1,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \sin\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*sin(b*x + a), x)","F",0
2,1,586,0,0.385345," ","integrate((d*x+c)^4*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{4 \, c^{4} \cos\left(b x + a\right)^{2} - \frac{16 \, a c^{3} d \cos\left(b x + a\right)^{2}}{b} + \frac{24 \, a^{2} c^{2} d^{2} \cos\left(b x + a\right)^{2}}{b^{2}} - \frac{16 \, a^{3} c d^{3} \cos\left(b x + a\right)^{2}}{b^{3}} + \frac{4 \, a^{4} d^{4} \cos\left(b x + a\right)^{2}}{b^{4}} + \frac{4 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b} - \frac{12 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{12 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{4 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{6 \, {\left({\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{12 \, {\left({\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{b^{3}} + \frac{6 \, {\left({\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{2 \, {\left(2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, 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^{3}}{b^{3}} - \frac{2 \, {\left(2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, 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^{4}}{b^{4}} + \frac{{\left({\left(2 \, {\left(b x + a\right)}^{4} - 6 \, {\left(b x + a\right)}^{2} + 3\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^{4}}{b^{4}}}{8 \, b}"," ",0,"-1/8*(4*c^4*cos(b*x + a)^2 - 16*a*c^3*d*cos(b*x + a)^2/b + 24*a^2*c^2*d^2*cos(b*x + a)^2/b^2 - 16*a^3*c*d^3*cos(b*x + a)^2/b^3 + 4*a^4*d^4*cos(b*x + a)^2/b^4 + 4*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*c^3*d/b - 12*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*a*c^2*d^2/b^2 + 12*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*a^2*c*d^3/b^3 - 4*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*a^3*d^4/b^4 + 6*((2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(b*x + a)*sin(2*b*x + 2*a))*c^2*d^2/b^2 - 12*((2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^3/b^3 + 6*((2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^4/b^4 + 2*(2*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c*d^3/b^3 - 2*(2*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*d^4/b^4 + ((2*(b*x + a)^4 - 6*(b*x + a)^2 + 3)*cos(2*b*x + 2*a) - 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*d^4/b^4)/b","B",0
3,1,342,0,0.364465," ","integrate((d*x+c)^3*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{8 \, c^{3} \cos\left(b x + a\right)^{2} - \frac{24 \, a c^{2} d \cos\left(b x + a\right)^{2}}{b} + \frac{24 \, a^{2} c d^{2} \cos\left(b x + a\right)^{2}}{b^{2}} - \frac{8 \, a^{3} d^{3} \cos\left(b x + a\right)^{2}}{b^{3}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{b} - \frac{12 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{b^{2}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{6 \, {\left({\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{b^{2}} - \frac{6 \, {\left({\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, 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^{3}}{b^{3}}}{16 \, b}"," ",0,"-1/16*(8*c^3*cos(b*x + a)^2 - 24*a*c^2*d*cos(b*x + a)^2/b + 24*a^2*c*d^2*cos(b*x + a)^2/b^2 - 8*a^3*d^3*cos(b*x + a)^2/b^3 + 6*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*c^2*d/b - 12*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*a*c*d^2/b^2 + 6*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*a^2*d^3/b^3 + 6*((2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(b*x + a)*sin(2*b*x + 2*a))*c*d^2/b^2 - 6*((2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(b*x + a)*sin(2*b*x + 2*a))*a*d^3/b^3 + (2*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*d^3/b^3)/b","B",0
4,1,171,0,0.362537," ","integrate((d*x+c)^2*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{4 \, c^{2} \cos\left(b x + a\right)^{2} - \frac{8 \, a c d \cos\left(b x + a\right)^{2}}{b} + \frac{4 \, a^{2} d^{2} \cos\left(b x + a\right)^{2}}{b^{2}} + \frac{2 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} c d}{b} - \frac{2 \, {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left({\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{b^{2}}}{8 \, b}"," ",0,"-1/8*(4*c^2*cos(b*x + a)^2 - 8*a*c*d*cos(b*x + a)^2/b + 4*a^2*d^2*cos(b*x + a)^2/b^2 + 2*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*c*d/b - 2*(2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*a*d^2/b^2 + ((2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 2*(b*x + a)*sin(2*b*x + 2*a))*d^2/b^2)/b","B",0
5,1,65,0,0.334727," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{4 \, c \cos\left(b x + a\right)^{2} - \frac{4 \, a d \cos\left(b x + a\right)^{2}}{b} + \frac{{\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} d}{b}}{8 \, b}"," ",0,"-1/8*(4*c*cos(b*x + a)^2 - 4*a*d*cos(b*x + a)^2/b + (2*(b*x + a)*cos(2*b*x + 2*a) - sin(2*b*x + 2*a))*d/b)/b","A",0
6,1,141,0,0.407845," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c),x, algorithm=""maxima"")","-\frac{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)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, b d}"," ",0,"-1/4*(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))*cos(-2*(b*c - a*d)/d) + 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))*sin(-2*(b*c - a*d)/d))/(b*d)","C",0
7,1,164,0,0.435642," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{b^{2} {\left(i \, E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - i \, 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(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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/4*(b^2*(I*exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - I*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*(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))*sin(-2*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
8,1,199,0,0.506191," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(i \, E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - i \, 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(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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\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,"-1/4*(b^3*(I*exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - I*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*(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))*sin(-2*(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
9,1,249,0,0.636356," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{b^{4} {\left(i \, E_{4}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - i \, 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(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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\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,"-1/4*(b^4*(I*exp_integral_e(4, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - I*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*(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))*sin(-2*(b*c - a*d)/d))/((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
10,1,13,0,0.374070," ","integrate(cos(x)*sin(x)/x,x, algorithm=""maxima"")","-\frac{1}{4} i \, {\rm Ei}\left(2 i \, x\right) + \frac{1}{4} i \, {\rm Ei}\left(-2 i \, x\right)"," ",0,"-1/4*I*Ei(2*I*x) + 1/4*I*Ei(-2*I*x)","C",0
11,1,15,0,0.384669," ","integrate(cos(x)*sin(x)/x^2,x, algorithm=""maxima"")","\frac{1}{2} \, \Gamma\left(-1, 2 i \, x\right) + \frac{1}{2} \, \Gamma\left(-1, -2 i \, x\right)"," ",0,"1/2*gamma(-1, 2*I*x) + 1/2*gamma(-1, -2*I*x)","C",0
12,1,15,0,0.393552," ","integrate(cos(x)*sin(x)/x^3,x, algorithm=""maxima"")","i \, \Gamma\left(-2, 2 i \, x\right) - i \, \Gamma\left(-2, -2 i \, x\right)"," ",0,"I*gamma(-2, 2*I*x) - I*gamma(-2, -2*I*x)","C",0
13,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*sin(b*x + a)^2, x)","F",0
14,1,880,0,0.416281," ","integrate((d*x+c)^4*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{108 \, c^{4} \sin\left(b x + a\right)^{3} - \frac{432 \, a c^{3} d \sin\left(b x + a\right)^{3}}{b} + \frac{648 \, a^{2} c^{2} d^{2} \sin\left(b x + a\right)^{3}}{b^{2}} - \frac{432 \, a^{3} c d^{3} \sin\left(b x + a\right)^{3}}{b^{3}} + \frac{108 \, a^{4} d^{4} \sin\left(b x + a\right)^{3}}{b^{4}} - \frac{36 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} c^{3} d}{b} + \frac{108 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} a c^{2} d^{2}}{b^{2}} - \frac{108 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} a^{2} c d^{3}}{b^{3}} + \frac{36 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} a^{3} d^{4}}{b^{4}} - \frac{18 \, {\left(6 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 54 \, {\left(b x + 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) - 27 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c^{2} d^{2}}{b^{2}} + \frac{36 \, {\left(6 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 54 \, {\left(b x + 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) - 27 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a c d^{3}}{b^{3}} - \frac{18 \, {\left(6 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 54 \, {\left(b x + 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) - 27 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a^{2} d^{4}}{b^{4}} - \frac{12 \, {\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) + 3 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) - 27 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} c d^{3}}{b^{3}} + \frac{12 \, {\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) + 3 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) - 27 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} a d^{4}}{b^{4}} - \frac{{\left(12 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 324 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) + {\left(27 \, {\left(b x + a\right)}^{4} - 36 \, {\left(b x + a\right)}^{2} + 8\right)} \sin\left(3 \, b x + 3 \, a\right) - 81 \, {\left({\left(b x + a\right)}^{4} - 12 \, {\left(b x + a\right)}^{2} + 24\right)} \sin\left(b x + a\right)\right)} d^{4}}{b^{4}}}{324 \, b}"," ",0,"1/324*(108*c^4*sin(b*x + a)^3 - 432*a*c^3*d*sin(b*x + a)^3/b + 648*a^2*c^2*d^2*sin(b*x + a)^3/b^2 - 432*a^3*c*d^3*sin(b*x + a)^3/b^3 + 108*a^4*d^4*sin(b*x + a)^3/b^4 - 36*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*c^3*d/b + 108*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*a*c^2*d^2/b^2 - 108*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*a^2*c*d^3/b^3 + 36*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*a^3*d^4/b^4 - 18*(6*(b*x + a)*cos(3*b*x + 3*a) - 54*(b*x + a)*cos(b*x + a) + (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 27*((b*x + a)^2 - 2)*sin(b*x + a))*c^2*d^2/b^2 + 36*(6*(b*x + a)*cos(3*b*x + 3*a) - 54*(b*x + a)*cos(b*x + a) + (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 27*((b*x + a)^2 - 2)*sin(b*x + a))*a*c*d^3/b^3 - 18*(6*(b*x + a)*cos(3*b*x + 3*a) - 54*(b*x + a)*cos(b*x + a) + (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 27*((b*x + a)^2 - 2)*sin(b*x + a))*a^2*d^4/b^4 - 12*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) + 3*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) - 27*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*c*d^3/b^3 + 12*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) + 3*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) - 27*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*a*d^4/b^4 - (12*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 324*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) + (27*(b*x + a)^4 - 36*(b*x + a)^2 + 8)*sin(3*b*x + 3*a) - 81*((b*x + a)^4 - 12*(b*x + a)^2 + 24)*sin(b*x + a))*d^4/b^4)/b","B",0
15,1,499,0,0.371404," ","integrate((d*x+c)^3*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{36 \, c^{3} \sin\left(b x + a\right)^{3} - \frac{108 \, a c^{2} d \sin\left(b x + a\right)^{3}}{b} + \frac{108 \, a^{2} c d^{2} \sin\left(b x + a\right)^{3}}{b^{2}} - \frac{36 \, a^{3} d^{3} \sin\left(b x + a\right)^{3}}{b^{3}} - \frac{9 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} c^{2} d}{b} + \frac{18 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} a c d^{2}}{b^{2}} - \frac{9 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} a^{2} d^{3}}{b^{3}} - \frac{3 \, {\left(6 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 54 \, {\left(b x + 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) - 27 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c d^{2}}{b^{2}} + \frac{3 \, {\left(6 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 54 \, {\left(b x + 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) - 27 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a d^{3}}{b^{3}} - \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) + 3 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) - 27 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} d^{3}}{b^{3}}}{108 \, b}"," ",0,"1/108*(36*c^3*sin(b*x + a)^3 - 108*a*c^2*d*sin(b*x + a)^3/b + 108*a^2*c*d^2*sin(b*x + a)^3/b^2 - 36*a^3*d^3*sin(b*x + a)^3/b^3 - 9*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*c^2*d/b + 18*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*a*c*d^2/b^2 - 9*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*a^2*d^3/b^3 - 3*(6*(b*x + a)*cos(3*b*x + 3*a) - 54*(b*x + a)*cos(b*x + a) + (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 27*((b*x + a)^2 - 2)*sin(b*x + a))*c*d^2/b^2 + 3*(6*(b*x + a)*cos(3*b*x + 3*a) - 54*(b*x + a)*cos(b*x + a) + (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 27*((b*x + a)^2 - 2)*sin(b*x + a))*a*d^3/b^3 - ((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 81*((b*x + a)^2 - 2)*cos(b*x + a) + 3*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) - 27*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^3/b^3)/b","B",0
16,1,240,0,0.373006," ","integrate((d*x+c)^2*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{36 \, c^{2} \sin\left(b x + a\right)^{3} - \frac{72 \, a c d \sin\left(b x + a\right)^{3}}{b} + \frac{36 \, a^{2} d^{2} \sin\left(b x + a\right)^{3}}{b^{2}} - \frac{6 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} c d}{b} + \frac{6 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} a d^{2}}{b^{2}} - \frac{{\left(6 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 54 \, {\left(b x + 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) - 27 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{108 \, b}"," ",0,"1/108*(36*c^2*sin(b*x + a)^3 - 72*a*c*d*sin(b*x + a)^3/b + 36*a^2*d^2*sin(b*x + a)^3/b^2 - 6*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*c*d/b + 6*(3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*a*d^2/b^2 - (6*(b*x + a)*cos(3*b*x + 3*a) - 54*(b*x + a)*cos(b*x + a) + (9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 27*((b*x + a)^2 - 2)*sin(b*x + a))*d^2/b^2)/b","B",0
17,1,85,0,0.339671," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{12 \, c \sin\left(b x + a\right)^{3} - \frac{12 \, a d \sin\left(b x + a\right)^{3}}{b} - \frac{{\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 9 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) - 9 \, \cos\left(b x + a\right)\right)} d}{b}}{36 \, b}"," ",0,"1/36*(12*c*sin(b*x + a)^3 - 12*a*d*sin(b*x + a)^3/b - (3*(b*x + a)*sin(3*b*x + 3*a) - 9*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) - 9*cos(b*x + a))*d/b)/b","A",0
18,1,274,0,0.447465," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","-\frac{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)} \cos\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)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 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)} \sin\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)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, b d}"," ",0,"-1/8*(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))*cos(-(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))*cos(-3*(b*c - a*d)/d) + 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))*sin(-(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))*sin(-3*(b*c - a*d)/d))/(b*d)","C",0
19,1,302,0,0.517751," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{8192 \, 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)} \cos\left(-\frac{b c - a d}{d}\right) - 8192 \, 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)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + b^{2} {\left(-8192 i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 8192 i \, 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(8192 i \, E_{2}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - 8192 i \, 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)}{65536 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/65536*(8192*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))*cos(-(b*c - a*d)/d) - 8192*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))*cos(-3*(b*c - a*d)/d) + b^2*(-8192*I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 8192*I*exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^2*(8192*I*exp_integral_e(2, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - 8192*I*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
20,1,337,0,0.676288," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{8192 \, 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)} \cos\left(-\frac{b c - a d}{d}\right) - 8192 \, 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)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + b^{3} {\left(-8192 i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 8192 i \, 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(8192 i \, E_{3}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - 8192 i \, 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)}{65536 \, {\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,"-1/65536*(8192*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))*cos(-(b*c - a*d)/d) - 8192*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))*cos(-3*(b*c - a*d)/d) + b^3*(-8192*I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 8192*I*exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^3*(8192*I*exp_integral_e(3, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - 8192*I*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
21,1,387,0,0.870969," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{8192 \, b^{4} {\left(E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{4}\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) - 8192 \, b^{4} {\left(E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{4}\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) + b^{4} {\left(-8192 i \, E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 8192 i \, E_{4}\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^{4} {\left(8192 i \, E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - 8192 i \, E_{4}\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)}{65536 \, {\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,"-1/65536*(8192*b^4*(exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) - 8192*b^4*(exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) + b^4*(-8192*I*exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 8192*I*exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^4*(8192*I*exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - 8192*I*exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d))/((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
22,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*sin(b*x + a)^3, x)","F",0
23,1,967,0,0.420583," ","integrate((d*x+c)^4*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{256 \, c^{4} \sin\left(b x + a\right)^{4} - \frac{1024 \, a c^{3} d \sin\left(b x + a\right)^{4}}{b} + \frac{1536 \, a^{2} c^{2} d^{2} \sin\left(b x + a\right)^{4}}{b^{2}} - \frac{1024 \, a^{3} c d^{3} \sin\left(b x + a\right)^{4}}{b^{3}} + \frac{256 \, a^{4} d^{4} \sin\left(b x + a\right)^{4}}{b^{4}} + \frac{32 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b} - \frac{96 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{96 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{32 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{24 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{48 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{b^{3}} + \frac{24 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{4 \, {\left(4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - 64 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) + 96 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{3}}{b^{3}} - \frac{4 \, {\left(4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - 64 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) + 96 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left({\left(32 \, {\left(b x + a\right)}^{4} - 24 \, {\left(b x + a\right)}^{2} + 3\right)} \cos\left(4 \, b x + 4 \, a\right) - 64 \, {\left(2 \, {\left(b x + a\right)}^{4} - 6 \, {\left(b x + a\right)}^{2} + 3\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right) + 128 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{4}}{b^{4}}}{1024 \, b}"," ",0,"1/1024*(256*c^4*sin(b*x + a)^4 - 1024*a*c^3*d*sin(b*x + a)^4/b + 1536*a^2*c^2*d^2*sin(b*x + a)^4/b^2 - 1024*a^3*c*d^3*sin(b*x + a)^4/b^3 + 256*a^4*d^4*sin(b*x + a)^4/b^4 + 32*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*c^3*d/b - 96*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a*c^2*d^2/b^2 + 96*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a^2*c*d^3/b^3 - 32*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a^3*d^4/b^4 + 24*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a))*c^2*d^2/b^2 - 48*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^3/b^3 + 24*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^4/b^4 + 4*(4*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) - 64*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) + 96*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c*d^3/b^3 - 4*(4*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) - 64*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) + 96*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*d^4/b^4 + ((32*(b*x + a)^4 - 24*(b*x + a)^2 + 3)*cos(4*b*x + 4*a) - 64*(2*(b*x + a)^4 - 6*(b*x + a)^2 + 3)*cos(2*b*x + 2*a) - 4*(8*(b*x + a)^3 - 3*b*x - 3*a)*sin(4*b*x + 4*a) + 128*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*d^4/b^4)/b","B",0
24,1,549,0,0.380002," ","integrate((d*x+c)^3*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{256 \, c^{3} \sin\left(b x + a\right)^{4} - \frac{768 \, a c^{2} d \sin\left(b x + a\right)^{4}}{b} + \frac{768 \, a^{2} c d^{2} \sin\left(b x + a\right)^{4}}{b^{2}} - \frac{256 \, a^{3} d^{3} \sin\left(b x + a\right)^{4}}{b^{3}} + \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{b} - \frac{48 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{b^{2}} + \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{12 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{b^{2}} - \frac{12 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - 64 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) + 96 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{3}}{b^{3}}}{1024 \, b}"," ",0,"1/1024*(256*c^3*sin(b*x + a)^4 - 768*a*c^2*d*sin(b*x + a)^4/b + 768*a^2*c*d^2*sin(b*x + a)^4/b^2 - 256*a^3*d^3*sin(b*x + a)^4/b^3 + 24*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*c^2*d/b - 48*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a*c*d^2/b^2 + 24*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a^2*d^3/b^3 + 12*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a))*c*d^2/b^2 - 12*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a))*a*d^3/b^3 + (4*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) - 64*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) + 96*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*d^3/b^3)/b","B",0
25,1,263,0,0.361879," ","integrate((d*x+c)^2*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{64 \, c^{2} \sin\left(b x + a\right)^{4} - \frac{128 \, a c d \sin\left(b x + a\right)^{4}}{b} + \frac{64 \, a^{2} d^{2} \sin\left(b x + a\right)^{4}}{b^{2}} + \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c d}{b} - \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{b^{2}}}{256 \, b}"," ",0,"1/256*(64*c^2*sin(b*x + a)^4 - 128*a*c*d*sin(b*x + a)^4/b + 64*a^2*d^2*sin(b*x + a)^4/b^2 + 4*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*c*d/b - 4*(4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a*d^2/b^2 + ((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a))*d^2/b^2)/b","B",0
26,1,92,0,0.336887," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{32 \, c \sin\left(b x + a\right)^{4} - \frac{32 \, a d \sin\left(b x + a\right)^{4}}{b} + \frac{{\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} d}{b}}{128 \, b}"," ",0,"1/128*(32*c*sin(b*x + a)^4 - 32*a*d*sin(b*x + a)^4/b + (4*(b*x + a)*cos(4*b*x + 4*a) - 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*d/b)/b","A",0
27,1,274,0,0.471447," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{b {\left(-2 i \, E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 2 i \, 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{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b {\left(E_{1}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{1}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, b d}"," ",0,"1/16*(b*(-2*I*exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 2*I*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, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(1, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - 2*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))*sin(-2*(b*c - a*d)/d) + b*(exp_integral_e(1, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(1, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d))/(b*d)","C",0
28,1,301,0,0.527105," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(-2 i \, E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 2 i \, 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(i \, E_{2}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{2}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{2} {\left(E_{2}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{2}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"1/16*(b^2*(-2*I*exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 2*I*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*(I*exp_integral_e(2, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(2, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - 2*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))*sin(-2*(b*c - a*d)/d) + b^2*(exp_integral_e(2, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(2, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
29,1,336,0,0.683311," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""maxima"")","\frac{b^{3} {\left(-2 i \, E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 2 i \, 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(i \, E_{3}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{3}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{3} {\left(E_{3}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{3}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\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,"1/16*(b^3*(-2*I*exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 2*I*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*(I*exp_integral_e(3, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(3, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - 2*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))*sin(-2*(b*c - a*d)/d) + b^3*(exp_integral_e(3, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(3, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(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
30,1,386,0,0.933196," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^4,x, algorithm=""maxima"")","\frac{b^{4} {\left(-2 i \, E_{4}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 2 i \, 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(i \, E_{4}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{4}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{4} {\left(E_{4}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{4}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\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,"1/16*(b^4*(-2*I*exp_integral_e(4, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 2*I*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*(I*exp_integral_e(4, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(4, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - 2*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))*sin(-2*(b*c - a*d)/d) + b^4*(exp_integral_e(4, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(4, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d))/((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
31,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*csc(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \csc\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*csc(b*x + a), x)","F",0
32,1,1262,0,0.619026," ","integrate((d*x+c)^4*cos(b*x+a)*csc(b*x+a),x, algorithm=""maxima"")","\frac{10 \, c^{4} \log\left(\sin\left(b x + a\right)\right) - \frac{40 \, a c^{3} d \log\left(\sin\left(b x + a\right)\right)}{b} + \frac{60 \, a^{2} c^{2} d^{2} \log\left(\sin\left(b x + a\right)\right)}{b^{2}} - \frac{40 \, a^{3} c d^{3} \log\left(\sin\left(b x + a\right)\right)}{b^{3}} + \frac{10 \, a^{4} d^{4} \log\left(\sin\left(b x + a\right)\right)}{b^{4}} + \frac{-2 i \, {\left(b x + a\right)}^{5} d^{4} + {\left(-10 i \, b c d^{3} + 10 i \, a d^{4}\right)} {\left(b x + a\right)}^{4} - 240 \, d^{4} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) - 240 \, d^{4} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) + {\left(-20 i \, b^{2} c^{2} d^{2} + 40 i \, a b c d^{3} - 20 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-20 i \, b^{3} c^{3} d + 60 i \, a b^{2} c^{2} d^{2} - 60 i \, a^{2} b c d^{3} + 20 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(10 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(40 i \, b c d^{3} - 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(60 i \, b^{2} c^{2} d^{2} - 120 i \, a b c d^{3} + 60 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(40 i \, b^{3} c^{3} d - 120 i \, a b^{2} c^{2} d^{2} + 120 i \, a^{2} b c d^{3} - 40 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(-10 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-40 i \, b c d^{3} + 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-40 i \, b^{3} c^{3} d + 120 i \, a b^{2} c^{2} d^{2} - 120 i \, a^{2} b c d^{3} + 40 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(-40 i \, b^{3} c^{3} d + 120 i \, a b^{2} c^{2} d^{2} - 120 i \, a^{2} b c d^{3} - 40 i \, {\left(b x + a\right)}^{3} d^{4} + 40 i \, a^{3} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} - 120 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(-40 i \, b^{3} c^{3} d + 120 i \, a b^{2} c^{2} d^{2} - 120 i \, a^{2} b c d^{3} - 40 i \, {\left(b x + a\right)}^{3} d^{4} + 40 i \, a^{3} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} - 120 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 5 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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) + 5 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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(240 i \, b c d^{3} + 240 i \, {\left(b x + a\right)} d^{4} - 240 i \, a d^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + {\left(240 i \, b c d^{3} + 240 i \, {\left(b x + a\right)} d^{4} - 240 i \, a d^{4}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)})}{b^{4}}}{10 \, b}"," ",0,"1/10*(10*c^4*log(sin(b*x + a)) - 40*a*c^3*d*log(sin(b*x + a))/b + 60*a^2*c^2*d^2*log(sin(b*x + a))/b^2 - 40*a^3*c*d^3*log(sin(b*x + a))/b^3 + 10*a^4*d^4*log(sin(b*x + a))/b^4 + (-2*I*(b*x + a)^5*d^4 + (-10*I*b*c*d^3 + 10*I*a*d^4)*(b*x + a)^4 - 240*d^4*polylog(5, -e^(I*b*x + I*a)) - 240*d^4*polylog(5, e^(I*b*x + I*a)) + (-20*I*b^2*c^2*d^2 + 40*I*a*b*c*d^3 - 20*I*a^2*d^4)*(b*x + a)^3 + (-20*I*b^3*c^3*d + 60*I*a*b^2*c^2*d^2 - 60*I*a^2*b*c*d^3 + 20*I*a^3*d^4)*(b*x + a)^2 + (10*I*(b*x + a)^4*d^4 + (40*I*b*c*d^3 - 40*I*a*d^4)*(b*x + a)^3 + (60*I*b^2*c^2*d^2 - 120*I*a*b*c*d^3 + 60*I*a^2*d^4)*(b*x + a)^2 + (40*I*b^3*c^3*d - 120*I*a*b^2*c^2*d^2 + 120*I*a^2*b*c*d^3 - 40*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (-10*I*(b*x + a)^4*d^4 + (-40*I*b*c*d^3 + 40*I*a*d^4)*(b*x + a)^3 + (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4)*(b*x + a)^2 + (-40*I*b^3*c^3*d + 120*I*a*b^2*c^2*d^2 - 120*I*a^2*b*c*d^3 + 40*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-40*I*b^3*c^3*d + 120*I*a*b^2*c^2*d^2 - 120*I*a^2*b*c*d^3 - 40*I*(b*x + a)^3*d^4 + 40*I*a^3*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a)^2 + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 - 120*I*a^2*d^4)*(b*x + a))*dilog(-e^(I*b*x + I*a)) + (-40*I*b^3*c^3*d + 120*I*a*b^2*c^2*d^2 - 120*I*a^2*b*c*d^3 - 40*I*(b*x + a)^3*d^4 + 40*I*a^3*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a)^2 + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 - 120*I*a^2*d^4)*(b*x + a))*dilog(e^(I*b*x + I*a)) + 5*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + 5*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (240*I*b*c*d^3 + 240*I*(b*x + a)*d^4 - 240*I*a*d^4)*polylog(4, -e^(I*b*x + I*a)) + (240*I*b*c*d^3 + 240*I*(b*x + a)*d^4 - 240*I*a*d^4)*polylog(4, e^(I*b*x + I*a)) + 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, -e^(I*b*x + I*a)) + 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, e^(I*b*x + I*a)))/b^4)/b","B",0
33,1,747,0,0.516143," ","integrate((d*x+c)^3*cos(b*x+a)*csc(b*x+a),x, algorithm=""maxima"")","\frac{4 \, c^{3} \log\left(\sin\left(b x + a\right)\right) - \frac{12 \, a c^{2} d \log\left(\sin\left(b x + a\right)\right)}{b} + \frac{12 \, a^{2} c d^{2} \log\left(\sin\left(b x + a\right)\right)}{b^{2}} - \frac{4 \, a^{3} d^{3} \log\left(\sin\left(b x + a\right)\right)}{b^{3}} + \frac{-i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-4 i \, b c d^{2} + 4 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + 24 i \, d^{3} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + 24 i \, d^{3} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\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)}^{2} + {\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} + 12 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(-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} - 12 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(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 12 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 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(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 12 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\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} + 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) + 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} + 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) + 24 \, {\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)}) + 24 \, {\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}}}{4 \, b}"," ",0,"1/4*(4*c^3*log(sin(b*x + a)) - 12*a*c^2*d*log(sin(b*x + a))/b + 12*a^2*c*d^2*log(sin(b*x + a))/b^2 - 4*a^3*d^3*log(sin(b*x + a))/b^3 + (-I*(b*x + a)^4*d^3 + (-4*I*b*c*d^2 + 4*I*a*d^3)*(b*x + a)^3 + 24*I*d^3*polylog(4, -e^(I*b*x + I*a)) + 24*I*d^3*polylog(4, e^(I*b*x + I*a)) + (-6*I*b^2*c^2*d + 12*I*a*b*c*d^2 - 6*I*a^2*d^3)*(b*x + a)^2 + (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*d^3)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (-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*d^3)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-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*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*dilog(-e^(I*b*x + I*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*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*dilog(e^(I*b*x + I*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*d^3)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + 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*d^3)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, -e^(I*b*x + I*a)) + 24*(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
34,1,404,0,0.469420," ","integrate((d*x+c)^2*cos(b*x+a)*csc(b*x+a),x, algorithm=""maxima"")","\frac{6 \, c^{2} \log\left(\sin\left(b x + a\right)\right) - \frac{12 \, a c d \log\left(\sin\left(b x + a\right)\right)}{b} + \frac{6 \, a^{2} d^{2} \log\left(\sin\left(b x + a\right)\right)}{b^{2}} + \frac{-2 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)}^{2} + 12 \, d^{2} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + 12 \, d^{2} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 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(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 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(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 3 \, {\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) + 3 \, {\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}}}{6 \, b}"," ",0,"1/6*(6*c^2*log(sin(b*x + a)) - 12*a*c*d*log(sin(b*x + a))/b + 6*a^2*d^2*log(sin(b*x + a))/b^2 + (-2*I*(b*x + a)^3*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a)^2 + 12*d^2*polylog(3, -e^(I*b*x + I*a)) + 12*d^2*polylog(3, e^(I*b*x + I*a)) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*dilog(-e^(I*b*x + I*a)) + (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*dilog(e^(I*b*x + I*a)) + 3*((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) + 3*((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
35,1,189,0,0.459111," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a),x, algorithm=""maxima"")","\frac{-i \, b^{2} d x^{2} - 2 i \, b^{2} c x - 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*(-I*b^2*d*x^2 - 2*I*b^2*c*x - 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
36,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right) \csc\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(cos(b*x + a)*csc(b*x + a)/(d*x + c), x)","F",0
37,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right) \csc\left(b x + a\right)}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)*csc(b*x + a)/(d*x + c)^2, x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \csc\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*csc(b*x + a)^2, x)","F",0
39,1,2944,0,0.838664," ","integrate((d*x+c)^4*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + a\right)\right)} c^{3} 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(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + a\right)\right)} a c^{2} 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{6 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + a\right)\right)} a^{2} c 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 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + a\right)\right)} a^{3} d^{4}}{{\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^{4}} + \frac{c^{4}}{\sin\left(b x + a\right)} - \frac{4 \, a c^{3} d}{b \sin\left(b x + a\right)} + \frac{6 \, a^{2} c^{2} d^{2}}{b^{2} \sin\left(b x + a\right)} - \frac{4 \, a^{3} c d^{3}}{b^{3} \sin\left(b x + a\right)} + \frac{a^{4} d^{4}}{b^{4} \sin\left(b x + a\right)} - \frac{{\left(4 \, {\left(b x + a\right)}^{3} d^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} - 4 \, {\left({\left(b x + a\right)}^{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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\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 \, {\left(b x + a\right)}^{3} d^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} - 4 \, {\left({\left(b x + a\right)}^{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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\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) - 2 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(b x + a\right) - {\left(12 \, b^{2} c^{2} d^{2} - 24 \, a b c d^{3} + 12 \, {\left(b x + a\right)}^{2} d^{4} + 12 \, a^{2} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} - 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, {\left(b x + a\right)}^{2} d^{4} - 12 i \, a^{2} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\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(12 \, b^{2} c^{2} d^{2} - 24 \, a b c d^{3} + 12 \, {\left(b x + a\right)}^{2} d^{4} + 12 \, a^{2} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} - 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, {\left(b x + a\right)}^{2} d^{4} + 12 i \, a^{2} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\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(2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(6 i \, b c d^{3} - 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(-2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} - 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{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)} \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 \, {\left(b x + a\right)}^{3} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} - 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(6 i \, b c d^{3} - 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left({\left(b x + a\right)}^{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)} \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) - 24 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - d^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + 24 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - d^{4}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(24 i \, b c d^{3} + 24 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4} + {\left(-24 i \, b c d^{3} - 24 i \, {\left(b x + a\right)} d^{4} + 24 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + 24 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, b c d^{3} - 24 i \, {\left(b x + a\right)} d^{4} + 24 i \, a d^{4} + {\left(24 i \, b c d^{3} + 24 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - 24 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(b x + a\right)}{-i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + b^{4} \sin\left(2 \, b x + 2 \, a\right) + i \, b^{4}}}{b}"," ",0,"-(2*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + a))*c^3*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*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + a))*a*c^2*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) + 6*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + a))*a^2*c*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*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + a))*a^3*d^4/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*b^4) + c^4/sin(b*x + a) - 4*a*c^3*d/(b*sin(b*x + a)) + 6*a^2*c^2*d^2/(b^2*sin(b*x + a)) - 4*a^3*c*d^3/(b^3*sin(b*x + a)) + a^4*d^4/(b^4*sin(b*x + a)) - ((4*(b*x + a)^3*d^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) - 4*((b*x + 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))*cos(2*b*x + 2*a) - (4*I*(b*x + a)^3*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^2 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(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^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) - 4*((b*x + 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))*cos(2*b*x + 2*a) - (4*I*(b*x + a)^3*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^2 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 2*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2)*cos(b*x + a) - (12*b^2*c^2*d^2 - 24*a*b*c*d^3 + 12*(b*x + a)^2*d^4 + 12*a^2*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a) - 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*(b*x + a)^2*d^4 - 12*I*a^2*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (12*b^2*c^2*d^2 - 24*a*b*c*d^3 + 12*(b*x + a)^2*d^4 + 12*a^2*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a) - 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*(b*x + a)^2*d^4 + 12*I*a^2*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (2*I*(b*x + a)^3*d^4 + (6*I*b*c*d^3 - 6*I*a*d^4)*(b*x + a)^2 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + 6*I*a^2*d^4)*(b*x + a) + (-2*I*(b*x + a)^3*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a)^2 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 - 6*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 2*((b*x + 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))*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*x + a)^3*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a)^2 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 - 6*I*a^2*d^4)*(b*x + a) + (2*I*(b*x + a)^3*d^4 + (6*I*b*c*d^3 - 6*I*a*d^4)*(b*x + a)^2 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + 6*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 2*((b*x + 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 24*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) - d^4)*polylog(4, -e^(I*b*x + I*a)) + 24*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) - d^4)*polylog(4, e^(I*b*x + I*a)) - (24*I*b*c*d^3 + 24*I*(b*x + a)*d^4 - 24*I*a*d^4 + (-24*I*b*c*d^3 - 24*I*(b*x + a)*d^4 + 24*I*a*d^4)*cos(2*b*x + 2*a) + 24*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) - (-24*I*b*c*d^3 - 24*I*(b*x + a)*d^4 + 24*I*a*d^4 + (24*I*b*c*d^3 + 24*I*(b*x + a)*d^4 - 24*I*a*d^4)*cos(2*b*x + 2*a) - 24*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) - (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a)^2)*sin(b*x + a))/(-I*b^4*cos(2*b*x + 2*a) + b^4*sin(2*b*x + 2*a) + I*b^4))/b","B",0
40,1,1770,0,0.560877," ","integrate((d*x+c)^3*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + 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(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + 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(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + 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}}{\sin\left(b x + a\right)} - \frac{6 \, a c^{2} d}{b \sin\left(b x + a\right)} + \frac{6 \, a^{2} c d^{2}}{b^{2} \sin\left(b x + a\right)} - \frac{2 \, a^{3} d^{3}}{b^{3} \sin\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(b x + 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(b x + 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*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + 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*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + 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*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + 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/sin(b*x + a) - 6*a*c^2*d/(b*sin(b*x + a)) + 6*a^2*c*d^2/(b^2*sin(b*x + a)) - 2*a^3*d^3/(b^3*sin(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(b*x + 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(b*x + 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
41,1,556,0,0.524685," ","integrate((d*x+c)^2*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\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 + b^{2} c^{2}\right)} \cos\left(b x + a\right) + 2 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 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 + 2 i \, b^{2} c^{2}\right)} \sin\left(b x + 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*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 + b^2*c^2)*cos(b*x + a) + 2*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) - d^2)*dilog(-e^(I*b*x + I*a)) - 2*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) - 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 + 2*I*b^2*c^2)*sin(b*x + a))/(-I*b^3*cos(2*b*x + 2*a) + b^3*sin(2*b*x + 2*a) + I*b^3)","B",0
42,1,259,0,0.377547," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\frac{{\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\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) - {\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(b x + 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}{\sin\left(b x + a\right)} - \frac{2 \, a d}{b \sin\left(b x + a\right)}}{2 \, b}"," ",0,"-1/2*((4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - 4*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + (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(b*x + 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/sin(b*x + a) - 2*a*d/(b*sin(b*x + a)))/b","B",0
43,0,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \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(b x + 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*cos(b*x + a)*sin(2*b*x + 2*a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + 2*sin(b*x + 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
44,-1,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \csc\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*csc(b*x + a)^3, x)","F",0
