x + 5 \, c\right) + 18 i \, d e \sin\left(4 \, d x + 4 \, c\right) - 72 \, d e \sin\left(3 \, d x + 3 \, c\right) - 18 i \, d e \sin\left(2 \, d x + 2 \, c\right) - 36 \, d e \sin\left(d x + c\right) - 18 \, d e\right)} \arctan\left(\sin\left(d x + c\right) + 1, \cos\left(d x + c\right)\right) - {\left(18 \, d e \cos\left(6 \, d x + 6 \, c\right) + 36 i \, d e \cos\left(5 \, d x + 5 \, c\right) + 18 \, d e \cos\left(4 \, d x + 4 \, c\right) + 72 i \, d e \cos\left(3 \, d x + 3 \, c\right) - 18 \, d e \cos\left(2 \, d x + 2 \, c\right) + 36 i \, d e \cos\left(d x + c\right) + 18 i \, d e \sin\left(6 \, d x + 6 \, c\right) - 36 \, d e \sin\left(5 \, d x + 5 \, c\right) + 18 i \, d e \sin\left(4 \, d x + 4 \, c\right) - 72 \, d e \sin\left(3 \, d x + 3 \, c\right) - 18 i \, d e \sin\left(2 \, d x + 2 \, c\right) - 36 \, d e \sin\left(d x + c\right) - 18 \, d e\right)} \arctan\left(\sin\left(d x + c\right) - 1, \cos\left(d x + c\right)\right) - {\left(18 \, d f x \cos\left(6 \, d x + 6 \, c\right) + 36 i \, d f x \cos\left(5 \, d x + 5 \, c\right) + 18 \, d f x \cos\left(4 \, d x + 4 \, c\right) + 72 i \, d f x \cos\left(3 \, d x + 3 \, c\right) - 18 \, d f x \cos\left(2 \, d x + 2 \, c\right) + 36 i \, d f x \cos\left(d x + c\right) + 18 i \, d f x \sin\left(6 \, d x + 6 \, c\right) - 36 \, d f x \sin\left(5 \, d x + 5 \, c\right) + 18 i \, d f x \sin\left(4 \, d x + 4 \, c\right) - 72 \, d f x \sin\left(3 \, d x + 3 \, c\right) - 18 i \, d f x \sin\left(2 \, d x + 2 \, c\right) - 36 \, d f x \sin\left(d x + c\right) - 18 \, d f x\right)} \arctan\left(\cos\left(d x + c\right), \sin\left(d x + c\right) + 1\right) - {\left(18 \, d f x \cos\left(6 \, d x + 6 \, c\right) + 36 i \, d f x \cos\left(5 \, d x + 5 \, c\right) + 18 \, d f x \cos\left(4 \, d x + 4 \, c\right) + 72 i \, d f x \cos\left(3 \, d x + 3 \, c\right) - 18 \, d f x \cos\left(2 \, d x + 2 \, c\right) + 36 i \, d f x \cos\left(d x + c\right) + 18 i \, d f x \sin\left(6 \, d x + 6 \, c\right) - 36 \, d f x \sin\left(5 \, d x + 5 \, c\right) + 18 i \, d f x \sin\left(4 \, d x + 4 \, c\right) - 72 \, d f x \sin\left(3 \, d x + 3 \, c\right) - 18 i \, d f x \sin\left(2 \, d x + 2 \, c\right) - 36 \, d f x \sin\left(d x + c\right) - 18 \, d f x\right)} \arctan\left(\cos\left(d x + c\right), -\sin\left(d x + c\right) + 1\right) - {\left(36 \, d f x + 36 \, d e - 36 i \, f\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-72 i \, d f x - 72 i \, d e - 72 \, f\right)} \cos\left(4 \, d x + 4 \, c\right) - {\left(24 \, d f x + 24 \, d e - 32 i \, f\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(72 i \, d f x + 72 i \, d e - 88 \, f\right)} \cos\left(2 \, d x + 2 \, c\right) - {\left(36 \, d f x + 36 \, d e + 4 i \, f\right)} \cos\left(d x + c\right) - {\left(18 \, f \cos\left(6 \, d x + 6 \, c\right) + 36 i \, f \cos\left(5 \, d x + 5 \, c\right) + 18 \, f \cos\left(4 \, d x + 4 \, c\right) + 72 i \, f \cos\left(3 \, d x + 3 \, c\right) - 18 \, f \cos\left(2 \, d x + 2 \, c\right) + 36 i \, f \cos\left(d x + c\right) + 18 i \, f \sin\left(6 \, d x + 6 \, c\right) - 36 \, f \sin\left(5 \, d x + 5 \, c\right) + 18 i \, f \sin\left(4 \, d x + 4 \, c\right) - 72 \, f \sin\left(3 \, d x + 3 \, c\right) - 18 i \, f \sin\left(2 \, d x + 2 \, c\right) - 36 \, f \sin\left(d x + c\right) - 18 \, f\right)} {\rm Li}_2\left(i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(18 \, f \cos\left(6 \, d x + 6 \, c\right) + 36 i \, f \cos\left(5 \, d x + 5 \, c\right) + 18 \, f \cos\left(4 \, d x + 4 \, c\right) + 72 i \, f \cos\left(3 \, d x + 3 \, c\right) - 18 \, f \cos\left(2 \, d x + 2 \, c\right) + 36 i \, f \cos\left(d x + c\right) + 18 i \, f \sin\left(6 \, d x + 6 \, c\right) - 36 \, f \sin\left(5 \, d x + 5 \, c\right) + 18 i \, f \sin\left(4 \, d x + 4 \, c\right) - 72 \, f \sin\left(3 \, d x + 3 \, c\right) - 18 i \, f \sin\left(2 \, d x + 2 \, c\right) - 36 \, f \sin\left(d x + c\right) - 18 \, f\right)} {\rm Li}_2\left(-i \, e^{\left(i \, d x + i \, c\right)}\right) + {\left(9 i \, d f x + 9 i \, d e + {\left(-9 i \, d f x - 9 i \, d e\right)} \cos\left(6 \, d x + 6 \, c\right) + 18 \, {\left(d f x + d e\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(-9 i \, d f x - 9 i \, d e\right)} \cos\left(4 \, d x + 4 \, c\right) + 36 \, {\left(d f x + d e\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(9 i \, d f x + 9 i \, d e\right)} \cos\left(2 \, d x + 2 \, c\right) + 18 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) + 9 \, {\left(d f x + d e\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(18 i \, d f x + 18 i \, d e\right)} \sin\left(5 \, d x + 5 \, c\right) + 9 \, {\left(d f x + d e\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(36 i \, d f x + 36 i \, d e\right)} \sin\left(3 \, d x + 3 \, c\right) - 9 \, {\left(d f x + d e\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(18 i \, d f x + 18 i \, d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1\right) + {\left(-9 i \, d f x - 9 i \, d e + {\left(9 i \, d f x + 9 i \, d e\right)} \cos\left(6 \, d x + 6 \, c\right) - 18 \, {\left(d f x + d e\right)} \cos\left(5 \, d x + 5 \, c\right) + {\left(9 i \, d f x + 9 i \, d e\right)} \cos\left(4 \, d x + 4 \, c\right) - 36 \, {\left(d f x + d e\right)} \cos\left(3 \, d x + 3 \, c\right) + {\left(-9 i \, d f x - 9 i \, d e\right)} \cos\left(2 \, d x + 2 \, c\right) - 18 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) - 9 \, {\left(d f x + d e\right)} \sin\left(6 \, d x + 6 \, c\right) + {\left(-18 i \, d f x - 18 i \, d e\right)} \sin\left(5 \, d x + 5 \, c\right) - 9 \, {\left(d f x + d e\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-36 i \, d f x - 36 i \, d e\right)} \sin\left(3 \, d x + 3 \, c\right) + 9 \, {\left(d f x + d e\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-18 i \, d f x - 18 i \, d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right)^{2} + \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right) + {\left(-36 i \, d f x - 36 i \, d e - 36 \, f\right)} \sin\left(5 \, d x + 5 \, c\right) + {\left(72 \, d f x + 72 \, d e - 72 i \, f\right)} \sin\left(4 \, d x + 4 \, c\right) + {\left(-24 i \, d f x - 24 i \, d e - 32 \, f\right)} \sin\left(3 \, d x + 3 \, c\right) - {\left(72 \, d f x + 72 \, d e + 88 i \, f\right)} \sin\left(2 \, d x + 2 \, c\right) + {\left(-36 i \, d f x - 36 i \, d e + 4 \, f\right)} \sin\left(d x + c\right) - 16 \, f}{-48 i \, a d^{2} \cos\left(6 \, d x + 6 \, c\right) + 96 \, a d^{2} \cos\left(5 \, d x + 5 \, c\right) - 48 i \, a d^{2} \cos\left(4 \, d x + 4 \, c\right) + 192 \, a d^{2} \cos\left(3 \, d x + 3 \, c\right) + 48 i \, a d^{2} \cos\left(2 \, d x + 2 \, c\right) + 96 \, a d^{2} \cos\left(d x + c\right) + 48 \, a d^{2} \sin\left(6 \, d x + 6 \, c\right) + 96 i \, a d^{2} \sin\left(5 \, d x + 5 \, c\right) + 48 \, a d^{2} \sin\left(4 \, d x + 4 \, c\right) + 192 i \, a d^{2} \sin\left(3 \, d x + 3 \, c\right) - 48 \, a d^{2} \sin\left(2 \, d x + 2 \, c\right) + 96 i \, a d^{2} \sin\left(d x + c\right) + 48 i \, a d^{2}}"," ",0,"((18*d*e*cos(6*d*x + 6*c) + 36*I*d*e*cos(5*d*x + 5*c) + 18*d*e*cos(4*d*x + 4*c) + 72*I*d*e*cos(3*d*x + 3*c) - 18*d*e*cos(2*d*x + 2*c) + 36*I*d*e*cos(d*x + c) + 18*I*d*e*sin(6*d*x + 6*c) - 36*d*e*sin(5*d*x + 5*c) + 18*I*d*e*sin(4*d*x + 4*c) - 72*d*e*sin(3*d*x + 3*c) - 18*I*d*e*sin(2*d*x + 2*c) - 36*d*e*sin(d*x + c) - 18*d*e)*arctan2(sin(d*x + c) + 1, cos(d*x + c)) - (18*d*e*cos(6*d*x + 6*c) + 36*I*d*e*cos(5*d*x + 5*c) + 18*d*e*cos(4*d*x + 4*c) + 72*I*d*e*cos(3*d*x + 3*c) - 18*d*e*cos(2*d*x + 2*c) + 36*I*d*e*cos(d*x + c) + 18*I*d*e*sin(6*d*x + 6*c) - 36*d*e*sin(5*d*x + 