46,1,4540,0,0.892729," ","integrate((d*x+c)^4*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{\frac{8 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b} - \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{2}} + \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{3}} - \frac{8 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{4}} + \frac{6 \, {\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) + b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{2}} - \frac{12 \, {\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) + b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{3}} + \frac{6 \, {\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) + b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{4}} - \frac{c^{4}}{\sin\left(b x + a\right)^{2}} + \frac{4 \, a c^{3} d}{b \sin\left(b x + a\right)^{2}} - \frac{6 \, a^{2} c^{2} d^{2}}{b^{2} \sin\left(b x + a\right)^{2}} + \frac{4 \, a^{3} c d^{3}}{b^{3} \sin\left(b x + a\right)^{2}} - \frac{a^{4} d^{4}}{b^{4} \sin\left(b x + a\right)^{2}} + \frac{2 \, {\left({\left(6 \, {\left(b x + a\right)}^{2} d^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\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^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\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^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\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^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\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^{4} + 3 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-8 i \, b c d^{3} - 4 \, {\left(-2 i \, a - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 \, b c d^{3} + 12 \, {\left(b x + a\right)} d^{4} - 12 \, a d^{4} + 12 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b c d^{3} - 12 i \, {\left(b x + a\right)} d^{4} + 12 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, b c d^{3} + 24 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4}\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^{3} + 12 \, {\left(b x + a\right)} d^{4} - 12 \, a d^{4} + 12 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b c d^{3} - 12 i \, {\left(b x + a\right)} d^{4} + 12 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, b c d^{3} + 24 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4}\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^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\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^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\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^{4} \cos\left(4 \, b x + 4 \, a\right) + 24 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) - 24 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, d^{4}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(-12 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) + 24 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) - 24 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, d^{4}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(2 \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 \, b c d^{3} - {\left(8 \, a - 4 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) + 2 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + b^{4} \sin\left(4 \, b x + 4 \, a\right) - 2 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - i \, b^{4}}}{2 \, b}"," ",0,"1/2*(8*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*c^3*d/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b) - 24*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*a*c^2*d^2/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^2) + 24*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*a^2*c*d^3/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^3) - 8*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*a^3*d^4/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^4) + 6*(8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 - 4*(b*x + a)^2*cos(2*b*x + 2*a) - 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*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)^2*sin(2*b*x + 2*a) + b*x - (b*x + a)*cos(2*b*x + 2*a) + a)*sin(4*b*x + 4*a) + 4*(b*x + a)*sin(2*b*x + 2*a))*c^2*d^2/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^2) - 12*(8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 - 4*(b*x + a)^2*cos(2*b*x + 2*a) - 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*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)^2*sin(2*b*x + 2*a) + b*x - (b*x + a)*cos(2*b*x + 2*a) + a)*sin(4*b*x + 4*a) + 4*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^3/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^3) + 6*(8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 - 4*(b*x + a)^2*cos(2*b*x + 2*a) - 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*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)^2*sin(2*b*x + 2*a) + b*x - (b*x + a)*cos(2*b*x + 2*a) + a)*sin(4*b*x + 4*a) + 4*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^4/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^4) - c^4/sin(b*x + a)^2 + 4*a*c^3*d/(b*sin(b*x + a)^2) - 6*a^2*c^2*d^2/(b^2*sin(b*x + a)^2) + 4*a^3*c*d^3/(b^3*sin(b*x + a)^2) - a^4*d^4/(b^4*sin(b*x + a)^2) + 2*((6*(b*x + a)^2*d^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a) + 6*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 12*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (-12*I*(b*x + a)^2*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(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^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a) + 6*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 12*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-6*I*(b*x + a)^2*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (12*I*(b*x + a)^2*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(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^4 + 3*(b*c*d^3 - a*d^4)*(b*x + a)^2)*cos(4*b*x + 4*a) + (-2*I*(b*x + a)^4*d^4 + (-8*I*b*c*d^3 - 4*(-2*I*a - 1)*d^4)*(b*x + a)^3 + 12*(b*c*d^3 - a*d^4)*(b*x + a)^2)*cos(2*b*x + 2*a) - (12*b*c*d^3 + 12*(b*x + a)*d^4 - 12*a*d^4 + 12*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) - 24*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-12*I*b*c*d^3 - 12*I*(b*x + a)*d^4 + 12*I*a*d^4)*sin(4*b*x + 4*a) - (24*I*b*c*d^3 + 24*I*(b*x + a)*d^4 - 24*I*a*d^4)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) - (12*b*c*d^3 + 12*(b*x + a)*d^4 - 12*a*d^4 + 12*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) - 24*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-12*I*b*c*d^3 - 12*I*(b*x + a)*d^4 + 12*I*a*d^4)*sin(4*b*x + 4*a) - (24*I*b*c*d^3 + 24*I*(b*x + a)*d^4 - 24*I*a*d^4)*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (-3*I*(b*x + a)^2*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a) + (-3*I*(b*x + a)^2*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 6*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(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^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a) + (-3*I*(b*x + a)^2*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 6*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(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^4*cos(4*b*x + 4*a) + 24*I*d^4*cos(2*b*x + 2*a) + 12*d^4*sin(4*b*x + 4*a) - 24*d^4*sin(2*b*x + 2*a) - 12*I*d^4)*polylog(3, -e^(I*b*x + I*a)) + (-12*I*d^4*cos(4*b*x + 4*a) + 24*I*d^4*cos(2*b*x + 2*a) + 12*d^4*sin(4*b*x + 4*a) - 24*d^4*sin(2*b*x + 2*a) - 12*I*d^4)*polylog(3, e^(I*b*x + I*a)) + (-4*I*(b*x + a)^3*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2)*sin(4*b*x + 4*a) + (2*(b*x + a)^4*d^4 + (8*b*c*d^3 - (8*a - 4*I)*d^4)*(b*x + a)^3 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-I*b^4*cos(4*b*x + 4*a) + 2*I*b^4*cos(2*b*x + 2*a) + b^4*sin(4*b*x + 4*a) - 2*b^4*sin(2*b*x + 2*a) - I*b^4))/b","B",0
47,1,1044,0,0.697312," ","integrate((d*x+c)^3*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{6 \, b^{2} c^{2} d + {\left(6 \, b d^{3} x + 6 \, b c d^{2} + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, b d^{3} x - 12 i \, b c 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(6 \, b c d^{2} \cos\left(4 \, b x + 4 \, a\right) - 12 \, b c d^{2} \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b c d^{2} \sin\left(4 \, b x + 4 \, a\right) - 12 i \, b c d^{2} \sin\left(2 \, b x + 2 \, a\right) + 6 \, b c d^{2}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) - {\left(6 \, b d^{3} x \cos\left(4 \, b x + 4 \, a\right) - 12 \, b d^{3} x \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b d^{3} x \sin\left(4 \, b x + 4 \, a\right) - 12 i \, b d^{3} x \sin\left(2 \, b x + 2 \, a\right) + 6 \, b d^{3} x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, b^{3} d^{3} x^{3} - 4 i \, b^{3} c^{3} - 6 \, b^{2} c^{2} d + {\left(-12 i \, b^{3} c d^{2} + 6 \, b^{2} d^{3}\right)} x^{2} + {\left(-12 i \, b^{3} c^{2} d + 12 \, b^{2} c d^{2}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(6 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 12 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 12 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 6 \, d^{3}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(6 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 12 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 12 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 6 \, d^{3}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-3 i \, b d^{3} x - 3 i \, b c d^{2} + {\left(-3 i \, b d^{3} x - 3 i \, b c d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b d^{3} x + b c d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left(b d^{3} x + b c 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(-3 i \, b d^{3} x - 3 i \, b c d^{2} + {\left(-3 i \, b d^{3} x - 3 i \, b c d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b d^{3} x + b c d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left(b d^{3} x + b c 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(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(4 \, b^{3} d^{3} x^{3} + 4 \, b^{3} c^{3} - 6 i \, b^{2} c^{2} d + 6 \, {\left(2 \, b^{3} c d^{2} + i \, b^{2} d^{3}\right)} x^{2} + 12 \, {\left(b^{3} c^{2} d + i \, b^{2} c d^{2}\right)} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{-2 i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{4} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{4}}"," ",0,"(6*b^2*c^2*d + (6*b*d^3*x + 6*b*c*d^2 + 6*(b*d^3*x + b*c*d^2)*cos(4*b*x + 4*a) - 12*(b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*sin(4*b*x + 4*a) + (-12*I*b*d^3*x - 12*I*b*c*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*b*c*d^2*cos(4*b*x + 4*a) - 12*b*c*d^2*cos(2*b*x + 2*a) + 6*I*b*c*d^2*sin(4*b*x + 4*a) - 12*I*b*c*d^2*sin(2*b*x + 2*a) + 6*b*c*d^2)*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*b*d^3*x*cos(4*b*x + 4*a) - 12*b*d^3*x*cos(2*b*x + 2*a) + 6*I*b*d^3*x*sin(4*b*x + 4*a) - 12*I*b*d^3*x*sin(2*b*x + 2*a) + 6*b*d^3*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x)*cos(4*b*x + 4*a) + (-4*I*b^3*d^3*x^3 - 4*I*b^3*c^3 - 6*b^2*c^2*d + (-12*I*b^3*c*d^2 + 6*b^2*d^3)*x^2 + (-12*I*b^3*c^2*d + 12*b^2*c*d^2)*x)*cos(2*b*x + 2*a) - (6*d^3*cos(4*b*x + 4*a) - 12*d^3*cos(2*b*x + 2*a) + 6*I*d^3*sin(4*b*x + 4*a) - 12*I*d^3*sin(2*b*x + 2*a) + 6*d^3)*dilog(-e^(I*b*x + I*a)) - (6*d^3*cos(4*b*x + 4*a) - 12*d^3*cos(2*b*x + 2*a) + 6*I*d^3*sin(4*b*x + 4*a) - 12*I*d^3*sin(2*b*x + 2*a) + 6*d^3)*dilog(e^(I*b*x + I*a)) + (-3*I*b*d^3*x - 3*I*b*c*d^2 + (-3*I*b*d^3*x - 3*I*b*c*d^2)*cos(4*b*x + 4*a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(2*b*x + 2*a) + 3*(b*d^3*x + b*c*d^2)*sin(4*b*x + 4*a) - 6*(b*d^3*x + b*c*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) + (-3*I*b*d^3*x - 3*I*b*c*d^2 + (-3*I*b*d^3*x - 3*I*b*c*d^2)*cos(4*b*x + 4*a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(2*b*x + 2*a) + 3*(b*d^3*x + b*c*d^2)*sin(4*b*x + 4*a) - 6*(b*d^3*x + b*c*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) + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x)*sin(4*b*x + 4*a) + (4*b^3*d^3*x^3 + 4*b^3*c^3 - 6*I*b^2*c^2*d + 6*(2*b^3*c*d^2 + I*b^2*d^3)*x^2 + 12*(b^3*c^2*d + I*b^2*c*d^2)*x)*sin(2*b*x + 2*a))/(-2*I*b^4*cos(4*b*x + 4*a) + 4*I*b^4*cos(2*b*x + 2*a) + 2*b^4*sin(4*b*x + 4*a) - 4*b^4*sin(2*b*x + 2*a) - 2*I*b^4)","B",0
48,1,1130,0,0.356075," ","integrate((d*x+c)^2*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} c d}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b} - \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{2}} + \frac{{\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \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({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) + b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b^{2}} - \frac{c^{2}}{\sin\left(b x + a\right)^{2}} + \frac{2 \, a c d}{b \sin\left(b x + a\right)^{2}} - \frac{a^{2} d^{2}}{b^{2} \sin\left(b x + a\right)^{2}}}{2 \, b}"," ",0,"1/2*(4*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*c*d/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b) - 4*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*a*d^2/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^2) + (8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 - 4*(b*x + a)^2*cos(2*b*x + 2*a) - 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*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)^2*sin(2*b*x + 2*a) + b*x - (b*x + a)*cos(2*b*x + 2*a) + a)*sin(4*b*x + 4*a) + 4*(b*x + a)*sin(2*b*x + 2*a))*d^2/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b^2) - c^2/sin(b*x + a)^2 + 2*a*c*d/(b*sin(b*x + a)^2) - a^2*d^2/(b^2*sin(b*x + a)^2))/b","B",0
49,1,287,0,0.393107," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \sin\left(4 \, b x + 4 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} d}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)^{2} - 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) - 1\right)} b} - \frac{c}{\sin\left(b x + a\right)^{2}} + \frac{a d}{b \sin\left(b x + a\right)^{2}}}{2 \, b}"," ",0,"1/2*(2*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 - (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - 2*(b*x + a)*cos(2*b*x + 2*a) - (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*sin(4*b*x + 4*a) + sin(2*b*x + 2*a))*d/((2*(2*cos(2*b*x + 2*a) - 1)*cos(4*b*x + 4*a) - cos(4*b*x + 4*a)^2 - 4*cos(2*b*x + 2*a)^2 - sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) - 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) - 1)*b) - c/sin(b*x + a)^2 + a*d/(b*sin(b*x + a)^2))/b","B",0
50,-1,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(cos(b*x+a)*csc(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,275,0,0.547917," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(160 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 8 \, {\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)} \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^{3} \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^{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(15 i + 15\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(15 i - 15\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)\right)}}{1024 \, b^{4}}"," ",0,"1/1024*sqrt(2)*(160*sqrt(2)*(d*x + c)^(3/2)*b^2*d*sin(2*((d*x + c)*b - b*c + a*d)/d) - 8*(16*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((15*I - 15)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (15*I + 15)*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)) + (-(15*I + 15)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (15*I - 15)*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)))/b^4","C",0
53,1,256,0,0.555955," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(32 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 24 \, \sqrt{2} \sqrt{d x + c} b d \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^{2} \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^{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(3 i - 3\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(3 i + 3\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)}}{256 \, b^{3}}"," ",0,"-1/256*sqrt(2)*(32*sqrt(2)*(d*x + c)^(3/2)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d) - 24*sqrt(2)*sqrt(d*x + c)*b*d*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(3*I + 3)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (3*I - 3)*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)) - ((3*I - 3)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (3*I + 3)*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
54,1,209,0,0.451721," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(8 \, \sqrt{2} \sqrt{d x + c} b \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(i - 1\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(i + 1\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(i + 1\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(i - 1\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)}}{64 \, b^{2}}"," ",0,"-1/64*sqrt(2)*(8*sqrt(2)*sqrt(d*x + c)*b*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((I - 1)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (I + 1)*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)) + (-(I + 1)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (I - 1)*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
55,1,209,0,0.600894," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(8 \, \sqrt{2} \sqrt{d x + c} b \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(i - 1\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(i + 1\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(i + 1\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(i - 1\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)}}{64 \, b^{2}}"," ",0,"-1/64*sqrt(2)*(8*sqrt(2)*sqrt(d*x + c)*b*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((I - 1)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (I + 1)*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)) + (-(I + 1)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (I - 1)*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
56,1,256,0,0.546545," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(32 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 24 \, \sqrt{2} \sqrt{d x + c} b d \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^{2} \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^{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(3 i - 3\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(3 i + 3\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)}}{256 \, b^{3}}"," ",0,"-1/256*sqrt(2)*(32*sqrt(2)*(d*x + c)^(3/2)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d) - 24*sqrt(2)*sqrt(d*x + c)*b*d*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(3*I + 3)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (3*I - 3)*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)) - ((3*I - 3)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (3*I + 3)*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
57,1,275,0,0.470167," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(160 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 8 \, {\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)} \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^{3} \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^{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(15 i + 15\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(15 i - 15\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)\right)}}{1024 \, b^{4}}"," ",0,"1/1024*sqrt(2)*(160*sqrt(2)*(d*x + c)^(3/2)*b^2*d*sin(2*((d*x + c)*b - b*c + a*d)/d) - 8*(16*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((15*I - 15)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (15*I + 15)*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)) + (-(15*I + 15)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (15*I - 15)*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)))/b^4","C",0
58,1,543,0,0.595803," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(240 \, {\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) - 2160 \, {\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) + {\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(405 i + 405\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(405 i - 405\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(405 i - 405\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(405 i + 405\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) + 24 \, {\left(\frac{12 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 5 \, \sqrt{d x + c} b^{2} d\right)} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 216 \, {\left(\frac{4 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)\right)} d}{3456 \, b^{5}}"," ",0,"-1/3456*(240*(d*x + c)^(3/2)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d) - 2160*(d*x + c)^(3/2)*b^3*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)) + (-(405*I + 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (405*I - 405)*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)) + ((405*I - 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (405*I + 405)*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)) + 24*(12*(d*x + c)^(5/2)*b^4/d - 5*sqrt(d*x + c)*b^2*d)*sin(3*((d*x + c)*b - b*c + a*d)/d) - 216*(4*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*sin(((d*x + c)*b - b*c + a*d)/d))*d/b^5","C",0
59,1,495,0,0.591712," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{48 \, {\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)}{d} - \frac{144 \, {\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)}{d} + 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) - 216 \, \sqrt{d x + c} b^{2} \cos\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(27 i - 27\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(27 i + 27\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(27 i + 27\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(27 i - 27\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*sin(3*((d*x + c)*b - b*c + a*d)/d)/d - 144*(d*x + c)^(3/2)*b^3*sin(((d*x + c)*b - b*c + a*d)/d)/d + 24*sqrt(d*x + c)*b^2*cos(3*((d*x + c)*b - b*c + a*d)/d) - 216*sqrt(d*x + c)*b^2*cos(((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)) + (-(27*I - 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (27*I + 27)*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)) + ((27*I + 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (27*I - 27)*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
60,1,422,0,0.569479," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{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)}{d} - \frac{72 \, \sqrt{d x + c} b^{2} \sin\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(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) - \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)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\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) + \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)\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*sin(3*((d*x + c)*b - b*c + a*d)/d)/d - 72*sqrt(d*x + c)*b^2*sin(((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)) + ((9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (9*I - 9)*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)) + (-(9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (9*I + 9)*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
61,1,422,0,0.579439," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{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)}{d} - \frac{72 \, \sqrt{d x + c} b^{2} \sin\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(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) - \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)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\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) + \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)\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*sin(3*((d*x + c)*b - b*c + a*d)/d)/d - 72*sqrt(d*x + c)*b^2*sin(((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)) + ((9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (9*I - 9)*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)) + (-(9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (9*I + 9)*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
62,1,495,0,0.606894," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(\frac{48 \, {\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)}{d} - \frac{144 \, {\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)}{d} + 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) - 216 \, \sqrt{d x + c} b^{2} \cos\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(27 i - 27\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(27 i + 27\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(27 i + 27\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(27 i - 27\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*sin(3*((d*x + c)*b - b*c + a*d)/d)/d - 144*(d*x + c)^(3/2)*b^3*sin(((d*x + c)*b - b*c + a*d)/d)/d + 24*sqrt(d*x + c)*b^2*cos(3*((d*x + c)*b - b*c + a*d)/d) - 216*sqrt(d*x + c)*b^2*cos(((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)) + (-(27*I - 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (27*I + 27)*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)) + ((27*I + 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (27*I - 27)*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
63,1,543,0,0.602978," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(240 \, {\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) - 2160 \, {\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) + {\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(405 i + 405\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(405 i - 405\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(405 i - 405\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(405 i + 405\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) + 24 \, {\left(\frac{12 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 5 \, \sqrt{d x + c} b^{2} d\right)} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 216 \, {\left(\frac{4 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)\right)} d}{3456 \, b^{5}}"," ",0,"-1/3456*(240*(d*x + c)^(3/2)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d) - 2160*(d*x + c)^(3/2)*b^3*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)) + (-(405*I + 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (405*I - 405)*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)) + ((405*I - 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (405*I + 405)*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)) + 24*(12*(d*x + c)^(5/2)*b^4/d - 5*sqrt(d*x + c)*b^2*d)*sin(3*((d*x + c)*b - b*c + a*d)/d) - 216*(4*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*sin(((d*x + c)*b - b*c + a*d)/d))*d/b^5","C",0
64,1,547,0,0.538616," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(1280 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 10240 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 32 \, {\left(\frac{64 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 512 \, {\left(\frac{16 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(-\left(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(\left(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{65536 \, b^{5}}"," ",0,"-1/65536*(1280*(d*x + c)^(3/2)*b^3*sin(4*((d*x + c)*b - b*c + a*d)/d) - 10240*(d*x + c)^(3/2)*b^3*sin(2*((d*x + c)*b - b*c + a*d)/d) - 32*(64*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(4*((d*x + c)*b - b*c + a*d)/d) + 512*(16*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(2*((d*x + c)*b - b*c + a*d)/d) + (-(480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + ((30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + ((480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)))*d/b^5","C",0
65,1,503,0,0.514385," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{256 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{1024 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - 96 \, \sqrt{d x + c} b^{2} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 768 \, \sqrt{d x + c} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - {\left(-\left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{8192 \, b^{4}}"," ",0,"1/8192*(256*(d*x + c)^(3/2)*b^3*cos(4*((d*x + c)*b - b*c + a*d)/d)/d - 1024*(d*x + c)^(3/2)*b^3*cos(2*((d*x + c)*b - b*c + a*d)/d)/d - 96*sqrt(d*x + c)*b^2*sin(4*((d*x + c)*b - b*c + a*d)/d) + 768*sqrt(d*x + c)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - ((48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - ((6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) - (-(48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^4","C",0
66,1,425,0,0.492397," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{32 \, \sqrt{d x + c} b^{2} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{128 \, \sqrt{d x + c} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + {\left(-\left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(\left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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)} d}{1024 \, b^{3}}"," ",0,"1/1024*(32*sqrt(d*x + c)*b^2*cos(4*((d*x + c)*b - b*c + a*d)/d)/d - 128*sqrt(d*x + c)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d)/d + (-(8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + ((8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^3","C",0
67,1,425,0,0.484295," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{32 \, \sqrt{d x + c} b^{2} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{128 \, \sqrt{d x + c} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + {\left(-\left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(\left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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)} d}{1024 \, b^{3}}"," ",0,"1/1024*(32*sqrt(d*x + c)*b^2*cos(4*((d*x + c)*b - b*c + a*d)/d)/d - 128*sqrt(d*x + c)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d)/d + (-(8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + ((8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^3","C",0
68,1,503,0,0.497239," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{256 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{1024 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - 96 \, \sqrt{d x + c} b^{2} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 768 \, \sqrt{d x + c} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - {\left(-\left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{8192 \, b^{4}}"," ",0,"1/8192*(256*(d*x + c)^(3/2)*b^3*cos(4*((d*x + c)*b - b*c + a*d)/d)/d - 1024*(d*x + c)^(3/2)*b^3*cos(2*((d*x + c)*b - b*c + a*d)/d)/d - 96*sqrt(d*x + c)*b^2*sin(4*((d*x + c)*b - b*c + a*d)/d) + 768*sqrt(d*x + c)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - ((48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - ((6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) - (-(48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^4","C",0
69,1,547,0,0.633799," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(1280 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 10240 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 32 \, {\left(\frac{64 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 512 \, {\left(\frac{16 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(-\left(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(\left(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{65536 \, b^{5}}"," ",0,"-1/65536*(1280*(d*x + c)^(3/2)*b^3*sin(4*((d*x + c)*b - b*c + a*d)/d) - 10240*(d*x + c)^(3/2)*b^3*sin(2*((d*x + c)*b - b*c + a*d)/d) - 32*(64*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(4*((d*x + c)*b - b*c + a*d)/d) + 512*(16*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(2*((d*x + c)*b - b*c + a*d)/d) + (-(480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + ((30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + ((480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)))*d/b^5","C",0
70,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^2*sin(b*x + a), x)","F",0
71,1,889,0,0.470753," ","integrate((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{108 \, c^{4} \cos\left(b x + a\right)^{3} - \frac{432 \, a c^{3} d \cos\left(b x + a\right)^{3}}{b} + \frac{648 \, a^{2} c^{2} d^{2} \cos\left(b x + a\right)^{3}}{b^{2}} - \frac{432 \, a^{3} c d^{3} \cos\left(b x + a\right)^{3}}{b^{3}} + \frac{108 \, a^{4} d^{4} \cos\left(b x + a\right)^{3}}{b^{4}} + \frac{36 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 27 \, {\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) - 54 \, {\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) + 27 \, {\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) - 54 \, {\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) + 27 \, {\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) - 54 \, {\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) + 27 \, {\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) - 81 \, {\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) + 27 \, {\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) - 81 \, {\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) + 81 \, {\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) - 324 \, {\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*c^4*cos(b*x + a)^3 - 432*a*c^3*d*cos(b*x + a)^3/b + 648*a^2*c^2*d^2*cos(b*x + a)^3/b^2 - 432*a^3*c*d^3*cos(b*x + a)^3/b^3 + 108*a^4*d^4*cos(b*x + a)^3/b^4 + 36*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*c^3*d/b - 108*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*a*c^2*d^2/b^2 + 108*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*a^2*c*d^3/b^3 - 36*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*a^3*d^4/b^4 + 18*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) + 27*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) - 54*(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) + 27*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) - 54*(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) + 27*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) - 54*(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) + 27*((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) - 81*((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) + 27*((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) - 81*((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) + 81*((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) - 324*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^4/b^4)/b","B",0
72,1,505,0,0.369982," ","integrate((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{36 \, c^{3} \cos\left(b x + a\right)^{3} - \frac{108 \, a c^{2} d \cos\left(b x + a\right)^{3}}{b} + \frac{108 \, a^{2} c d^{2} \cos\left(b x + a\right)^{3}}{b^{2}} - \frac{36 \, a^{3} d^{3} \cos\left(b x + a\right)^{3}}{b^{3}} + \frac{9 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 27 \, {\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) - 54 \, {\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) + 27 \, {\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) - 54 \, {\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) + 27 \, {\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) - 81 \, {\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*c^3*cos(b*x + a)^3 - 108*a*c^2*d*cos(b*x + a)^3/b + 108*a^2*c*d^2*cos(b*x + a)^3/b^2 - 36*a^3*d^3*cos(b*x + a)^3/b^3 + 9*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*c^2*d/b - 18*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*a*c*d^2/b^2 + 9*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*a^2*d^3/b^3 + 3*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) + 27*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) - 54*(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) + 27*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) - 54*(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) + 27*((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) - 81*((b*x + a)^2 - 2)*sin(b*x + a))*d^3/b^3)/b","B",0
73,1,243,0,0.374054," ","integrate((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{36 \, c^{2} \cos\left(b x + a\right)^{3} - \frac{72 \, a c d \cos\left(b x + a\right)^{3}}{b} + \frac{36 \, a^{2} d^{2} \cos\left(b x + a\right)^{3}}{b^{2}} + \frac{6 \, {\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \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) + 27 \, {\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) - 54 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{108 \, b}"," ",0,"-1/108*(36*c^2*cos(b*x + a)^3 - 72*a*c*d*cos(b*x + a)^3/b + 36*a^2*d^2*cos(b*x + a)^3/b^2 + 6*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*c*d/b - 6*(3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*a*d^2/b^2 + ((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) + 27*((b*x + a)^2 - 2)*cos(b*x + a) - 6*(b*x + a)*sin(3*b*x + 3*a) - 54*(b*x + a)*sin(b*x + a))*d^2/b^2)/b","B",0
74,1,86,0,0.385935," ","integrate((d*x+c)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""maxima"")","-\frac{12 \, c \cos\left(b x + a\right)^{3} - \frac{12 \, a d \cos\left(b x + a\right)^{3}}{b} + \frac{{\left(3 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 9 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(3 \, b x + 3 \, a\right) - 9 \, \sin\left(b x + a\right)\right)} d}{b}}{36 \, b}"," ",0,"-1/36*(12*c*cos(b*x + a)^3 - 12*a*d*cos(b*x + a)^3/b + (3*(b*x + a)*cos(3*b*x + 3*a) + 9*(b*x + a)*cos(b*x + a) - sin(3*b*x + 3*a) - 9*sin(b*x + a))*d/b)/b","A",0
75,1,273,0,0.431597," ","integrate(cos(b*x+a)^2*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(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) + 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*(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*(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) + 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
76,1,300,0,0.523241," ","integrate(cos(b*x+a)^2*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(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) + 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*(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*(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) + 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
77,1,335,0,0.649916," ","integrate(cos(b*x+a)^2*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(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) + 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*(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*(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) + 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
78,1,385,0,0.876729," ","integrate(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{b^{4} {\left(i \, E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - i \, E_{4}\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^{4} {\left(i \, E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - i \, E_{4}\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) + b^{4} {\left(E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{4}\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^{4} {\left(E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{4}\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^{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,"-1/8*(b^4*(I*exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - I*exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b^4*(I*exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - I*exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) + b^4*(exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^4*(exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d))/((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
79,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(4 \, b x + 4 \, a\right)\,{d x} - e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)}}{8 \, {\left(d m + d\right)}}"," ",0,"-1/8*((d*m + d)*integrate((d*x + c)^m*cos(4*b*x + 4*a), x) - e^(m*log(d*x + c) + log(d*x + c)))/(d*m + d)","F",0
80,1,735,0,0.373139," ","integrate((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{160 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} c^{4} - \frac{640 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a c^{3} d}{b} + \frac{960 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{640 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a^{3} c d^{3}}{b^{3}} + \frac{160 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a^{4} d^{4}}{b^{4}} + \frac{160 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} c^{3} d}{b} - \frac{480 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{480 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{160 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{40 \, {\left(32 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{80 \, {\left(32 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} a c d^{3}}{b^{3}} + \frac{40 \, {\left(32 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{20 \, {\left(32 \, {\left(b x + a\right)}^{4} - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} c d^{3}}{b^{3}} - \frac{20 \, {\left(32 \, {\left(b x + a\right)}^{4} - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left(128 \, {\left(b x + a\right)}^{5} - 20 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - 5 \, {\left(32 \, {\left(b x + a\right)}^{4} - 24 \, {\left(b x + a\right)}^{2} + 3\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} d^{4}}{b^{4}}}{5120 \, b}"," ",0,"1/5120*(160*(4*b*x + 4*a - sin(4*b*x + 4*a))*c^4 - 640*(4*b*x + 4*a - sin(4*b*x + 4*a))*a*c^3*d/b + 960*(4*b*x + 4*a - sin(4*b*x + 4*a))*a^2*c^2*d^2/b^2 - 640*(4*b*x + 4*a - sin(4*b*x + 4*a))*a^3*c*d^3/b^3 + 160*(4*b*x + 4*a - sin(4*b*x + 4*a))*a^4*d^4/b^4 + 160*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*c^3*d/b - 480*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*a*c^2*d^2/b^2 + 480*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*a^2*c*d^3/b^3 - 160*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*a^3*d^4/b^4 + 40*(32*(b*x + a)^3 - 12*(b*x + a)*cos(4*b*x + 4*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a))*c^2*d^2/b^2 - 80*(32*(b*x + a)^3 - 12*(b*x + a)*cos(4*b*x + 4*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a))*a*c*d^3/b^3 + 40*(32*(b*x + a)^3 - 12*(b*x + a)*cos(4*b*x + 4*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a))*a^2*d^4/b^4 + 20*(32*(b*x + a)^4 - 3*(8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 4*(8*(b*x + a)^3 - 3*b*x - 3*a)*sin(4*b*x + 4*a))*c*d^3/b^3 - 20*(32*(b*x + a)^4 - 3*(8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 4*(8*(b*x + a)^3 - 3*b*x - 3*a)*sin(4*b*x + 4*a))*a*d^4/b^4 + (128*(b*x + a)^5 - 20*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) - 5*(32*(b*x + a)^4 - 24*(b*x + a)^2 + 3)*sin(4*b*x + 4*a))*d^4/b^4)/b","B",0
81,1,442,0,0.363921," ","integrate((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{32 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} c^{3} - \frac{96 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a c^{2} d}{b} + \frac{96 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{32 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a^{3} d^{3}}{b^{3}} + \frac{24 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} c^{2} d}{b} - \frac{48 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} a c d^{2}}{b^{2}} + \frac{24 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{4 \, {\left(32 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} c d^{2}}{b^{2}} - \frac{4 \, {\left(32 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(32 \, {\left(b x + a\right)}^{4} - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} d^{3}}{b^{3}}}{1024 \, b}"," ",0,"1/1024*(32*(4*b*x + 4*a - sin(4*b*x + 4*a))*c^3 - 96*(4*b*x + 4*a - sin(4*b*x + 4*a))*a*c^2*d/b + 96*(4*b*x + 4*a - sin(4*b*x + 4*a))*a^2*c*d^2/b^2 - 32*(4*b*x + 4*a - sin(4*b*x + 4*a))*a^3*d^3/b^3 + 24*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*c^2*d/b - 48*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*a*c*d^2/b^2 + 24*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*a^2*d^3/b^3 + 4*(32*(b*x + a)^3 - 12*(b*x + a)*cos(4*b*x + 4*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a))*c*d^2/b^2 - 4*(32*(b*x + a)^3 - 12*(b*x + a)*cos(4*b*x + 4*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a))*a*d^3/b^3 + (32*(b*x + a)^4 - 3*(8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) - 4*(8*(b*x + a)^3 - 3*b*x - 3*a)*sin(4*b*x + 4*a))*d^3/b^3)/b","B",0
82,1,232,0,0.340764," ","integrate((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{24 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} c^{2} - \frac{48 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a c d}{b} + \frac{24 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a^{2} d^{2}}{b^{2}} + \frac{12 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} c d}{b} - \frac{12 \, {\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left(32 \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} d^{2}}{b^{2}}}{768 \, b}"," ",0,"1/768*(24*(4*b*x + 4*a - sin(4*b*x + 4*a))*c^2 - 48*(4*b*x + 4*a - sin(4*b*x + 4*a))*a*c*d/b + 24*(4*b*x + 4*a - sin(4*b*x + 4*a))*a^2*d^2/b^2 + 12*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*c*d/b - 12*(8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*a*d^2/b^2 + (32*(b*x + a)^3 - 12*(b*x + a)*cos(4*b*x + 4*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a))*d^2/b^2)/b","B",0
83,1,96,0,0.325696," ","integrate((d*x+c)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} c - \frac{4 \, {\left(4 \, b x + 4 \, a - \sin\left(4 \, b x + 4 \, a\right)\right)} a d}{b} + \frac{{\left(8 \, {\left(b x + a\right)}^{2} - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - \cos\left(4 \, b x + 4 \, a\right)\right)} d}{b}}{128 \, b}"," ",0,"1/128*(4*(4*b*x + 4*a - sin(4*b*x + 4*a))*c - 4*(4*b*x + 4*a - sin(4*b*x + 4*a))*a*d/b + (8*(b*x + a)^2 - 4*(b*x + a)*sin(4*b*x + 4*a) - cos(4*b*x + 4*a))*d/b)/b","B",0
84,1,160,0,0.409918," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{b {\left(E_{1}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{1}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + b {\left(-i \, E_{1}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + i \, E_{1}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 2 \, b \log\left(b c + {\left(b x + a\right)} d - a d\right)}{16 \, b d}"," ",0,"1/16*(b*(exp_integral_e(1, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(1, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) + b*(-I*exp_integral_e(1, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + I*exp_integral_e(1, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d) + 2*b*log(b*c + (b*x + a)*d - a*d))/(b*d)","C",0
85,1,171,0,0.443841," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\frac{64 \, b^{2} {\left(E_{2}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{2}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - b^{2} {\left(64 i \, E_{2}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - 64 i \, E_{2}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 128 \, b^{2}}{1024 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"1/1024*(64*b^2*(exp_integral_e(2, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(2, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - b^2*(64*I*exp_integral_e(2, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - 64*I*exp_integral_e(2, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d) - 128*b^2)/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
86,1,206,0,0.490891," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""maxima"")","\frac{64 \, b^{3} {\left(E_{3}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{3}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - b^{3} {\left(64 i \, E_{3}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - 64 i \, E_{3}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 64 \, b^{3}}{1024 \, {\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,"1/1024*(64*b^3*(exp_integral_e(3, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(3, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - b^3*(64*I*exp_integral_e(3, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - 64*I*exp_integral_e(3, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d) - 64*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
87,1,256,0,0.609947," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""maxima"")","\frac{3 \, b^{4} {\left(E_{4}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{4}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - b^{4} {\left(3 i \, E_{4}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - 3 i \, E_{4}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, b^{4}}{48 \, {\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,"1/48*(3*b^4*(exp_integral_e(4, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(4, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) - b^4*(3*I*exp_integral_e(4, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - 3*I*exp_integral_e(4, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(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
88,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^2*sin(b*x + a)^3, x)","F",0
89,1,1339,0,0.419507," ","integrate((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{270000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} c^{4} - \frac{1080000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a c^{3} d}{b} + \frac{1620000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{1080000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a^{3} c d^{3}}{b^{3}} + \frac{270000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a^{4} d^{4}}{b^{4}} + \frac{4500 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} c^{3} d}{b} - \frac{13500 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{13500 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{4500 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{450 \, {\left(27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) - 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 270 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 13500 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{900 \, {\left(27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) - 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 270 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 13500 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a c d^{3}}{b^{3}} + \frac{450 \, {\left(27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) - 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 270 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 13500 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{60 \, {\left(135 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(5 \, b x + 5 \, a\right) - 1875 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 33750 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 81 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 625 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) + 101250 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c d^{3}}{b^{3}} - \frac{60 \, {\left(135 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(5 \, b x + 5 \, a\right) - 1875 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 33750 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 81 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 625 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) + 101250 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left(81 \, {\left(625 \, {\left(b x + a\right)}^{4} - 300 \, {\left(b x + a\right)}^{2} + 24\right)} \cos\left(5 \, b x + 5 \, a\right) - 3125 \, {\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) - 506250 \, {\left({\left(b x + a\right)}^{4} - 12 \, {\left(b x + a\right)}^{2} + 24\right)} \cos\left(b x + a\right) - 1620 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(5 \, b x + 5 \, a\right) + 37500 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) + 2025000 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} d^{4}}{b^{4}}}{4050000 \, b}"," ",0,"1/4050000*(270000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*c^4 - 1080000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a*c^3*d/b + 1620000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a^2*c^2*d^2/b^2 - 1080000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a^3*c*d^3/b^3 + 270000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a^4*d^4/b^4 + 4500*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*c^3*d/b - 13500*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*a*c^2*d^2/b^2 + 13500*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*a^2*c*d^3/b^3 - 4500*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*a^3*d^4/b^4 + 450*(27*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) - 125*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*cos(b*x + a) - 270*(b*x + a)*sin(5*b*x + 5*a) + 750*(b*x + a)*sin(3*b*x + 3*a) + 13500*(b*x + a)*sin(b*x + a))*c^2*d^2/b^2 - 900*(27*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) - 125*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*cos(b*x + a) - 270*(b*x + a)*sin(5*b*x + 5*a) + 750*(b*x + a)*sin(3*b*x + 3*a) + 13500*(b*x + a)*sin(b*x + a))*a*c*d^3/b^3 + 450*(27*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) - 125*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*cos(b*x + a) - 270*(b*x + a)*sin(5*b*x + 5*a) + 750*(b*x + a)*sin(3*b*x + 3*a) + 13500*(b*x + a)*sin(b*x + a))*a^2*d^4/b^4 + 60*(135*(25*(b*x + a)^3 - 6*b*x - 6*a)*cos(5*b*x + 5*a) - 1875*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 33750*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 81*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 625*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) + 101250*((b*x + a)^2 - 2)*sin(b*x + a))*c*d^3/b^3 - 60*(135*(25*(b*x + a)^3 - 6*b*x - 6*a)*cos(5*b*x + 5*a) - 1875*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 33750*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 81*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 625*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) + 101250*((b*x + a)^2 - 2)*sin(b*x + a))*a*d^4/b^4 + (81*(625*(b*x + a)^4 - 300*(b*x + a)^2 + 24)*cos(5*b*x + 5*a) - 3125*(27*(b*x + a)^4 - 36*(b*x + a)^2 + 8)*cos(3*b*x + 3*a) - 506250*((b*x + a)^4 - 12*(b*x + a)^2 + 24)*cos(b*x + a) - 1620*(25*(b*x + a)^3 - 6*b*x - 6*a)*sin(5*b*x + 5*a) + 37500*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) + 2025000*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^4/b^4)/b","B",0
90,1,766,0,0.378860," ","integrate((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{18000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} c^{3} - \frac{54000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a c^{2} d}{b} + \frac{54000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a^{2} c d^{2}}{b^{2}} - \frac{18000 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a^{3} d^{3}}{b^{3}} + \frac{225 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} c^{2} d}{b} - \frac{450 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} a c d^{2}}{b^{2}} + \frac{225 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{15 \, {\left(27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) - 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 270 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 13500 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} c d^{2}}{b^{2}} - \frac{15 \, {\left(27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) - 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 270 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 13500 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(135 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(5 \, b x + 5 \, a\right) - 1875 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 33750 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) - 81 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 625 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) + 101250 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} d^{3}}{b^{3}}}{270000 \, b}"," ",0,"1/270000*(18000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*c^3 - 54000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a*c^2*d/b + 54000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a^2*c*d^2/b^2 - 18000*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a^3*d^3/b^3 + 225*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*c^2*d/b - 450*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*a*c*d^2/b^2 + 225*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*a^2*d^3/b^3 + 15*(27*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) - 125*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*cos(b*x + a) - 270*(b*x + a)*sin(5*b*x + 5*a) + 750*(b*x + a)*sin(3*b*x + 3*a) + 13500*(b*x + a)*sin(b*x + a))*c*d^2/b^2 - 15*(27*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) - 125*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*cos(b*x + a) - 270*(b*x + a)*sin(5*b*x + 5*a) + 750*(b*x + a)*sin(3*b*x + 3*a) + 13500*(b*x + a)*sin(b*x + a))*a*d^3/b^3 + (135*(25*(b*x + a)^3 - 6*b*x - 6*a)*cos(5*b*x + 5*a) - 1875*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 33750*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) - 81*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 625*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) + 101250*((b*x + a)^2 - 2)*sin(b*x + a))*d^3/b^3)/b","B",0
91,1,375,0,0.348423," ","integrate((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{3600 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} c^{2} - \frac{7200 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a c d}{b} + \frac{3600 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a^{2} d^{2}}{b^{2}} + \frac{30 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} c d}{b} - \frac{30 \, {\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left(27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) - 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) - 270 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 13500 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{54000 \, b}"," ",0,"1/54000*(3600*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*c^2 - 7200*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a*c*d/b + 3600*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a^2*d^2/b^2 + 30*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*c*d/b - 30*(45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*a*d^2/b^2 + (27*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) - 125*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*cos(b*x + a) - 270*(b*x + a)*sin(5*b*x + 5*a) + 750*(b*x + a)*sin(3*b*x + 3*a) + 13500*(b*x + a)*sin(b*x + a))*d^2/b^2)/b","B",0
92,1,139,0,0.336558," ","integrate((d*x+c)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{240 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} c - \frac{240 \, {\left(3 \, \cos\left(b x + a\right)^{5} - 5 \, \cos\left(b x + a\right)^{3}\right)} a d}{b} + \frac{{\left(45 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) - 75 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 9 \, \sin\left(5 \, b x + 5 \, a\right) + 25 \, \sin\left(3 \, b x + 3 \, a\right) + 450 \, \sin\left(b x + a\right)\right)} d}{b}}{3600 \, b}"," ",0,"1/3600*(240*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*c - 240*(3*cos(b*x + a)^5 - 5*cos(b*x + a)^3)*a*d/b + (45*(b*x + a)*cos(5*b*x + 5*a) - 75*(b*x + a)*cos(3*b*x + 3*a) - 450*(b*x + a)*cos(b*x + a) - 9*sin(5*b*x + 5*a) + 25*sin(3*b*x + 3*a) + 450*sin(b*x + a))*d/b)/b","A",0
93,1,407,0,0.470902," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{b {\left(-2 i \, E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 2 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) + b {\left(i \, E_{1}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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) + b {\left(E_{1}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{1}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{32 \, b d}"," ",0,"1/32*(b*(-2*I*exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 2*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) + b*(I*exp_integral_e(1, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - I*exp_integral_e(1, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) - 2*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*(exp_integral_e(1, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(1, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(b*c - a*d)/d))/(b*d)","C",0
94,1,438,0,0.583910," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(-2 i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 2 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) + b^{2} {\left(i \, E_{2}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - i \, E_{2}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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) + b^{2} {\left(E_{2}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{2}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{32 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"1/32*(b^2*(-2*I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 2*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) + b^2*(I*exp_integral_e(2, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - I*exp_integral_e(2, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) - 2*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^2*(exp_integral_e(2, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(2, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
95,1,473,0,0.779113," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""maxima"")","\frac{b^{3} {\left(-2 i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 2 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) + b^{3} {\left(i \, E_{3}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - i \, E_{3}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 2 \, 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) + b^{3} {\left(E_{3}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{3}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{32 \, {\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,"1/32*(b^3*(-2*I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 2*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) + b^3*(I*exp_integral_e(3, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - I*exp_integral_e(3, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) - 2*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^3*(exp_integral_e(3, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(3, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(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
96,1,523,0,1.103761," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^4,x, algorithm=""maxima"")","\frac{b^{4} {\left(-2 i \, E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 2 i \, E_{4}\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^{4} {\left(-i \, E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + i \, E_{4}\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) + b^{4} {\left(i \, E_{4}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - i \, E_{4}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 2 \, b^{4} {\left(E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{4}\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^{4} {\left(E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{4}\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) + b^{4} {\left(E_{4}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{4}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{32 \, {\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,"1/32*(b^4*(-2*I*exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 2*I*exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) + b^4*(-I*exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + I*exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) + b^4*(I*exp_integral_e(4, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - I*exp_integral_e(4, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) - 2*b^4*(exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) - b^4*(exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d) + b^4*(exp_integral_e(4, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(4, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(b*c - a*d)/d))/((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
97,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*cot(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \cot\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*cot(b*x + a), x)","F",0
98,1,1538,0,0.638476," ","integrate((d*x+c)^4*cos(b*x+a)*cot(b*x+a),x, algorithm=""maxima"")","\frac{c^{4} {\left(2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{4 \, a c^{3} d {\left(2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b} + \frac{6 \, a^{2} c^{2} d^{2} {\left(2 \, \cos\left(b x + a\right) - \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 \, a^{3} c d^{3} {\left(2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{3}} + \frac{a^{4} d^{4} {\left(2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{4}} + \frac{48 \, d^{4} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) - 48 \, d^{4} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) - {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 24 i \, a^{2} b c d^{3} - 8 i \, a^{3} d^{4}\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)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 24 i \, a^{2} b c d^{3} - 8 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, {\left(a^{2} - 2\right)} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) - {\left(-8 i \, b^{3} c^{3} d + 24 i \, a b^{2} c^{2} d^{2} - 24 i \, a^{2} b c d^{3} - 8 i \, {\left(b x + a\right)}^{3} d^{4} + 8 i \, a^{3} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 24 i \, a^{2} b c d^{3} + 8 i \, {\left(b x + a\right)}^{3} d^{4} - 8 i \, a^{3} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, a^{2} d^{4}\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)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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(48 i \, b c d^{3} + 48 i \, {\left(b x + a\right)} d^{4} - 48 i \, a d^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-48 i \, b c d^{3} - 48 i \, {\left(b x + a\right)} d^{4} + 48 i \, a d^{4}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} 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} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)}{b^{4}}}{2 \, b}"," ",0,"1/2*(c^4*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 4*a*c^3*d*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + 6*a^2*c^2*d^2*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 - 4*a^3*c*d^3*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^3 + a^4*d^4*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^4 + (48*d^4*polylog(5, -e^(I*b*x + I*a)) - 48*d^4*polylog(5, e^(I*b*x + I*a)) - (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 24*I*a^2*b*c*d^3 - 8*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 24*I*a^2*b*c*d^3 - 8*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 2*((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*(a^2 - 2)*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*cos(b*x + a) - (-8*I*b^3*c^3*d + 24*I*a*b^2*c^2*d^2 - 24*I*a^2*b*c*d^3 - 8*I*(b*x + a)^3*d^4 + 8*I*a^3*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^2 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*a^2*d^4)*(b*x + a))*dilog(-e^(I*b*x + I*a)) - (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 24*I*a^2*b*c*d^3 + 8*I*(b*x + a)^3*d^4 - 8*I*a^3*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^2 + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*a^2*d^4)*(b*x + a))*dilog(e^(I*b*x + I*a)) - ((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + ((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (48*I*b*c*d^3 + 48*I*(b*x + a)*d^4 - 48*I*a*d^4)*polylog(4, -e^(I*b*x + I*a)) - (-48*I*b*c*d^3 - 48*I*(b*x + a)*d^4 + 48*I*a*d^4)*polylog(4, e^(I*b*x + I*a)) - 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, -e^(I*b*x + I*a)) + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, e^(I*b*x + I*a)) - 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*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 - 2)*d^4)*(b*x + a))*sin(b*x + a))/b^4)/b","B",0
99,1,919,0,0.516912," ","integrate((d*x+c)^3*cos(b*x+a)*cot(b*x+a),x, algorithm=""maxima"")","\frac{c^{3} {\left(2 \, \cos\left(b x + a\right) - \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(2 \, \cos\left(b x + a\right) - \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(2 \, \cos\left(b x + a\right) - \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(2 \, \cos\left(b x + a\right) - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\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) - 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(b x + 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} - 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)}) + 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)} \sin\left(b x + a\right)}{b^{3}}}{2 \, b}"," ",0,"1/2*(c^3*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 3*a*c^2*d*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + 3*a^2*c*d^2*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 - a^3*d^3*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/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) - 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(b*x + 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)) + (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)) + 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))*sin(b*x + a))/b^3)/b","B",0
100,1,507,0,0.469620," ","integrate((d*x+c)^2*cos(b*x+a)*cot(b*x+a),x, algorithm=""maxima"")","\frac{c^{2} {\left(2 \, \cos\left(b x + a\right) - \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(2 \, \cos\left(b x + a\right) - \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(2 \, \cos\left(b x + a\right) - \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 \, 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) - 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(b x + a\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) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(b x + a\right)}{b^{2}}}{2 \, b}"," ",0,"1/2*(c^2*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 2*a*c*d*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + a^2*d^2*(2*cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/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) - 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - 2*d^2)*cos(b*x + 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)) + (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) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(b*x + a))/b^2)/b","B",0
101,1,199,0,0.453896," ","integrate((d*x+c)*cos(b*x+a)*cot(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 \, {\left(b d x + b c\right)} \cos\left(b x + a\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 \, d \sin\left(b x + a\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*(b*d*x + b*c)*cos(b*x + a) - 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) + 2*d*sin(b*x + a))/b^2","B",0
102,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\frac{{\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 2 \, d \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} + 2 \, d \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} + {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{2 \, d}"," ",0,"1/2*((I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) + 2*d*integrate(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x + 2*(d*x + c)*cos(b*x + a) + c), x) + 2*d*integrate(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x - 2*(d*x + c)*cos(b*x + a) + c), x) + (exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))/d","F",0
103,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(i \, E_{2}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{2}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 2 \, {\left(d^{2} x + c d\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} + 2 \, {\left(d^{2} x + c d\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} + {\left(E_{2}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{2}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{2 \, {\left(d^{2} x + c d\right)}}"," ",0,"1/2*((I*exp_integral_e(2, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(2, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) + 2*(d^2*x + c*d)*integrate(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) + 2*(d^2*x + c*d)*integrate(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 - 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) + (exp_integral_e(2, (I*b*d*x + I*b*c)/d) + exp_integral_e(2, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))/(d^2*x + c*d)","F",0
104,0,0,0,0.000000," ","integrate((d*x+c)^m*cot(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cot\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*cot(b*x + a)^2, x)","F",0
105,1,3229,0,1.205276," ","integrate((d*x+c)^4*cot(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} c^{4} - \frac{4 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a c^{3} d}{b} + \frac{6 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{4 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a^{3} c d^{3}}{b^{3}} + \frac{{\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a^{4} d^{4}}{b^{4}} + \frac{2 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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^{3} 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(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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^{2} 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{6 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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} c 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 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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^{3} d^{4}}{{\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^{4}} - \frac{-i \, {\left(b x + a\right)}^{5} d^{4} + {\left(-5 i \, b c d^{3} + 5 i \, a d^{4}\right)} {\left(b x + a\right)}^{4} + {\left(-10 i \, b^{2} c^{2} d^{2} + 20 i \, a b c d^{3} - 10 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{3} - {\left(20 \, {\left(b x + a\right)}^{3} d^{4} + 60 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} - 20 \, {\left({\left(b x + a\right)}^{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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(20 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(60 i \, b c d^{3} - 60 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(60 i \, b^{2} c^{2} d^{2} - 120 i \, a b c d^{3} + 60 i \, a^{2} d^{4}\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(20 \, {\left(b x + a\right)}^{3} d^{4} + 60 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} - 20 \, {\left({\left(b x + a\right)}^{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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-20 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-60 i \, b c d^{3} + 60 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4}\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(i \, {\left(b x + a\right)}^{5} d^{4} + {\left(5 i \, b c d^{3} - 5 \, {\left(i \, a + 2\right)} d^{4}\right)} {\left(b x + a\right)}^{4} + {\left(10 i \, b^{2} c^{2} d^{2} - 20 \, {\left(i \, a + 2\right)} b c d^{3} + {\left(10 i \, a^{2} + 40 \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{3} - 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(60 \, b^{2} c^{2} d^{2} - 120 \, a b c d^{3} + 60 \, {\left(b x + a\right)}^{2} d^{4} + 60 \, a^{2} d^{4} + 120 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} - 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, {\left(b x + a\right)}^{2} d^{4} - 60 i \, a^{2} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\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(60 \, b^{2} c^{2} d^{2} - 120 \, a b c d^{3} + 60 \, {\left(b x + a\right)}^{2} d^{4} + 60 \, a^{2} d^{4} + 120 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} - 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, {\left(b x + a\right)}^{2} d^{4} - 60 i \, a^{2} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\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(10 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(30 i \, b c d^{3} - 30 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(30 i \, b^{2} c^{2} d^{2} - 60 i \, a b c d^{3} + 30 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(-10 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-30 i \, b c d^{3} + 30 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} - 30 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 10 \, {\left({\left(b x + a\right)}^{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)} \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(10 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(30 i \, b c d^{3} - 30 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(30 i \, b^{2} c^{2} d^{2} - 60 i \, a b c d^{3} + 30 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(-10 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-30 i \, b c d^{3} + 30 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} - 30 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 10 \, {\left({\left(b x + a\right)}^{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)} \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) + 120 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - d^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + 120 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - d^{4}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(120 i \, b c d^{3} + 120 i \, {\left(b x + a\right)} d^{4} - 120 i \, a d^{4} + {\left(-120 i \, b c d^{3} - 120 i \, {\left(b x + a\right)} d^{4} + 120 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + 120 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(120 i \, b c d^{3} + 120 i \, {\left(b x + a\right)} d^{4} - 120 i \, a d^{4} + {\left(-120 i \, b c d^{3} - 120 i \, {\left(b x + a\right)} d^{4} + 120 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + 120 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left({\left(b x + a\right)}^{5} d^{4} + {\left(5 \, b c d^{3} - {\left(5 \, a - 10 i\right)} d^{4}\right)} {\left(b x + a\right)}^{4} + {\left(10 \, b^{2} c^{2} d^{2} - {\left(20 \, a - 40 i\right)} b c d^{3} + 10 \, {\left(a^{2} - 4 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{3} - {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)}{-5 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 5 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) + 5 i \, b^{4}}}{b}"," ",0,"-((b*x + a + 1/tan(b*x + a))*c^4 - 4*(b*x + a + 1/tan(b*x + a))*a*c^3*d/b + 6*(b*x + a + 1/tan(b*x + a))*a^2*c^2*d^2/b^2 - 4*(b*x + a + 1/tan(b*x + a))*a^3*c*d^3/b^3 + (b*x + a + 1/tan(b*x + a))*a^4*d^4/b^4 + 2*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*c^3*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*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*a*c^2*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) + 6*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*a^2*c*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*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*a^3*d^4/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*b^4) - (-I*(b*x + a)^5*d^4 + (-5*I*b*c*d^3 + 5*I*a*d^4)*(b*x + a)^4 + (-10*I*b^2*c^2*d^2 + 20*I*a*b*c*d^3 - 10*I*a^2*d^4)*(b*x + a)^3 - (20*(b*x + a)^3*d^4 + 60*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) - 20*((b*x + 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))*cos(2*b*x + 2*a) - (20*I*(b*x + a)^3*d^4 + (60*I*b*c*d^3 - 60*I*a*d^4)*(b*x + a)^2 + (60*I*b^2*c^2*d^2 - 120*I*a*b*c*d^3 + 60*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (20*(b*x + a)^3*d^4 + 60*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) - 20*((b*x + 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))*cos(2*b*x + 2*a) + (-20*I*(b*x + a)^3*d^4 + (-60*I*b*c*d^3 + 60*I*a*d^4)*(b*x + a)^2 + (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (I*(b*x + a)^5*d^4 + (5*I*b*c*d^3 - 5*(I*a + 2)*d^4)*(b*x + a)^4 + (10*I*b^2*c^2*d^2 - 20*(I*a + 2)*b*c*d^3 + (10*I*a^2 + 40*a)*d^4)*(b*x + a)^3 - 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2)*cos(2*b*x + 2*a) + (60*b^2*c^2*d^2 - 120*a*b*c*d^3 + 60*(b*x + a)^2*d^4 + 60*a^2*d^4 + 120*(b*c*d^3 - a*d^4)*(b*x + a) - 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*(b*x + a)^2*d^4 - 60*I*a^2*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (60*b^2*c^2*d^2 - 120*a*b*c*d^3 + 60*(b*x + a)^2*d^4 + 60*a^2*d^4 + 120*(b*c*d^3 - a*d^4)*(b*x + a) - 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*(b*x + a)^2*d^4 - 60*I*a^2*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (10*I*(b*x + a)^3*d^4 + (30*I*b*c*d^3 - 30*I*a*d^4)*(b*x + a)^2 + (30*I*b^2*c^2*d^2 - 60*I*a*b*c*d^3 + 30*I*a^2*d^4)*(b*x + a) + (-10*I*(b*x + a)^3*d^4 + (-30*I*b*c*d^3 + 30*I*a*d^4)*(b*x + a)^2 + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 - 30*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 10*((b*x + 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (10*I*(b*x + a)^3*d^4 + (30*I*b*c*d^3 - 30*I*a*d^4)*(b*x + a)^2 + (30*I*b^2*c^2*d^2 - 60*I*a*b*c*d^3 + 30*I*a^2*d^4)*(b*x + a) + (-10*I*(b*x + a)^3*d^4 + (-30*I*b*c*d^3 + 30*I*a*d^4)*(b*x + a)^2 + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 - 30*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 10*((b*x + 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 120*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) - d^4)*polylog(4, -e^(I*b*x + I*a)) + 120*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) - d^4)*polylog(4, e^(I*b*x + I*a)) + (120*I*b*c*d^3 + 120*I*(b*x + a)*d^4 - 120*I*a*d^4 + (-120*I*b*c*d^3 - 120*I*(b*x + a)*d^4 + 120*I*a*d^4)*cos(2*b*x + 2*a) + 120*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) + (120*I*b*c*d^3 + 120*I*(b*x + a)*d^4 - 120*I*a*d^4 + (-120*I*b*c*d^3 - 120*I*(b*x + a)*d^4 + 120*I*a*d^4)*cos(2*b*x + 2*a) + 120*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) - ((b*x + a)^5*d^4 + (5*b*c*d^3 - (5*a - 10*I)*d^4)*(b*x + a)^4 + (10*b^2*c^2*d^2 - (20*a - 40*I)*b*c*d^3 + 10*(a^2 - 4*I*a)*d^4)*(b*x + a)^3 - (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-5*I*b^4*cos(2*b*x + 2*a) + 5*b^4*sin(2*b*x + 2*a) + 5*I*b^4))/b","B",0
106,1,1945,0,0.741509," ","integrate((d*x+c)^3*cot(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} c^{3} - \frac{6 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a c^{2} d}{b} + \frac{6 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a^{2} c d^{2}}{b^{2}} - \frac{2 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a^{3} d^{3}}{b^{3}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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 \, {\left(-i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-4 i \, b c d^{2} + 4 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} - {\left(12 \, {\left(b x + a\right)}^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 12 \, {\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(12 i \, {\left(b x + a\right)}^{2} 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)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(12 \, {\left(b x + a\right)}^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 12 \, {\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(-12 i \, {\left(b x + a\right)}^{2} 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)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(i \, {\left(b x + a\right)}^{4} d^{3} + {\left(4 i \, b c d^{2} - 4 \, {\left(i \, a + 2\right)} d^{3}\right)} {\left(b x + a\right)}^{3} - 24 \, {\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(24 \, b c d^{2} + 24 \, {\left(b x + a\right)} d^{3} - 24 \, a d^{3} - 24 \, {\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(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 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(24 \, b c d^{2} + 24 \, {\left(b x + a\right)} d^{3} - 24 \, a d^{3} - 24 \, {\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(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 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(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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \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(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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \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(-24 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 24 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 24 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(-24 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 24 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 24 i \, d^{3}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left({\left(b x + a\right)}^{4} d^{3} + {\left(4 \, b c d^{2} - {\left(4 \, a - 8 i\right)} d^{3}\right)} {\left(b x + a\right)}^{3} - {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-4 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) + 4 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(2*(b*x + a + 1/tan(b*x + a))*c^3 - 6*(b*x + a + 1/tan(b*x + a))*a*c^2*d/b + 6*(b*x + a + 1/tan(b*x + a))*a^2*c*d^2/b^2 - 2*(b*x + a + 1/tan(b*x + a))*a^3*d^3/b^3 + 3*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*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*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*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*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))*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*(-I*(b*x + a)^4*d^3 + (-4*I*b*c*d^2 + 4*I*a*d^3)*(b*x + a)^3 - (12*(b*x + a)^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) - 12*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (12*I*(b*x + a)^2*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (12*(b*x + a)^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) - 12*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-12*I*(b*x + a)^2*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (I*(b*x + a)^4*d^3 + (4*I*b*c*d^2 - 4*(I*a + 2)*d^3)*(b*x + a)^3 - 24*(b*c*d^2 - a*d^3)*(b*x + a)^2)*cos(2*b*x + 2*a) + (24*b*c*d^2 + 24*(b*x + a)*d^3 - 24*a*d^3 - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (24*b*c*d^2 + 24*(b*x + a)*d^3 - 24*a*d^3 - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 6*((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) + (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 6*((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) + (-24*I*d^3*cos(2*b*x + 2*a) + 24*d^3*sin(2*b*x + 2*a) + 24*I*d^3)*polylog(3, -e^(I*b*x + I*a)) + (-24*I*d^3*cos(2*b*x + 2*a) + 24*d^3*sin(2*b*x + 2*a) + 24*I*d^3)*polylog(3, e^(I*b*x + I*a)) - ((b*x + a)^4*d^3 + (4*b*c*d^2 - (4*a - 8*I)*d^3)*(b*x + a)^3 - (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-4*I*b^3*cos(2*b*x + 2*a) + 4*b^3*sin(2*b*x + 2*a) + 4*I*b^3))/b","B",0
107,1,646,0,0.741559," ","integrate((d*x+c)^2*cot(b*x+a)^2,x, algorithm=""maxima"")","\frac{-i \, b^{3} d^{2} x^{3} - 3 i \, b^{3} c d x^{2} - 3 i \, b^{3} c^{2} x - 6 \, b^{2} c^{2} - {\left(6 \, b d^{2} x + 6 \, b c d - 6 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(6 i \, b d^{2} x + 6 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(6 \, b c d \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b c d \sin\left(2 \, b x + 2 \, a\right) - 6 \, b c d\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) - {\left(6 \, b d^{2} x \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b d^{2} x \sin\left(2 \, b x + 2 \, a\right) - 6 \, b d^{2} x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(i \, b^{3} d^{2} x^{3} + {\left(3 i \, b^{3} c d - 6 \, b^{2} d^{2}\right)} x^{2} - 3 \, {\left(-i \, b^{3} c^{2} + 4 \, b^{2} c d\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 6 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(3 i \, b d^{2} x + 3 i \, b c d + {\left(-3 i \, b d^{2} x - 3 i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\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(3 i \, b d^{2} x + 3 i \, b c d + {\left(-3 i \, b d^{2} x - 3 i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\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(b^{3} d^{2} x^{3} + 3 \, {\left(b^{3} c d + 2 i \, b^{2} d^{2}\right)} x^{2} + {\left(3 \, b^{3} c^{2} + 12 i \, b^{2} c d\right)} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{-3 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 3 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) + 3 i \, b^{3}}"," ",0,"(-I*b^3*d^2*x^3 - 3*I*b^3*c*d*x^2 - 3*I*b^3*c^2*x - 6*b^2*c^2 - (6*b*d^2*x + 6*b*c*d - 6*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a) - (6*I*b*d^2*x + 6*I*b*c*d)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*b*c*d*cos(2*b*x + 2*a) + 6*I*b*c*d*sin(2*b*x + 2*a) - 6*b*c*d)*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*b*d^2*x*cos(2*b*x + 2*a) + 6*I*b*d^2*x*sin(2*b*x + 2*a) - 6*b*d^2*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (I*b^3*d^2*x^3 + (3*I*b^3*c*d - 6*b^2*d^2)*x^2 - 3*(-I*b^3*c^2 + 4*b^2*c*d)*x)*cos(2*b*x + 2*a) - 6*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) - d^2)*dilog(-e^(I*b*x + I*a)) - 6*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) - d^2)*dilog(e^(I*b*x + I*a)) + (3*I*b*d^2*x + 3*I*b*c*d + (-3*I*b*d^2*x - 3*I*b*c*d)*cos(2*b*x + 2*a) + 3*(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) + (3*I*b*d^2*x + 3*I*b*c*d + (-3*I*b*d^2*x - 3*I*b*c*d)*cos(2*b*x + 2*a) + 3*(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) - (b^3*d^2*x^3 + 3*(b^3*c*d + 2*I*b^2*d^2)*x^2 + (3*b^3*c^2 + 12*I*b^2*c*d)*x)*sin(2*b*x + 2*a))/(-3*I*b^3*cos(2*b*x + 2*a) + 3*b^3*sin(2*b*x + 2*a) + 3*I*b^3)","B",0
108,1,292,0,0.584091," ","integrate((d*x+c)*cot(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} c - \frac{2 \, {\left(b x + a + \frac{1}{\tan\left(b x + a\right)}\right)} a d}{b} + \frac{{\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \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}}{2 \, b}"," ",0,"-1/2*(2*(b*x + a + 1/tan(b*x + a))*c - 2*(b*x + a + 1/tan(b*x + a))*a*d/b + ((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 - 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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))/b","B",0
109,0,0,0,0.000000," ","integrate(cot(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{-{\left(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)\right)} \log\left(d x + c\right) - 2 \, d \sin\left(2 \, b x + 2 \, a\right) + \frac{{\left(b d^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{3} x + b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\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^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{3} x + b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\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}}{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)}"," ",0,"((b*d^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a)^2 + (b*d^3*x + b*c*d^2)*sin(2*b*x + 2*a)^2 - 2*(b*d^3*x + b*c*d^2)*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^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a)^2 + (b*d^3*x + b*c*d^2)*sin(2*b*x + 2*a)^2 - 2*(b*d^3*x + b*c*d^2)*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*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))*log(d*x + c) - 2*d*sin(2*b*x + 2*a))/(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))","F",0
110,-1,0,0,0.000000," ","integrate(cot(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,0,0,0,0.000000," ","integrate((d*x+c)^m*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cot\left(b x + a\right)^{2} \csc\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cot(b*x + a)^2*csc(b*x + a), x)","F",0
112,1,6952,0,5.491726," ","integrate((d*x+c)^4*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""maxima"")","\frac{c^{4} {\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{4 \, a c^{3} 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{6 \, a^{2} c^{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 \, a^{3} c 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{a^{4} d^{4} {\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^{4}} + \frac{4 \, {\left({\left(2 \, {\left(b x + a\right)}^{4} d^{4} - 24 \, b^{2} c^{2} d^{2} + 48 \, a b c d^{3} - 24 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} - 24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, a^{2} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + {\left(12 i \, a^{2} - 24 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + {\left(24 i \, a^{2} - 48 i\right)} b c d^{3} + {\left(-8 i \, a^{3} + 48 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{4} d^{4} + 48 i \, b^{2} c^{2} d^{2} - 96 i \, a b c d^{3} + 48 i \, a^{2} d^{4} + {\left(-16 i \, b c d^{3} + 16 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} + {\left(-24 i \, a^{2} + 48 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-16 i \, b^{3} c^{3} d + 48 i \, a b^{2} c^{2} d^{2} + {\left(-48 i \, a^{2} + 96 i\right)} b c d^{3} + {\left(16 i \, a^{3} - 96 i \, a\right)} d^{4}\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(24 \, b^{2} c^{2} d^{2} - 48 \, a b c d^{3} + 24 \, a^{2} d^{4} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 48 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, a^{2} d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-48 i \, b^{2} c^{2} d^{2} + 96 i \, a b c d^{3} - 48 i \, a^{2} d^{4}\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)}^{4} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + {\left(12 i \, a^{2} - 24 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + {\left(24 i \, a^{2} - 48 i\right)} b c d^{3} + {\left(-8 i \, a^{3} + 48 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-16 i \, b c d^{3} + 16 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} + {\left(-24 i \, a^{2} + 48 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-16 i \, b^{3} c^{3} d + 48 i \, a b^{2} c^{2} d^{2} + {\left(-48 i \, a^{2} + 96 i\right)} b c d^{3} + {\left(16 i \, a^{3} - 96 i \, a\right)} d^{4}\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)}^{4} d^{4} - 16 \, b^{3} c^{3} d + 48 \, a b^{2} c^{2} d^{2} - 48 \, a^{2} b c d^{3} + 16 \, a^{3} d^{4} - 16 \, {\left(i \, b c d^{3} + {\left(-i \, a + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-24 i \, b^{2} c^{2} d^{2} - 48 \, {\left(-i \, a + 1\right)} b c d^{3} + {\left(-24 i \, a^{2} + 48 \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-16 i \, b^{3} c^{3} d - 48 \, {\left(-i \, a + 1\right)} b^{2} c^{2} d^{2} + {\left(-48 i \, a^{2} + 96 \, a\right)} b c d^{3} + {\left(16 i \, a^{3} - 48 \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(-4 i \, {\left(b x + a\right)}^{4} d^{4} + 16 \, b^{3} c^{3} d - 48 \, a b^{2} c^{2} d^{2} + 48 \, a^{2} b c d^{3} - 16 \, a^{3} d^{4} + {\left(-16 i \, b c d^{3} - 16 \, {\left(-i \, a - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-24 i \, b^{2} c^{2} d^{2} - 48 \, {\left(-i \, a - 1\right)} b c d^{3} + {\left(-24 i \, a^{2} - 48 \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-16 i \, b^{3} c^{3} d - 48 \, {\left(-i \, a - 1\right)} b^{2} c^{2} d^{2} + {\left(-48 i \, a^{2} - 96 \, a\right)} b c d^{3} + {\left(16 i \, a^{3} + 48 \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) - {\left(8 \, b^{3} c^{3} d - 24 \, a b^{2} c^{2} d^{2} + 8 \, {\left(b x + a\right)}^{3} d^{4} + 24 \, {\left(a^{2} - 2\right)} b c d^{3} - 8 \, {\left(a^{3} - 6 \, a\right)} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)} + 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} 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} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} 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} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-8 i \, b^{3} c^{3} d + 24 i \, a b^{2} c^{2} d^{2} - 8 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-24 i \, a^{2} + 48 i\right)} b c d^{3} + {\left(8 i \, a^{3} - 48 i \, a\right)} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} + {\left(-24 i \, a^{2} + 48 i\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(16 i \, b^{3} c^{3} d - 48 i \, a b^{2} c^{2} d^{2} + 16 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(48 i \, a^{2} - 96 i\right)} b c d^{3} + {\left(-16 i \, a^{3} + 96 i \, a\right)} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(48 i \, b^{2} c^{2} d^{2} - 96 i \, a b c d^{3} + {\left(48 i \, a^{2} - 96 i\right)} d^{4}\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(8 \, b^{3} c^{3} d - 24 \, a b^{2} c^{2} d^{2} + 8 \, {\left(b x + a\right)}^{3} d^{4} + 24 \, {\left(a^{2} - 2\right)} b c d^{3} - 8 \, {\left(a^{3} - 6 \, a\right)} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)} + 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} 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} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 16 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} 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} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 8 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(24 i \, a^{2} - 48 i\right)} b c d^{3} + {\left(-8 i \, a^{3} + 48 i \, a\right)} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + {\left(24 i \, a^{2} - 48 i\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-16 i \, b^{3} c^{3} d + 48 i \, a b^{2} c^{2} d^{2} - 16 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-48 i \, a^{2} + 96 i\right)} b c d^{3} + {\left(16 i \, a^{3} - 96 i \, a\right)} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-48 i \, b^{2} c^{2} d^{2} + 96 i \, a b c d^{3} + {\left(-48 i \, a^{2} + 96 i\right)} d^{4}\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)}^{4} d^{4} + 12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4} + {\left(-4 i \, b c d^{3} + 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} + {\left(-6 i \, a^{2} + 12 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-4 i \, b^{3} c^{3} d + 12 i \, a b^{2} c^{2} d^{2} + {\left(-12 i \, a^{2} + 24 i\right)} b c d^{3} + {\left(4 i \, a^{3} - 24 i \, a\right)} d^{4}\right)} {\left(b x + a\right)} + {\left(-i \, {\left(b x + a\right)}^{4} d^{4} + 12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4} + {\left(-4 i \, b c d^{3} + 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} + {\left(-6 i \, a^{2} + 12 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-4 i \, b^{3} c^{3} d + 12 i \, a b^{2} c^{2} d^{2} + {\left(-12 i \, a^{2} + 24 i\right)} b c d^{3} + {\left(4 i \, a^{3} - 24 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} - 24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, a^{2} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + {\left(12 i \, a^{2} - 24 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + {\left(24 i \, a^{2} - 48 i\right)} b c d^{3} + {\left(-8 i \, a^{3} + 48 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 2 \, {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\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)}^{4} d^{4} - 12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, a^{2} d^{4} + {\left(4 i \, b c d^{3} - 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + {\left(6 i \, a^{2} - 12 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(4 i \, b^{3} c^{3} d - 12 i \, a b^{2} c^{2} d^{2} + {\left(12 i \, a^{2} - 24 i\right)} b c d^{3} + {\left(-4 i \, a^{3} + 24 i \, a\right)} d^{4}\right)} {\left(b x + a\right)} + {\left(i \, {\left(b x + a\right)}^{4} d^{4} - 12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, a^{2} d^{4} + {\left(4 i \, b c d^{3} - 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + {\left(6 i \, a^{2} - 12 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(4 i \, b^{3} c^{3} d - 12 i \, a b^{2} c^{2} d^{2} + {\left(12 i \, a^{2} - 24 i\right)} b c d^{3} + {\left(-4 i \, a^{3} + 24 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-2 i \, {\left(b x + a\right)}^{4} d^{4} + 24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, a^{2} d^{4} + {\left(-8 i \, b c d^{3} + 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} + {\left(-12 i \, a^{2} + 24 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-8 i \, b^{3} c^{3} d + 24 i \, a b^{2} c^{2} d^{2} + {\left(-24 i \, a^{2} + 48 i\right)} b c d^{3} + {\left(8 i \, a^{3} - 48 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, a b c d^{3} - 12 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\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(48 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) - 96 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) - 48 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) + 96 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + 48 i \, d^{4}\right)} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) + {\left(-48 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) + 96 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 48 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) - 96 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 48 i \, d^{4}\right)} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) + {\left(48 \, b c d^{3} + 48 \, {\left(b x + a\right)} d^{4} - 48 \, a d^{4} + 48 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 96 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(48 i \, b c d^{3} + 48 i \, {\left(b x + a\right)} d^{4} - 48 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-96 i \, b c d^{3} - 96 i \, {\left(b x + a\right)} d^{4} + 96 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(48 \, b c d^{3} + 48 \, {\left(b x + a\right)} d^{4} - 48 \, a d^{4} + 48 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 96 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-48 i \, b c d^{3} - 48 i \, {\left(b x + a\right)} d^{4} + 48 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(96 i \, b c d^{3} + 96 i \, {\left(b x + a\right)} d^{4} - 96 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-24 i \, a^{2} + 48 i\right)} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-24 i \, a^{2} + 48 i\right)} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(48 i \, b^{2} c^{2} d^{2} - 96 i \, a b c d^{3} + 48 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(48 i \, a^{2} - 96 i\right)} d^{4} + {\left(96 i \, b c d^{3} - 96 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 2\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 48 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 2\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(24 i \, a^{2} - 48 i\right)} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(24 i \, a^{2} - 48 i\right)} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-48 i \, b^{2} c^{2} d^{2} + 96 i \, a b c d^{3} - 48 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-48 i \, a^{2} + 96 i\right)} d^{4} + {\left(-96 i \, b c d^{3} + 96 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 2\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 48 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 2\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\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)}^{4} d^{4} - 16 i \, b^{3} c^{3} d + 48 i \, a b^{2} c^{2} d^{2} - 48 i \, a^{2} b c d^{3} + 16 i \, a^{3} d^{4} + {\left(16 \, b c d^{3} - {\left(16 \, a + 16 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(24 \, b^{2} c^{2} d^{2} - {\left(48 \, a + 48 i\right)} b c d^{3} + 24 \, {\left(a^{2} + 2 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(16 \, b^{3} c^{3} d - {\left(48 \, a + 48 i\right)} b^{2} c^{2} d^{2} + 48 \, {\left(a^{2} + 2 i \, a\right)} b c d^{3} - 16 \, {\left(a^{3} + 3 i \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(4 \, {\left(b x + a\right)}^{4} d^{4} + 16 i \, b^{3} c^{3} d - 48 i \, a b^{2} c^{2} d^{2} + 48 i \, a^{2} b c d^{3} - 16 i \, a^{3} d^{4} + {\left(16 \, b c d^{3} - {\left(16 \, a - 16 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(24 \, b^{2} c^{2} d^{2} - {\left(48 \, a - 48 i\right)} b c d^{3} + 24 \, {\left(a^{2} - 2 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(16 \, b^{3} c^{3} d - {\left(48 \, a - 48 i\right)} b^{2} c^{2} d^{2} + 48 \, {\left(a^{2} - 2 i \, a\right)} b c d^{3} - 16 \, {\left(a^{3} - 3 i \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)}}{-4 i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) + 8 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{4} \sin\left(4 \, b x + 4 \, a\right) - 8 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{4}}}{4 \, b}"," ",0,"1/4*(c^4*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) + log(cos(b*x + a) + 1) - log(cos(b*x + a) - 1)) - 4*a*c^3*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 + 6*a^2*c^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*a^3*c*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 + a^4*d^4*(2*cos(b*x + a)/(cos(b*x + a)^2 - 1) + log(cos(b*x + a) + 1) - log(cos(b*x + a) - 1))/b^4 + 4*((2*(b*x + a)^4*d^4 - 24*b^2*c^2*d^2 + 48*a*b*c*d^3 - 24*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a) + 2*((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 4*((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^4*d^4 - 24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*a^2*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + (12*I*a^2 - 24*I)*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + (24*I*a^2 - 48*I)*b*c*d^3 + (-8*I*a^3 + 48*I*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (-4*I*(b*x + a)^4*d^4 + 48*I*b^2*c^2*d^2 - 96*I*a*b*c*d^3 + 48*I*a^2*d^4 + (-16*I*b*c*d^3 + 16*I*a*d^4)*(b*x + a)^3 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 + (-24*I*a^2 + 48*I)*d^4)*(b*x + a)^2 + (-16*I*b^3*c^3*d + 48*I*a*b^2*c^2*d^2 + (-48*I*a^2 + 96*I)*b*c*d^3 + (16*I*a^3 - 96*I*a)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (24*b^2*c^2*d^2 - 48*a*b*c*d^3 + 24*a^2*d^4 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(4*b*x + 4*a) - 48*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(2*b*x + 2*a) + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*a^2*d^4)*sin(4*b*x + 4*a) + (-48*I*b^2*c^2*d^2 + 96*I*a*b*c*d^3 - 48*I*a^2*d^4)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*(b*x + a)^4*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a) + 2*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 4*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + (12*I*a^2 - 24*I)*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + (24*I*a^2 - 48*I)*b*c*d^3 + (-8*I*a^3 + 48*I*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (-4*I*(b*x + a)^4*d^4 + (-16*I*b*c*d^3 + 16*I*a*d^4)*(b*x + a)^3 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 + (-24*I*a^2 + 48*I)*d^4)*(b*x + a)^2 + (-16*I*b^3*c^3*d + 48*I*a*b^2*c^2*d^2 + (-48*I*a^2 + 96*I)*b*c*d^3 + (16*I*a^3 - 96*I*a)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-4*I*(b*x + a)^4*d^4 - 16*b^3*c^3*d + 48*a*b^2*c^2*d^2 - 48*a^2*b*c*d^3 + 16*a^3*d^4 - 16*(I*b*c*d^3 + (-I*a + 1)*d^4)*(b*x + a)^3 + (-24*I*b^2*c^2*d^2 - 48*(-I*a + 1)*b*c*d^3 + (-24*I*a^2 + 48*a)*d^4)*(b*x + a)^2 + (-16*I*b^3*c^3*d - 48*(-I*a + 1)*b^2*c^2*d^2 + (-48*I*a^2 + 96*a)*b*c*d^3 + (16*I*a^3 - 48*a^2)*d^4)*(b*x + a))*cos(3*b*x + 3*a) + (-4*I*(b*x + a)^4*d^4 + 16*b^3*c^3*d - 48*a*b^2*c^2*d^2 + 48*a^2*b*c*d^3 - 16*a^3*d^4 + (-16*I*b*c*d^3 - 16*(-I*a - 1)*d^4)*(b*x + a)^3 + (-24*I*b^2*c^2*d^2 - 48*(-I*a - 1)*b*c*d^3 + (-24*I*a^2 - 48*a)*d^4)*(b*x + a)^2 + (-16*I*b^3*c^3*d - 48*(-I*a - 1)*b^2*c^2*d^2 + (-48*I*a^2 - 96*a)*b*c*d^3 + (16*I*a^3 + 48*a^2)*d^4)*(b*x + a))*cos(b*x + a) - (8*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 8*(b*x + a)^3*d^4 + 24*(a^2 - 2)*b*c*d^3 - 8*(a^3 - 6*a)*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a) + 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*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 - 2)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 16*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*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 - 2)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-8*I*b^3*c^3*d + 24*I*a*b^2*c^2*d^2 - 8*I*(b*x + a)^3*d^4 + (-24*I*a^2 + 48*I)*b*c*d^3 + (8*I*a^3 - 48*I*a)*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^2 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 + (-24*I*a^2 + 48*I)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (16*I*b^3*c^3*d - 48*I*a*b^2*c^2*d^2 + 16*I*(b*x + a)^3*d^4 + (48*I*a^2 - 96*I)*b*c*d^3 + (-16*I*a^3 + 96*I*a)*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a)^2 + (48*I*b^2*c^2*d^2 - 96*I*a*b*c*d^3 + (48*I*a^2 - 96*I)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (8*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 8*(b*x + a)^3*d^4 + 24*(a^2 - 2)*b*c*d^3 - 8*(a^3 - 6*a)*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a) + 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*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 - 2)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 16*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*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 - 2)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 8*I*(b*x + a)^3*d^4 + (24*I*a^2 - 48*I)*b*c*d^3 + (-8*I*a^3 + 48*I*a)*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^2 + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + (24*I*a^2 - 48*I)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (-16*I*b^3*c^3*d + 48*I*a*b^2*c^2*d^2 - 16*I*(b*x + a)^3*d^4 + (-48*I*a^2 + 96*I)*b*c*d^3 + (16*I*a^3 - 96*I*a)*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a)^2 + (-48*I*b^2*c^2*d^2 + 96*I*a*b*c*d^3 + (-48*I*a^2 + 96*I)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (-I*(b*x + a)^4*d^4 + 12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4 + (-4*I*b*c*d^3 + 4*I*a*d^4)*(b*x + a)^3 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 + (-6*I*a^2 + 12*I)*d^4)*(b*x + a)^2 + (-4*I*b^3*c^3*d + 12*I*a*b^2*c^2*d^2 + (-12*I*a^2 + 24*I)*b*c*d^3 + (4*I*a^3 - 24*I*a)*d^4)*(b*x + a) + (-I*(b*x + a)^4*d^4 + 12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4 + (-4*I*b*c*d^3 + 4*I*a*d^4)*(b*x + a)^3 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 + (-6*I*a^2 + 12*I)*d^4)*(b*x + a)^2 + (-4*I*b^3*c^3*d + 12*I*a*b^2*c^2*d^2 + (-12*I*a^2 + 24*I)*b*c*d^3 + (4*I*a^3 - 24*I*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (2*I*(b*x + a)^4*d^4 - 24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*a^2*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + (12*I*a^2 - 24*I)*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + (24*I*a^2 - 48*I)*b*c*d^3 + (-8*I*a^3 + 48*I*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 2*((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(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)^4*d^4 - 12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*a^2*d^4 + (4*I*b*c*d^3 - 4*I*a*d^4)*(b*x + a)^3 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + (6*I*a^2 - 12*I)*d^4)*(b*x + a)^2 + (4*I*b^3*c^3*d - 12*I*a*b^2*c^2*d^2 + (12*I*a^2 - 24*I)*b*c*d^3 + (-4*I*a^3 + 24*I*a)*d^4)*(b*x + a) + (I*(b*x + a)^4*d^4 - 12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*a^2*d^4 + (4*I*b*c*d^3 - 4*I*a*d^4)*(b*x + a)^3 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + (6*I*a^2 - 12*I)*d^4)*(b*x + a)^2 + (4*I*b^3*c^3*d - 12*I*a*b^2*c^2*d^2 + (12*I*a^2 - 24*I)*b*c*d^3 + (-4*I*a^3 + 24*I*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (-2*I*(b*x + a)^4*d^4 + 24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*a^2*d^4 + (-8*I*b*c*d^3 + 8*I*a*d^4)*(b*x + a)^3 + (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 + (-12*I*a^2 + 24*I)*d^4)*(b*x + a)^2 + (-8*I*b^3*c^3*d + 24*I*a*b^2*c^2*d^2 + (-24*I*a^2 + 48*I)*b*c*d^3 + (8*I*a^3 - 48*I*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - ((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + 2*((b*x + a)^4*d^4 - 12*b^2*c^2*d^2 + 24*a*b*c*d^3 - 12*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(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) + (48*I*d^4*cos(4*b*x + 4*a) - 96*I*d^4*cos(2*b*x + 2*a) - 48*d^4*sin(4*b*x + 4*a) + 96*d^4*sin(2*b*x + 2*a) + 48*I*d^4)*polylog(5, -e^(I*b*x + I*a)) + (-48*I*d^4*cos(4*b*x + 4*a) + 96*I*d^4*cos(2*b*x + 2*a) + 48*d^4*sin(4*b*x + 4*a) - 96*d^4*sin(2*b*x + 2*a) - 48*I*d^4)*polylog(5, e^(I*b*x + I*a)) + (48*b*c*d^3 + 48*(b*x + a)*d^4 - 48*a*d^4 + 48*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) - 96*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) + (48*I*b*c*d^3 + 48*I*(b*x + a)*d^4 - 48*I*a*d^4)*sin(4*b*x + 4*a) + (-96*I*b*c*d^3 - 96*I*(b*x + a)*d^4 + 96*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, -e^(I*b*x + I*a)) - (48*b*c*d^3 + 48*(b*x + a)*d^4 - 48*a*d^4 + 48*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) - 96*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-48*I*b*c*d^3 - 48*I*(b*x + a)*d^4 + 48*I*a*d^4)*sin(4*b*x + 4*a) - (96*I*b*c*d^3 + 96*I*(b*x + a)*d^4 - 96*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, e^(I*b*x + I*a)) + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*(b*x + a)^2*d^4 + (-24*I*a^2 + 48*I)*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a) + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*(b*x + a)^2*d^4 + (-24*I*a^2 + 48*I)*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (48*I*b^2*c^2*d^2 - 96*I*a*b*c*d^3 + 48*I*(b*x + a)^2*d^4 + (48*I*a^2 - 96*I)*d^4 + (96*I*b*c*d^3 - 96*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 2)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 48*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 2)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*(b*x + a)^2*d^4 + (24*I*a^2 - 48*I)*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a) + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*(b*x + a)^2*d^4 + (24*I*a^2 - 48*I)*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (-48*I*b^2*c^2*d^2 + 96*I*a*b*c*d^3 - 48*I*(b*x + a)^2*d^4 + (-48*I*a^2 + 96*I)*d^4 + (-96*I*b*c*d^3 + 96*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 2)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) + 48*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 2)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) + (4*(b*x + a)^4*d^4 - 16*I*b^3*c^3*d + 48*I*a*b^2*c^2*d^2 - 48*I*a^2*b*c*d^3 + 16*I*a^3*d^4 + (16*b*c*d^3 - (16*a + 16*I)*d^4)*(b*x + a)^3 + (24*b^2*c^2*d^2 - (48*a + 48*I)*b*c*d^3 + 24*(a^2 + 2*I*a)*d^4)*(b*x + a)^2 + (16*b^3*c^3*d - (48*a + 48*I)*b^2*c^2*d^2 + 48*(a^2 + 2*I*a)*b*c*d^3 - 16*(a^3 + 3*I*a^2)*d^4)*(b*x + a))*sin(3*b*x + 3*a) + (4*(b*x + a)^4*d^4 + 16*I*b^3*c^3*d - 48*I*a*b^2*c^2*d^2 + 48*I*a^2*b*c*d^3 - 16*I*a^3*d^4 + (16*b*c*d^3 - (16*a - 16*I)*d^4)*(b*x + a)^3 + (24*b^2*c^2*d^2 - (48*a - 48*I)*b*c*d^3 + 24*(a^2 - 2*I*a)*d^4)*(b*x + a)^2 + (16*b^3*c^3*d - (48*a - 48*I)*b^2*c^2*d^2 + 48*(a^2 - 2*I*a)*b*c*d^3 - 16*(a^3 - 3*I*a^2)*d^4)*(b*x + a))*sin(b*x + a))/(-4*I*b^4*cos(4*b*x + 4*a) + 8*I*b^4*cos(2*b*x + 2*a) + 4*b^4*sin(4*b*x + 4*a) - 8*b^4*sin(2*b*x + 2*a) - 4*I*b^4))/b","B",0
113,1,3872,0,1.919932," ","integrate((d*x+c)^3*cot(b*x+a)^2*csc(b*x+a),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} - 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(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} + {\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(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 + (-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 - 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(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
114,1,1932,0,0.809212," ","integrate((d*x+c)^2*cot(b*x+a)^2*csc(b*x+a),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) - 4 \, {\left(i \, {\left(b x + a\right)}^{2} d^{2} + 2 \, b c d - 2 \, a d^{2} + 2 \, {\left(i \, b c d + {\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} + {\left(-8 i \, b c d - 8 \, {\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 + 2*b*c*d - 2*a*d^2 + 2*(I*b*c*d + (-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 - 8*(-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
115,1,770,0,0.536305," ","integrate((d*x+c)*cot(b*x+a)^2*csc(b*x+a),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) + {\left(4 \, b d x + 4 \, b c - 4 i \, d\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(4 \, b d x + 4 \, b c + 4 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 + 4*b*c - 4*I*d)*sin(3*b*x + 3*a) + (4*b*d*x + 4*b*c + 4*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
116,0,0,0,0.000000," ","integrate(cot(b*x+a)^2*csc(b*x+a)/(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
117,0,0,0,0.000000," ","integrate(cot(b*x+a)^2*csc(b*x+a)/(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
118,1,543,0,0.532783," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a),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) + 2160 \, {\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) - 216 \, {\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(405 i - 405\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(405 i + 405\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(405 i + 405\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(405 i - 405\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) + 2160*(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) - 216*(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)) + ((405*I - 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (405*I + 405)*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)) + (-(405*I + 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (405*I - 405)*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
119,1,499,0,0.510108," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a),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{144 \, {\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) - 216 \, \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(27 i + 27\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(27 i - 27\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(27 i - 27\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(27 i + 27\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 + 144*(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) - 216*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)) - (-(27*I + 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (27*I - 27)*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)) - ((27*I - 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (27*I + 27)*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
120,1,422,0,0.499029," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a),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{72 \, \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(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) + \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)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\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) - \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)\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 + 72*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)) + ((9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (9*I + 9)*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)) + (-(9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (9*I - 9)*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
121,1,422,0,0.497190," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a),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{72 \, \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(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) + \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)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\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) - \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)\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 + 72*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)) + ((9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (9*I + 9)*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)) + (-(9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (9*I - 9)*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
122,1,499,0,0.529647," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a),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{144 \, {\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) - 216 \, \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(27 i + 27\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(27 i - 27\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(27 i - 27\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(27 i + 27\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 + 144*(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) - 216*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)) - (-(27*I + 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (27*I - 27)*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)) - ((27*I - 27)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (27*I + 27)*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
123,1,543,0,0.521253," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a),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) + 2160 \, {\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) - 216 \, {\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(405 i - 405\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(405 i + 405\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(405 i + 405\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(405 i - 405\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) + 2160*(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) - 216*(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)) + ((405*I - 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (405*I + 405)*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)) + (-(405*I + 405)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (405*I - 405)*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
124,1,285,0,0.472570," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{4096 \, \sqrt{2} {\left(d x + c\right)}^{\frac{7}{2}} b^{4}}{d} - 2240 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(105 i + 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(105 i - 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(-\left(105 i - 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(105 i + 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - 56 \, {\left(64 \, \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{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)\right)}}{229376 \, b^{4}}"," ",0,"1/229376*sqrt(2)*(4096*sqrt(2)*(d*x + c)^(7/2)*b^4/d - 2240*sqrt(2)*(d*x + c)^(3/2)*b^2*d*cos(4*((d*x + c)*b - b*c + a*d)/d) - ((105*I + 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (105*I - 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - (-(105*I - 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (105*I + 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) - 56*(64*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*sin(4*((d*x + c)*b - b*c + a*d)/d))/b^4","C",0
125,1,264,0,0.479793," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{512 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3}}{d} - 320 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \sin\left(\frac{4 \, {\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{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(15 i - 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(15 i + 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(-\left(15 i + 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(15 i - 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{20480 \, b^{3}}"," ",0,"1/20480*sqrt(2)*(512*sqrt(2)*(d*x + c)^(5/2)*b^3/d - 320*sqrt(2)*(d*x + c)^(3/2)*b^2*sin(4*((d*x + c)*b - b*c + a*d)/d) - 120*sqrt(2)*sqrt(d*x + c)*b*d*cos(4*((d*x + c)*b - b*c + a*d)/d) - ((15*I - 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (15*I + 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - (-(15*I + 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (15*I - 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)))/b^3","C",0
126,1,219,0,0.462434," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{64 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2}}{d} - 24 \, \sqrt{2} \sqrt{d x + c} b \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(3 i + 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(3 i - 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(3 i - 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(3 i + 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{1536 \, b^{2}}"," ",0,"1/1536*sqrt(2)*(64*sqrt(2)*(d*x + c)^(3/2)*b^2/d - 24*sqrt(2)*sqrt(d*x + c)*b*sin(4*((d*x + c)*b - b*c + a*d)/d) - (-(3*I + 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (3*I - 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - ((3*I - 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (3*I + 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)))/b^2","C",0
127,1,219,0,0.461586," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{64 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2}}{d} - 24 \, \sqrt{2} \sqrt{d x + c} b \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(3 i + 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(3 i - 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(3 i - 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(3 i + 3\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{1536 \, b^{2}}"," ",0,"1/1536*sqrt(2)*(64*sqrt(2)*(d*x + c)^(3/2)*b^2/d - 24*sqrt(2)*sqrt(d*x + c)*b*sin(4*((d*x + c)*b - b*c + a*d)/d) - (-(3*I + 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (3*I - 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - ((3*I - 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (3*I + 3)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)))/b^2","C",0
128,1,264,0,0.781667," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{512 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3}}{d} - 320 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \sin\left(\frac{4 \, {\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{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(15 i - 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(15 i + 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(-\left(15 i + 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(15 i - 15\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{20480 \, b^{3}}"," ",0,"1/20480*sqrt(2)*(512*sqrt(2)*(d*x + c)^(5/2)*b^3/d - 320*sqrt(2)*(d*x + c)^(3/2)*b^2*sin(4*((d*x + c)*b - b*c + a*d)/d) - 120*sqrt(2)*sqrt(d*x + c)*b*d*cos(4*((d*x + c)*b - b*c + a*d)/d) - ((15*I - 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (15*I + 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - (-(15*I + 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (15*I - 15)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)))/b^3","C",0
129,1,285,0,2.022235," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{4096 \, \sqrt{2} {\left(d x + c\right)}^{\frac{7}{2}} b^{4}}{d} - 2240 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(\left(105 i + 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(105 i - 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(-\left(105 i - 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(105 i + 105\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - 56 \, {\left(64 \, \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{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)\right)}}{229376 \, b^{4}}"," ",0,"1/229376*sqrt(2)*(4096*sqrt(2)*(d*x + c)^(7/2)*b^4/d - 2240*sqrt(2)*(d*x + c)^(3/2)*b^2*d*cos(4*((d*x + c)*b - b*c + a*d)/d) - ((105*I + 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (105*I - 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - (-(105*I - 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (105*I + 105)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) - 56*(64*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*sin(4*((d*x + c)*b - b*c + a*d)/d))/b^4","C",0
130,1,820,0,0.902413," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{10800 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{30000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{540000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} - 1080 \, {\left(\frac{20 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 3 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 3000 \, {\left(\frac{12 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 5 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 54000 \, {\left(\frac{4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 15 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(-\left(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(202500 i - 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(202500 i + 202500\right) \, \sqrt{\pi} b^{2} 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(202500 i + 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(202500 i - 202500\right) \, \sqrt{\pi} b^{2} 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(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{3456000 \, b^{6}}"," ",0,"-1/3456000*sqrt(2)*(10800*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(5*((d*x + c)*b - b*c + a*d)/d)/d - 30000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(3*((d*x + c)*b - b*c + a*d)/d)/d - 540000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(((d*x + c)*b - b*c + a*d)/d)/d - 1080*(20*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 3*sqrt(2)*sqrt(d*x + c)*b^3)*cos(5*((d*x + c)*b - b*c + a*d)/d) + 3000*(12*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 5*sqrt(2)*sqrt(d*x + c)*b^3)*cos(3*((d*x + c)*b - b*c + a*d)/d) + 54000*(4*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 15*sqrt(2)*sqrt(d*x + c)*b^3)*cos(((d*x + c)*b - b*c + a*d)/d) + ((162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + (-(1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^6","C",0
131,1,760,0,0.924233," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{3600 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{6000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{36000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} - \frac{1080 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{3000 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{54000 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} - {\left(-\left(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) - {\left(\left(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(13500 i + 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(13500 i - 13500\right) \, \sqrt{\pi} b^{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(13500 i - 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(13500 i + 13500\right) \, \sqrt{\pi} b^{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(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{576000 \, b^{5}}"," ",0,"1/576000*sqrt(2)*(3600*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(5*((d*x + c)*b - b*c + a*d)/d)/d^2 - 6000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 36000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(((d*x + c)*b - b*c + a*d)/d)/d^2 - 1080*sqrt(2)*sqrt(d*x + c)*b^3*sin(5*((d*x + c)*b - b*c + a*d)/d)/d + 3000*sqrt(2)*sqrt(d*x + c)*b^3*sin(3*((d*x + c)*b - b*c + a*d)/d)/d + 54000*sqrt(2)*sqrt(d*x + c)*b^3*sin(((d*x + c)*b - b*c + a*d)/d)/d - (-(54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) - ((250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) - ((13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) - (-(13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) - (-(250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) - ((54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^5","C",0
132,1,674,0,0.835939," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{360 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{600 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{3600 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} + {\left(\frac{\left(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} + \frac{\left(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(-\frac{\left(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(900 i - 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} - \frac{\left(900 i + 900\right) \, \sqrt{\pi} b^{2} \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(900 i + 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} + \frac{\left(900 i - 900\right) \, \sqrt{\pi} b^{2} \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(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} - \frac{\left(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{57600 \, b^{4}}"," ",0,"1/57600*sqrt(2)*(360*sqrt(2)*sqrt(d*x + c)*b^3*cos(5*((d*x + c)*b - b*c + a*d)/d)/d^2 - 600*sqrt(2)*sqrt(d*x + c)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 3600*sqrt(2)*sqrt(d*x + c)*b^3*cos(((d*x + c)*b - b*c + a*d)/d)/d^2 + ((18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d + (18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + (-(50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d - (50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d - (900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d + (900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d + (50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d - (18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^4","C",0
133,1,674,0,0.570425," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{360 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{600 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{3600 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} + {\left(\frac{\left(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} + \frac{\left(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(-\frac{\left(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(900 i - 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} - \frac{\left(900 i + 900\right) \, \sqrt{\pi} b^{2} \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(900 i + 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} + \frac{\left(900 i - 900\right) \, \sqrt{\pi} b^{2} \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(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} - \frac{\left(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{57600 \, b^{4}}"," ",0,"1/57600*sqrt(2)*(360*sqrt(2)*sqrt(d*x + c)*b^3*cos(5*((d*x + c)*b - b*c + a*d)/d)/d^2 - 600*sqrt(2)*sqrt(d*x + c)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 3600*sqrt(2)*sqrt(d*x + c)*b^3*cos(((d*x + c)*b - b*c + a*d)/d)/d^2 + ((18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d + (18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + (-(50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d - (50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d - (900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d + (900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d + (50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d - (18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^4","C",0
134,1,760,0,0.797848," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{3600 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{6000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{36000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} - \frac{1080 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{3000 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{54000 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} - {\left(-\left(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) - {\left(\left(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(13500 i + 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(13500 i - 13500\right) \, \sqrt{\pi} b^{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(13500 i - 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(13500 i + 13500\right) \, \sqrt{\pi} b^{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(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{576000 \, b^{5}}"," ",0,"1/576000*sqrt(2)*(3600*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(5*((d*x + c)*b - b*c + a*d)/d)/d^2 - 6000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 36000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(((d*x + c)*b - b*c + a*d)/d)/d^2 - 1080*sqrt(2)*sqrt(d*x + c)*b^3*sin(5*((d*x + c)*b - b*c + a*d)/d)/d + 3000*sqrt(2)*sqrt(d*x + c)*b^3*sin(3*((d*x + c)*b - b*c + a*d)/d)/d + 54000*sqrt(2)*sqrt(d*x + c)*b^3*sin(((d*x + c)*b - b*c + a*d)/d)/d - (-(54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) - ((250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) - ((13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) - (-(13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) - (-(250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) - ((54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^5","C",0
135,1,820,0,1.787367," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{10800 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{30000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{540000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} - 1080 \, {\left(\frac{20 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 3 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 3000 \, {\left(\frac{12 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 5 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 54000 \, {\left(\frac{4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 15 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(-\left(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(202500 i - 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(202500 i + 202500\right) \, \sqrt{\pi} b^{2} 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(202500 i + 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(202500 i - 202500\right) \, \sqrt{\pi} b^{2} 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(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{3456000 \, b^{6}}"," ",0,"-1/3456000*sqrt(2)*(10800*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(5*((d*x + c)*b - b*c + a*d)/d)/d - 30000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(3*((d*x + c)*b - b*c + a*d)/d)/d - 540000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(((d*x + c)*b - b*c + a*d)/d)/d - 1080*(20*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 3*sqrt(2)*sqrt(d*x + c)*b^3)*cos(5*((d*x + c)*b - b*c + a*d)/d) + 3000*(12*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 5*sqrt(2)*sqrt(d*x + c)*b^3)*cos(3*((d*x + c)*b - b*c + a*d)/d) + 54000*(4*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 15*sqrt(2)*sqrt(d*x + c)*b^3)*cos(((d*x + c)*b - b*c + a*d)/d) + ((162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + (-(1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^6","C",0
136,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^3*sin(b*x + a), x)","F",0
137,1,967,0,0.391981," ","integrate((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{256 \, c^{4} \cos\left(b x + a\right)^{4} - \frac{1024 \, a c^{3} d \cos\left(b x + a\right)^{4}}{b} + \frac{1536 \, a^{2} c^{2} d^{2} \cos\left(b x + a\right)^{4}}{b^{2}} - \frac{1024 \, a^{3} c d^{3} \cos\left(b x + a\right)^{4}}{b^{3}} + \frac{256 \, a^{4} d^{4} \cos\left(b x + a\right)^{4}}{b^{4}} + \frac{32 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b} - \frac{96 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{96 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{32 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{24 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{48 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{b^{3}} + \frac{24 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{4 \, {\left(4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + 64 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - 96 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{3}}{b^{3}} - \frac{4 \, {\left(4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + 64 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - 96 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left({\left(32 \, {\left(b x + a\right)}^{4} - 24 \, {\left(b x + a\right)}^{2} + 3\right)} \cos\left(4 \, b x + 4 \, a\right) + 64 \, {\left(2 \, {\left(b x + a\right)}^{4} - 6 \, {\left(b x + a\right)}^{2} + 3\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(4 \, b x + 4 \, a\right) - 128 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{4}}{b^{4}}}{1024 \, b}"," ",0,"-1/1024*(256*c^4*cos(b*x + a)^4 - 1024*a*c^3*d*cos(b*x + a)^4/b + 1536*a^2*c^2*d^2*cos(b*x + a)^4/b^2 - 1024*a^3*c*d^3*cos(b*x + a)^4/b^3 + 256*a^4*d^4*cos(b*x + a)^4/b^4 + 32*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*c^3*d/b - 96*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*a*c^2*d^2/b^2 + 96*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*a^2*c*d^3/b^3 - 32*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*a^3*d^4/b^4 + 24*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) - 32*(b*x + a)*sin(2*b*x + 2*a))*c^2*d^2/b^2 - 48*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) - 32*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^3/b^3 + 24*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) - 32*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^4/b^4 + 4*(4*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) + 64*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) - 96*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c*d^3/b^3 - 4*(4*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) + 64*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) - 96*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*d^4/b^4 + ((32*(b*x + a)^4 - 24*(b*x + a)^2 + 3)*cos(4*b*x + 4*a) + 64*(2*(b*x + a)^4 - 6*(b*x + a)^2 + 3)*cos(2*b*x + 2*a) - 4*(8*(b*x + a)^3 - 3*b*x - 3*a)*sin(4*b*x + 4*a) - 128*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*d^4/b^4)/b","B",0
138,1,549,0,0.361467," ","integrate((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{256 \, c^{3} \cos\left(b x + a\right)^{4} - \frac{768 \, a c^{2} d \cos\left(b x + a\right)^{4}}{b} + \frac{768 \, a^{2} c d^{2} \cos\left(b x + a\right)^{4}}{b^{2}} - \frac{256 \, a^{3} d^{3} \cos\left(b x + a\right)^{4}}{b^{3}} + \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{b} - \frac{48 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{b^{2}} + \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{12 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{b^{2}} - \frac{12 \, {\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(4 \, {\left(8 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + 64 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - 96 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{3}}{b^{3}}}{1024 \, b}"," ",0,"-1/1024*(256*c^3*cos(b*x + a)^4 - 768*a*c^2*d*cos(b*x + a)^4/b + 768*a^2*c*d^2*cos(b*x + a)^4/b^2 - 256*a^3*d^3*cos(b*x + a)^4/b^3 + 24*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*c^2*d/b - 48*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*a*c*d^2/b^2 + 24*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*a^2*d^3/b^3 + 12*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) - 32*(b*x + a)*sin(2*b*x + 2*a))*c*d^2/b^2 - 12*((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) - 32*(b*x + a)*sin(2*b*x + 2*a))*a*d^3/b^3 + (4*(8*(b*x + a)^3 - 3*b*x - 3*a)*cos(4*b*x + 4*a) + 64*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - 3*(8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) - 96*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*d^3/b^3)/b","B",0
139,1,263,0,0.340341," ","integrate((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{64 \, c^{2} \cos\left(b x + a\right)^{4} - \frac{128 \, a c d \cos\left(b x + a\right)^{4}}{b} + \frac{64 \, a^{2} d^{2} \cos\left(b x + a\right)^{4}}{b^{2}} + \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c d}{b} - \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left({\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right) - 32 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{b^{2}}}{256 \, b}"," ",0,"-1/256*(64*c^2*cos(b*x + a)^4 - 128*a*c*d*cos(b*x + a)^4/b + 64*a^2*d^2*cos(b*x + a)^4/b^2 + 4*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*c*d/b - 4*(4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*a*d^2/b^2 + ((8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 16*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 4*(b*x + a)*sin(4*b*x + 4*a) - 32*(b*x + a)*sin(2*b*x + 2*a))*d^2/b^2)/b","B",0
140,1,92,0,0.321129," ","integrate((d*x+c)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{32 \, c \cos\left(b x + a\right)^{4} - \frac{32 \, a d \cos\left(b x + a\right)^{4}}{b} + \frac{{\left(4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 16 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(4 \, b x + 4 \, a\right) - 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} d}{b}}{128 \, b}"," ",0,"-1/128*(32*c*cos(b*x + a)^4 - 32*a*d*cos(b*x + a)^4/b + (4*(b*x + a)*cos(4*b*x + 4*a) + 16*(b*x + a)*cos(2*b*x + 2*a) - sin(4*b*x + 4*a) - 8*sin(2*b*x + 2*a))*d/b)/b","A",0
141,1,274,0,0.494080," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c),x, algorithm=""maxima"")","-\frac{b {\left(2 i \, E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 2 i \, 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{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b {\left(E_{1}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{1}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, b d}"," ",0,"-1/16*(b*(2*I*exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 2*I*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, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(1, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) + 2*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))*sin(-2*(b*c - a*d)/d) + b*(exp_integral_e(1, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(1, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d))/(b*d)","C",0
142,1,301,0,0.559399," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{b^{2} {\left(2 i \, E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 2 i \, 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(i \, E_{2}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{2}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{2} {\left(E_{2}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{2}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/16*(b^2*(2*I*exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 2*I*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*(I*exp_integral_e(2, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(2, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) + 2*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))*sin(-2*(b*c - a*d)/d) + b^2*(exp_integral_e(2, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(2, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
143,1,336,0,0.686766," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{b^{3} {\left(2 i \, E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 2 i \, 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(i \, E_{3}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{3}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{3} {\left(E_{3}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{3}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\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,"-1/16*(b^3*(2*I*exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 2*I*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*(I*exp_integral_e(3, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(3, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) + 2*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))*sin(-2*(b*c - a*d)/d) + b^3*(exp_integral_e(3, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(3, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(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
144,1,386,0,1.896297," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{b^{4} {\left(2 i \, E_{4}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 2 i \, 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(i \, E_{4}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) - i \, E_{4}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 2 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{4} {\left(E_{4}\left(\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right) + E_{4}\left(-\frac{4 i \, b c + 4 i \, {\left(b x + a\right)} d - 4 i \, a d}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\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,"-1/16*(b^4*(2*I*exp_integral_e(4, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 2*I*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*(I*exp_integral_e(4, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) - I*exp_integral_e(4, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*cos(-4*(b*c - a*d)/d) + 2*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))*sin(-2*(b*c - a*d)/d) + b^4*(exp_integral_e(4, (4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d) + exp_integral_e(4, -(4*I*b*c + 4*I*(b*x + a)*d - 4*I*a*d)/d))*sin(-4*(b*c - a*d)/d))/((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
145,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^3*sin(b*x + a)^2, x)","F",0