5*c) + 18*I*d*e*sin(4*d*x + 4*c) - 72*d*e*sin(3*d*x + 3*c) - 18*I*d*e*sin(2*d*x + 2*c) - 36*d*e*sin(d*x + c) - 18*d*e)*arctan2(sin(d*x + c) - 1, cos(d*x + c)) - (18*d*f*x*cos(6*d*x + 6*c) + 36*I*d*f*x*cos(5*d*x + 5*c) + 18*d*f*x*cos(4*d*x + 4*c) + 72*I*d*f*x*cos(3*d*x + 3*c) - 18*d*f*x*cos(2*d*x + 2*c) + 36*I*d*f*x*cos(d*x + c) + 18*I*d*f*x*sin(6*d*x + 6*c) - 36*d*f*x*sin(5*d*x + 5*c) + 18*I*d*f*x*sin(4*d*x + 4*c) - 72*d*f*x*sin(3*d*x + 3*c) - 18*I*d*f*x*sin(2*d*x + 2*c) - 36*d*f*x*sin(d*x + c) - 18*d*f*x)*arctan2(cos(d*x + c), sin(d*x + c) + 1) - (18*d*f*x*cos(6*d*x + 6*c) + 36*I*d*f*x*cos(5*d*x + 5*c) + 18*d*f*x*cos(4*d*x + 4*c) + 72*I*d*f*x*cos(3*d*x + 3*c) - 18*d*f*x*cos(2*d*x + 2*c) + 36*I*d*f*x*cos(d*x + c) + 18*I*d*f*x*sin(6*d*x + 6*c) - 36*d*f*x*sin(5*d*x + 5*c) + 18*I*d*f*x*sin(4*d*x + 4*c) - 72*d*f*x*sin(3*d*x + 3*c) - 18*I*d*f*x*sin(2*d*x + 2*c) - 36*d*f*x*sin(d*x + c) - 18*d*f*x)*arctan2(cos(d*x + c), -sin(d*x + c) + 1) - (36*d*f*x + 36*d*e - 36*I*f)*cos(5*d*x + 5*c) + (-72*I*d*f*x - 72*I*d*e - 72*f)*cos(4*d*x + 4*c) - (24*d*f*x + 24*d*e - 32*I*f)*cos(3*d*x + 3*c) + (72*I*d*f*x + 72*I*d*e - 88*f)*cos(2*d*x + 2*c) - (36*d*f*x + 36*d*e + 4*I*f)*cos(d*x + c) - (18*f*cos(6*d*x + 6*c) + 36*I*f*cos(5*d*x + 5*c) + 18*f*cos(4*d*x + 4*c) + 72*I*f*cos(3*d*x + 3*c) - 18*f*cos(2*d*x + 2*c) + 36*I*f*cos(d*x + c) + 18*I*f*sin(6*d*x + 6*c) - 36*f*sin(5*d*x + 5*c) + 18*I*f*sin(4*d*x + 4*c) - 72*f*sin(3*d*x + 3*c) - 18*I*f*sin(2*d*x + 2*c) - 36*f*sin(d*x + c) - 18*f)*dilog(I*e^(I*d*x + I*c)) + (18*f*cos(6*d*x + 6*c) + 36*I*f*cos(5*d*x + 5*c) + 18*f*cos(4*d*x + 4*c) + 72*I*f*cos(3*d*x + 3*c) - 18*f*cos(2*d*x + 2*c) + 36*I*f*cos(d*x + c) + 18*I*f*sin(6*d*x + 6*c) - 36*f*sin(5*d*x + 5*c) + 18*I*f*sin(4*d*x + 4*c) - 72*f*sin(3*d*x + 3*c) - 18*I*f*sin(2*d*x + 2*c) - 36*f*sin(d*x + c) - 18*f)*dilog(-I*e^(I*d*x + I*c)) + (9*I*d*f*x + 9*I*d*e + (-9*I*d*f*x - 9*I*d*e)*cos(6*d*x + 6*c) + 18*(d*f*x + d*e)*cos(5*d*x + 5*c) + (-9*I*d*f*x - 9*I*d*e)*cos(4*d*x + 4*c) + 36*(d*f*x + d*e)*cos(3*d*x + 3*c) + (9*I*d*f*x + 9*I*d*e)*cos(2*d*x + 2*c) + 18*(d*f*x + d*e)*cos(d*x + c) + 9*(d*f*x + d*e)*sin(6*d*x + 6*c) + (18*I*d*f*x + 18*I*d*e)*sin(5*d*x + 5*c) + 9*(d*f*x + d*e)*sin(4*d*x + 4*c) + (36*I*d*f*x + 36*I*d*e)*sin(3*d*x + 3*c) - 9*(d*f*x + d*e)*sin(2*d*x + 2*c) + (18*I*d*f*x + 18*I*d*e)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 + 2*sin(d*x + c) + 1) + (-9*I*d*f*x - 9*I*d*e + (9*I*d*f*x + 9*I*d*e)*cos(6*d*x + 6*c) - 18*(d*f*x + d*e)*cos(5*d*x + 5*c) + (9*I*d*f*x + 9*I*d*e)*cos(4*d*x + 4*c) - 36*(d*f*x + d*e)*cos(3*d*x + 3*c) + (-9*I*d*f*x - 9*I*d*e)*cos(2*d*x + 2*c) - 18*(d*f*x + d*e)*cos(d*x + c) - 9*(d*f*x + d*e)*sin(6*d*x + 6*c) + (-18*I*d*f*x - 18*I*d*e)*sin(5*d*x + 5*c) - 9*(d*f*x + d*e)*sin(4*d*x + 4*c) + (-36*I*d*f*x - 36*I*d*e)*sin(3*d*x + 3*c) + 9*(d*f*x + d*e)*sin(2*d*x + 2*c) + (-18*I*d*f*x - 18*I*d*e)*sin(d*x + c))*log(cos(d*x + c)^2 + sin(d*x + c)^2 - 2*sin(d*x + c) + 1) + (-36*I*d*f*x - 36*I*d*e - 36*f)*sin(5*d*x + 5*c) + (72*d*f*x + 72*d*e - 72*I*f)*sin(4*d*x + 4*c) + (-24*I*d*f*x - 24*I*d*e - 32*f)*sin(3*d*x + 3*c) - (72*d*f*x + 72*d*e + 88*I*f)*sin(2*d*x + 2*c) + (-36*I*d*f*x - 36*I*d*e + 4*f)*sin(d*x + c) - 16*f)/(-48*I*a*d^2*cos(6*d*x + 6*c) + 96*a*d^2*cos(5*d*x + 5*c) - 48*I*a*d^2*cos(4*d*x + 4*c) + 192*a*d^2*cos(3*d*x + 3*c) + 48*I*a*d^2*cos(2*d*x + 2*c) + 96*a*d^2*cos(d*x + c) + 48*a*d^2*sin(6*d*x + 6*c) + 96*I*a*d^2*sin(5*d*x + 5*c) + 48*a*d^2*sin(4*d*x + 4*c) + 192*I*a*d^2*sin(3*d*x + 3*c) - 48*a*d^2*sin(2*d*x + 2*c) + 96*I*a*d^2*sin(d*x + c) + 48*I*a*d^2)","B",0
284,1,91,0,0.741931," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2\right)}}{a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{3 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{3 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{16 \, d}"," ",0,"-1/16*(2*(3*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*sin(d*x + c)^3 + a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 3*log(sin(d*x + c) + 1)/a + 3*log(sin(d*x + c) - 1)/a)/d","A",0
285,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate(sec(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,0,0,0,0.000000," ","integrate((f*x+e)^m*cos(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)^{4}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*cos(d*x + c)^4/(a*sin(d*x + c) + a), x)","F",0
288,0,0,0,0.000000," ","integrate((f*x+e)^m*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)^{3}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*cos(d*x + c)^3/(a*sin(d*x + c) + a), x)","F",0
289,0,0,0,0.000000," ","integrate((f*x+e)^m*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)^{2}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*cos(d*x + c)^2/(a*sin(d*x + c) + a), x)","F",0
290,0,0,0,0.000000," ","integrate((f*x+e)^m*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*cos(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
291,0,0,0,0.000000," ","integrate((f*x+e)^m/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m/(a*sin(d*x + c) + a), x)","F",0
292,-2,0,0,0.000000," ","integrate((f*x+e)^m*sec(d*x+c)/(a+a*sin(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
293,-2,0,0,0.000000," ","integrate((f*x+e)^m*sec(d*x+c)^2/(a+a*sin(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
294,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
295,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
296,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
297,1,18,0,0.775230," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\log\left(b \sin\left(d x + c\right) + a\right)}{b d}"," ",0,"log(b*sin(d*x + c) + a)/(b*d)","A",0
298,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
299,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
300,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
301,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
302,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
303,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
304,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)^3/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
305,1,55,0,0.414613," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{3}}}{2 \, d}"," ",0,"-1/2*((b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 + 2*(a^2 - b^2)*log(b*sin(d*x + c) + a)/b^3)/d","A",0
306,-2,0,0,0.000000," ","integrate((f*x+e)^3*sec(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
307,-2,0,0,0.000000," ","integrate((f*x+e)^2*sec(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
308,-2,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
309,1,64,0,1.318224," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} - b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(2*b*log(b*sin(d*x + c) + a)/(a^2 - b^2) - log(sin(d*x + c) + 1)/(a - b) + log(sin(d*x + c) - 1)/(a + b))/d","A",0
310,-2,0,0,0.000000," ","integrate((f*x+e)^3*sec(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
311,-2,0,0,0.000000," ","integrate((f*x+e)^2*sec(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
312,-2,0,0,0.000000," ","integrate((f*x+e)*sec(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
313,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
314,0,0,0,0.000000," ","integrate((f*x+e)^m*cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*cos(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
315,0,0,0,0.000000," ","integrate((f*x+e)^m*cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*cos(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
316,0,0,0,0.000000," ","integrate((f*x+e)^m/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m/(b*sin(d*x + c) + a), x)","F",0