146,1,1339,0,0.426782," ","integrate((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{270000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} c^{4} - \frac{1080000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a c^{3} d}{b} + \frac{1620000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{1080000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a^{3} c d^{3}}{b^{3}} + \frac{270000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a^{4} d^{4}}{b^{4}} + \frac{4500 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} c^{3} d}{b} - \frac{13500 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{13500 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{4500 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{450 \, {\left(270 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 13500 \, {\left(b x + a\right)} \cos\left(b x + a\right) + 27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{900 \, {\left(270 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 13500 \, {\left(b x + a\right)} \cos\left(b x + a\right) + 27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a c d^{3}}{b^{3}} + \frac{450 \, {\left(270 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 13500 \, {\left(b x + a\right)} \cos\left(b x + a\right) + 27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{60 \, {\left(81 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) + 625 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 101250 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) + 135 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(5 \, b x + 5 \, a\right) + 1875 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) - 33750 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} c d^{3}}{b^{3}} - \frac{60 \, {\left(81 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) + 625 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 101250 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) + 135 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(5 \, b x + 5 \, a\right) + 1875 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) - 33750 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left(1620 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(5 \, b x + 5 \, a\right) + 37500 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \cos\left(3 \, b x + 3 \, a\right) - 2025000 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) + 81 \, {\left(625 \, {\left(b x + a\right)}^{4} - 300 \, {\left(b x + a\right)}^{2} + 24\right)} \sin\left(5 \, b x + 5 \, a\right) + 3125 \, {\left(27 \, {\left(b x + a\right)}^{4} - 36 \, {\left(b x + a\right)}^{2} + 8\right)} \sin\left(3 \, b x + 3 \, a\right) - 506250 \, {\left({\left(b x + a\right)}^{4} - 12 \, {\left(b x + a\right)}^{2} + 24\right)} \sin\left(b x + a\right)\right)} d^{4}}{b^{4}}}{4050000 \, b}"," ",0,"-1/4050000*(270000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*c^4 - 1080000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a*c^3*d/b + 1620000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a^2*c^2*d^2/b^2 - 1080000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a^3*c*d^3/b^3 + 270000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a^4*d^4/b^4 + 4500*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*c^3*d/b - 13500*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*a*c^2*d^2/b^2 + 13500*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*a^2*c*d^3/b^3 - 4500*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*a^3*d^4/b^4 + 450*(270*(b*x + a)*cos(5*b*x + 5*a) + 750*(b*x + a)*cos(3*b*x + 3*a) - 13500*(b*x + a)*cos(b*x + a) + 27*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 125*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*sin(b*x + a))*c^2*d^2/b^2 - 900*(270*(b*x + a)*cos(5*b*x + 5*a) + 750*(b*x + a)*cos(3*b*x + 3*a) - 13500*(b*x + a)*cos(b*x + a) + 27*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 125*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*sin(b*x + a))*a*c*d^3/b^3 + 450*(270*(b*x + a)*cos(5*b*x + 5*a) + 750*(b*x + a)*cos(3*b*x + 3*a) - 13500*(b*x + a)*cos(b*x + a) + 27*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 125*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*sin(b*x + a))*a^2*d^4/b^4 + 60*(81*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) + 625*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 101250*((b*x + a)^2 - 2)*cos(b*x + a) + 135*(25*(b*x + a)^3 - 6*b*x - 6*a)*sin(5*b*x + 5*a) + 1875*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) - 33750*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*c*d^3/b^3 - 60*(81*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) + 625*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 101250*((b*x + a)^2 - 2)*cos(b*x + a) + 135*(25*(b*x + a)^3 - 6*b*x - 6*a)*sin(5*b*x + 5*a) + 1875*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) - 33750*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*a*d^4/b^4 + (1620*(25*(b*x + a)^3 - 6*b*x - 6*a)*cos(5*b*x + 5*a) + 37500*(3*(b*x + a)^3 - 2*b*x - 2*a)*cos(3*b*x + 3*a) - 2025000*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) + 81*(625*(b*x + a)^4 - 300*(b*x + a)^2 + 24)*sin(5*b*x + 5*a) + 3125*(27*(b*x + a)^4 - 36*(b*x + a)^2 + 8)*sin(3*b*x + 3*a) - 506250*((b*x + a)^4 - 12*(b*x + a)^2 + 24)*sin(b*x + a))*d^4/b^4)/b","B",0
147,1,766,0,0.852177," ","integrate((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{18000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} c^{3} - \frac{54000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a c^{2} d}{b} + \frac{54000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a^{2} c d^{2}}{b^{2}} - \frac{18000 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a^{3} d^{3}}{b^{3}} + \frac{225 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} c^{2} d}{b} - \frac{450 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} a c d^{2}}{b^{2}} + \frac{225 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{15 \, {\left(270 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 13500 \, {\left(b x + a\right)} \cos\left(b x + a\right) + 27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c d^{2}}{b^{2}} - \frac{15 \, {\left(270 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 13500 \, {\left(b x + a\right)} \cos\left(b x + a\right) + 27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(81 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(5 \, b x + 5 \, a\right) + 625 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \cos\left(3 \, b x + 3 \, a\right) - 101250 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) + 135 \, {\left(25 \, {\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(5 \, b x + 5 \, a\right) + 1875 \, {\left(3 \, {\left(b x + a\right)}^{3} - 2 \, b x - 2 \, a\right)} \sin\left(3 \, b x + 3 \, a\right) - 33750 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} d^{3}}{b^{3}}}{270000 \, b}"," ",0,"-1/270000*(18000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*c^3 - 54000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a*c^2*d/b + 54000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a^2*c*d^2/b^2 - 18000*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a^3*d^3/b^3 + 225*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*c^2*d/b - 450*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*a*c*d^2/b^2 + 225*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*a^2*d^3/b^3 + 15*(270*(b*x + a)*cos(5*b*x + 5*a) + 750*(b*x + a)*cos(3*b*x + 3*a) - 13500*(b*x + a)*cos(b*x + a) + 27*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 125*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*sin(b*x + a))*c*d^2/b^2 - 15*(270*(b*x + a)*cos(5*b*x + 5*a) + 750*(b*x + a)*cos(3*b*x + 3*a) - 13500*(b*x + a)*cos(b*x + a) + 27*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 125*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*sin(b*x + a))*a*d^3/b^3 + (81*(25*(b*x + a)^2 - 2)*cos(5*b*x + 5*a) + 625*(9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) - 101250*((b*x + a)^2 - 2)*cos(b*x + a) + 135*(25*(b*x + a)^3 - 6*b*x - 6*a)*sin(5*b*x + 5*a) + 1875*(3*(b*x + a)^3 - 2*b*x - 2*a)*sin(3*b*x + 3*a) - 33750*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^3/b^3)/b","B",0
148,1,375,0,0.599684," ","integrate((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{3600 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} c^{2} - \frac{7200 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a c d}{b} + \frac{3600 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a^{2} d^{2}}{b^{2}} + \frac{30 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} c d}{b} - \frac{30 \, {\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left(270 \, {\left(b x + a\right)} \cos\left(5 \, b x + 5 \, a\right) + 750 \, {\left(b x + a\right)} \cos\left(3 \, b x + 3 \, a\right) - 13500 \, {\left(b x + a\right)} \cos\left(b x + a\right) + 27 \, {\left(25 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(5 \, b x + 5 \, a\right) + 125 \, {\left(9 \, {\left(b x + a\right)}^{2} - 2\right)} \sin\left(3 \, b x + 3 \, a\right) - 6750 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{54000 \, b}"," ",0,"-1/54000*(3600*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*c^2 - 7200*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a*c*d/b + 3600*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a^2*d^2/b^2 + 30*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*c*d/b - 30*(45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*a*d^2/b^2 + (270*(b*x + a)*cos(5*b*x + 5*a) + 750*(b*x + a)*cos(3*b*x + 3*a) - 13500*(b*x + a)*cos(b*x + a) + 27*(25*(b*x + a)^2 - 2)*sin(5*b*x + 5*a) + 125*(9*(b*x + a)^2 - 2)*sin(3*b*x + 3*a) - 6750*((b*x + a)^2 - 2)*sin(b*x + a))*d^2/b^2)/b","B",0
149,1,139,0,0.947049," ","integrate((d*x+c)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{240 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} c - \frac{240 \, {\left(3 \, \sin\left(b x + a\right)^{5} - 5 \, \sin\left(b x + a\right)^{3}\right)} a d}{b} + \frac{{\left(45 \, {\left(b x + a\right)} \sin\left(5 \, b x + 5 \, a\right) + 75 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 450 \, {\left(b x + a\right)} \sin\left(b x + a\right) + 9 \, \cos\left(5 \, b x + 5 \, a\right) + 25 \, \cos\left(3 \, b x + 3 \, a\right) - 450 \, \cos\left(b x + a\right)\right)} d}{b}}{3600 \, b}"," ",0,"-1/3600*(240*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*c - 240*(3*sin(b*x + a)^5 - 5*sin(b*x + a)^3)*a*d/b + (45*(b*x + a)*sin(5*b*x + 5*a) + 75*(b*x + a)*sin(3*b*x + 3*a) - 450*(b*x + a)*sin(b*x + a) + 9*cos(5*b*x + 5*a) + 25*cos(3*b*x + 3*a) - 450*cos(b*x + a))*d/b)/b","A",0
150,1,408,0,0.506834," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","-\frac{2 \, 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)} \cos\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)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - b {\left(E_{1}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{1}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + b {\left(-2 i \, E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 2 i \, 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(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)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + b {\left(i \, E_{1}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{32 \, b d}"," ",0,"-1/32*(2*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))*cos(-(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))*cos(-3*(b*c - a*d)/d) - b*(exp_integral_e(1, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(1, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) + b*(-2*I*exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 2*I*exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(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))*sin(-3*(b*c - a*d)/d) + b*(I*exp_integral_e(1, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - I*exp_integral_e(1, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(b*c - a*d)/d))/(b*d)","C",0
151,1,439,0,0.566115," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{1073741824 \, 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)} \cos\left(-\frac{b c - a d}{d}\right) - 536870912 \, 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)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 536870912 \, b^{2} {\left(E_{2}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{2}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + b^{2} {\left(-1073741824 i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 1073741824 i \, 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(536870912 i \, E_{2}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - 536870912 i \, 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) + b^{2} {\left(536870912 i \, E_{2}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - 536870912 i \, E_{2}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{17179869184 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/17179869184*(1073741824*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))*cos(-(b*c - a*d)/d) - 536870912*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))*cos(-3*(b*c - a*d)/d) - 536870912*b^2*(exp_integral_e(2, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(2, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) + b^2*(-1073741824*I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 1073741824*I*exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^2*(536870912*I*exp_integral_e(2, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - 536870912*I*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^2*(536870912*I*exp_integral_e(2, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - 536870912*I*exp_integral_e(2, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
152,1,474,0,1.372131," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{1073741824 \, 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)} \cos\left(-\frac{b c - a d}{d}\right) - 536870912 \, 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)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 536870912 \, b^{3} {\left(E_{3}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{3}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + b^{3} {\left(-1073741824 i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 1073741824 i \, 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(536870912 i \, E_{3}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - 536870912 i \, 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) + b^{3} {\left(536870912 i \, E_{3}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - 536870912 i \, E_{3}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{17179869184 \, {\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,"-1/17179869184*(1073741824*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))*cos(-(b*c - a*d)/d) - 536870912*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))*cos(-3*(b*c - a*d)/d) - 536870912*b^3*(exp_integral_e(3, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(3, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) + b^3*(-1073741824*I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 1073741824*I*exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^3*(536870912*I*exp_integral_e(3, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - 536870912*I*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^3*(536870912*I*exp_integral_e(3, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - 536870912*I*exp_integral_e(3, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(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
153,1,524,0,1.272222," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{1073741824 \, b^{4} {\left(E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{4}\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) - 536870912 \, b^{4} {\left(E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) + E_{4}\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) - 536870912 \, b^{4} {\left(E_{4}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) + E_{4}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + b^{4} {\left(-1073741824 i \, E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + 1073741824 i \, E_{4}\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^{4} {\left(536870912 i \, E_{4}\left(\frac{3 i \, b c + 3 i \, {\left(b x + a\right)} d - 3 i \, a d}{d}\right) - 536870912 i \, E_{4}\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) + b^{4} {\left(536870912 i \, E_{4}\left(\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right) - 536870912 i \, E_{4}\left(-\frac{5 i \, b c + 5 i \, {\left(b x + a\right)} d - 5 i \, a d}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{17179869184 \, {\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,"-1/17179869184*(1073741824*b^4*(exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*cos(-(b*c - a*d)/d) - 536870912*b^4*(exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) + exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*cos(-3*(b*c - a*d)/d) - 536870912*b^4*(exp_integral_e(4, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) + exp_integral_e(4, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*cos(-5*(b*c - a*d)/d) + b^4*(-1073741824*I*exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + 1073741824*I*exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d) + b^4*(536870912*I*exp_integral_e(4, (3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d) - 536870912*I*exp_integral_e(4, -(3*I*b*c + 3*I*(b*x + a)*d - 3*I*a*d)/d))*sin(-3*(b*c - a*d)/d) + b^4*(536870912*I*exp_integral_e(4, (5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d) - 536870912*I*exp_integral_e(4, -(5*I*b*c + 5*I*(b*x + a)*d - 5*I*a*d)/d))*sin(-5*(b*c - a*d)/d))/((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
154,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{3} \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^3*sin(b*x + a)^3, x)","F",0
155,1,1033,0,0.390748," ","integrate((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{864 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} c^{4} - \frac{3456 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a c^{3} d}{b} + \frac{5184 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{3456 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a^{3} c d^{3}}{b^{3}} + \frac{864 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a^{4} d^{4}}{b^{4}} - \frac{36 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b} + \frac{108 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} - \frac{108 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} + \frac{36 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{b^{4}} - \frac{18 \, {\left({\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 81 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \sin\left(6 \, b x + 6 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{2}} + \frac{36 \, {\left({\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 81 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \sin\left(6 \, b x + 6 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{b^{3}} - \frac{18 \, {\left({\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 81 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \sin\left(6 \, b x + 6 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{b^{4}} - \frac{6 \, {\left(6 \, {\left(6 \, {\left(b x + a\right)}^{3} - b x - a\right)} \cos\left(6 \, b x + 6 \, a\right) - 162 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(6 \, b x + 6 \, a\right) + 243 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{3}}{b^{3}} + \frac{6 \, {\left(6 \, {\left(6 \, {\left(b x + a\right)}^{3} - b x - a\right)} \cos\left(6 \, b x + 6 \, a\right) - 162 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(6 \, b x + 6 \, a\right) + 243 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{4}}{b^{4}} - \frac{{\left({\left(54 \, {\left(b x + a\right)}^{4} - 18 \, {\left(b x + a\right)}^{2} + 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 243 \, {\left(2 \, {\left(b x + a\right)}^{4} - 6 \, {\left(b x + a\right)}^{2} + 3\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(6 \, {\left(b x + a\right)}^{3} - b x - a\right)} \sin\left(6 \, b x + 6 \, a\right) + 486 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{4}}{b^{4}}}{10368 \, b}"," ",0,"-1/10368*(864*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*c^4 - 3456*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a*c^3*d/b + 5184*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a^2*c^2*d^2/b^2 - 3456*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a^3*c*d^3/b^3 + 864*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a^4*d^4/b^4 - 36*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*c^3*d/b + 108*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*a*c^2*d^2/b^2 - 108*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*a^2*c*d^3/b^3 + 36*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*a^3*d^4/b^4 - 18*((18*(b*x + a)^2 - 1)*cos(6*b*x + 6*a) - 81*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 6*(b*x + a)*sin(6*b*x + 6*a) + 162*(b*x + a)*sin(2*b*x + 2*a))*c^2*d^2/b^2 + 36*((18*(b*x + a)^2 - 1)*cos(6*b*x + 6*a) - 81*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 6*(b*x + a)*sin(6*b*x + 6*a) + 162*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^3/b^3 - 18*((18*(b*x + a)^2 - 1)*cos(6*b*x + 6*a) - 81*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 6*(b*x + a)*sin(6*b*x + 6*a) + 162*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^4/b^4 - 6*(6*(6*(b*x + a)^3 - b*x - a)*cos(6*b*x + 6*a) - 162*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - (18*(b*x + a)^2 - 1)*sin(6*b*x + 6*a) + 243*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c*d^3/b^3 + 6*(6*(6*(b*x + a)^3 - b*x - a)*cos(6*b*x + 6*a) - 162*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - (18*(b*x + a)^2 - 1)*sin(6*b*x + 6*a) + 243*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*d^4/b^4 - ((54*(b*x + a)^4 - 18*(b*x + a)^2 + 1)*cos(6*b*x + 6*a) - 243*(2*(b*x + a)^4 - 6*(b*x + a)^2 + 3)*cos(2*b*x + 2*a) - 6*(6*(b*x + a)^3 - b*x - a)*sin(6*b*x + 6*a) + 486*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*d^4/b^4)/b","B",0
156,1,602,0,0.349316," ","integrate((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{576 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} c^{3} - \frac{1728 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a c^{2} d}{b} + \frac{1728 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a^{2} c d^{2}}{b^{2}} - \frac{576 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a^{3} d^{3}}{b^{3}} - \frac{18 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{b} + \frac{36 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{b^{2}} - \frac{18 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{b^{3}} - \frac{6 \, {\left({\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 81 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \sin\left(6 \, b x + 6 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{b^{2}} + \frac{6 \, {\left({\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 81 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \sin\left(6 \, b x + 6 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{3}}{b^{3}} - \frac{{\left(6 \, {\left(6 \, {\left(b x + a\right)}^{3} - b x - a\right)} \cos\left(6 \, b x + 6 \, a\right) - 162 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(6 \, b x + 6 \, a\right) + 243 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{3}}{b^{3}}}{6912 \, b}"," ",0,"-1/6912*(576*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*c^3 - 1728*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a*c^2*d/b + 1728*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a^2*c*d^2/b^2 - 576*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a^3*d^3/b^3 - 18*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*c^2*d/b + 36*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*a*c*d^2/b^2 - 18*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*a^2*d^3/b^3 - 6*((18*(b*x + a)^2 - 1)*cos(6*b*x + 6*a) - 81*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 6*(b*x + a)*sin(6*b*x + 6*a) + 162*(b*x + a)*sin(2*b*x + 2*a))*c*d^2/b^2 + 6*((18*(b*x + a)^2 - 1)*cos(6*b*x + 6*a) - 81*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 6*(b*x + a)*sin(6*b*x + 6*a) + 162*(b*x + a)*sin(2*b*x + 2*a))*a*d^3/b^3 - (6*(6*(b*x + a)^3 - b*x - a)*cos(6*b*x + 6*a) - 162*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) - (18*(b*x + a)^2 - 1)*sin(6*b*x + 6*a) + 243*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*d^3/b^3)/b","B",0
157,1,303,0,0.406601," ","integrate((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{288 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} c^{2} - \frac{576 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a c d}{b} + \frac{288 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a^{2} d^{2}}{b^{2}} - \frac{6 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} c d}{b} + \frac{6 \, {\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{b^{2}} - \frac{{\left({\left(18 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(6 \, b x + 6 \, a\right) - 81 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b x + a\right)} \sin\left(6 \, b x + 6 \, a\right) + 162 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{b^{2}}}{3456 \, b}"," ",0,"-1/3456*(288*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*c^2 - 576*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a*c*d/b + 288*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a^2*d^2/b^2 - 6*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*c*d/b + 6*(6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*a*d^2/b^2 - ((18*(b*x + a)^2 - 1)*cos(6*b*x + 6*a) - 81*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) - 6*(b*x + a)*sin(6*b*x + 6*a) + 162*(b*x + a)*sin(2*b*x + 2*a))*d^2/b^2)/b","B",0
158,1,119,0,0.795947," ","integrate((d*x+c)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{96 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} c - \frac{96 \, {\left(2 \, \sin\left(b x + a\right)^{6} - 3 \, \sin\left(b x + a\right)^{4}\right)} a d}{b} - \frac{{\left(6 \, {\left(b x + a\right)} \cos\left(6 \, b x + 6 \, a\right) - 54 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - \sin\left(6 \, b x + 6 \, a\right) + 27 \, \sin\left(2 \, b x + 2 \, a\right)\right)} d}{b}}{1152 \, b}"," ",0,"-1/1152*(96*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*c - 96*(2*sin(b*x + a)^6 - 3*sin(b*x + a)^4)*a*d/b - (6*(b*x + a)*cos(6*b*x + 6*a) - 54*(b*x + a)*cos(2*b*x + 2*a) - sin(6*b*x + 6*a) + 27*sin(2*b*x + 2*a))*d/b)/b","A",0
159,1,274,0,0.724399," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{b {\left(-3 i \, E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 3 i \, 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{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 3 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b {\left(E_{1}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) + E_{1}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)}{64 \, b d}"," ",0,"1/64*(b*(-3*I*exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 3*I*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, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) - I*exp_integral_e(1, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*cos(-6*(b*c - a*d)/d) - 3*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))*sin(-2*(b*c - a*d)/d) + b*(exp_integral_e(1, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) + exp_integral_e(1, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*sin(-6*(b*c - a*d)/d))/(b*d)","C",0
160,1,301,0,0.484592," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{b^{2} {\left(-3 i \, E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 3 i \, 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(i \, E_{2}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) - i \, E_{2}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 3 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{2} {\left(E_{2}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) + E_{2}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)}{64 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"1/64*(b^2*(-3*I*exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 3*I*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*(I*exp_integral_e(2, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) - I*exp_integral_e(2, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*cos(-6*(b*c - a*d)/d) - 3*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))*sin(-2*(b*c - a*d)/d) + b^2*(exp_integral_e(2, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) + exp_integral_e(2, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*sin(-6*(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
161,1,336,0,0.685728," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""maxima"")","\frac{b^{3} {\left(-3 i \, E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + 3 i \, 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(i \, E_{3}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) - i \, E_{3}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 3 \, 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{3} {\left(E_{3}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) + E_{3}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)}{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*(b^3*(-3*I*exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + 3*I*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*(I*exp_integral_e(3, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) - I*exp_integral_e(3, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*cos(-6*(b*c - a*d)/d) - 3*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))*sin(-2*(b*c - a*d)/d) + b^3*(exp_integral_e(3, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) + exp_integral_e(3, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*sin(-6*(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
162,1,386,0,0.859464," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^4,x, algorithm=""maxima"")","\frac{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)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{4} {\left(i \, E_{4}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) - i \, E_{4}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 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)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + b^{4} {\left(E_{4}\left(\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right) + E_{4}\left(-\frac{6 i \, b c + 6 i \, {\left(b x + a\right)} d - 6 i \, a d}{d}\right)\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)}{64 \, {\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,"1/64*(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))*cos(-2*(b*c - a*d)/d) + b^4*(I*exp_integral_e(4, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) - I*exp_integral_e(4, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*cos(-6*(b*c - a*d)/d) - 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))*sin(-2*(b*c - a*d)/d) + b^4*(exp_integral_e(4, (6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d) + exp_integral_e(4, -(6*I*b*c + 6*I*(b*x + a)*d - 6*I*a*d)/d))*sin(-6*(b*c - a*d)/d))/((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
163,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{2} \cot\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^2*cot(b*x + a), x)","F",0
164,1,1635,0,1.061842," ","integrate((d*x+c)^4*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""maxima"")","-\frac{20 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} c^{4} - \frac{80 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a c^{3} d}{b} + \frac{120 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{80 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a^{3} c d^{3}}{b^{3}} + \frac{20 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a^{4} d^{4}}{b^{4}} - \frac{-8 i \, {\left(b x + a\right)}^{5} d^{4} + {\left(-40 i \, b c d^{3} + 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{4} - 960 \, d^{4} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) - 960 \, d^{4} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) + {\left(-80 i \, b^{2} c^{2} d^{2} + 160 i \, a b c d^{3} - 80 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-80 i \, b^{3} c^{3} d + 240 i \, a b^{2} c^{2} d^{2} - 240 i \, a^{2} b c d^{3} + 80 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(40 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(160 i \, b c d^{3} - 160 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(240 i \, b^{2} c^{2} d^{2} - 480 i \, a b c d^{3} + 240 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(160 i \, b^{3} c^{3} d - 480 i \, a b^{2} c^{2} d^{2} + 480 i \, a^{2} b c d^{3} - 160 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(-40 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-160 i \, b c d^{3} + 160 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-240 i \, b^{2} c^{2} d^{2} + 480 i \, a b c d^{3} - 240 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-160 i \, b^{3} c^{3} d + 480 i \, a b^{2} c^{2} d^{2} - 480 i \, a^{2} b c d^{3} + 160 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 5 \, {\left(2 \, {\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 3 \, {\left(2 \, a^{2} - 1\right)} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(2 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + {\left(2 \, a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(2 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 3 \, {\left(2 \, a^{2} - 1\right)} b c d^{3} - {\left(2 \, a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-160 i \, b^{3} c^{3} d + 480 i \, a b^{2} c^{2} d^{2} - 480 i \, a^{2} b c d^{3} - 160 i \, {\left(b x + a\right)}^{3} d^{4} + 160 i \, a^{3} d^{4} + {\left(-480 i \, b c d^{3} + 480 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-480 i \, b^{2} c^{2} d^{2} + 960 i \, a b c d^{3} - 480 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(-160 i \, b^{3} c^{3} d + 480 i \, a b^{2} c^{2} d^{2} - 480 i \, a^{2} b c d^{3} - 160 i \, {\left(b x + a\right)}^{3} d^{4} + 160 i \, a^{3} d^{4} + {\left(-480 i \, b c d^{3} + 480 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-480 i \, b^{2} c^{2} d^{2} + 960 i \, a b c d^{3} - 480 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 20 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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) + 20 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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(960 i \, b c d^{3} + 960 i \, {\left(b x + a\right)} d^{4} - 960 i \, a d^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + {\left(960 i \, b c d^{3} + 960 i \, {\left(b x + a\right)} d^{4} - 960 i \, a d^{4}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + 480 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + 480 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - 10 \, {\left(2 \, b^{3} c^{3} d - 6 \, a b^{2} c^{2} d^{2} + 2 \, {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(2 \, a^{2} - 1\right)} b c d^{3} - {\left(2 \, a^{3} - 3 \, a\right)} d^{4} + 6 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d^{2} - 4 \, a b c d^{3} + {\left(2 \, a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)}{b^{4}}}{40 \, b}"," ",0,"-1/40*(20*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*c^4 - 80*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a*c^3*d/b + 120*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a^2*c^2*d^2/b^2 - 80*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a^3*c*d^3/b^3 + 20*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a^4*d^4/b^4 - (-8*I*(b*x + a)^5*d^4 + (-40*I*b*c*d^3 + 40*I*a*d^4)*(b*x + a)^4 - 960*d^4*polylog(5, -e^(I*b*x + I*a)) - 960*d^4*polylog(5, e^(I*b*x + I*a)) + (-80*I*b^2*c^2*d^2 + 160*I*a*b*c*d^3 - 80*I*a^2*d^4)*(b*x + a)^3 + (-80*I*b^3*c^3*d + 240*I*a*b^2*c^2*d^2 - 240*I*a^2*b*c*d^3 + 80*I*a^3*d^4)*(b*x + a)^2 + (40*I*(b*x + a)^4*d^4 + (160*I*b*c*d^3 - 160*I*a*d^4)*(b*x + a)^3 + (240*I*b^2*c^2*d^2 - 480*I*a*b*c*d^3 + 240*I*a^2*d^4)*(b*x + a)^2 + (160*I*b^3*c^3*d - 480*I*a*b^2*c^2*d^2 + 480*I*a^2*b*c*d^3 - 160*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (-40*I*(b*x + a)^4*d^4 + (-160*I*b*c*d^3 + 160*I*a*d^4)*(b*x + a)^3 + (-240*I*b^2*c^2*d^2 + 480*I*a*b*c*d^3 - 240*I*a^2*d^4)*(b*x + a)^2 + (-160*I*b^3*c^3*d + 480*I*a*b^2*c^2*d^2 - 480*I*a^2*b*c*d^3 + 160*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 5*(2*(b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 3*(2*a^2 - 1)*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(2*b^2*c^2*d^2 - 4*a*b*c*d^3 + (2*a^2 - 1)*d^4)*(b*x + a)^2 + 4*(2*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 3*(2*a^2 - 1)*b*c*d^3 - (2*a^3 - 3*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (-160*I*b^3*c^3*d + 480*I*a*b^2*c^2*d^2 - 480*I*a^2*b*c*d^3 - 160*I*(b*x + a)^3*d^4 + 160*I*a^3*d^4 + (-480*I*b*c*d^3 + 480*I*a*d^4)*(b*x + a)^2 + (-480*I*b^2*c^2*d^2 + 960*I*a*b*c*d^3 - 480*I*a^2*d^4)*(b*x + a))*dilog(-e^(I*b*x + I*a)) + (-160*I*b^3*c^3*d + 480*I*a*b^2*c^2*d^2 - 480*I*a^2*b*c*d^3 - 160*I*(b*x + a)^3*d^4 + 160*I*a^3*d^4 + (-480*I*b*c*d^3 + 480*I*a*d^4)*(b*x + a)^2 + (-480*I*b^2*c^2*d^2 + 960*I*a*b*c*d^3 - 480*I*a^2*d^4)*(b*x + a))*dilog(e^(I*b*x + I*a)) + 20*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + 20*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (960*I*b*c*d^3 + 960*I*(b*x + a)*d^4 - 960*I*a*d^4)*polylog(4, -e^(I*b*x + I*a)) + (960*I*b*c*d^3 + 960*I*(b*x + a)*d^4 - 960*I*a*d^4)*polylog(4, e^(I*b*x + I*a)) + 480*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, -e^(I*b*x + I*a)) + 480*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, e^(I*b*x + I*a)) - 10*(2*b^3*c^3*d - 6*a*b^2*c^2*d^2 + 2*(b*x + a)^3*d^4 + 3*(2*a^2 - 1)*b*c*d^3 - (2*a^3 - 3*a)*d^4 + 6*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 3*(2*b^2*c^2*d^2 - 4*a*b*c*d^3 + (2*a^2 - 1)*d^4)*(b*x + a))*sin(2*b*x + 2*a))/b^4)/b","B",0
165,1,967,0,0.797892," ","integrate((d*x+c)^3*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""maxima"")","-\frac{8 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} c^{3} - \frac{24 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a c^{2} d}{b} + \frac{24 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{8 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a^{3} d^{3}}{b^{3}} - \frac{-4 i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-16 i \, b c d^{2} + 16 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + 96 i \, d^{3} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + 96 i \, d^{3} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(-24 i \, b^{2} c^{2} d + 48 i \, a b c d^{2} - 24 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(16 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(48 i \, b c d^{2} - 48 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(48 i \, b^{2} c^{2} d - 96 i \, a b c d^{2} + 48 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(-16 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-48 i \, b c d^{2} + 48 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-48 i \, b^{2} c^{2} d + 96 i \, a b c d^{2} - 48 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) + 2 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-48 i \, b^{2} c^{2} d + 96 i \, a b c d^{2} - 48 i \, {\left(b x + a\right)}^{2} d^{3} - 48 i \, a^{2} d^{3} + {\left(-96 i \, b c d^{2} + 96 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(-48 i \, b^{2} c^{2} d + 96 i \, a b c d^{2} - 48 i \, {\left(b x + a\right)}^{2} d^{3} - 48 i \, a^{2} d^{3} + {\left(-96 i \, b c d^{2} + 96 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 8 \, {\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) + 8 \, {\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) + 96 \, {\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)}) + 96 \, {\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)}) - 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, {\left(b x + a\right)}^{2} d^{3} + {\left(2 \, a^{2} - 1\right)} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)}{b^{3}}}{16 \, b}"," ",0,"-1/16*(8*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*c^3 - 24*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a*c^2*d/b + 24*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a^2*c*d^2/b^2 - 8*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a^3*d^3/b^3 - (-4*I*(b*x + a)^4*d^3 + (-16*I*b*c*d^2 + 16*I*a*d^3)*(b*x + a)^3 + 96*I*d^3*polylog(4, -e^(I*b*x + I*a)) + 96*I*d^3*polylog(4, e^(I*b*x + I*a)) + (-24*I*b^2*c^2*d + 48*I*a*b*c*d^2 - 24*I*a^2*d^3)*(b*x + a)^2 + (16*I*(b*x + a)^3*d^3 + (48*I*b*c*d^2 - 48*I*a*d^3)*(b*x + a)^2 + (48*I*b^2*c^2*d - 96*I*a*b*c*d^2 + 48*I*a^2*d^3)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (-16*I*(b*x + a)^3*d^3 + (-48*I*b*c*d^2 + 48*I*a*d^3)*(b*x + a)^2 + (-48*I*b^2*c^2*d + 96*I*a*b*c*d^2 - 48*I*a^2*d^3)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 2*(2*(b*x + a)^3*d^3 - 3*b*c*d^2 + 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 - 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-48*I*b^2*c^2*d + 96*I*a*b*c*d^2 - 48*I*(b*x + a)^2*d^3 - 48*I*a^2*d^3 + (-96*I*b*c*d^2 + 96*I*a*d^3)*(b*x + a))*dilog(-e^(I*b*x + I*a)) + (-48*I*b^2*c^2*d + 96*I*a*b*c*d^2 - 48*I*(b*x + a)^2*d^3 - 48*I*a^2*d^3 + (-96*I*b*c*d^2 + 96*I*a*d^3)*(b*x + a))*dilog(e^(I*b*x + I*a)) + 8*((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) + 8*((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) + 96*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, -e^(I*b*x + I*a)) + 96*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, e^(I*b*x + I*a)) - 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + 2*(b*x + a)^2*d^3 + (2*a^2 - 1)*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))/b^3)/b","B",0
166,1,522,0,0.460256," ","integrate((d*x+c)^2*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""maxima"")","-\frac{12 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} c^{2} - \frac{24 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a c d}{b} + \frac{12 \, {\left(\sin\left(b x + a\right)^{2} - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} a^{2} d^{2}}{b^{2}} - \frac{-8 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-24 i \, b c d + 24 i \, a d^{2}\right)} {\left(b x + a\right)}^{2} + 48 \, d^{2} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + 48 \, d^{2} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(24 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(48 i \, b c d - 48 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(-24 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-48 i \, b c d + 48 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) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-48 i \, b c d - 48 i \, {\left(b x + a\right)} d^{2} + 48 i \, a d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(-48 i \, b c d - 48 i \, {\left(b x + a\right)} d^{2} + 48 i \, a d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 12 \, {\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) + 12 \, {\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) - 6 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)}{b^{2}}}{24 \, b}"," ",0,"-1/24*(12*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*c^2 - 24*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a*c*d/b + 12*(sin(b*x + a)^2 - log(sin(b*x + a)^2))*a^2*d^2/b^2 - (-8*I*(b*x + a)^3*d^2 + (-24*I*b*c*d + 24*I*a*d^2)*(b*x + a)^2 + 48*d^2*polylog(3, -e^(I*b*x + I*a)) + 48*d^2*polylog(3, e^(I*b*x + I*a)) + (24*I*(b*x + a)^2*d^2 + (48*I*b*c*d - 48*I*a*d^2)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (-24*I*(b*x + a)^2*d^2 + (-48*I*b*c*d + 48*I*a*d^2)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 3*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) - d^2)*cos(2*b*x + 2*a) + (-48*I*b*c*d - 48*I*(b*x + a)*d^2 + 48*I*a*d^2)*dilog(-e^(I*b*x + I*a)) + (-48*I*b*c*d - 48*I*(b*x + a)*d^2 + 48*I*a*d^2)*dilog(e^(I*b*x + I*a)) + 12*((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) + 12*((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) - 6*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(2*b*x + 2*a))/b^2)/b","B",0
167,1,222,0,0.786680," ","integrate((d*x+c)*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""maxima"")","\frac{-4 i \, b^{2} d x^{2} - 8 i \, b^{2} c x - 8 i \, b d x \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 8 i \, b c \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(8 i \, b d x + 8 i \, b c\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + 2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - 8 i \, d {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 8 i \, d {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 4 \, {\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) + 4 \, {\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) - d \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{2}}"," ",0,"1/8*(-4*I*b^2*d*x^2 - 8*I*b^2*c*x - 8*I*b*d*x*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 8*I*b*c*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (8*I*b*d*x + 8*I*b*c)*arctan2(sin(b*x + a), cos(b*x + a) + 1) + 2*(b*d*x + b*c)*cos(2*b*x + 2*a) - 8*I*d*dilog(-e^(I*b*x + I*a)) - 8*I*d*dilog(e^(I*b*x + I*a)) + 4*(b*d*x + b*c)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + 4*(b*d*x + b*c)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - d*sin(2*b*x + 2*a))/b^2","B",0
168,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*cot(b*x+a)/(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(-i \, E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + i \, E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 4 \, d \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} - 4 \, d \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} - {\left(E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, d}"," ",0,"-1/4*((-I*exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) + I*exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 4*d*integrate(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x + 2*(d*x + c)*cos(b*x + a) + c), x) - 4*d*integrate(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x - 2*(d*x + c)*cos(b*x + a) + c), x) - (exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/d","F",0
169,0,0,0,0.000000," ","integrate(cos(b*x+a)^2*cot(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(-i \, E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + i \, E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left(d^{2} x + c d\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} - 4 \, {\left(d^{2} x + c d\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} - {\left(E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{2} x + c d\right)}}"," ",0,"-1/4*((-I*exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) + I*exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 4*(d^2*x + c*d)*integrate(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) - 4*(d^2*x + c*d)*integrate(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 - 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) - (exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/(d^2*x + c*d)","F",0
170,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right) \cot\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)*cot(b*x + a)^2, x)","F",0