317,0,0,0,0.000000," ","integrate((f*x+e)^m*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \sec\left(d x + c\right)}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*sec(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
318,0,0,0,0.000000," ","integrate((f*x+e)^m*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{{\left(f x + e\right)}^{m} \sec\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate((f*x + e)^m*sec(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
319,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))^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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
320,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c))^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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
321,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
322,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
323,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
324,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
325,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
326,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
327,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
328,-2,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
329,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
330,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
331,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
332,1,54,0,0.588765," ","integrate(cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right)\right)}{a} - \frac{\sin\left(d x + c\right)}{b} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a b^{2}}}{d}"," ",0,"(log(sin(d*x + c))/a - sin(d*x + c)/b + (a^2 - b^2)*log(b*sin(d*x + c) + a)/(a*b^2))/d","A",0
333,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
334,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
335,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
336,-2,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
337,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
338,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
339,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
340,1,57,0,0.770674," ","integrate(cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b \log\left(\sin\left(d x + c\right)\right)}{a^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b} + \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"-(b*log(sin(d*x + c))/a^2 + (a^2 - b^2)*log(b*sin(d*x + c) + a)/(a^2*b) + 1/(a*sin(d*x + c)))/d","A",0
341,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
342,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
343,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
344,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(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(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
345,-2,0,0,0.000000," ","integrate((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(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
346,-2,0,0,0.000000," ","integrate((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(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
347,-2,0,0,0.000000," ","integrate((f*x+e)*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(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
348,1,91,0,0.748114," ","integrate(cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b \log\left(\sin\left(d x + c\right)\right)}{a^{2}} - \frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}} + \frac{2}{a \sin\left(d x + c\right)} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(2*b*log(sin(d*x + c))/a^2 - (b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 + 2/(a*sin(d*x + c)) - 2*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/(a^2*b^3))/d","A",0