171,-1,0,0,0.000000," ","integrate((d*x+c)^4*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,1,11018,0,1.961710," ","integrate((d*x+c)^3*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c^{3} {\left(\frac{1}{\sin\left(b x + a\right)} + \sin\left(b x + a\right)\right)} - \frac{6 \, a c^{2} d {\left(\frac{1}{\sin\left(b x + a\right)} + \sin\left(b x + a\right)\right)}}{b} + \frac{6 \, a^{2} c d^{2} {\left(\frac{1}{\sin\left(b x + a\right)} + \sin\left(b x + a\right)\right)}}{b^{2}} - \frac{2 \, a^{3} d^{3} {\left(\frac{1}{\sin\left(b x + a\right)} + \sin\left(b x + a\right)\right)}}{b^{3}} - \frac{3 \, {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + {\left(b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} - 6 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} - 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - 8 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)^{2} + \cos\left(b x + a\right)^{2} + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(b x + a\right)^{2} + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} + {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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(\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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 - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + 2 \, {\left({\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(b x + a\right)} \cos\left(b x + a\right) - {\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - {\left(6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} c^{2} d}{{\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b} + \frac{6 \, {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + {\left(b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} - 6 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} - 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - 8 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)^{2} + \cos\left(b x + a\right)^{2} + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(b x + a\right)^{2} + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} + {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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(\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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 - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + 2 \, {\left({\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(b x + a\right)} \cos\left(b x + a\right) - {\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - {\left(6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} a c d^{2}}{{\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b^{2}} - \frac{3 \, {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + {\left(b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} - 6 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} - 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - 8 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)^{2} + \cos\left(b x + a\right)^{2} + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(b x + a\right)^{2} + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} + {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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(\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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 - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + 2 \, {\left({\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(b x + a\right)} \cos\left(b x + a\right) - {\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - {\left(6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} a^{2} d^{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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b^{3}} - \frac{2 \, {\left(-i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 \, {\left(i \, a - 1\right)} d^{3} - 3 \, {\left(i \, b c d^{2} + {\left(-i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} - 6 \, {\left(-i \, a - 1\right)} d^{3} + {\left(3 i \, b c d^{2} - 3 \, {\left(i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(6 \, b c d^{2} - {\left(6 \, a - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(-i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 \, {\left(i \, a + 1\right)} d^{3} + {\left(-3 i \, b c d^{2} - 3 \, {\left(-i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 \, b c d^{2} - {\left(6 \, a - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} - 12 \, {\left({\left(b x + a\right)}^{3} d^{3} - 2 \, b c d^{2} - 2 \, {\left(b x + a\right)} d^{3} + 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} + 12 i \, b c d^{2} + 12 i \, {\left(b x + a\right)} d^{3} - 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(b x + a\right)^{2} - {\left(6 \, b c d^{2} - {\left(6 \, a + 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left({\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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\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)} \cos\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)} \sin\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)} \cos\left(b x + a\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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\left(b x + a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left({\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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\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)} \cos\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)} \sin\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)} \cos\left(b x + a\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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\left(b x + a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left({\left(-7 i \, {\left(b x + a\right)}^{3} d^{3} + 18 i \, b c d^{2} - 6 \, {\left(3 i \, a + 1\right)} d^{3} + {\left(-21 i \, b c d^{2} - 3 \, {\left(-7 i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 \, b c d^{2} - {\left(6 \, a - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(7 \, {\left(b x + a\right)}^{3} d^{3} - 18 \, b c d^{2} + {\left(18 \, a - 6 i\right)} d^{3} + {\left(21 \, b c d^{2} - {\left(21 \, a - 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b c d^{2} - 6 \, {\left(i \, a + 3\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} - 6 \, {\left(-i \, a + 1\right)} d^{3} - 3 \, {\left(-i \, b c d^{2} + {\left(i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 \, b c d^{2} - {\left(6 \, a + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\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(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(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\left(-12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3}\right)} \cos\left(b x + a\right) + 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(b x + a\right)\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)} \cos\left(b x + 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)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(b x + 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(b x + a\right)\right)} \sin\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(b x + a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left({\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(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(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\left(12 i \, b c d^{2} + 12 i \, {\left(b x + a\right)} d^{3} - 12 i \, a d^{3}\right)} \cos\left(b x + a\right) - 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(b x + a\right)\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)} \cos\left(b x + 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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(b x + 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(b x + a\right)\right)} \sin\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(b x + a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left({\left(3 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + 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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(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)} \cos\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)} \sin\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)} \cos\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)} + {\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)} \sin\left(3 \, b x + 3 \, a\right) + {\left({\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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\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(3 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + 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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(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)} \cos\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)} \sin\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)} \cos\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)} + {\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)} \sin\left(3 \, b x + 3 \, a\right) - {\left({\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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\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(12 \, d^{3} \cos\left(b x + a\right) + 12 i \, d^{3} \sin\left(b x + a\right) + 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - d^{3}\right)} \cos\left(3 \, b x + 3 \, a\right) - 12 \, {\left(d^{3} \cos\left(b x + a\right) + i \, d^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(12 i \, d^{3} \cos\left(b x + a\right) - 12 \, d^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(12 \, d^{3} \cos\left(b x + a\right) + 12 i \, d^{3} \sin\left(b x + a\right) + 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - d^{3}\right)} \cos\left(3 \, b x + 3 \, a\right) - 12 \, {\left(d^{3} \cos\left(b x + a\right) + i \, d^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(3 \, b x + 3 \, a\right) + {\left(-12 i \, d^{3} \cos\left(b x + a\right) + 12 \, d^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left({\left(2 \, {\left(b x + a\right)}^{3} d^{3} - 12 \, b c d^{2} + {\left(12 \, a - 12 i\right)} d^{3} + {\left(6 \, b c d^{2} - {\left(6 \, a - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(-12 i \, b c d^{2} - 12 \, {\left(-i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(7 \, {\left(b x + a\right)}^{3} d^{3} - 18 \, b c d^{2} + {\left(18 \, a - 6 i\right)} d^{3} + {\left(21 \, b c d^{2} - {\left(21 \, a - 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b c d^{2} - 6 \, {\left(i \, a + 3\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) - {\left(7 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} - 6 \, {\left(-3 i \, a - 1\right)} d^{3} + {\left(21 i \, b c d^{2} - 3 \, {\left(7 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(6 \, b c d^{2} - {\left(6 \, a - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left({\left(b x + a\right)}^{3} d^{3} - 6 \, b c d^{2} + {\left(6 \, a + 6 i\right)} d^{3} + {\left(3 \, b c d^{2} - {\left(3 \, a + 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(-i \, b c d^{2} + {\left(i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{2 \, b^{3} \cos\left(b x + a\right) + 2 i \, b^{3} \sin\left(b x + a\right) + {\left(2 \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 2 \, b^{3}\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(b^{3} \cos\left(b x + a\right) + i \, b^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-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}\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(2 i \, b^{3} \cos\left(b x + a\right) - 2 \, b^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)}}{2 \, b}"," ",0,"-1/2*(2*c^3*(1/sin(b*x + a) + sin(b*x + a)) - 6*a*c^2*d*(1/sin(b*x + a) + sin(b*x + a))/b + 6*a^2*c*d^2*(1/sin(b*x + a) + sin(b*x + a))/b^2 - 2*a^3*d^3*(1/sin(b*x + a) + sin(b*x + a))/b^3 - 3*(((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^3 + (b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*sin(3*b*x + 3*a)^3 - 6*(b*x + a)*sin(b*x + a)^3 - 2*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) + 3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) - 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a) - 8*(b*x + a)*sin(b*x + a))*sin(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a)^2 + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2 + 2)*cos(2*b*x + 2*a) + cos(2*b*x + 2*a)^2 + cos(b*x + a)^2 + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + sin(b*x + a)^2 + 1)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*sin(b*x + a)^3 + (3*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + ((b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + (b*x + a)*cos(2*b*x + 2*a)^2 + (b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + b*x + 2*(((b*x + a)*cos(b*x + a) + sin(b*x + a))*cos(2*b*x + 2*a) - (b*x + a)*cos(b*x + a) - ((b*x + a)*sin(b*x + a) - cos(b*x + a))*sin(2*b*x + 2*a) - sin(b*x + a))*cos(3*b*x + 3*a) - ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*sin(3*b*x + 3*a) - 6*((b*x + a)*cos(b*x + a)^3 + (b*x + a)*cos(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - (6*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) - cos(b*x + 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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b) + 6*(((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^3 + (b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*sin(3*b*x + 3*a)^3 - 6*(b*x + a)*sin(b*x + a)^3 - 2*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) + 3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) - 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a) - 8*(b*x + a)*sin(b*x + a))*sin(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a)^2 + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2 + 2)*cos(2*b*x + 2*a) + cos(2*b*x + 2*a)^2 + cos(b*x + a)^2 + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + sin(b*x + a)^2 + 1)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*sin(b*x + a)^3 + (3*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + ((b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + (b*x + a)*cos(2*b*x + 2*a)^2 + (b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + b*x + 2*(((b*x + a)*cos(b*x + a) + sin(b*x + a))*cos(2*b*x + 2*a) - (b*x + a)*cos(b*x + a) - ((b*x + a)*sin(b*x + a) - cos(b*x + a))*sin(2*b*x + 2*a) - sin(b*x + a))*cos(3*b*x + 3*a) - ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*sin(3*b*x + 3*a) - 6*((b*x + a)*cos(b*x + a)^3 + (b*x + a)*cos(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - (6*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) - cos(b*x + 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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b^2) - 3*(((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^3 + (b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*sin(3*b*x + 3*a)^3 - 6*(b*x + a)*sin(b*x + a)^3 - 2*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) + 3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) - 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a) - 8*(b*x + a)*sin(b*x + a))*sin(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a)^2 + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2 + 2)*cos(2*b*x + 2*a) + cos(2*b*x + 2*a)^2 + cos(b*x + a)^2 + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + sin(b*x + a)^2 + 1)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*sin(b*x + a)^3 + (3*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + ((b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + (b*x + a)*cos(2*b*x + 2*a)^2 + (b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + b*x + 2*(((b*x + a)*cos(b*x + a) + sin(b*x + a))*cos(2*b*x + 2*a) - (b*x + a)*cos(b*x + a) - ((b*x + a)*sin(b*x + a) - cos(b*x + a))*sin(2*b*x + 2*a) - sin(b*x + a))*cos(3*b*x + 3*a) - ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*sin(3*b*x + 3*a) - 6*((b*x + a)*cos(b*x + a)^3 + (b*x + a)*cos(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - (6*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) - cos(b*x + 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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b^3) - 2*(-I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*(I*a - 1)*d^3 - 3*(I*b*c*d^2 + (-I*a + 1)*d^3)*(b*x + a)^2 + (I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 - 6*(-I*a - 1)*d^3 + (3*I*b*c*d^2 - 3*(I*a + 1)*d^3)*(b*x + a)^2 - (6*b*c*d^2 - (6*a - 6*I)*d^3)*(b*x + a))*cos(3*b*x + 3*a)^2 + (6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2)*cos(b*x + a)^2 + (-I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*(I*a + 1)*d^3 + (-3*I*b*c*d^2 - 3*(-I*a - 1)*d^3)*(b*x + a)^2 + (6*b*c*d^2 - (6*a - 6*I)*d^3)*(b*x + a))*sin(3*b*x + 3*a)^2 - 12*((b*x + a)^3*d^3 - 2*b*c*d^2 - 2*(b*x + a)*d^3 + 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*cos(b*x + a)*sin(b*x + a) + (-6*I*(b*x + a)^3*d^3 + 12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2)*sin(b*x + a)^2 - (6*b*c*d^2 - (6*a + 6*I)*d^3)*(b*x + a) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*cos(b*x + a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(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))*cos(b*x + a) - (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))*sin(3*b*x + 3*a) - (6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(b*x + a) - (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) + 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*cos(b*x + a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(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))*cos(b*x + a) - (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))*sin(3*b*x + 3*a) - (6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(b*x + a) - (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) + 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + ((-7*I*(b*x + a)^3*d^3 + 18*I*b*c*d^2 - 6*(3*I*a + 1)*d^3 + (-21*I*b*c*d^2 - 3*(-7*I*a - 1)*d^3)*(b*x + a)^2 + (6*b*c*d^2 - (6*a - 18*I)*d^3)*(b*x + a))*cos(b*x + a) + (7*(b*x + a)^3*d^3 - 18*b*c*d^2 + (18*a - 6*I)*d^3 + (21*b*c*d^2 - (21*a - 3*I)*d^3)*(b*x + a)^2 + (6*I*b*c*d^2 - 6*(I*a + 3)*d^3)*(b*x + a))*sin(b*x + a))*cos(3*b*x + 3*a) + (I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 - 6*(-I*a + 1)*d^3 - 3*(-I*b*c*d^2 + (I*a - 1)*d^3)*(b*x + a)^2 + (6*b*c*d^2 - (6*a + 6*I)*d^3)*(b*x + a))*cos(2*b*x + 2*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(2*b*x + 2*a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*cos(b*x + a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*cos(2*b*x + 2*a) + (12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*cos(b*x + 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))*sin(3*b*x + 3*a) + (12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(b*x + a) + (12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*sin(b*x + a))*sin(2*b*x + 2*a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*dilog(-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(2*b*x + 2*a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*cos(b*x + a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*cos(2*b*x + 2*a) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*cos(b*x + 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))*sin(3*b*x + 3*a) - (12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(b*x + a) - (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*sin(b*x + a))*sin(2*b*x + 2*a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*dilog(e^(I*b*x + I*a)) + ((3*(b*x + a)^2*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a) - 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + (3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(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))*sin(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))*cos(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) + (-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))*sin(3*b*x + 3*a) + ((3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a))*cos(b*x + a) - 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) + (-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*sin(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - ((3*(b*x + a)^2*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a) - 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + (3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(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))*sin(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))*cos(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) + (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))*sin(3*b*x + 3*a) - ((-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*cos(b*x + a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) - (3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a))*sin(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (12*d^3*cos(b*x + a) + 12*I*d^3*sin(b*x + a) + 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) - d^3)*cos(3*b*x + 3*a) - 12*(d^3*cos(b*x + a) + I*d^3*sin(b*x + a))*cos(2*b*x + 2*a) - (-12*I*d^3*cos(2*b*x + 2*a) + 12*d^3*sin(2*b*x + 2*a) + 12*I*d^3)*sin(3*b*x + 3*a) - (12*I*d^3*cos(b*x + a) - 12*d^3*sin(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) + (12*d^3*cos(b*x + a) + 12*I*d^3*sin(b*x + a) + 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) - d^3)*cos(3*b*x + 3*a) - 12*(d^3*cos(b*x + a) + I*d^3*sin(b*x + a))*cos(2*b*x + 2*a) + (12*I*d^3*cos(2*b*x + 2*a) - 12*d^3*sin(2*b*x + 2*a) - 12*I*d^3)*sin(3*b*x + 3*a) + (-12*I*d^3*cos(b*x + a) + 12*d^3*sin(b*x + a))*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) - ((2*(b*x + a)^3*d^3 - 12*b*c*d^2 + (12*a - 12*I)*d^3 + (6*b*c*d^2 - (6*a - 6*I)*d^3)*(b*x + a)^2 - (-12*I*b*c*d^2 - 12*(-I*a - 1)*d^3)*(b*x + a))*cos(3*b*x + 3*a) - (7*(b*x + a)^3*d^3 - 18*b*c*d^2 + (18*a - 6*I)*d^3 + (21*b*c*d^2 - (21*a - 3*I)*d^3)*(b*x + a)^2 + (6*I*b*c*d^2 - 6*(I*a + 3)*d^3)*(b*x + a))*cos(b*x + a) - (7*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 - 6*(-3*I*a - 1)*d^3 + (21*I*b*c*d^2 - 3*(7*I*a + 1)*d^3)*(b*x + a)^2 - (6*b*c*d^2 - (6*a - 18*I)*d^3)*(b*x + a))*sin(b*x + a))*sin(3*b*x + 3*a) - ((b*x + a)^3*d^3 - 6*b*c*d^2 + (6*a + 6*I)*d^3 + (3*b*c*d^2 - (3*a + 3*I)*d^3)*(b*x + a)^2 + 6*(-I*b*c*d^2 + (I*a - 1)*d^3)*(b*x + a))*sin(2*b*x + 2*a))/(2*b^3*cos(b*x + a) + 2*I*b^3*sin(b*x + a) + (2*b^3*cos(2*b*x + 2*a) + 2*I*b^3*sin(2*b*x + 2*a) - 2*b^3)*cos(3*b*x + 3*a) - 2*(b^3*cos(b*x + a) + I*b^3*sin(b*x + a))*cos(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)*sin(3*b*x + 3*a) - (2*I*b^3*cos(b*x + a) - 2*b^3*sin(b*x + a))*sin(2*b*x + 2*a)))/b","B",0
173,1,3284,0,1.664957," ","integrate((d*x+c)^2*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""maxima"")","\frac{b^{2} d^{2} x^{2} {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + b^{2} c^{2} {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} - b c d {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} - 2 \, d^{2} {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} - {\left(2 \, b^{2} c d {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} + b d^{2} {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)}\right)} x - {\left({\left(4 \, b d^{2} x {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + 4 \, b c d {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} - {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(2 \, b x + 3 \, a\right) - 4 \, {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left({\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right) - 4 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 4 \, {\left(b d^{2} x {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} + b c d {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)}\right)} \cos\left(b x + a\right) + {\left(b d^{2} x {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} + b c d {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} - 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 3 \, a\right) - {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) - {\left(b d^{2} x {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} + b c d {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)}\right)} \sin\left(b x + a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(4 \, b c d {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} \cos\left(b x + a\right) + b c d {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} \sin\left(b x + a\right) + {\left(4 \, b c d {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} - 4 i \, b c d \cos\left(2 \, b x + 3 \, a\right) + 4 \, b c d \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(-4 i \, b c d \cos\left(b x + a\right) + 4 \, b c d \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) - {\left(b c d {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} - 4 \, b c d \cos\left(2 \, b x + 3 \, a\right) - 4 i \, b c d \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) - 4 \, {\left(b c d \cos\left(b x + a\right) + i \, b c d \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) - {\left(4 \, b d^{2} x {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} \cos\left(b x + a\right) - b d^{2} x {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} \sin\left(b x + a\right) + 4 \, {\left(b d^{2} x {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + i \, b d^{2} x \cos\left(2 \, b x + 3 \, a\right) - b d^{2} x \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 4 \, {\left(-i \, b d^{2} x \cos\left(b x + a\right) + b d^{2} x \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left(b d^{2} x {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} - 4 \, b d^{2} x \cos\left(2 \, b x + 3 \, a\right) - 4 i \, b d^{2} x \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(4 \, b d^{2} x \cos\left(b x + a\right) + 4 i \, b d^{2} x \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left({\left(i \, b^{2} d^{2} x^{2} + i \, b^{2} c^{2} - 2 \, b c d - 2 i \, d^{2} + {\left(2 i \, b^{2} c d - 2 \, b d^{2}\right)} x\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(-i \, b^{2} d^{2} x^{2} - i \, b^{2} c^{2} + 2 \, b c d + 2 i \, d^{2} + {\left(-2 i \, b^{2} c d + 2 \, b d^{2}\right)} x\right)} \cos\left(b x + a\right) - {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 i \, b c d - 2 \, d^{2} + 2 \, {\left(b^{2} c d + i \, b d^{2}\right)} x\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 i \, b c d - 2 \, d^{2} + 2 \, {\left(b^{2} c d + i \, b d^{2}\right)} x\right)} \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 4 \, a\right) + {\left({\left(-6 i \, b^{2} d^{2} x^{2} - 12 i \, b^{2} c d x - 6 i \, b^{2} c^{2} + 4 i \, d^{2}\right)} \cos\left(b x + 2 \, a\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} - 2 \, d^{2}\right)} \sin\left(b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(i \, b^{2} d^{2} x^{2} + i \, b^{2} c^{2} + 2 \, b c d - 2 i \, d^{2} + {\left(2 i \, b^{2} c d + 2 \, b d^{2}\right)} x\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left({\left(6 i \, b^{2} d^{2} x^{2} + 12 i \, b^{2} c d x + 6 i \, b^{2} c^{2} - 4 i \, d^{2}\right)} \cos\left(b x + a\right) - 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} - 2 \, d^{2}\right)} \sin\left(b x + a\right)\right)} \cos\left(b x + 2 \, a\right) - {\left(4 \, d^{2} {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} \cos\left(b x + a\right) + d^{2} {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} \sin\left(b x + a\right) + {\left(4 \, d^{2} {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} - 4 i \, d^{2} \cos\left(2 \, b x + 3 \, a\right) + 4 \, d^{2} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(-4 i \, d^{2} \cos\left(b x + a\right) + 4 \, d^{2} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) - {\left(d^{2} {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} - 4 \, d^{2} \cos\left(2 \, b x + 3 \, a\right) - 4 i \, d^{2} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) - 4 \, {\left(d^{2} \cos\left(b x + a\right) + i \, d^{2} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(4 \, d^{2} {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} \cos\left(b x + a\right) - d^{2} {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} \sin\left(b x + a\right) + {\left(4 \, d^{2} {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + 4 i \, d^{2} \cos\left(2 \, b x + 3 \, a\right) - 4 \, d^{2} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(4 i \, d^{2} \cos\left(b x + a\right) - 4 \, d^{2} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left(d^{2} {\left(4 \, \cos\left(a\right) + 4 i \, \sin\left(a\right)\right)} - 4 \, d^{2} \cos\left(2 \, b x + 3 \, a\right) - 4 i \, d^{2} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 4 \, {\left(d^{2} \cos\left(b x + a\right) + i \, d^{2} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left({\left(b d^{2} x {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} + b c d {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) - {\left(b d^{2} x {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} + b c d {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)}\right)} \cos\left(b x + a\right) - {\left(2 \, b d^{2} x {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + 2 \, b c d {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(2 \, b x + 3 \, a\right) - 2 \, {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left({\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right) - 2 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) - 2 \, {\left(b d^{2} x {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} + b c d {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)}\right)} \sin\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 d^{2} x {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} + b c d {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 3 \, a\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) - {\left(b d^{2} x {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} + b c d {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)}\right)} \cos\left(b x + a\right) + {\left(2 \, b d^{2} x {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} + 2 \, b c d {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left({\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right) + 2 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b d^{2} x {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + b c d {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)}\right)} \sin\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^{2} d^{2} x^{2} + b^{2} c^{2} + 2 i \, b c d - 2 \, d^{2} + 2 \, {\left(b^{2} c d + i \, b d^{2}\right)} x\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 i \, b c d - 2 \, d^{2} + 2 \, {\left(b^{2} c d + i \, b d^{2}\right)} x\right)} \cos\left(b x + a\right) - {\left(-i \, b^{2} d^{2} x^{2} - i \, b^{2} c^{2} + 2 \, b c d + 2 i \, d^{2} + {\left(-2 i \, b^{2} c d + 2 \, b d^{2}\right)} x\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(i \, b^{2} d^{2} x^{2} + i \, b^{2} c^{2} - 2 \, b c d - 2 i \, d^{2} + {\left(2 i \, b^{2} c d - 2 \, b d^{2}\right)} x\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 4 \, a\right) + {\left(2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + 2 \, a\right) + {\left(6 i \, b^{2} d^{2} x^{2} + 12 i \, b^{2} c d x + 6 i \, b^{2} c^{2} - 4 i \, d^{2}\right)} \sin\left(b x + 2 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} - 2 i \, b c d - 2 \, d^{2} + 2 \, {\left(b^{2} c d - i \, b d^{2}\right)} x\right)} \sin\left(2 \, b x + 3 \, a\right) - {\left(2 \, {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right) - {\left(-6 i \, b^{2} d^{2} x^{2} - 12 i \, b^{2} c d x - 6 i \, b^{2} c^{2} + 4 i \, d^{2}\right)} \sin\left(b x + a\right)\right)} \sin\left(b x + 2 \, a\right)}{b^{3} {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} \cos\left(b x + a\right) + 2 \, b^{3} {\left(i \, \cos\left(a\right) - \sin\left(a\right)\right)} \sin\left(b x + a\right) - {\left(b^{3} {\left(2 \, \cos\left(a\right) + 2 i \, \sin\left(a\right)\right)} - 2 \, b^{3} \cos\left(2 \, b x + 3 \, a\right) - 2 i \, b^{3} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(b^{3} \cos\left(b x + a\right) + i \, b^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left(2 \, b^{3} {\left(-i \, \cos\left(a\right) + \sin\left(a\right)\right)} + 2 i \, b^{3} \cos\left(2 \, b x + 3 \, a\right) - 2 \, b^{3} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(2 i \, b^{3} \cos\left(b x + a\right) - 2 \, b^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)}"," ",0,"(b^2*d^2*x^2*(-I*cos(a) + sin(a)) + b^2*c^2*(-I*cos(a) + sin(a)) - b*c*d*(2*cos(a) + 2*I*sin(a)) - 2*d^2*(-I*cos(a) + sin(a)) - (2*b^2*c*d*(I*cos(a) - sin(a)) + b*d^2*(2*cos(a) + 2*I*sin(a)))*x - ((4*b*d^2*x*(-I*cos(a) + sin(a)) + 4*b*c*d*(-I*cos(a) + sin(a)) - (-4*I*b*d^2*x - 4*I*b*c*d)*cos(2*b*x + 3*a) - 4*(b*d^2*x + b*c*d)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) - ((4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a) - 4*(b*d^2*x + b*c*d)*sin(b*x + a))*cos(2*b*x + 3*a) + 4*(b*d^2*x*(I*cos(a) - sin(a)) + b*c*d*(I*cos(a) - sin(a)))*cos(b*x + a) + (b*d^2*x*(4*cos(a) + 4*I*sin(a)) + b*c*d*(4*cos(a) + 4*I*sin(a)) - 4*(b*d^2*x + b*c*d)*cos(2*b*x + 3*a) - (4*I*b*d^2*x + 4*I*b*c*d)*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) + (4*(b*d^2*x + b*c*d)*cos(b*x + a) - (-4*I*b*d^2*x - 4*I*b*c*d)*sin(b*x + a))*sin(2*b*x + 3*a) - (b*d^2*x*(4*cos(a) + 4*I*sin(a)) + b*c*d*(4*cos(a) + 4*I*sin(a)))*sin(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (4*b*c*d*(-I*cos(a) + sin(a))*cos(b*x + a) + b*c*d*(4*cos(a) + 4*I*sin(a))*sin(b*x + a) + (4*b*c*d*(I*cos(a) - sin(a)) - 4*I*b*c*d*cos(2*b*x + 3*a) + 4*b*c*d*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) - (-4*I*b*c*d*cos(b*x + a) + 4*b*c*d*sin(b*x + a))*cos(2*b*x + 3*a) - (b*c*d*(4*cos(a) + 4*I*sin(a)) - 4*b*c*d*cos(2*b*x + 3*a) - 4*I*b*c*d*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) - 4*(b*c*d*cos(b*x + a) + I*b*c*d*sin(b*x + a))*sin(2*b*x + 3*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (4*b*d^2*x*(I*cos(a) - sin(a))*cos(b*x + a) - b*d^2*x*(4*cos(a) + 4*I*sin(a))*sin(b*x + a) + 4*(b*d^2*x*(-I*cos(a) + sin(a)) + I*b*d^2*x*cos(2*b*x + 3*a) - b*d^2*x*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + 4*(-I*b*d^2*x*cos(b*x + a) + b*d^2*x*sin(b*x + a))*cos(2*b*x + 3*a) + (b*d^2*x*(4*cos(a) + 4*I*sin(a)) - 4*b*d^2*x*cos(2*b*x + 3*a) - 4*I*b*d^2*x*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) + (4*b*d^2*x*cos(b*x + a) + 4*I*b*d^2*x*sin(b*x + a))*sin(2*b*x + 3*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + ((I*b^2*d^2*x^2 + I*b^2*c^2 - 2*b*c*d - 2*I*d^2 + (2*I*b^2*c*d - 2*b*d^2)*x)*cos(3*b*x + 3*a) + (-I*b^2*d^2*x^2 - I*b^2*c^2 + 2*b*c*d + 2*I*d^2 + (-2*I*b^2*c*d + 2*b*d^2)*x)*cos(b*x + a) - (b^2*d^2*x^2 + b^2*c^2 + 2*I*b*c*d - 2*d^2 + 2*(b^2*c*d + I*b*d^2)*x)*sin(3*b*x + 3*a) + (b^2*d^2*x^2 + b^2*c^2 + 2*I*b*c*d - 2*d^2 + 2*(b^2*c*d + I*b*d^2)*x)*sin(b*x + a))*cos(3*b*x + 4*a) + ((-6*I*b^2*d^2*x^2 - 12*I*b^2*c*d*x - 6*I*b^2*c^2 + 4*I*d^2)*cos(b*x + 2*a) + 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 - 2*d^2)*sin(b*x + 2*a))*cos(3*b*x + 3*a) + (I*b^2*d^2*x^2 + I*b^2*c^2 + 2*b*c*d - 2*I*d^2 + (2*I*b^2*c*d + 2*b*d^2)*x)*cos(2*b*x + 3*a) + ((6*I*b^2*d^2*x^2 + 12*I*b^2*c*d*x + 6*I*b^2*c^2 - 4*I*d^2)*cos(b*x + a) - 2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 - 2*d^2)*sin(b*x + a))*cos(b*x + 2*a) - (4*d^2*(-I*cos(a) + sin(a))*cos(b*x + a) + d^2*(4*cos(a) + 4*I*sin(a))*sin(b*x + a) + (4*d^2*(I*cos(a) - sin(a)) - 4*I*d^2*cos(2*b*x + 3*a) + 4*d^2*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) - (-4*I*d^2*cos(b*x + a) + 4*d^2*sin(b*x + a))*cos(2*b*x + 3*a) - (d^2*(4*cos(a) + 4*I*sin(a)) - 4*d^2*cos(2*b*x + 3*a) - 4*I*d^2*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) - 4*(d^2*cos(b*x + a) + I*d^2*sin(b*x + a))*sin(2*b*x + 3*a))*dilog(-e^(I*b*x + I*a)) - (4*d^2*(I*cos(a) - sin(a))*cos(b*x + a) - d^2*(4*cos(a) + 4*I*sin(a))*sin(b*x + a) + (4*d^2*(-I*cos(a) + sin(a)) + 4*I*d^2*cos(2*b*x + 3*a) - 4*d^2*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) - (4*I*d^2*cos(b*x + a) - 4*d^2*sin(b*x + a))*cos(2*b*x + 3*a) + (d^2*(4*cos(a) + 4*I*sin(a)) - 4*d^2*cos(2*b*x + 3*a) - 4*I*d^2*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) + 4*(d^2*cos(b*x + a) + I*d^2*sin(b*x + a))*sin(2*b*x + 3*a))*dilog(e^(I*b*x + I*a)) + ((b*d^2*x*(2*cos(a) + 2*I*sin(a)) + b*c*d*(2*cos(a) + 2*I*sin(a)) - 2*(b*d^2*x + b*c*d)*cos(2*b*x + 3*a) + (-2*I*b*d^2*x - 2*I*b*c*d)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + (2*(b*d^2*x + b*c*d)*cos(b*x + a) + (2*I*b*d^2*x + 2*I*b*c*d)*sin(b*x + a))*cos(2*b*x + 3*a) - (b*d^2*x*(2*cos(a) + 2*I*sin(a)) + b*c*d*(2*cos(a) + 2*I*sin(a)))*cos(b*x + a) - (2*b*d^2*x*(-I*cos(a) + sin(a)) + 2*b*c*d*(-I*cos(a) + sin(a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*cos(2*b*x + 3*a) - 2*(b*d^2*x + b*c*d)*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) + ((2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a) - 2*(b*d^2*x + b*c*d)*sin(b*x + a))*sin(2*b*x + 3*a) - 2*(b*d^2*x*(I*cos(a) - sin(a)) + b*c*d*(I*cos(a) - sin(a)))*sin(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - ((b*d^2*x*(2*cos(a) + 2*I*sin(a)) + b*c*d*(2*cos(a) + 2*I*sin(a)) - 2*(b*d^2*x + b*c*d)*cos(2*b*x + 3*a) - (2*I*b*d^2*x + 2*I*b*c*d)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + (2*(b*d^2*x + b*c*d)*cos(b*x + a) - (-2*I*b*d^2*x - 2*I*b*c*d)*sin(b*x + a))*cos(2*b*x + 3*a) - (b*d^2*x*(2*cos(a) + 2*I*sin(a)) + b*c*d*(2*cos(a) + 2*I*sin(a)))*cos(b*x + a) + (2*b*d^2*x*(I*cos(a) - sin(a)) + 2*b*c*d*(I*cos(a) - sin(a)) - (2*I*b*d^2*x + 2*I*b*c*d)*cos(2*b*x + 3*a) + 2*(b*d^2*x + b*c*d)*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) - ((-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a) + 2*(b*d^2*x + b*c*d)*sin(b*x + a))*sin(2*b*x + 3*a) + 2*(b*d^2*x*(-I*cos(a) + sin(a)) + b*c*d*(-I*cos(a) + sin(a)))*sin(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - ((b^2*d^2*x^2 + b^2*c^2 + 2*I*b*c*d - 2*d^2 + 2*(b^2*c*d + I*b*d^2)*x)*cos(3*b*x + 3*a) - (b^2*d^2*x^2 + b^2*c^2 + 2*I*b*c*d - 2*d^2 + 2*(b^2*c*d + I*b*d^2)*x)*cos(b*x + a) - (-I*b^2*d^2*x^2 - I*b^2*c^2 + 2*b*c*d + 2*I*d^2 + (-2*I*b^2*c*d + 2*b*d^2)*x)*sin(3*b*x + 3*a) - (I*b^2*d^2*x^2 + I*b^2*c^2 - 2*b*c*d - 2*I*d^2 + (2*I*b^2*c*d - 2*b*d^2)*x)*sin(b*x + a))*sin(3*b*x + 4*a) + (2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 - 2*d^2)*cos(b*x + 2*a) + (6*I*b^2*d^2*x^2 + 12*I*b^2*c*d*x + 6*I*b^2*c^2 - 4*I*d^2)*sin(b*x + 2*a))*sin(3*b*x + 3*a) - (b^2*d^2*x^2 + b^2*c^2 - 2*I*b*c*d - 2*d^2 + 2*(b^2*c*d - I*b*d^2)*x)*sin(2*b*x + 3*a) - (2*(3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 - 2*d^2)*cos(b*x + a) - (-6*I*b^2*d^2*x^2 - 12*I*b^2*c*d*x - 6*I*b^2*c^2 + 4*I*d^2)*sin(b*x + a))*sin(b*x + 2*a))/(b^3*(2*cos(a) + 2*I*sin(a))*cos(b*x + a) + 2*b^3*(I*cos(a) - sin(a))*sin(b*x + a) - (b^3*(2*cos(a) + 2*I*sin(a)) - 2*b^3*cos(2*b*x + 3*a) - 2*I*b^3*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) - 2*(b^3*cos(b*x + a) + I*b^3*sin(b*x + a))*cos(2*b*x + 3*a) + (2*b^3*(-I*cos(a) + sin(a)) + 2*I*b^3*cos(2*b*x + 3*a) - 2*b^3*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) - (2*I*b^3*cos(b*x + a) - 2*b^3*sin(b*x + a))*sin(2*b*x + 3*a))","B",0
174,1,2110,0,0.394371," ","integrate((d*x+c)*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c {\left(\frac{1}{\sin\left(b x + a\right)} + \sin\left(b x + a\right)\right)} - \frac{2 \, a d {\left(\frac{1}{\sin\left(b x + a\right)} + \sin\left(b x + a\right)\right)}}{b} - \frac{{\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + {\left(b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} - 6 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} - 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - 8 \, {\left(b x + a\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} - {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)^{2} + \cos\left(b x + a\right)^{2} + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(b x + a\right)^{2} + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{3} + {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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(\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\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 - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a - \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + 2 \, {\left({\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(b x + a\right)} \cos\left(b x + a\right) - {\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \sin\left(3 \, b x + 3 \, a\right) - 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - {\left(6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} d}{{\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} - 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) - 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b}}{2 \, b}"," ",0,"-1/2*(2*c*(1/sin(b*x + a) + sin(b*x + a)) - 2*a*d*(1/sin(b*x + a) + sin(b*x + a))/b - (((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^3 + (b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*sin(3*b*x + 3*a)^3 - 6*(b*x + a)*sin(b*x + a)^3 - 2*(4*(b*x + a)*cos(b*x + a)*sin(2*b*x + 2*a) - (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) + 3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*cos(2*b*x + 2*a)*sin(b*x + a) + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) - 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a) - 8*(b*x + a)*sin(b*x + a))*sin(3*b*x + 3*a)^2 - ((b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a)^2 + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2 + 2)*cos(2*b*x + 2*a) + cos(2*b*x + 2*a)^2 + cos(b*x + a)^2 + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) + sin(2*b*x + 2*a)^2 + sin(b*x + a)^2 + 1)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*sin(b*x + a)^3 + (3*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) + cos(b*x + a))*cos(2*b*x + 2*a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + ((b*x - (b*x + a)*cos(2*b*x + 2*a) + a - sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + (b*x + a)*cos(2*b*x + 2*a)^2 + (b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + b*x + 2*(((b*x + a)*cos(b*x + a) + sin(b*x + a))*cos(2*b*x + 2*a) - (b*x + a)*cos(b*x + a) - ((b*x + a)*sin(b*x + a) - cos(b*x + a))*sin(2*b*x + 2*a) - sin(b*x + a))*cos(3*b*x + 3*a) - ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*sin(3*b*x + 3*a) - 6*((b*x + a)*cos(b*x + a)^3 + (b*x + a)*cos(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - (6*(b*x + a)*cos(b*x + a)^2 + b*x + a)*sin(b*x + a) - cos(b*x + a))*d/(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 - 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 - 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) - 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 - 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) - 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b))/b","B",0
175,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{b c {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - b c {\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + {\left(b c {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - b c {\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + {\left(b d {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - b d {\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} - 4 \, d \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right) + {\left(b c {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - b c {\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + {\left(b d {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - b d {\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} x\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - b d {\left(i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} x - {\left(2 \, b c {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b c {\left(-2 i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + 2 i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + {\left(2 \, b d {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + b d {\left(-2 i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + 2 i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} x - 4 \, d \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, d \sin\left(b x + a\right) - \frac{2 \, {\left(b d^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{3} x + b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\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{2 \, {\left(b d^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{3} x + b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\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 \, {\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)}}"," ",0,"1/2*(b*c*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) - b*c*(I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d) + (b*c*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) - b*c*(I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d) + (b*d*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) - b*d*(I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))*x)*cos(2*b*x + 2*a)^2 - 4*d*cos(b*x + a)*sin(2*b*x + 2*a) + (b*c*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) - b*c*(I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d) + (b*d*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) - b*d*(I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))*x)*sin(2*b*x + 2*a)^2 + (b*d*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) - b*d*(I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))*x - (2*b*c*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) + b*c*(-2*I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) + 2*I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d) + (2*b*d*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) + b*d*(-2*I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) + 2*I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))*x - 4*d*sin(b*x + a))*cos(2*b*x + 2*a) - 2*(b*d^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a)^2 + (b*d^3*x + b*c*d^2)*sin(2*b*x + 2*a)^2 - 2*(b*d^3*x + b*c*d^2)*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*(b*d^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a)^2 + (b*d^3*x + b*c*d^2)*sin(2*b*x + 2*a)^2 - 2*(b*d^3*x + b*c*d^2)*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) - 4*d*sin(b*x + a))/(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))","F",0
176,-1,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,0,0,0,0.000000," ","integrate((d*x+c)^m*cot(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cot\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cot(b*x + a)^3, x)","F",0
178,1,7111,0,4.852071," ","integrate((d*x+c)^4*cot(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{4} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{4 \, a c^{3} d {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{6 \, a^{2} c^{2} d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{4 \, a^{3} c d^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} + \frac{a^{4} d^{4} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{4}} - \frac{2 \, {\left(2 \, {\left(b x + a\right)}^{5} d^{4} + 40 \, b^{3} c^{3} d - 120 \, a b^{2} c^{2} d^{2} + 120 \, a^{2} b c d^{3} - 40 \, a^{3} d^{4} + 10 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{4} + 20 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{3} + 20 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}^{2} - {\left(10 \, {\left(b x + a\right)}^{4} d^{4} - 60 \, b^{2} c^{2} d^{2} + 120 \, a b c d^{3} - 60 \, a^{2} d^{4} + 40 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 40 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)} + 10 \, {\left({\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 6 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 20 \, {\left({\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 6 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(10 i \, {\left(b x + a\right)}^{4} d^{4} - 60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4} + {\left(40 i \, b c d^{3} - 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(60 i \, b^{2} c^{2} d^{2} - 120 i \, a b c d^{3} + {\left(60 i \, a^{2} - 60 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(40 i \, b^{3} c^{3} d - 120 i \, a b^{2} c^{2} d^{2} + {\left(120 i \, a^{2} - 120 i\right)} b c d^{3} + {\left(-40 i \, a^{3} + 120 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-20 i \, {\left(b x + a\right)}^{4} d^{4} + 120 i \, b^{2} c^{2} d^{2} - 240 i \, a b c d^{3} + 120 i \, a^{2} d^{4} + {\left(-80 i \, b c d^{3} + 80 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-80 i \, b^{3} c^{3} d + 240 i \, a b^{2} c^{2} d^{2} + {\left(-240 i \, a^{2} + 240 i\right)} b c d^{3} + {\left(80 i \, a^{3} - 240 i \, a\right)} d^{4}\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(60 \, b^{2} c^{2} d^{2} - 120 \, a b c d^{3} + 60 \, a^{2} d^{4} + 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(120 i \, b^{2} c^{2} d^{2} - 240 i \, a b c d^{3} + 120 i \, a^{2} d^{4}\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(10 \, {\left(b x + a\right)}^{4} d^{4} + 40 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 40 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)} + 10 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 20 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-10 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-40 i \, b c d^{3} + 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} + {\left(-60 i \, a^{2} + 60 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-40 i \, b^{3} c^{3} d + 120 i \, a b^{2} c^{2} d^{2} + {\left(-120 i \, a^{2} + 120 i\right)} b c d^{3} + {\left(40 i \, a^{3} - 120 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(20 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(80 i \, b c d^{3} - 80 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(120 i \, b^{2} c^{2} d^{2} - 240 i \, a b c d^{3} + {\left(120 i \, a^{2} - 120 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(80 i \, b^{3} c^{3} d - 240 i \, a b^{2} c^{2} d^{2} + {\left(240 i \, a^{2} - 240 i\right)} b c d^{3} + {\left(-80 i \, a^{3} + 240 i \, a\right)} d^{4}\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) + 2 \, {\left({\left(b x + a\right)}^{5} d^{4} + 5 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{4} + 10 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 2\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + 10 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 2\right)} b c d^{3} - {\left(a^{3} - 6 \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} - 60 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(4 \, {\left(b x + a\right)}^{5} d^{4} + 40 \, b^{3} c^{3} d - 120 \, a b^{2} c^{2} d^{2} + 120 \, a^{2} b c d^{3} - 40 \, a^{3} d^{4} + {\left(20 \, b c d^{3} - {\left(20 \, a - 20 i\right)} d^{4}\right)} {\left(b x + a\right)}^{4} + {\left(40 \, b^{2} c^{2} d^{2} - {\left(80 \, a - 80 i\right)} b c d^{3} + 40 \, {\left(a^{2} - 2 i \, a - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(40 \, b^{3} c^{3} d - {\left(120 \, a - 120 i\right)} b^{2} c^{2} d^{2} + 120 \, {\left(a^{2} - 2 i \, a - 1\right)} b c d^{3} - {\left(40 \, a^{3} - 120 i \, a^{2} - 120 \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(80 i \, b^{3} c^{3} d - 120 \, {\left(2 i \, a + 1\right)} b^{2} c^{2} d^{2} + {\left(240 i \, a^{2} + 240 \, a\right)} b c d^{3} + {\left(-80 i \, a^{3} - 120 \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(40 \, b^{3} c^{3} d - 120 \, a b^{2} c^{2} d^{2} + 40 \, {\left(b x + a\right)}^{3} d^{4} + 120 \, {\left(a^{2} - 1\right)} b c d^{3} - 40 \, {\left(a^{3} - 3 \, a\right)} d^{4} + 120 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)} + 40 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} 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} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 80 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} 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} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-40 i \, b^{3} c^{3} d + 120 i \, a b^{2} c^{2} d^{2} - 40 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-120 i \, a^{2} + 120 i\right)} b c d^{3} + {\left(40 i \, a^{3} - 120 i \, a\right)} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(80 i \, b^{3} c^{3} d - 240 i \, a b^{2} c^{2} d^{2} + 80 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(240 i \, a^{2} - 240 i\right)} b c d^{3} + {\left(-80 i \, a^{3} + 240 i \, a\right)} d^{4} + {\left(240 i \, b c d^{3} - 240 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(240 i \, b^{2} c^{2} d^{2} - 480 i \, a b c d^{3} + {\left(240 i \, a^{2} - 240 i\right)} d^{4}\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(40 \, b^{3} c^{3} d - 120 \, a b^{2} c^{2} d^{2} + 40 \, {\left(b x + a\right)}^{3} d^{4} + 120 \, {\left(a^{2} - 1\right)} b c d^{3} - 40 \, {\left(a^{3} - 3 \, a\right)} d^{4} + 120 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)} + 40 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} 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} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 80 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} 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} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-40 i \, b^{3} c^{3} d + 120 i \, a b^{2} c^{2} d^{2} - 40 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-120 i \, a^{2} + 120 i\right)} b c d^{3} + {\left(40 i \, a^{3} - 120 i \, a\right)} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(80 i \, b^{3} c^{3} d - 240 i \, a b^{2} c^{2} d^{2} + 80 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(240 i \, a^{2} - 240 i\right)} b c d^{3} + {\left(-80 i \, a^{3} + 240 i \, a\right)} d^{4} + {\left(240 i \, b c d^{3} - 240 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(240 i \, b^{2} c^{2} d^{2} - 480 i \, a b c d^{3} + {\left(240 i \, a^{2} - 240 i\right)} d^{4}\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(-5 i \, {\left(b x + a\right)}^{4} d^{4} + 30 i \, b^{2} c^{2} d^{2} - 60 i \, a b c d^{3} + 30 i \, a^{2} d^{4} + {\left(-20 i \, b c d^{3} + 20 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} + {\left(-30 i \, a^{2} + 30 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-20 i \, b^{3} c^{3} d + 60 i \, a b^{2} c^{2} d^{2} + {\left(-60 i \, a^{2} + 60 i\right)} b c d^{3} + {\left(20 i \, a^{3} - 60 i \, a\right)} d^{4}\right)} {\left(b x + a\right)} + {\left(-5 i \, {\left(b x + a\right)}^{4} d^{4} + 30 i \, b^{2} c^{2} d^{2} - 60 i \, a b c d^{3} + 30 i \, a^{2} d^{4} + {\left(-20 i \, b c d^{3} + 20 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} + {\left(-30 i \, a^{2} + 30 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-20 i \, b^{3} c^{3} d + 60 i \, a b^{2} c^{2} d^{2} + {\left(-60 i \, a^{2} + 60 i\right)} b c d^{3} + {\left(20 i \, a^{3} - 60 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(10 i \, {\left(b x + a\right)}^{4} d^{4} - 60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4} + {\left(40 i \, b c d^{3} - 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(60 i \, b^{2} c^{2} d^{2} - 120 i \, a b c d^{3} + {\left(60 i \, a^{2} - 60 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(40 i \, b^{3} c^{3} d - 120 i \, a b^{2} c^{2} d^{2} + {\left(120 i \, a^{2} - 120 i\right)} b c d^{3} + {\left(-40 i \, a^{3} + 120 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 5 \, {\left({\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 6 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 10 \, {\left({\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 6 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\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(-5 i \, {\left(b x + a\right)}^{4} d^{4} + 30 i \, b^{2} c^{2} d^{2} - 60 i \, a b c d^{3} + 30 i \, a^{2} d^{4} + {\left(-20 i \, b c d^{3} + 20 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} + {\left(-30 i \, a^{2} + 30 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-20 i \, b^{3} c^{3} d + 60 i \, a b^{2} c^{2} d^{2} + {\left(-60 i \, a^{2} + 60 i\right)} b c d^{3} + {\left(20 i \, a^{3} - 60 i \, a\right)} d^{4}\right)} {\left(b x + a\right)} + {\left(-5 i \, {\left(b x + a\right)}^{4} d^{4} + 30 i \, b^{2} c^{2} d^{2} - 60 i \, a b c d^{3} + 30 i \, a^{2} d^{4} + {\left(-20 i \, b c d^{3} + 20 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} + {\left(-30 i \, a^{2} + 30 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-20 i \, b^{3} c^{3} d + 60 i \, a b^{2} c^{2} d^{2} + {\left(-60 i \, a^{2} + 60 i\right)} b c d^{3} + {\left(20 i \, a^{3} - 60 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(10 i \, {\left(b x + a\right)}^{4} d^{4} - 60 i \, b^{2} c^{2} d^{2} + 120 i \, a b c d^{3} - 60 i \, a^{2} d^{4} + {\left(40 i \, b c d^{3} - 40 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(60 i \, b^{2} c^{2} d^{2} - 120 i \, a b c d^{3} + {\left(60 i \, a^{2} - 60 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(40 i \, b^{3} c^{3} d - 120 i \, a b^{2} c^{2} d^{2} + {\left(120 i \, a^{2} - 120 i\right)} b c d^{3} + {\left(-40 i \, a^{3} + 120 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 5 \, {\left({\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 6 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 10 \, {\left({\left(b x + a\right)}^{4} d^{4} - 6 \, b^{2} c^{2} d^{2} + 12 \, a b c d^{3} - 6 \, a^{2} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} - 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} - 1\right)} b c d^{3} - {\left(a^{3} - 3 \, a\right)} d^{4}\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(240 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) - 480 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) - 240 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) + 480 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + 240 i \, d^{4}\right)} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) - {\left(240 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) - 480 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) - 240 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) + 480 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + 240 i \, d^{4}\right)} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) - {\left(240 \, b c d^{3} + 240 \, {\left(b x + a\right)} d^{4} - 240 \, a d^{4} + 240 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 480 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(240 i \, b c d^{3} + 240 i \, {\left(b x + a\right)} d^{4} - 240 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-480 i \, b c d^{3} - 480 i \, {\left(b x + a\right)} d^{4} + 480 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(240 \, b c d^{3} + 240 \, {\left(b x + a\right)} d^{4} - 240 \, a d^{4} + 240 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) - 480 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(240 i \, b c d^{3} + 240 i \, {\left(b x + a\right)} d^{4} - 240 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-480 i \, b c d^{3} - 480 i \, {\left(b x + a\right)} d^{4} + 480 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} - 120 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4} + {\left(-240 i \, b c d^{3} + 240 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} - 120 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4} + {\left(-240 i \, b c d^{3} + 240 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(240 i \, b^{2} c^{2} d^{2} - 480 i \, a b c d^{3} + 240 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(240 i \, a^{2} - 240 i\right)} d^{4} + {\left(480 i \, b c d^{3} - 480 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 1\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 240 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 1\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} - 120 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4} + {\left(-240 i \, b c d^{3} + 240 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-120 i \, b^{2} c^{2} d^{2} + 240 i \, a b c d^{3} - 120 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-120 i \, a^{2} + 120 i\right)} d^{4} + {\left(-240 i \, b c d^{3} + 240 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(240 i \, b^{2} c^{2} d^{2} - 480 i \, a b c d^{3} + 240 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(240 i \, a^{2} - 240 i\right)} d^{4} + {\left(480 i \, b c d^{3} - 480 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 120 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 1\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 240 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + {\left(a^{2} - 1\right)} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(-2 i \, {\left(b x + a\right)}^{5} d^{4} + {\left(-10 i \, b c d^{3} + 10 i \, a d^{4}\right)} {\left(b x + a\right)}^{4} + {\left(-20 i \, b^{2} c^{2} d^{2} + 40 i \, a b c d^{3} + {\left(-20 i \, a^{2} + 40 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-20 i \, b^{3} c^{3} d + 60 i \, a b^{2} c^{2} d^{2} + {\left(-60 i \, a^{2} + 120 i\right)} b c d^{3} + {\left(20 i \, a^{3} - 120 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(120 i \, b^{2} c^{2} d^{2} - 240 i \, a b c d^{3} + 120 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{5} d^{4} + 40 i \, b^{3} c^{3} d - 120 i \, a b^{2} c^{2} d^{2} + 120 i \, a^{2} b c d^{3} - 40 i \, a^{3} d^{4} + {\left(20 i \, b c d^{3} - 20 \, {\left(i \, a + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{4} + {\left(40 i \, b^{2} c^{2} d^{2} - 80 \, {\left(i \, a + 1\right)} b c d^{3} + {\left(40 i \, a^{2} + 80 \, a - 40 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(40 i \, b^{3} c^{3} d - 120 \, {\left(i \, a + 1\right)} b^{2} c^{2} d^{2} + {\left(120 i \, a^{2} + 240 \, a - 120 i\right)} b c d^{3} + {\left(-40 i \, a^{3} - 120 \, a^{2} + 120 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} - {\left(80 \, b^{3} c^{3} d - {\left(240 \, a - 120 i\right)} b^{2} c^{2} d^{2} + 240 \, {\left(a^{2} - i \, a\right)} b c d^{3} - 40 \, {\left(2 \, a^{3} - 3 i \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-10 i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) + 20 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 10 \, b^{4} \sin\left(4 \, b x + 4 \, a\right) - 20 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - 10 i \, b^{4}}}{2 \, b}"," ",0,"-1/2*(c^4*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2)) - 4*a*c^3*d*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b + 6*a^2*c^2*d^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b^2 - 4*a^3*c*d^3*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b^3 + a^4*d^4*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b^4 - 2*(2*(b*x + a)^5*d^4 + 40*b^3*c^3*d - 120*a*b^2*c^2*d^2 + 120*a^2*b*c*d^3 - 40*a^3*d^4 + 10*(b*c*d^3 - a*d^4)*(b*x + a)^4 + 20*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^3 + 20*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a)^2 - (10*(b*x + a)^4*d^4 - 60*b^2*c^2*d^2 + 120*a*b*c*d^3 - 60*a^2*d^4 + 40*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 40*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a) + 10*((b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 6*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 20*((b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 6*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (10*I*(b*x + a)^4*d^4 - 60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4 + (40*I*b*c*d^3 - 40*I*a*d^4)*(b*x + a)^3 + (60*I*b^2*c^2*d^2 - 120*I*a*b*c*d^3 + (60*I*a^2 - 60*I)*d^4)*(b*x + a)^2 + (40*I*b^3*c^3*d - 120*I*a*b^2*c^2*d^2 + (120*I*a^2 - 120*I)*b*c*d^3 + (-40*I*a^3 + 120*I*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (-20*I*(b*x + a)^4*d^4 + 120*I*b^2*c^2*d^2 - 240*I*a*b*c*d^3 + 120*I*a^2*d^4 + (-80*I*b*c*d^3 + 80*I*a*d^4)*(b*x + a)^3 + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 + (-120*I*a^2 + 120*I)*d^4)*(b*x + a)^2 + (-80*I*b^3*c^3*d + 240*I*a*b^2*c^2*d^2 + (-240*I*a^2 + 240*I)*b*c*d^3 + (80*I*a^3 - 240*I*a)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (60*b^2*c^2*d^2 - 120*a*b*c*d^3 + 60*a^2*d^4 + 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(4*b*x + 4*a) - 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(2*b*x + 2*a) - (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4)*sin(4*b*x + 4*a) - (120*I*b^2*c^2*d^2 - 240*I*a*b*c*d^3 + 120*I*a^2*d^4)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (10*(b*x + a)^4*d^4 + 40*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 40*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a) + 10*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 20*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-10*I*(b*x + a)^4*d^4 + (-40*I*b*c*d^3 + 40*I*a*d^4)*(b*x + a)^3 + (-60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 + (-60*I*a^2 + 60*I)*d^4)*(b*x + a)^2 + (-40*I*b^3*c^3*d + 120*I*a*b^2*c^2*d^2 + (-120*I*a^2 + 120*I)*b*c*d^3 + (40*I*a^3 - 120*I*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (20*I*(b*x + a)^4*d^4 + (80*I*b*c*d^3 - 80*I*a*d^4)*(b*x + a)^3 + (120*I*b^2*c^2*d^2 - 240*I*a*b*c*d^3 + (120*I*a^2 - 120*I)*d^4)*(b*x + a)^2 + (80*I*b^3*c^3*d - 240*I*a*b^2*c^2*d^2 + (240*I*a^2 - 240*I)*b*c*d^3 + (-80*I*a^3 + 240*I*a)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 2*((b*x + a)^5*d^4 + 5*(b*c*d^3 - a*d^4)*(b*x + a)^4 + 10*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 2)*d^4)*(b*x + a)^3 + 10*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 2)*b*c*d^3 - (a^3 - 6*a)*d^4)*(b*x + a)^2 - 60*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a))*cos(4*b*x + 4*a) - (4*(b*x + a)^5*d^4 + 40*b^3*c^3*d - 120*a*b^2*c^2*d^2 + 120*a^2*b*c*d^3 - 40*a^3*d^4 + (20*b*c*d^3 - (20*a - 20*I)*d^4)*(b*x + a)^4 + (40*b^2*c^2*d^2 - (80*a - 80*I)*b*c*d^3 + 40*(a^2 - 2*I*a - 1)*d^4)*(b*x + a)^3 + (40*b^3*c^3*d - (120*a - 120*I)*b^2*c^2*d^2 + 120*(a^2 - 2*I*a - 1)*b*c*d^3 - (40*a^3 - 120*I*a^2 - 120*a)*d^4)*(b*x + a)^2 + (80*I*b^3*c^3*d - 120*(2*I*a + 1)*b^2*c^2*d^2 + (240*I*a^2 + 240*a)*b*c*d^3 + (-80*I*a^3 - 120*a^2)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (40*b^3*c^3*d - 120*a*b^2*c^2*d^2 + 40*(b*x + a)^3*d^4 + 120*(a^2 - 1)*b*c*d^3 - 40*(a^3 - 3*a)*d^4 + 120*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a) + 40*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*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 - 1)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 80*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*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 - 1)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-40*I*b^3*c^3*d + 120*I*a*b^2*c^2*d^2 - 40*I*(b*x + a)^3*d^4 + (-120*I*a^2 + 120*I)*b*c*d^3 + (40*I*a^3 - 120*I*a)*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a)^2 + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 + (-120*I*a^2 + 120*I)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (80*I*b^3*c^3*d - 240*I*a*b^2*c^2*d^2 + 80*I*(b*x + a)^3*d^4 + (240*I*a^2 - 240*I)*b*c*d^3 + (-80*I*a^3 + 240*I*a)*d^4 + (240*I*b*c*d^3 - 240*I*a*d^4)*(b*x + a)^2 + (240*I*b^2*c^2*d^2 - 480*I*a*b*c*d^3 + (240*I*a^2 - 240*I)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (40*b^3*c^3*d - 120*a*b^2*c^2*d^2 + 40*(b*x + a)^3*d^4 + 120*(a^2 - 1)*b*c*d^3 - 40*(a^3 - 3*a)*d^4 + 120*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a) + 40*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*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 - 1)*d^4)*(b*x + a))*cos(4*b*x + 4*a) - 80*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + (b*x + a)^3*d^4 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*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 - 1)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-40*I*b^3*c^3*d + 120*I*a*b^2*c^2*d^2 - 40*I*(b*x + a)^3*d^4 + (-120*I*a^2 + 120*I)*b*c*d^3 + (40*I*a^3 - 120*I*a)*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a)^2 + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 + (-120*I*a^2 + 120*I)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (80*I*b^3*c^3*d - 240*I*a*b^2*c^2*d^2 + 80*I*(b*x + a)^3*d^4 + (240*I*a^2 - 240*I)*b*c*d^3 + (-80*I*a^3 + 240*I*a)*d^4 + (240*I*b*c*d^3 - 240*I*a*d^4)*(b*x + a)^2 + (240*I*b^2*c^2*d^2 - 480*I*a*b*c*d^3 + (240*I*a^2 - 240*I)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (-5*I*(b*x + a)^4*d^4 + 30*I*b^2*c^2*d^2 - 60*I*a*b*c*d^3 + 30*I*a^2*d^4 + (-20*I*b*c*d^3 + 20*I*a*d^4)*(b*x + a)^3 + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 + (-30*I*a^2 + 30*I)*d^4)*(b*x + a)^2 + (-20*I*b^3*c^3*d + 60*I*a*b^2*c^2*d^2 + (-60*I*a^2 + 60*I)*b*c*d^3 + (20*I*a^3 - 60*I*a)*d^4)*(b*x + a) + (-5*I*(b*x + a)^4*d^4 + 30*I*b^2*c^2*d^2 - 60*I*a*b*c*d^3 + 30*I*a^2*d^4 + (-20*I*b*c*d^3 + 20*I*a*d^4)*(b*x + a)^3 + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 + (-30*I*a^2 + 30*I)*d^4)*(b*x + a)^2 + (-20*I*b^3*c^3*d + 60*I*a*b^2*c^2*d^2 + (-60*I*a^2 + 60*I)*b*c*d^3 + (20*I*a^3 - 60*I*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (10*I*(b*x + a)^4*d^4 - 60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4 + (40*I*b*c*d^3 - 40*I*a*d^4)*(b*x + a)^3 + (60*I*b^2*c^2*d^2 - 120*I*a*b*c*d^3 + (60*I*a^2 - 60*I)*d^4)*(b*x + a)^2 + (40*I*b^3*c^3*d - 120*I*a*b^2*c^2*d^2 + (120*I*a^2 - 120*I)*b*c*d^3 + (-40*I*a^3 + 120*I*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 5*((b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 6*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 10*((b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 6*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(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) - (-5*I*(b*x + a)^4*d^4 + 30*I*b^2*c^2*d^2 - 60*I*a*b*c*d^3 + 30*I*a^2*d^4 + (-20*I*b*c*d^3 + 20*I*a*d^4)*(b*x + a)^3 + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 + (-30*I*a^2 + 30*I)*d^4)*(b*x + a)^2 + (-20*I*b^3*c^3*d + 60*I*a*b^2*c^2*d^2 + (-60*I*a^2 + 60*I)*b*c*d^3 + (20*I*a^3 - 60*I*a)*d^4)*(b*x + a) + (-5*I*(b*x + a)^4*d^4 + 30*I*b^2*c^2*d^2 - 60*I*a*b*c*d^3 + 30*I*a^2*d^4 + (-20*I*b*c*d^3 + 20*I*a*d^4)*(b*x + a)^3 + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 + (-30*I*a^2 + 30*I)*d^4)*(b*x + a)^2 + (-20*I*b^3*c^3*d + 60*I*a*b^2*c^2*d^2 + (-60*I*a^2 + 60*I)*b*c*d^3 + (20*I*a^3 - 60*I*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (10*I*(b*x + a)^4*d^4 - 60*I*b^2*c^2*d^2 + 120*I*a*b*c*d^3 - 60*I*a^2*d^4 + (40*I*b*c*d^3 - 40*I*a*d^4)*(b*x + a)^3 + (60*I*b^2*c^2*d^2 - 120*I*a*b*c*d^3 + (60*I*a^2 - 60*I)*d^4)*(b*x + a)^2 + (40*I*b^3*c^3*d - 120*I*a*b^2*c^2*d^2 + (120*I*a^2 - 120*I)*b*c*d^3 + (-40*I*a^3 + 120*I*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 5*((b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 6*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 10*((b*x + a)^4*d^4 - 6*b^2*c^2*d^2 + 12*a*b*c*d^3 - 6*a^2*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 - 1)*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 - 1)*b*c*d^3 - (a^3 - 3*a)*d^4)*(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) - (240*I*d^4*cos(4*b*x + 4*a) - 480*I*d^4*cos(2*b*x + 2*a) - 240*d^4*sin(4*b*x + 4*a) + 480*d^4*sin(2*b*x + 2*a) + 240*I*d^4)*polylog(5, -e^(I*b*x + I*a)) - (240*I*d^4*cos(4*b*x + 4*a) - 480*I*d^4*cos(2*b*x + 2*a) - 240*d^4*sin(4*b*x + 4*a) + 480*d^4*sin(2*b*x + 2*a) + 240*I*d^4)*polylog(5, e^(I*b*x + I*a)) - (240*b*c*d^3 + 240*(b*x + a)*d^4 - 240*a*d^4 + 240*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) - 480*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) + (240*I*b*c*d^3 + 240*I*(b*x + a)*d^4 - 240*I*a*d^4)*sin(4*b*x + 4*a) + (-480*I*b*c*d^3 - 480*I*(b*x + a)*d^4 + 480*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, -e^(I*b*x + I*a)) - (240*b*c*d^3 + 240*(b*x + a)*d^4 - 240*a*d^4 + 240*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) - 480*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) + (240*I*b*c*d^3 + 240*I*(b*x + a)*d^4 - 240*I*a*d^4)*sin(4*b*x + 4*a) + (-480*I*b*c*d^3 - 480*I*(b*x + a)*d^4 + 480*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, e^(I*b*x + I*a)) - (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 - 120*I*(b*x + a)^2*d^4 + (-120*I*a^2 + 120*I)*d^4 + (-240*I*b*c*d^3 + 240*I*a*d^4)*(b*x + a) + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 - 120*I*(b*x + a)^2*d^4 + (-120*I*a^2 + 120*I)*d^4 + (-240*I*b*c*d^3 + 240*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (240*I*b^2*c^2*d^2 - 480*I*a*b*c*d^3 + 240*I*(b*x + a)^2*d^4 + (240*I*a^2 - 240*I)*d^4 + (480*I*b*c*d^3 - 480*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 1)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 240*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 1)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) - (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 - 120*I*(b*x + a)^2*d^4 + (-120*I*a^2 + 120*I)*d^4 + (-240*I*b*c*d^3 + 240*I*a*d^4)*(b*x + a) + (-120*I*b^2*c^2*d^2 + 240*I*a*b*c*d^3 - 120*I*(b*x + a)^2*d^4 + (-120*I*a^2 + 120*I)*d^4 + (-240*I*b*c*d^3 + 240*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (240*I*b^2*c^2*d^2 - 480*I*a*b*c*d^3 + 240*I*(b*x + a)^2*d^4 + (240*I*a^2 - 240*I)*d^4 + (480*I*b*c*d^3 - 480*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 120*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 1)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 240*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + (a^2 - 1)*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) - (-2*I*(b*x + a)^5*d^4 + (-10*I*b*c*d^3 + 10*I*a*d^4)*(b*x + a)^4 + (-20*I*b^2*c^2*d^2 + 40*I*a*b*c*d^3 + (-20*I*a^2 + 40*I)*d^4)*(b*x + a)^3 + (-20*I*b^3*c^3*d + 60*I*a*b^2*c^2*d^2 + (-60*I*a^2 + 120*I)*b*c*d^3 + (20*I*a^3 - 120*I*a)*d^4)*(b*x + a)^2 + (120*I*b^2*c^2*d^2 - 240*I*a*b*c*d^3 + 120*I*a^2*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (4*I*(b*x + a)^5*d^4 + 40*I*b^3*c^3*d - 120*I*a*b^2*c^2*d^2 + 120*I*a^2*b*c*d^3 - 40*I*a^3*d^4 + (20*I*b*c*d^3 - 20*(I*a + 1)*d^4)*(b*x + a)^4 + (40*I*b^2*c^2*d^2 - 80*(I*a + 1)*b*c*d^3 + (40*I*a^2 + 80*a - 40*I)*d^4)*(b*x + a)^3 + (40*I*b^3*c^3*d - 120*(I*a + 1)*b^2*c^2*d^2 + (120*I*a^2 + 240*a - 120*I)*b*c*d^3 + (-40*I*a^3 - 120*a^2 + 120*I*a)*d^4)*(b*x + a)^2 - (80*b^3*c^3*d - (240*a - 120*I)*b^2*c^2*d^2 + 240*(a^2 - I*a)*b*c*d^3 - 40*(2*a^3 - 3*I*a^2)*d^4)*(b*x + a))*sin(2*b*x + 2*a))/(-10*I*b^4*cos(4*b*x + 4*a) + 20*I*b^4*cos(2*b*x + 2*a) + 10*b^4*sin(4*b*x + 4*a) - 20*b^4*sin(2*b*x + 2*a) - 10*I*b^4))/b","B",0
179,1,3952,0,1.737284," ","integrate((d*x+c)^3*cot(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} - \frac{2 \, {\left({\left(b x + a\right)}^{4} d^{3} + 12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, a^{2} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(4 \, {\left(b x + a\right)}^{3} d^{3} - 12 \, b c d^{2} + 12 \, a d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)} + 4 \, {\left({\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, 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} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\left({\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, 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} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 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} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} + 24 i \, b c d^{2} - 24 i \, a d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d + 48 i \, a b c d^{2} + {\left(-24 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(4 \, {\left(b x + a\right)}^{3} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + 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} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\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} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, 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} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(24 i \, b c d^{2} - 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{2} c^{2} d - 48 i \, a b c d^{2} + {\left(24 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({\left(b x + a\right)}^{4} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{3} + 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} - 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(b x + a\right)}^{4} d^{3} + 12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, a^{2} d^{3} + {\left(8 \, b c d^{2} - {\left(8 \, a - 8 i\right)} d^{3}\right)} {\left(b x + a\right)}^{3} + {\left(12 \, b^{2} c^{2} d - {\left(24 \, a - 24 i\right)} b c d^{2} + 12 \, {\left(a^{2} - 2 i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{2} c^{2} d - 24 \, {\left(2 i \, a + 1\right)} b c d^{2} + {\left(24 i \, a^{2} + 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, {\left(a^{2} - 1\right)} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + 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} - 1\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) - 24 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} - 1\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(-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} + 12 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(4 \, b x + 4 \, a\right) - {\left(24 i \, b^{2} c^{2} d - 48 i \, a b c d^{2} + 24 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(24 i \, a^{2} - 24 i\right)} d^{3} + {\left(48 i \, b c d^{2} - 48 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(12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, {\left(a^{2} - 1\right)} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + 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} - 1\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) - 24 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} - 1\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(-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} + 12 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(4 \, b x + 4 \, a\right) - {\left(24 i \, b^{2} c^{2} d - 48 i \, a b c d^{2} + 24 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(24 i \, a^{2} - 24 i\right)} d^{3} + {\left(48 i \, b c d^{2} - 48 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(-2 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 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} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-2 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 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} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 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} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, 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} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, 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} - 1\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(-2 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 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} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-2 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 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} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 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} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, 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} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left({\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, 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} - 1\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(24 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 48 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 24 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 48 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 24 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(24 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 48 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 24 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 48 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 24 \, d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3} + {\left(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(48 i \, b c d^{2} + 48 i \, {\left(b x + a\right)} d^{3} - 48 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 48 \, {\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(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3} + {\left(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(48 i \, b c d^{2} + 48 i \, {\left(b x + a\right)} d^{3} - 48 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 48 \, {\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(-i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-4 i \, b c d^{2} + 4 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + {\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)}^{2} + {\left(24 i \, b c d^{2} - 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(2 i \, {\left(b x + a\right)}^{4} d^{3} + 12 i \, b^{2} c^{2} d - 24 i \, a b c d^{2} + 12 i \, a^{2} d^{3} + {\left(8 i \, b c d^{2} - 8 \, {\left(i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{3} + {\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 - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(24 \, b^{2} c^{2} d - {\left(48 \, a - 24 i\right)} b c d^{2} + 24 \, {\left(a^{2} - i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, 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}}}{2 \, b}"," ",0,"-1/2*(c^3*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2)) - 3*a*c^2*d*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b + 3*a^2*c*d^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b^2 - a^3*d^3*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b^3 - 2*((b*x + a)^4*d^3 + 12*b^2*c^2*d - 24*a*b*c*d^2 + 12*a^2*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a)^3 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a)^2 - (4*(b*x + a)^3*d^3 - 12*b*c*d^2 + 12*a*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 12*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + a) + 4*((b*x + a)^3*d^3 - 3*b*c*d^2 + 3*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 - 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 8*((b*x + a)^3*d^3 - 3*b*c*d^2 + 3*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 - 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (4*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*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 - 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-8*I*(b*x + a)^3*d^3 + 24*I*b*c*d^2 - 24*I*a*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a)^2 + (-24*I*b^2*c^2*d + 48*I*a*b*c*d^2 + (-24*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) + (4*(b*x + a)^3*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 12*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + 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 - 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 8*((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 - 1)*d^3)*(b*x + a))*cos(2*b*x + 2*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 + 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (8*I*(b*x + a)^3*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a)^2 + (24*I*b^2*c^2*d - 48*I*a*b*c*d^2 + (24*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) + ((b*x + a)^4*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a)^3 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 2)*d^3)*(b*x + a)^2 - 24*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - (2*(b*x + a)^4*d^3 + 12*b^2*c^2*d - 24*a*b*c*d^2 + 12*a^2*d^3 + (8*b*c*d^2 - (8*a - 8*I)*d^3)*(b*x + a)^3 + (12*b^2*c^2*d - (24*a - 24*I)*b*c*d^2 + 12*(a^2 - 2*I*a - 1)*d^3)*(b*x + a)^2 + (24*I*b^2*c^2*d - 24*(2*I*a + 1)*b*c*d^2 + (24*I*a^2 + 24*a)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (12*b^2*c^2*d - 24*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 12*(a^2 - 1)*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) + 12*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 - 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 24*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 - 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*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 + 12*I)*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (24*I*b^2*c^2*d - 48*I*a*b*c*d^2 + 24*I*(b*x + a)^2*d^3 + (24*I*a^2 - 24*I)*d^3 + (48*I*b*c*d^2 - 48*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (12*b^2*c^2*d - 24*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 12*(a^2 - 1)*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) + 12*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 - 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 24*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 - 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*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 + 12*I)*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (24*I*b^2*c^2*d - 48*I*a*b*c*d^2 + 24*I*(b*x + a)^2*d^3 + (24*I*a^2 - 24*I)*d^3 + (48*I*b*c*d^2 - 48*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(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 + (-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 + 6*I)*d^3)*(b*x + a) + (-2*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*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 + 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (4*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*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 - 12*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 2*((b*x + a)^3*d^3 - 3*b*c*d^2 + 3*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 - 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - 4*((b*x + a)^3*d^3 - 3*b*c*d^2 + 3*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 - 1)*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) - (-2*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*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 + 6*I)*d^3)*(b*x + a) + (-2*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*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 + 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (4*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*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 - 12*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 2*((b*x + a)^3*d^3 - 3*b*c*d^2 + 3*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 - 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - 4*((b*x + a)^3*d^3 - 3*b*c*d^2 + 3*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 - 1)*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) - (24*d^3*cos(4*b*x + 4*a) - 48*d^3*cos(2*b*x + 2*a) + 24*I*d^3*sin(4*b*x + 4*a) - 48*I*d^3*sin(2*b*x + 2*a) + 24*d^3)*polylog(4, -e^(I*b*x + I*a)) - (24*d^3*cos(4*b*x + 4*a) - 48*d^3*cos(2*b*x + 2*a) + 24*I*d^3*sin(4*b*x + 4*a) - 48*I*d^3*sin(2*b*x + 2*a) + 24*d^3)*polylog(4, e^(I*b*x + I*a)) - (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3 + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*cos(4*b*x + 4*a) + (48*I*b*c*d^2 + 48*I*(b*x + a)*d^3 - 48*I*a*d^3)*cos(2*b*x + 2*a) + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 48*(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)) - (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3 + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*cos(4*b*x + 4*a) + (48*I*b*c*d^2 + 48*I*(b*x + a)*d^3 - 48*I*a*d^3)*cos(2*b*x + 2*a) + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 48*(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)) - (-I*(b*x + a)^4*d^3 + (-4*I*b*c*d^2 + 4*I*a*d^3)*(b*x + a)^3 + (-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)^2 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (2*I*(b*x + a)^4*d^3 + 12*I*b^2*c^2*d - 24*I*a*b*c*d^2 + 12*I*a^2*d^3 + (8*I*b*c*d^2 - 8*(I*a + 1)*d^3)*(b*x + a)^3 + (12*I*b^2*c^2*d - 24*(I*a + 1)*b*c*d^2 + (12*I*a^2 + 24*a - 12*I)*d^3)*(b*x + a)^2 - (24*b^2*c^2*d - (48*a - 24*I)*b*c*d^2 + 24*(a^2 - I*a)*d^3)*(b*x + a))*sin(2*b*x + 2*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
180,1,1966,0,0.709496," ","integrate((d*x+c)^2*cot(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{2 \, a c d {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{2 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}^{2} + 12 \, b c d - 12 \, a d^{2} - {\left(6 \, {\left(b x + a\right)}^{2} d^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - 6 \, d^{2} + 6 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 6 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-24 i \, b c d + 24 i \, a d^{2}\right)} {\left(b x + a\right)} + 12 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(6 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 12 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 12 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 6 \, d^{2}\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^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 6 \, {\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) - 12 \, {\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(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(24 i \, b c d - 24 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) + 2 \, {\left({\left(b x + a\right)}^{3} d^{2} + 3 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(4 \, {\left(b x + a\right)}^{3} d^{2} + {\left(12 \, b c d - {\left(12 \, a - 12 i\right)} d^{2}\right)} {\left(b x + a\right)}^{2} + 12 \, b c d - 12 \, a d^{2} + {\left(24 i \, b c d - 12 \, {\left(2 i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, b c d + 12 \, {\left(b x + a\right)} d^{2} - 12 \, a d^{2} + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, b c d + 24 i \, {\left(b x + a\right)} d^{2} - 24 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(12 \, b c d + 12 \, {\left(b x + a\right)} d^{2} - 12 \, a d^{2} + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(24 i \, b c d + 24 i \, {\left(b x + a\right)} d^{2} - 24 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(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 3 i \, d^{2} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 3 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 6 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - 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(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 3 i \, d^{2} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 3 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 6 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - 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(-12 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 24 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 24 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-12 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 24 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 24 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(-2 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(12 i \, b c d - 12 \, {\left(i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}^{2} + 12 i \, b c d - 12 i \, a d^{2} - {\left(24 \, b c d - {\left(24 \, a - 12 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-6 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 12 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 6 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 12 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, b^{2}}}{2 \, b}"," ",0,"-1/2*(c^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2)) - 2*a*c*d*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b + a^2*d^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2))/b^2 - 2*(2*(b*x + a)^3*d^2 + 6*(b*c*d - a*d^2)*(b*x + a)^2 + 12*b*c*d - 12*a*d^2 - (6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) - 6*d^2 + 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*cos(4*b*x + 4*a) - 12*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) - 6*I*d^2)*sin(4*b*x + 4*a) + (-12*I*(b*x + a)^2*d^2 + (-24*I*b*c*d + 24*I*a*d^2)*(b*x + a) + 12*I*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*d^2*cos(4*b*x + 4*a) - 12*d^2*cos(2*b*x + 2*a) + 6*I*d^2*sin(4*b*x + 4*a) - 12*I*d^2*sin(2*b*x + 2*a) + 6*d^2)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) + 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(4*b*x + 4*a) - 12*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(2*b*x + 2*a) - (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a))*sin(4*b*x + 4*a) - (12*I*(b*x + a)^2*d^2 + (24*I*b*c*d - 24*I*a*d^2)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 2*((b*x + a)^3*d^2 + 3*(b*c*d - a*d^2)*(b*x + a)^2 - 6*(b*x + a)*d^2)*cos(4*b*x + 4*a) - (4*(b*x + a)^3*d^2 + (12*b*c*d - (12*a - 12*I)*d^2)*(b*x + a)^2 + 12*b*c*d - 12*a*d^2 + (24*I*b*c*d - 12*(2*I*a + 1)*d^2)*(b*x + a))*cos(2*b*x + 2*a) + (12*b*c*d + 12*(b*x + a)*d^2 - 12*a*d^2 + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 24*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(4*b*x + 4*a) - (24*I*b*c*d + 24*I*(b*x + a)*d^2 - 24*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (12*b*c*d + 12*(b*x + a)*d^2 - 12*a*d^2 + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 24*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(4*b*x + 4*a) - (24*I*b*c*d + 24*I*(b*x + a)*d^2 - 24*I*a*d^2)*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) + 3*I*d^2 + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) + 3*I*d^2)*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) - 6*I*d^2)*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*sin(4*b*x + 4*a) - 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - 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) - (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) + 3*I*d^2 + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) + 3*I*d^2)*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) - 6*I*d^2)*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*sin(4*b*x + 4*a) - 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - 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) - (-12*I*d^2*cos(4*b*x + 4*a) + 24*I*d^2*cos(2*b*x + 2*a) + 12*d^2*sin(4*b*x + 4*a) - 24*d^2*sin(2*b*x + 2*a) - 12*I*d^2)*polylog(3, -e^(I*b*x + I*a)) - (-12*I*d^2*cos(4*b*x + 4*a) + 24*I*d^2*cos(2*b*x + 2*a) + 12*d^2*sin(4*b*x + 4*a) - 24*d^2*sin(2*b*x + 2*a) - 12*I*d^2)*polylog(3, e^(I*b*x + I*a)) - (-2*I*(b*x + a)^3*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a)^2 + 12*I*(b*x + a)*d^2)*sin(4*b*x + 4*a) - (4*I*(b*x + a)^3*d^2 + (12*I*b*c*d - 12*(I*a + 1)*d^2)*(b*x + a)^2 + 12*I*b*c*d - 12*I*a*d^2 - (24*b*c*d - (24*a - 12*I)*d^2)*(b*x + a))*sin(2*b*x + 2*a))/(-6*I*b^2*cos(4*b*x + 4*a) + 12*I*b^2*cos(2*b*x + 2*a) + 6*b^2*sin(4*b*x + 4*a) - 12*b^2*sin(2*b*x + 2*a) - 6*I*b^2))/b","B",0
181,1,839,0,0.527879," ","integrate((d*x+c)*cot(b*x+a)^3,x, algorithm=""maxima"")","\frac{b^{2} d x^{2} + 2 \, b^{2} c x - {\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(b^{2} d x^{2} + 2 \, b^{2} c x\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, b^{2} d x^{2} + 4 i \, b c + {\left(4 \, b^{2} c + 4 i \, b d\right)} x + 2 \, d\right)} \cos\left(2 \, b x + 2 \, 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) - {\left(-i \, b^{2} d x^{2} - 2 i \, b^{2} c x\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(2 i \, b^{2} d x^{2} - 4 \, b c - 4 \, {\left(-i \, b^{2} c + b d\right)} x + 2 i \, d\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}"," ",0,"(b^2*d*x^2 + 2*b^2*c*x - (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) + (b^2*d*x^2 + 2*b^2*c*x)*cos(4*b*x + 4*a) - (2*b^2*d*x^2 + 4*I*b*c + (4*b^2*c + 4*I*b*d)*x + 2*d)*cos(2*b*x + 2*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) - (-I*b^2*d*x^2 - 2*I*b^2*c*x)*sin(4*b*x + 4*a) - (2*I*b^2*d*x^2 - 4*b*c - 4*(-I*b^2*c + b*d)*x + 2*I*d)*sin(2*b*x + 2*a) + 2*d)/(-2*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2)","B",0
182,-1,0,0,0.000000," ","integrate(cot(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(cot(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,1,547,0,0.562699," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","\frac{{\left(1280 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 10240 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 32 \, {\left(\frac{64 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 512 \, {\left(\frac{16 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{65536 \, b^{5}}"," ",0,"1/65536*(1280*(d*x + c)^(3/2)*b^3*sin(4*((d*x + c)*b - b*c + a*d)/d) + 10240*(d*x + c)^(3/2)*b^3*sin(2*((d*x + c)*b - b*c + a*d)/d) - 32*(64*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(4*((d*x + c)*b - b*c + a*d)/d) - 512*(16*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + ((30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + (-(480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)))*d/b^5","C",0
185,1,503,0,0.510960," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{256 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{1024 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - 96 \, \sqrt{d x + c} b^{2} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 768 \, \sqrt{d x + c} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - {\left(\left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{8192 \, b^{4}}"," ",0,"-1/8192*(256*(d*x + c)^(3/2)*b^3*cos(4*((d*x + c)*b - b*c + a*d)/d)/d + 1024*(d*x + c)^(3/2)*b^3*cos(2*((d*x + c)*b - b*c + a*d)/d)/d - 96*sqrt(d*x + c)*b^2*sin(4*((d*x + c)*b - b*c + a*d)/d) - 768*sqrt(d*x + c)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - ((6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) - ((48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^4","C",0
186,1,425,0,0.537122," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{32 \, \sqrt{d x + c} b^{2} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{128 \, \sqrt{d x + c} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + {\left(\left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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)} d}{1024 \, b^{3}}"," ",0,"-1/1024*(32*sqrt(d*x + c)*b^2*cos(4*((d*x + c)*b - b*c + a*d)/d)/d + 128*sqrt(d*x + c)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d)/d + ((8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + (-(8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^3","C",0
187,1,425,0,0.511240," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{32 \, \sqrt{d x + c} b^{2} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{128 \, \sqrt{d x + c} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + {\left(\left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(2 i + 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i - 2\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(8 i + 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(8 i - 8\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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)} d}{1024 \, b^{3}}"," ",0,"-1/1024*(32*sqrt(d*x + c)*b^2*cos(4*((d*x + c)*b - b*c + a*d)/d)/d + 128*sqrt(d*x + c)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d)/d + ((8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(2*I + 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (2*I - 2)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + (-(8*I + 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (8*I - 8)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^3","C",0
188,1,503,0,0.534700," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","-\frac{{\left(\frac{256 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{1024 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - 96 \, \sqrt{d x + c} b^{2} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 768 \, \sqrt{d x + c} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) - {\left(\left(6 i - 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(6 i + 6\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) - {\left(\left(48 i - 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(48 i + 48\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{8192 \, b^{4}}"," ",0,"-1/8192*(256*(d*x + c)^(3/2)*b^3*cos(4*((d*x + c)*b - b*c + a*d)/d)/d + 1024*(d*x + c)^(3/2)*b^3*cos(2*((d*x + c)*b - b*c + a*d)/d)/d - 96*sqrt(d*x + c)*b^2*sin(4*((d*x + c)*b - b*c + a*d)/d) - 768*sqrt(d*x + c)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) - ((6*I - 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (6*I + 6)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) - ((48*I - 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (48*I + 48)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))*d/b^4","C",0
189,1,547,0,0.518853," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""maxima"")","\frac{{\left(1280 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 10240 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 32 \, {\left(\frac{64 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{4 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 512 \, {\left(\frac{16 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + \left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(30 i + 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - \left(30 i - 30\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(2 \, \sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(480 i + 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(480 i - 480\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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)} d}{65536 \, b^{5}}"," ",0,"1/65536*(1280*(d*x + c)^(3/2)*b^3*sin(4*((d*x + c)*b - b*c + a*d)/d) + 10240*(d*x + c)^(3/2)*b^3*sin(2*((d*x + c)*b - b*c + a*d)/d) - 32*(64*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(4*((d*x + c)*b - b*c + a*d)/d) - 512*(16*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + ((30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) + (30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(I*b/d)) + (-(30*I + 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-4*(b*c - a*d)/d) - (30*I - 30)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-4*(b*c - a*d)/d))*erf(2*sqrt(d*x + c)*sqrt(-I*b/d)) + (-(480*I + 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (480*I - 480)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)))*d/b^5","C",0
190,1,820,0,0.566341," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{10800 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{30000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{540000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} + {\left(\left(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(\left(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(202500 i + 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(202500 i - 202500\right) \, \sqrt{\pi} b^{2} 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(202500 i - 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(202500 i + 202500\right) \, \sqrt{\pi} b^{2} 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(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right) + 1080 \, {\left(\frac{20 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 3 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 3000 \, {\left(\frac{12 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 5 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 54000 \, {\left(\frac{4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 15 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)\right)} d^{2}}{3456000 \, b^{6}}"," ",0,"-1/3456000*sqrt(2)*(10800*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(5*((d*x + c)*b - b*c + a*d)/d)/d + 30000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(3*((d*x + c)*b - b*c + a*d)/d)/d - 540000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(((d*x + c)*b - b*c + a*d)/d)/d + ((162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + ((1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)) + 1080*(20*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 3*sqrt(2)*sqrt(d*x + c)*b^3)*sin(5*((d*x + c)*b - b*c + a*d)/d) + 3000*(12*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 5*sqrt(2)*sqrt(d*x + c)*b^3)*sin(3*((d*x + c)*b - b*c + a*d)/d) - 54000*(4*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 15*sqrt(2)*sqrt(d*x + c)*b^3)*sin(((d*x + c)*b - b*c + a*d)/d))*d^2/b^6","C",0
191,1,754,0,0.583761," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{3600 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} + \frac{6000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{36000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} + \frac{1080 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{3000 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{54000 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} + {\left(\left(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(\left(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(13500 i - 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(13500 i + 13500\right) \, \sqrt{\pi} b^{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(13500 i + 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(13500 i - 13500\right) \, \sqrt{\pi} b^{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(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{576000 \, b^{5}}"," ",0,"-1/576000*sqrt(2)*(3600*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(5*((d*x + c)*b - b*c + a*d)/d)/d^2 + 6000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 36000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(((d*x + c)*b - b*c + a*d)/d)/d^2 + 1080*sqrt(2)*sqrt(d*x + c)*b^3*cos(5*((d*x + c)*b - b*c + a*d)/d)/d + 3000*sqrt(2)*sqrt(d*x + c)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d)/d - 54000*sqrt(2)*sqrt(d*x + c)*b^3*cos(((d*x + c)*b - b*c + a*d)/d)/d + ((54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + ((250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^5","C",0
192,1,674,0,0.518628," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{360 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} + \frac{600 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{3600 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} + {\left(-\frac{\left(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} + \frac{\left(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(-\frac{\left(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(900 i + 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} - \frac{\left(900 i - 900\right) \, \sqrt{\pi} b^{2} \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(900 i - 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} + \frac{\left(900 i + 900\right) \, \sqrt{\pi} b^{2} \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(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} - \frac{\left(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{57600 \, b^{4}}"," ",0,"-1/57600*sqrt(2)*(360*sqrt(2)*sqrt(d*x + c)*b^3*sin(5*((d*x + c)*b - b*c + a*d)/d)/d^2 + 600*sqrt(2)*sqrt(d*x + c)*b^3*sin(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 3600*sqrt(2)*sqrt(d*x + c)*b^3*sin(((d*x + c)*b - b*c + a*d)/d)/d^2 + (-(18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d + (18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + (-(50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d + (50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + ((900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d - (900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d + (900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d - (50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + ((18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d - (18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^4","C",0
193,1,674,0,0.512506," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{360 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} + \frac{600 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{3600 \, \sqrt{2} \sqrt{d x + c} b^{3} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} + {\left(-\frac{\left(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} + \frac{\left(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(-\frac{\left(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(900 i + 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} - \frac{\left(900 i - 900\right) \, \sqrt{\pi} b^{2} \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(900 i - 900\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} + \frac{\left(900 i + 900\right) \, \sqrt{\pi} b^{2} \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(50 i - 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(50 i + 50\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \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(18 i - 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d} - \frac{\left(18 i + 18\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{57600 \, b^{4}}"," ",0,"-1/57600*sqrt(2)*(360*sqrt(2)*sqrt(d*x + c)*b^3*sin(5*((d*x + c)*b - b*c + a*d)/d)/d^2 + 600*sqrt(2)*sqrt(d*x + c)*b^3*sin(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 3600*sqrt(2)*sqrt(d*x + c)*b^3*sin(((d*x + c)*b - b*c + a*d)/d)/d^2 + (-(18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d + (18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + (-(50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d + (50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + ((900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d - (900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(900*I - 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d + (900*I + 900)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((50*I - 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d - (50*I + 50)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + ((18*I - 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d)/d - (18*I + 18)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^4","C",0
194,1,754,0,0.534578," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{3600 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} + \frac{6000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d^{2}} - \frac{36000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d^{2}} + \frac{1080 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{3000 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{54000 \, \sqrt{2} \sqrt{d x + c} b^{3} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} + {\left(\left(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(\left(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(13500 i - 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(13500 i + 13500\right) \, \sqrt{\pi} b^{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(13500 i + 13500\right) \, \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(13500 i - 13500\right) \, \sqrt{\pi} b^{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(250 i + 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(250 i - 250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{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(54 i + 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(54 i - 54\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right)\right)} d^{2}}{576000 \, b^{5}}"," ",0,"-1/576000*sqrt(2)*(3600*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(5*((d*x + c)*b - b*c + a*d)/d)/d^2 + 6000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(3*((d*x + c)*b - b*c + a*d)/d)/d^2 - 36000*sqrt(2)*(d*x + c)^(3/2)*b^4*sin(((d*x + c)*b - b*c + a*d)/d)/d^2 + 1080*sqrt(2)*sqrt(d*x + c)*b^3*cos(5*((d*x + c)*b - b*c + a*d)/d)/d + 3000*sqrt(2)*sqrt(d*x + c)*b^3*cos(3*((d*x + c)*b - b*c + a*d)/d)/d - 54000*sqrt(2)*sqrt(d*x + c)*b^3*cos(((d*x + c)*b - b*c + a*d)/d)/d + ((54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + ((250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((13500*I + 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (13500*I - 13500)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(250*I + 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (250*I - 250)*9^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(54*I + 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (54*I - 54)*25^(1/4)*sqrt(pi)*b^2*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)))*d^2/b^5","C",0
195,1,820,0,0.576702," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left(\frac{10800 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + \frac{30000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{540000 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{4} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)}{d} + {\left(\left(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - \left(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{5 i \, b}{d}}\right) + {\left(\left(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(202500 i + 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(202500 i - 202500\right) \, \sqrt{\pi} b^{2} 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(202500 i - 202500\right) \, \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(202500 i + 202500\right) \, \sqrt{\pi} b^{2} 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(1250 i - 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(1250 i + 1250\right) \cdot 9^{\frac{1}{4}} \sqrt{\pi} b^{2} 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(162 i - 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + \left(162 i + 162\right) \cdot 25^{\frac{1}{4}} \sqrt{\pi} b^{2} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{5 i \, b}{d}}\right) + 1080 \, {\left(\frac{20 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 3 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \sin\left(\frac{5 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 3000 \, {\left(\frac{12 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 5 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \sin\left(\frac{3 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 54000 \, {\left(\frac{4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{5}}{d^{2}} - 15 \, \sqrt{2} \sqrt{d x + c} b^{3}\right)} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)\right)} d^{2}}{3456000 \, b^{6}}"," ",0,"-1/3456000*sqrt(2)*(10800*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(5*((d*x + c)*b - b*c + a*d)/d)/d + 30000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(3*((d*x + c)*b - b*c + a*d)/d)/d - 540000*sqrt(2)*(d*x + c)^(3/2)*b^4*cos(((d*x + c)*b - b*c + a*d)/d)/d + ((162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) - (162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(5*I*b/d)) + ((1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + (-(202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((202500*I - 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (202500*I + 202500)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(1250*I - 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (1250*I + 1250)*9^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + (-(162*I - 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*cos(-5*(b*c - a*d)/d) + (162*I + 162)*25^(1/4)*sqrt(pi)*b^2*d*(b^2/d^2)^(1/4)*sin(-5*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-5*I*b/d)) + 1080*(20*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 3*sqrt(2)*sqrt(d*x + c)*b^3)*sin(5*((d*x + c)*b - b*c + a*d)/d) + 3000*(12*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 5*sqrt(2)*sqrt(d*x + c)*b^3)*sin(3*((d*x + c)*b - b*c + a*d)/d) - 54000*(4*sqrt(2)*(d*x + c)^(5/2)*b^5/d^2 - 15*sqrt(2)*sqrt(d*x + c)*b^3)*sin(((d*x + c)*b - b*c + a*d)/d))*d^2/b^6","C",0
196,1,557,0,0.534397," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(1920 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 51840 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 96 \, {\left(\frac{48 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 5 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 2592 \, {\left(\frac{16 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(10 i - 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + \left(10 i + 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{6 i \, b}{d}}\right) + {\left(-\left(2430 i - 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2430 i + 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2430 i + 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2430 i - 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(10 i + 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - \left(10 i - 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{6 i \, b}{d}}\right)\right)} d}{884736 \, b^{5}}"," ",0,"-1/884736*(1920*(d*x + c)^(3/2)*b^3*sin(6*((d*x + c)*b - b*c + a*d)/d) - 51840*(d*x + c)^(3/2)*b^3*sin(2*((d*x + c)*b - b*c + a*d)/d) - 96*(48*(d*x + c)^(5/2)*b^4/d - 5*sqrt(d*x + c)*b^2*d)*cos(6*((d*x + c)*b - b*c + a*d)/d) + 2592*(16*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((10*I - 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) + (10*I + 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(6*I*b/d)) + (-(2430*I - 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (2430*I + 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + ((2430*I + 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (2430*I - 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + (-(10*I + 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) - (10*I - 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-6*I*b/d)))*d/b^5","C",0
197,1,513,0,0.514085," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{384 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{3456 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - 96 \, \sqrt{d x + c} b^{2} \sin\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 2592 \, \sqrt{d x + c} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{6 i \, b}{d}}\right) - {\left(\left(162 i + 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(162 i - 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(162 i - 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(162 i + 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{6 i \, b}{d}}\right)\right)} d}{73728 \, b^{4}}"," ",0,"1/73728*(384*(d*x + c)^(3/2)*b^3*cos(6*((d*x + c)*b - b*c + a*d)/d)/d - 3456*(d*x + c)^(3/2)*b^3*cos(2*((d*x + c)*b - b*c + a*d)/d)/d - 96*sqrt(d*x + c)*b^2*sin(6*((d*x + c)*b - b*c + a*d)/d) + 2592*sqrt(d*x + c)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) + (2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(6*I*b/d)) - ((162*I + 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (162*I - 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(162*I - 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (162*I + 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) - ((2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) - (2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-6*I*b/d)))*d/b^4","C",0
198,1,435,0,0.524637," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{96 \, \sqrt{d x + c} b^{2} \cos\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{864 \, \sqrt{d x + c} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + {\left(\left(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{6 i \, b}{d}}\right) + {\left(-\left(54 i - 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(54 i + 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(54 i + 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(54 i - 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{6 i \, b}{d}}\right)\right)} d}{18432 \, b^{3}}"," ",0,"1/18432*(96*sqrt(d*x + c)*b^2*cos(6*((d*x + c)*b - b*c + a*d)/d)/d - 864*sqrt(d*x + c)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d)/d + ((2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) + (2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(6*I*b/d)) + (-(54*I - 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (54*I + 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((54*I + 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (54*I - 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) + (-(2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) - (2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-6*I*b/d)))*d/b^3","C",0
199,1,435,0,0.511771," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{96 \, \sqrt{d x + c} b^{2} \cos\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{864 \, \sqrt{d x + c} b^{2} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} + {\left(\left(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{6 i \, b}{d}}\right) + {\left(-\left(54 i - 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(54 i + 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(54 i + 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(54 i - 54\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \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(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{6 i \, b}{d}}\right)\right)} d}{18432 \, b^{3}}"," ",0,"1/18432*(96*sqrt(d*x + c)*b^2*cos(6*((d*x + c)*b - b*c + a*d)/d)/d - 864*sqrt(d*x + c)*b^2*cos(2*((d*x + c)*b - b*c + a*d)/d)/d + ((2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) + (2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(6*I*b/d)) + (-(54*I - 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (54*I + 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((54*I + 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (54*I - 54)*4^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) + (-(2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) - (2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-6*I*b/d)))*d/b^3","C",0
200,1,513,0,0.541825," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","\frac{{\left(\frac{384 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - \frac{3456 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)}{d} - 96 \, \sqrt{d x + c} b^{2} \sin\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 2592 \, \sqrt{d x + c} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - {\left(-\left(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + \left(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{6 i \, b}{d}}\right) - {\left(\left(162 i + 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(162 i - 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(162 i - 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(162 i + 162\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2 i - 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - \left(2 i + 2\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{6 i \, b}{d}}\right)\right)} d}{73728 \, b^{4}}"," ",0,"1/73728*(384*(d*x + c)^(3/2)*b^3*cos(6*((d*x + c)*b - b*c + a*d)/d)/d - 3456*(d*x + c)^(3/2)*b^3*cos(2*((d*x + c)*b - b*c + a*d)/d)/d - 96*sqrt(d*x + c)*b^2*sin(6*((d*x + c)*b - b*c + a*d)/d) + 2592*sqrt(d*x + c)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) - (-(2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) + (2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(6*I*b/d)) - ((162*I + 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (162*I - 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) - (-(162*I - 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (162*I + 162)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) - ((2*I - 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) - (2*I + 2)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-6*I*b/d)))*d/b^4","C",0
201,1,557,0,0.564172," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{{\left(1920 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 51840 \, {\left(d x + c\right)}^{\frac{3}{2}} b^{3} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) - 96 \, {\left(\frac{48 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 5 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{6 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 2592 \, {\left(\frac{16 \, {\left(d x + c\right)}^{\frac{5}{2}} b^{4}}{d} - 15 \, \sqrt{d x + c} b^{2} d\right)} \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(10 i - 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + \left(10 i + 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{6 i \, b}{d}}\right) + {\left(-\left(2430 i - 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2430 i + 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2430 i + 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(2430 i - 2430\right) \cdot 4^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b 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(10 i + 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - \left(10 i - 10\right) \cdot 36^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{6 i \, b}{d}}\right)\right)} d}{884736 \, b^{5}}"," ",0,"-1/884736*(1920*(d*x + c)^(3/2)*b^3*sin(6*((d*x + c)*b - b*c + a*d)/d) - 51840*(d*x + c)^(3/2)*b^3*sin(2*((d*x + c)*b - b*c + a*d)/d) - 96*(48*(d*x + c)^(5/2)*b^4/d - 5*sqrt(d*x + c)*b^2*d)*cos(6*((d*x + c)*b - b*c + a*d)/d) + 2592*(16*(d*x + c)^(5/2)*b^4/d - 15*sqrt(d*x + c)*b^2*d)*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((10*I - 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) + (10*I + 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(6*I*b/d)) + (-(2430*I - 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (2430*I + 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + ((2430*I + 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (2430*I - 2430)*4^(1/4)*sqrt(2)*sqrt(pi)*b*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)) + (-(10*I + 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-6*(b*c - a*d)/d) - (10*I - 10)*36^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-6*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-6*I*b/d)))*d/b^5","C",0
202,-2,0,0,0.000000," ","integrate(x^3*cos(x)^2*cot(x)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
203,-2,0,0,0.000000," ","integrate(x^2*cos(x)^2*cot(x)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
204,-2,0,0,0.000000," ","integrate(x*cos(x)^2*cot(x)^2,x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
205,1,3719,0,0.945246," ","integrate(x^3*cos(x)^2*cot(x)^3,x, algorithm=""maxima"")","-\frac{4 \, x^{3} + {\left(4 \, x^{3} + 6 i \, x^{2} - 6 \, x - 3 i\right)} \cos\left(6 \, x\right)^{2} - {\left(-32 i \, x^{4} - 16 \, x^{3} + 168 i \, x^{2} + 24 \, x + 12 i\right)} \cos\left(4 \, x\right)^{2} - {\left(-32 i \, x^{4} + 56 \, x^{3} + 96 i \, x^{2} + 12 \, x\right)} \cos\left(2 \, x\right)^{2} - {\left(4 \, x^{3} + 6 i \, x^{2} - 6 \, x - 3 i\right)} \sin\left(6 \, x\right)^{2} - {\left(32 i \, x^{4} + 16 \, x^{3} - 168 i \, x^{2} - 24 \, x - 12 i\right)} \sin\left(4 \, x\right)^{2} - {\left(32 i \, x^{4} - 56 \, x^{3} - 96 i \, x^{2} - 12 \, x\right)} \sin\left(2 \, x\right)^{2} - 6 i \, x^{2} - {\left({\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(4 \, x\right)^{2} + {\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(2 \, x\right)^{2} + {\left(-128 i \, x^{3} + 192 i \, x\right)} \sin\left(4 \, x\right)^{2} + {\left(-128 i \, x^{3} + 192 i \, x\right)} \sin\left(2 \, x\right)^{2} + {\left(-64 i \, x^{3} + {\left(-64 i \, x^{3} + 96 i \, x\right)} \cos\left(4 \, x\right) + {\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(2 \, x\right) + 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(4 \, x\right) - 64 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) + 96 i \, x\right)} \cos\left(6 \, x\right) + {\left(128 i \, x^{3} + {\left(-320 i \, x^{3} + 480 i \, x\right)} \cos\left(2 \, x\right) + 160 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) - 192 i \, x\right)} \cos\left(4 \, x\right) + {\left(-64 i \, x^{3} + 96 i \, x\right)} \cos\left(2 \, x\right) + {\left(64 \, x^{3} + 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right) - 64 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + {\left(64 i \, x^{3} - 96 i \, x\right)} \sin\left(4 \, x\right) + {\left(-128 i \, x^{3} + 192 i \, x\right)} \sin\left(2 \, x\right) - 96 \, x\right)} \sin\left(6 \, x\right) - {\left(128 \, x^{3} + 128 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right) - 160 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) - {\left(320 i \, x^{3} - 480 i \, x\right)} \sin\left(2 \, x\right) - 192 \, x\right)} \sin\left(4 \, x\right) + 32 \, {\left(2 \, x^{3} - 4 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) - 3 \, x\right)} \sin\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left({\left(-128 i \, x^{3} + 192 i \, x\right)} \cos\left(4 \, x\right)^{2} + {\left(-128 i \, x^{3} + 192 i \, x\right)} \cos\left(2 \, x\right)^{2} + {\left(128 i \, x^{3} - 192 i \, x\right)} \sin\left(4 \, x\right)^{2} + {\left(128 i \, x^{3} - 192 i \, x\right)} \sin\left(2 \, x\right)^{2} + {\left(64 i \, x^{3} + {\left(64 i \, x^{3} - 96 i \, x\right)} \cos\left(4 \, x\right) + {\left(-128 i \, x^{3} + 192 i \, x\right)} \cos\left(2 \, x\right) - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(4 \, x\right) + 64 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) - 96 i \, x\right)} \cos\left(6 \, x\right) + {\left(-128 i \, x^{3} + {\left(320 i \, x^{3} - 480 i \, x\right)} \cos\left(2 \, x\right) - 160 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) + 192 i \, x\right)} \cos\left(4 \, x\right) + {\left(64 i \, x^{3} - 96 i \, x\right)} \cos\left(2 \, x\right) - {\left(64 \, x^{3} + 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right) - 64 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) - {\left(-64 i \, x^{3} + 96 i \, x\right)} \sin\left(4 \, x\right) - {\left(128 i \, x^{3} - 192 i \, x\right)} \sin\left(2 \, x\right) - 96 \, x\right)} \sin\left(6 \, x\right) + {\left(128 \, x^{3} + 128 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right) - 160 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + {\left(-320 i \, x^{3} + 480 i \, x\right)} \sin\left(2 \, x\right) - 192 \, x\right)} \sin\left(4 \, x\right) - 32 \, {\left(2 \, x^{3} - 4 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) - 3 \, x\right)} \sin\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - {\left(16 i \, x^{4} + 8 \, x^{3} - 12 i \, x^{2} + {\left(16 i \, x^{4} + 16 \, x^{3} - 72 i \, x^{2} - 24 \, x - 12 i\right)} \cos\left(4 \, x\right) + {\left(-32 i \, x^{4} + 52 \, x^{3} + 90 i \, x^{2} + 18 \, x + 3 i\right)} \cos\left(2 \, x\right) - {\left(16 \, x^{4} - 16 i \, x^{3} - 72 \, x^{2} + 24 i \, x - 12\right)} \sin\left(4 \, x\right) + {\left(32 \, x^{4} + 52 i \, x^{3} - 90 \, x^{2} + 18 i \, x - 3\right)} \sin\left(2 \, x\right) - 12 \, x + 6 i\right)} \cos\left(6 \, x\right) - {\left(-32 i \, x^{4} - 20 \, x^{3} + 30 i \, x^{2} + {\left(80 i \, x^{4} - 104 \, x^{3} - 276 i \, x^{2} - 36 \, x - 6 i\right)} \cos\left(2 \, x\right) - {\left(80 \, x^{4} + 104 i \, x^{3} - 276 \, x^{2} + 36 i \, x - 6\right)} \sin\left(2 \, x\right) + 30 \, x - 15 i\right)} \cos\left(4 \, x\right) - {\left(16 i \, x^{4} + 16 \, x^{3} - 24 i \, x^{2} - 24 \, x + 12 i\right)} \cos\left(2 \, x\right) - {\left({\left(-384 i \, x^{2} + 192 i\right)} \cos\left(4 \, x\right)^{2} + {\left(-384 i \, x^{2} + 192 i\right)} \cos\left(2 \, x\right)^{2} + {\left(384 i \, x^{2} - 192 i\right)} \sin\left(4 \, x\right)^{2} + {\left(384 i \, x^{2} - 192 i\right)} \sin\left(2 \, x\right)^{2} + {\left(192 i \, x^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(4 \, x\right) + {\left(-384 i \, x^{2} + 192 i\right)} \cos\left(2 \, x\right) - 96 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right) + 192 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) - 96 i\right)} \cos\left(6 \, x\right) + {\left(-384 i \, x^{2} + {\left(960 i \, x^{2} - 480 i\right)} \cos\left(2 \, x\right) - 480 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) + 192 i\right)} \cos\left(4 \, x\right) + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(2 \, x\right) - {\left(192 \, x^{2} + 96 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 192 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - {\left(-192 i \, x^{2} + 96 i\right)} \sin\left(4 \, x\right) - {\left(384 i \, x^{2} - 192 i\right)} \sin\left(2 \, x\right) - 96\right)} \sin\left(6 \, x\right) + {\left(384 \, x^{2} + 384 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 480 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(-960 i \, x^{2} + 480 i\right)} \sin\left(2 \, x\right) - 192\right)} \sin\left(4 \, x\right) - 96 \, {\left(2 \, x^{2} - 4 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right)\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - {\left({\left(-384 i \, x^{2} + 192 i\right)} \cos\left(4 \, x\right)^{2} + {\left(-384 i \, x^{2} + 192 i\right)} \cos\left(2 \, x\right)^{2} + {\left(384 i \, x^{2} - 192 i\right)} \sin\left(4 \, x\right)^{2} + {\left(384 i \, x^{2} - 192 i\right)} \sin\left(2 \, x\right)^{2} + {\left(192 i \, x^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(4 \, x\right) + {\left(-384 i \, x^{2} + 192 i\right)} \cos\left(2 \, x\right) - 96 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right) + 192 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) - 96 i\right)} \cos\left(6 \, x\right) + {\left(-384 i \, x^{2} + {\left(960 i \, x^{2} - 480 i\right)} \cos\left(2 \, x\right) - 480 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) + 192 i\right)} \cos\left(4 \, x\right) + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(2 \, x\right) - {\left(192 \, x^{2} + 96 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 192 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - {\left(-192 i \, x^{2} + 96 i\right)} \sin\left(4 \, x\right) - {\left(384 i \, x^{2} - 192 i\right)} \sin\left(2 \, x\right) - 96\right)} \sin\left(6 \, x\right) + {\left(384 \, x^{2} + 384 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 480 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(-960 i \, x^{2} + 480 i\right)} \sin\left(2 \, x\right) - 192\right)} \sin\left(4 \, x\right) - 96 \, {\left(2 \, x^{2} - 4 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right)\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) - {\left(32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right)^{2} + 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right)^{2} - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(4 \, x\right)^{2} - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right)^{2} - {\left(32 \, x^{3} + 16 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right) - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) - {\left(-32 i \, x^{3} + 48 i \, x\right)} \sin\left(4 \, x\right) - {\left(64 i \, x^{3} - 96 i \, x\right)} \sin\left(2 \, x\right) - 48 \, x\right)} \cos\left(6 \, x\right) + {\left(64 \, x^{3} - 80 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + {\left(-160 i \, x^{3} + 240 i \, x\right)} \sin\left(2 \, x\right) - 96 \, x\right)} \cos\left(4 \, x\right) - 16 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + {\left(-32 i \, x^{3} + {\left(-32 i \, x^{3} + 48 i \, x\right)} \cos\left(4 \, x\right) + {\left(64 i \, x^{3} - 96 i \, x\right)} \cos\left(2 \, x\right) + 16 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(4 \, x\right) - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) + 48 i \, x\right)} \sin\left(6 \, x\right) + {\left(64 i \, x^{3} + {\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(4 \, x\right) + {\left(-160 i \, x^{3} + 240 i \, x\right)} \cos\left(2 \, x\right) + 80 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) - 96 i \, x\right)} \sin\left(4 \, x\right) + {\left(-32 i \, x^{3} + {\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(2 \, x\right) + 48 i \, x\right)} \sin\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right)^{2} + 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right)^{2} - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(4 \, x\right)^{2} - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right)^{2} - {\left(32 \, x^{3} + 16 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(4 \, x\right) - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) - {\left(-32 i \, x^{3} + 48 i \, x\right)} \sin\left(4 \, x\right) - {\left(64 i \, x^{3} - 96 i \, x\right)} \sin\left(2 \, x\right) - 48 \, x\right)} \cos\left(6 \, x\right) + {\left(64 \, x^{3} - 80 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + {\left(-160 i \, x^{3} + 240 i \, x\right)} \sin\left(2 \, x\right) - 96 \, x\right)} \cos\left(4 \, x\right) - 16 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + {\left(-32 i \, x^{3} + {\left(-32 i \, x^{3} + 48 i \, x\right)} \cos\left(4 \, x\right) + {\left(64 i \, x^{3} - 96 i \, x\right)} \cos\left(2 \, x\right) + 16 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(4 \, x\right) - 32 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) + 48 i \, x\right)} \sin\left(6 \, x\right) + {\left(64 i \, x^{3} + {\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(4 \, x\right) + {\left(-160 i \, x^{3} + 240 i \, x\right)} \cos\left(2 \, x\right) + 80 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right) - 96 i \, x\right)} \sin\left(4 \, x\right) + {\left(-32 i \, x^{3} + {\left(128 i \, x^{3} - 192 i \, x\right)} \cos\left(2 \, x\right) + 48 i \, x\right)} \sin\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) - {\left({\left(-384 i \, \cos\left(4 \, x\right) + 768 i \, \cos\left(2 \, x\right) + 384 \, \sin\left(4 \, x\right) - 768 \, \sin\left(2 \, x\right) - 384 i\right)} \cos\left(6 \, x\right) + {\left(-1920 i \, \cos\left(2 \, x\right) + 1920 \, \sin\left(2 \, x\right) + 768 i\right)} \cos\left(4 \, x\right) + 768 i \, \cos\left(4 \, x\right)^{2} + 768 i \, \cos\left(2 \, x\right)^{2} + {\left(384 \, \cos\left(4 \, x\right) - 768 \, \cos\left(2 \, x\right) + 384 i \, \sin\left(4 \, x\right) - 768 i \, \sin\left(2 \, x\right) + 384\right)} \sin\left(6 \, x\right) - {\left(1536 \, \cos\left(4 \, x\right) - 1920 \, \cos\left(2 \, x\right) - 1920 i \, \sin\left(2 \, x\right) + 768\right)} \sin\left(4 \, x\right) - 768 i \, \sin\left(4 \, x\right)^{2} - 384 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right) - 768 i \, \sin\left(2 \, x\right)^{2} - 384 i \, \cos\left(2 \, x\right)\right)} {\rm Li}_{4}(-e^{\left(i \, x\right)}) - {\left({\left(-384 i \, \cos\left(4 \, x\right) + 768 i \, \cos\left(2 \, x\right) + 384 \, \sin\left(4 \, x\right) - 768 \, \sin\left(2 \, x\right) - 384 i\right)} \cos\left(6 \, x\right) + {\left(-1920 i \, \cos\left(2 \, x\right) + 1920 \, \sin\left(2 \, x\right) + 768 i\right)} \cos\left(4 \, x\right) + 768 i \, \cos\left(4 \, x\right)^{2} + 768 i \, \cos\left(2 \, x\right)^{2} + {\left(384 \, \cos\left(4 \, x\right) - 768 \, \cos\left(2 \, x\right) + 384 i \, \sin\left(4 \, x\right) - 768 i \, \sin\left(2 \, x\right) + 384\right)} \sin\left(6 \, x\right) - {\left(1536 \, \cos\left(4 \, x\right) - 1920 \, \cos\left(2 \, x\right) - 1920 i \, \sin\left(2 \, x\right) + 768\right)} \sin\left(4 \, x\right) - 768 i \, \sin\left(4 \, x\right)^{2} - 384 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right) - 768 i \, \sin\left(2 \, x\right)^{2} - 384 i \, \cos\left(2 \, x\right)\right)} {\rm Li}_{4}(e^{\left(i \, x\right)}) - {\left(768 \, x \cos\left(4 \, x\right)^{2} + 768 \, x \cos\left(2 \, x\right)^{2} - 768 \, x \sin\left(4 \, x\right)^{2} - 768 \, x \sin\left(2 \, x\right)^{2} - {\left(384 \, x \cos\left(4 \, x\right) - 768 \, x \cos\left(2 \, x\right) + 384 i \, x \sin\left(4 \, x\right) - 768 i \, x \sin\left(2 \, x\right) + 384 \, x\right)} \cos\left(6 \, x\right) - 384 \, {\left(5 \, x \cos\left(2 \, x\right) + 5 i \, x \sin\left(2 \, x\right) - 2 \, x\right)} \cos\left(4 \, x\right) - 384 \, x \cos\left(2 \, x\right) + {\left(-384 i \, x \cos\left(4 \, x\right) + 768 i \, x \cos\left(2 \, x\right) + 384 \, x \sin\left(4 \, x\right) - 768 \, x \sin\left(2 \, x\right) - 384 i \, x\right)} \sin\left(6 \, x\right) + {\left(1536 i \, x \cos\left(4 \, x\right) - 1920 i \, x \cos\left(2 \, x\right) + 1920 \, x \sin\left(2 \, x\right) + 768 i \, x\right)} \sin\left(4 \, x\right) + {\left(1536 i \, x \cos\left(2 \, x\right) - 384 i \, x\right)} \sin\left(2 \, x\right)\right)} {\rm Li}_{3}(-e^{\left(i \, x\right)}) - {\left(768 \, x \cos\left(4 \, x\right)^{2} + 768 \, x \cos\left(2 \, x\right)^{2} - 768 \, x \sin\left(4 \, x\right)^{2} - 768 \, x \sin\left(2 \, x\right)^{2} - {\left(384 \, x \cos\left(4 \, x\right) - 768 \, x \cos\left(2 \, x\right) + 384 i \, x \sin\left(4 \, x\right) - 768 i \, x \sin\left(2 \, x\right) + 384 \, x\right)} \cos\left(6 \, x\right) - 384 \, {\left(5 \, x \cos\left(2 \, x\right) + 5 i \, x \sin\left(2 \, x\right) - 2 \, x\right)} \cos\left(4 \, x\right) - 384 \, x \cos\left(2 \, x\right) + {\left(-384 i \, x \cos\left(4 \, x\right) + 768 i \, x \cos\left(2 \, x\right) + 384 \, x \sin\left(4 \, x\right) - 768 \, x \sin\left(2 \, x\right) - 384 i \, x\right)} \sin\left(6 \, x\right) + {\left(1536 i \, x \cos\left(4 \, x\right) - 1920 i \, x \cos\left(2 \, x\right) + 1920 \, x \sin\left(2 \, x\right) + 768 i \, x\right)} \sin\left(4 \, x\right) + {\left(1536 i \, x \cos\left(2 \, x\right) - 384 i \, x\right)} \sin\left(2 \, x\right)\right)} {\rm Li}_{3}(e^{\left(i \, x\right)}) + {\left(16 \, x^{4} - 8 i \, x^{3} - 12 \, x^{2} - {\left(-8 i \, x^{3} + 12 \, x^{2} + 12 i \, x - 6\right)} \cos\left(6 \, x\right) + {\left(16 \, x^{4} - 16 i \, x^{3} - 72 \, x^{2} + 24 i \, x - 12\right)} \cos\left(4 \, x\right) - {\left(32 \, x^{4} + 52 i \, x^{3} - 90 \, x^{2} + 18 i \, x - 3\right)} \cos\left(2 \, x\right) - {\left(-16 i \, x^{4} - 16 \, x^{3} + 72 i \, x^{2} + 24 \, x + 12 i\right)} \sin\left(4 \, x\right) - {\left(32 i \, x^{4} - 52 \, x^{3} - 90 i \, x^{2} - 18 \, x - 3 i\right)} \sin\left(2 \, x\right) + 12 i \, x + 6\right)} \sin\left(6 \, x\right) - {\left(32 \, x^{4} - 20 i \, x^{3} - 30 \, x^{2} + {\left(64 \, x^{4} - 32 i \, x^{3} - 336 \, x^{2} + 48 i \, x - 24\right)} \cos\left(4 \, x\right) - {\left(80 \, x^{4} + 104 i \, x^{3} - 276 \, x^{2} + 36 i \, x - 6\right)} \cos\left(2 \, x\right) + {\left(-80 i \, x^{4} + 104 \, x^{3} + 276 i \, x^{2} + 36 \, x + 6 i\right)} \sin\left(2 \, x\right) + 30 i \, x + 15\right)} \sin\left(4 \, x\right) + {\left(16 \, x^{4} - 16 i \, x^{3} - 24 \, x^{2} - {\left(64 \, x^{4} + 112 i \, x^{3} - 192 \, x^{2} + 24 i \, x\right)} \cos\left(2 \, x\right) + 24 i \, x + 12\right)} \sin\left(2 \, x\right) - 6 \, x + 3 i}{{\left(32 \, \cos\left(4 \, x\right) - 64 \, \cos\left(2 \, x\right) + 32 i \, \sin\left(4 \, x\right) - 64 i \, \sin\left(2 \, x\right) + 32\right)} \cos\left(6 \, x\right) + {\left(160 \, \cos\left(2 \, x\right) + 160 i \, \sin\left(2 \, x\right) - 64\right)} \cos\left(4 \, x\right) - 64 \, \cos\left(4 \, x\right)^{2} - 64 \, \cos\left(2 \, x\right)^{2} - {\left(-32 i \, \cos\left(4 \, x\right) + 64 i \, \cos\left(2 \, x\right) + 32 \, \sin\left(4 \, x\right) - 64 \, \sin\left(2 \, x\right) - 32 i\right)} \sin\left(6 \, x\right) - {\left(128 i \, \cos\left(4 \, x\right) - 160 i \, \cos\left(2 \, x\right) + 160 \, \sin\left(2 \, x\right) + 64 i\right)} \sin\left(4 \, x\right) + 64 \, \sin\left(4 \, x\right)^{2} - {\left(128 i \, \cos\left(2 \, x\right) - 32 i\right)} \sin\left(2 \, x\right) + 64 \, \sin\left(2 \, x\right)^{2} + 32 \, \cos\left(2 \, x\right)}"," ",0,"-(4*x^3 + (4*x^3 + 6*I*x^2 - 6*x - 3*I)*cos(6*x)^2 - (-32*I*x^4 - 16*x^3 + 168*I*x^2 + 24*x + 12*I)*cos(4*x)^2 - (-32*I*x^4 + 56*x^3 + 96*I*x^2 + 12*x)*cos(2*x)^2 - (4*x^3 + 6*I*x^2 - 6*x - 3*I)*sin(6*x)^2 - (32*I*x^4 + 16*x^3 - 168*I*x^2 - 24*x - 12*I)*sin(4*x)^2 - (32*I*x^4 - 56*x^3 - 96*I*x^2 - 12*x)*sin(2*x)^2 - 6*I*x^2 - ((128*I*x^3 - 192*I*x)*cos(4*x)^2 + (128*I*x^3 - 192*I*x)*cos(2*x)^2 + (-128*I*x^3 + 192*I*x)*sin(4*x)^2 + (-128*I*x^3 + 192*I*x)*sin(2*x)^2 + (-64*I*x^3 + (-64*I*x^3 + 96*I*x)*cos(4*x) + (128*I*x^3 - 192*I*x)*cos(2*x) + 32*(2*x^3 - 3*x)*sin(4*x) - 64*(2*x^3 - 3*x)*sin(2*x) + 96*I*x)*cos(6*x) + (128*I*x^3 + (-320*I*x^3 + 480*I*x)*cos(2*x) + 160*(2*x^3 - 3*x)*sin(2*x) - 192*I*x)*cos(4*x) + (-64*I*x^3 + 96*I*x)*cos(2*x) + (64*x^3 + 32*(2*x^3 - 3*x)*cos(4*x) - 64*(2*x^3 - 3*x)*cos(2*x) + (64*I*x^3 - 96*I*x)*sin(4*x) + (-128*I*x^3 + 192*I*x)*sin(2*x) - 96*x)*sin(6*x) - (128*x^3 + 128*(2*x^3 - 3*x)*cos(4*x) - 160*(2*x^3 - 3*x)*cos(2*x) - (320*I*x^3 - 480*I*x)*sin(2*x) - 192*x)*sin(4*x) + 32*(2*x^3 - 4*(2*x^3 - 3*x)*cos(2*x) - 3*x)*sin(2*x))*arctan2(sin(x), cos(x) + 1) - ((-128*I*x^3 + 192*I*x)*cos(4*x)^2 + (-128*I*x^3 + 192*I*x)*cos(2*x)^2 + (128*I*x^3 - 192*I*x)*sin(4*x)^2 + (128*I*x^3 - 192*I*x)*sin(2*x)^2 + (64*I*x^3 + (64*I*x^3 - 96*I*x)*cos(4*x) + (-128*I*x^3 + 192*I*x)*cos(2*x) - 32*(2*x^3 - 3*x)*sin(4*x) + 64*(2*x^3 - 3*x)*sin(2*x) - 96*I*x)*cos(6*x) + (-128*I*x^3 + (320*I*x^3 - 480*I*x)*cos(2*x) - 160*(2*x^3 - 3*x)*sin(2*x) + 192*I*x)*cos(4*x) + (64*I*x^3 - 96*I*x)*cos(2*x) - (64*x^3 + 32*(2*x^3 - 3*x)*cos(4*x) - 64*(2*x^3 - 3*x)*cos(2*x) - (-64*I*x^3 + 96*I*x)*sin(4*x) - (128*I*x^3 - 192*I*x)*sin(2*x) - 96*x)*sin(6*x) + (128*x^3 + 128*(2*x^3 - 3*x)*cos(4*x) - 160*(2*x^3 - 3*x)*cos(2*x) + (-320*I*x^3 + 480*I*x)*sin(2*x) - 192*x)*sin(4*x) - 32*(2*x^3 - 4*(2*x^3 - 3*x)*cos(2*x) - 3*x)*sin(2*x))*arctan2(sin(x), -cos(x) + 1) - (16*I*x^4 + 8*x^3 - 12*I*x^2 + (16*I*x^4 + 16*x^3 - 72*I*x^2 - 24*x - 12*I)*cos(4*x) + (-32*I*x^4 + 52*x^3 + 90*I*x^2 + 18*x + 3*I)*cos(2*x) - (16*x^4 - 16*I*x^3 - 72*x^2 + 24*I*x - 12)*sin(4*x) + (32*x^4 + 52*I*x^3 - 90*x^2 + 18*I*x - 3)*sin(2*x) - 12*x + 6*I)*cos(6*x) - (-32*I*x^4 - 20*x^3 + 30*I*x^2 + (80*I*x^4 - 104*x^3 - 276*I*x^2 - 36*x - 6*I)*cos(2*x) - (80*x^4 + 104*I*x^3 - 276*x^2 + 36*I*x - 6)*sin(2*x) + 30*x - 15*I)*cos(4*x) - (16*I*x^4 + 16*x^3 - 24*I*x^2 - 24*x + 12*I)*cos(2*x) - ((-384*I*x^2 + 192*I)*cos(4*x)^2 + (-384*I*x^2 + 192*I)*cos(2*x)^2 + (384*I*x^2 - 192*I)*sin(4*x)^2 + (384*I*x^2 - 192*I)*sin(2*x)^2 + (192*I*x^2 + (192*I*x^2 - 96*I)*cos(4*x) + (-384*I*x^2 + 192*I)*cos(2*x) - 96*(2*x^2 - 1)*sin(4*x) + 192*(2*x^2 - 1)*sin(2*x) - 96*I)*cos(6*x) + (-384*I*x^2 + (960*I*x^2 - 480*I)*cos(2*x) - 480*(2*x^2 - 1)*sin(2*x) + 192*I)*cos(4*x) + (192*I*x^2 - 96*I)*cos(2*x) - (192*x^2 + 96*(2*x^2 - 1)*cos(4*x) - 192*(2*x^2 - 1)*cos(2*x) - (-192*I*x^2 + 96*I)*sin(4*x) - (384*I*x^2 - 192*I)*sin(2*x) - 96)*sin(6*x) + (384*x^2 + 384*(2*x^2 - 1)*cos(4*x) - 480*(2*x^2 - 1)*cos(2*x) + (-960*I*x^2 + 480*I)*sin(2*x) - 192)*sin(4*x) - 96*(2*x^2 - 4*(2*x^2 - 1)*cos(2*x) - 1)*sin(2*x))*dilog(-e^(I*x)) - ((-384*I*x^2 + 192*I)*cos(4*x)^2 + (-384*I*x^2 + 192*I)*cos(2*x)^2 + (384*I*x^2 - 192*I)*sin(4*x)^2 + (384*I*x^2 - 192*I)*sin(2*x)^2 + (192*I*x^2 + (192*I*x^2 - 96*I)*cos(4*x) + (-384*I*x^2 + 192*I)*cos(2*x) - 96*(2*x^2 - 1)*sin(4*x) + 192*(2*x^2 - 1)*sin(2*x) - 96*I)*cos(6*x) + (-384*I*x^2 + (960*I*x^2 - 480*I)*cos(2*x) - 480*(2*x^2 - 1)*sin(2*x) + 192*I)*cos(4*x) + (192*I*x^2 - 96*I)*cos(2*x) - (192*x^2 + 96*(2*x^2 - 1)*cos(4*x) - 192*(2*x^2 - 1)*cos(2*x) - (-192*I*x^2 + 96*I)*sin(4*x) - (384*I*x^2 - 192*I)*sin(2*x) - 96)*sin(6*x) + (384*x^2 + 384*(2*x^2 - 1)*cos(4*x) - 480*(2*x^2 - 1)*cos(2*x) + (-960*I*x^2 + 480*I)*sin(2*x) - 192)*sin(4*x) - 96*(2*x^2 - 4*(2*x^2 - 1)*cos(2*x) - 1)*sin(2*x))*dilog(e^(I*x)) - (32*(2*x^3 - 3*x)*cos(4*x)^2 + 32*(2*x^3 - 3*x)*cos(2*x)^2 - 32*(2*x^3 - 3*x)*sin(4*x)^2 - 32*(2*x^3 - 3*x)*sin(2*x)^2 - (32*x^3 + 16*(2*x^3 - 3*x)*cos(4*x) - 32*(2*x^3 - 3*x)*cos(2*x) - (-32*I*x^3 + 48*I*x)*sin(4*x) - (64*I*x^3 - 96*I*x)*sin(2*x) - 48*x)*cos(6*x) + (64*x^3 - 80*(2*x^3 - 3*x)*cos(2*x) + (-160*I*x^3 + 240*I*x)*sin(2*x) - 96*x)*cos(4*x) - 16*(2*x^3 - 3*x)*cos(2*x) + (-32*I*x^3 + (-32*I*x^3 + 48*I*x)*cos(4*x) + (64*I*x^3 - 96*I*x)*cos(2*x) + 16*(2*x^3 - 3*x)*sin(4*x) - 32*(2*x^3 - 3*x)*sin(2*x) + 48*I*x)*sin(6*x) + (64*I*x^3 + (128*I*x^3 - 192*I*x)*cos(4*x) + (-160*I*x^3 + 240*I*x)*cos(2*x) + 80*(2*x^3 - 3*x)*sin(2*x) - 96*I*x)*sin(4*x) + (-32*I*x^3 + (128*I*x^3 - 192*I*x)*cos(2*x) + 48*I*x)*sin(2*x))*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (32*(2*x^3 - 3*x)*cos(4*x)^2 + 32*(2*x^3 - 3*x)*cos(2*x)^2 - 32*(2*x^3 - 3*x)*sin(4*x)^2 - 32*(2*x^3 - 3*x)*sin(2*x)^2 - (32*x^3 + 16*(2*x^3 - 3*x)*cos(4*x) - 32*(2*x^3 - 3*x)*cos(2*x) - (-32*I*x^3 + 48*I*x)*sin(4*x) - (64*I*x^3 - 96*I*x)*sin(2*x) - 48*x)*cos(6*x) + (64*x^3 - 80*(2*x^3 - 3*x)*cos(2*x) + (-160*I*x^3 + 240*I*x)*sin(2*x) - 96*x)*cos(4*x) - 16*(2*x^3 - 3*x)*cos(2*x) + (-32*I*x^3 + (-32*I*x^3 + 48*I*x)*cos(4*x) + (64*I*x^3 - 96*I*x)*cos(2*x) + 16*(2*x^3 - 3*x)*sin(4*x) - 32*(2*x^3 - 3*x)*sin(2*x) + 48*I*x)*sin(6*x) + (64*I*x^3 + (128*I*x^3 - 192*I*x)*cos(4*x) + (-160*I*x^3 + 240*I*x)*cos(2*x) + 80*(2*x^3 - 3*x)*sin(2*x) - 96*I*x)*sin(4*x) + (-32*I*x^3 + (128*I*x^3 - 192*I*x)*cos(2*x) + 48*I*x)*sin(2*x))*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) - ((-384*I*cos(4*x) + 768*I*cos(2*x) + 384*sin(4*x) - 768*sin(2*x) - 384*I)*cos(6*x) + (-1920*I*cos(2*x) + 1920*sin(2*x) + 768*I)*cos(4*x) + 768*I*cos(4*x)^2 + 768*I*cos(2*x)^2 + (384*cos(4*x) - 768*cos(2*x) + 384*I*sin(4*x) - 768*I*sin(2*x) + 384)*sin(6*x) - (1536*cos(4*x) - 1920*cos(2*x) - 1920*I*sin(2*x) + 768)*sin(4*x) - 768*I*sin(4*x)^2 - 384*(4*cos(2*x) - 1)*sin(2*x) - 768*I*sin(2*x)^2 - 384*I*cos(2*x))*polylog(4, -e^(I*x)) - ((-384*I*cos(4*x) + 768*I*cos(2*x) + 384*sin(4*x) - 768*sin(2*x) - 384*I)*cos(6*x) + (-1920*I*cos(2*x) + 1920*sin(2*x) + 768*I)*cos(4*x) + 768*I*cos(4*x)^2 + 768*I*cos(2*x)^2 + (384*cos(4*x) - 768*cos(2*x) + 384*I*sin(4*x) - 768*I*sin(2*x) + 384)*sin(6*x) - (1536*cos(4*x) - 1920*cos(2*x) - 1920*I*sin(2*x) + 768)*sin(4*x) - 768*I*sin(4*x)^2 - 384*(4*cos(2*x) - 1)*sin(2*x) - 768*I*sin(2*x)^2 - 384*I*cos(2*x))*polylog(4, e^(I*x)) - (768*x*cos(4*x)^2 + 768*x*cos(2*x)^2 - 768*x*sin(4*x)^2 - 768*x*sin(2*x)^2 - (384*x*cos(4*x) - 768*x*cos(2*x) + 384*I*x*sin(4*x) - 768*I*x*sin(2*x) + 384*x)*cos(6*x) - 384*(5*x*cos(2*x) + 5*I*x*sin(2*x) - 2*x)*cos(4*x) - 384*x*cos(2*x) + (-384*I*x*cos(4*x) + 768*I*x*cos(2*x) + 384*x*sin(4*x) - 768*x*sin(2*x) - 384*I*x)*sin(6*x) + (1536*I*x*cos(4*x) - 1920*I*x*cos(2*x) + 1920*x*sin(2*x) + 768*I*x)*sin(4*x) + (1536*I*x*cos(2*x) - 384*I*x)*sin(2*x))*polylog(3, -e^(I*x)) - (768*x*cos(4*x)^2 + 768*x*cos(2*x)^2 - 768*x*sin(4*x)^2 - 768*x*sin(2*x)^2 - (384*x*cos(4*x) - 768*x*cos(2*x) + 384*I*x*sin(4*x) - 768*I*x*sin(2*x) + 384*x)*cos(6*x) - 384*(5*x*cos(2*x) + 5*I*x*sin(2*x) - 2*x)*cos(4*x) - 384*x*cos(2*x) + (-384*I*x*cos(4*x) + 768*I*x*cos(2*x) + 384*x*sin(4*x) - 768*x*sin(2*x) - 384*I*x)*sin(6*x) + (1536*I*x*cos(4*x) - 1920*I*x*cos(2*x) + 1920*x*sin(2*x) + 768*I*x)*sin(4*x) + (1536*I*x*cos(2*x) - 384*I*x)*sin(2*x))*polylog(3, e^(I*x)) + (16*x^4 - 8*I*x^3 - 12*x^2 - (-8*I*x^3 + 12*x^2 + 12*I*x - 6)*cos(6*x) + (16*x^4 - 16*I*x^3 - 72*x^2 + 24*I*x - 12)*cos(4*x) - (32*x^4 + 52*I*x^3 - 90*x^2 + 18*I*x - 3)*cos(2*x) - (-16*I*x^4 - 16*x^3 + 72*I*x^2 + 24*x + 12*I)*sin(4*x) - (32*I*x^4 - 52*x^3 - 90*I*x^2 - 18*x - 3*I)*sin(2*x) + 12*I*x + 6)*sin(6*x) - (32*x^4 - 20*I*x^3 - 30*x^2 + (64*x^4 - 32*I*x^3 - 336*x^2 + 48*I*x - 24)*cos(4*x) - (80*x^4 + 104*I*x^3 - 276*x^2 + 36*I*x - 6)*cos(2*x) + (-80*I*x^4 + 104*x^3 + 276*I*x^2 + 36*x + 6*I)*sin(2*x) + 30*I*x + 15)*sin(4*x) + (16*x^4 - 16*I*x^3 - 24*x^2 - (64*x^4 + 112*I*x^3 - 192*x^2 + 24*I*x)*cos(2*x) + 24*I*x + 12)*sin(2*x) - 6*x + 3*I)/((32*cos(4*x) - 64*cos(2*x) + 32*I*sin(4*x) - 64*I*sin(2*x) + 32)*cos(6*x) + (160*cos(2*x) + 160*I*sin(2*x) - 64)*cos(4*x) - 64*cos(4*x)^2 - 64*cos(2*x)^2 - (-32*I*cos(4*x) + 64*I*cos(2*x) + 32*sin(4*x) - 64*sin(2*x) - 32*I)*sin(6*x) - (128*I*cos(4*x) - 160*I*cos(2*x) + 160*sin(2*x) + 64*I)*sin(4*x) + 64*sin(4*x)^2 - (128*I*cos(2*x) - 32*I)*sin(2*x) + 64*sin(2*x)^2 + 32*cos(2*x))","B",0
206,1,2855,0,0.751609," ","integrate(x^2*cos(x)^2*cot(x)^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(2 \, x^{2} + 2 i \, x - 1\right)} \cos\left(6 \, x\right)^{2} - {\left(-64 i \, x^{3} - 24 \, x^{2} + 168 i \, x + 12\right)} \cos\left(4 \, x\right)^{2} - {\left(-64 i \, x^{3} + 84 \, x^{2} + 96 i \, x + 6\right)} \cos\left(2 \, x\right)^{2} - 3 \, {\left(2 \, x^{2} + 2 i \, x - 1\right)} \sin\left(6 \, x\right)^{2} - {\left(64 i \, x^{3} + 24 \, x^{2} - 168 i \, x - 12\right)} \sin\left(4 \, x\right)^{2} - {\left(64 i \, x^{3} - 84 \, x^{2} - 96 i \, x - 6\right)} \sin\left(2 \, x\right)^{2} + 6 \, x^{2} - {\left({\left(192 i \, x^{2} - 96 i\right)} \cos\left(4 \, x\right)^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(2 \, x\right)^{2} + {\left(-192 i \, x^{2} + 96 i\right)} \sin\left(4 \, x\right)^{2} + {\left(-192 i \, x^{2} + 96 i\right)} \sin\left(2 \, x\right)^{2} + {\left(-96 i \, x^{2} + {\left(-96 i \, x^{2} + 48 i\right)} \cos\left(4 \, x\right) + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(2 \, x\right) + 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right) - 96 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) + 48 i\right)} \cos\left(6 \, x\right) + {\left(192 i \, x^{2} + {\left(-480 i \, x^{2} + 240 i\right)} \cos\left(2 \, x\right) + 240 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) - 96 i\right)} \cos\left(4 \, x\right) + {\left(-96 i \, x^{2} + 48 i\right)} \cos\left(2 \, x\right) + {\left(96 \, x^{2} + 48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 96 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(96 i \, x^{2} - 48 i\right)} \sin\left(4 \, x\right) + {\left(-192 i \, x^{2} + 96 i\right)} \sin\left(2 \, x\right) - 48\right)} \sin\left(6 \, x\right) - {\left(192 \, x^{2} + 192 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 240 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - {\left(480 i \, x^{2} - 240 i\right)} \sin\left(2 \, x\right) - 96\right)} \sin\left(4 \, x\right) + 48 \, {\left(2 \, x^{2} - 4 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left({\left(48 i \, \cos\left(4 \, x\right) - 96 i \, \cos\left(2 \, x\right) - 48 \, \sin\left(4 \, x\right) + 96 \, \sin\left(2 \, x\right) + 48 i\right)} \cos\left(6 \, x\right) + {\left(240 i \, \cos\left(2 \, x\right) - 240 \, \sin\left(2 \, x\right) - 96 i\right)} \cos\left(4 \, x\right) - 96 i \, \cos\left(4 \, x\right)^{2} - 96 i \, \cos\left(2 \, x\right)^{2} - {\left(48 \, \cos\left(4 \, x\right) - 96 \, \cos\left(2 \, x\right) + 48 i \, \sin\left(4 \, x\right) - 96 i \, \sin\left(2 \, x\right) + 48\right)} \sin\left(6 \, x\right) + {\left(192 \, \cos\left(4 \, x\right) - 240 \, \cos\left(2 \, x\right) - 240 i \, \sin\left(2 \, x\right) + 96\right)} \sin\left(4 \, x\right) + 96 i \, \sin\left(4 \, x\right)^{2} + 48 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right) + 96 i \, \sin\left(2 \, x\right)^{2} + 48 i \, \cos\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) - 1\right) - {\left(-192 i \, x^{2} \cos\left(4 \, x\right)^{2} - 192 i \, x^{2} \cos\left(2 \, x\right)^{2} + 192 i \, x^{2} \sin\left(4 \, x\right)^{2} + 192 i \, x^{2} \sin\left(2 \, x\right)^{2} + 96 i \, x^{2} \cos\left(2 \, x\right) + {\left(96 i \, x^{2} \cos\left(4 \, x\right) - 192 i \, x^{2} \cos\left(2 \, x\right) - 96 \, x^{2} \sin\left(4 \, x\right) + 192 \, x^{2} \sin\left(2 \, x\right) + 96 i \, x^{2}\right)} \cos\left(6 \, x\right) + {\left(480 i \, x^{2} \cos\left(2 \, x\right) - 480 \, x^{2} \sin\left(2 \, x\right) - 192 i \, x^{2}\right)} \cos\left(4 \, x\right) - {\left(96 \, x^{2} \cos\left(4 \, x\right) - 192 \, x^{2} \cos\left(2 \, x\right) + 96 i \, x^{2} \sin\left(4 \, x\right) - 192 i \, x^{2} \sin\left(2 \, x\right) + 96 \, x^{2}\right)} \sin\left(6 \, x\right) + 96 \, {\left(4 \, x^{2} \cos\left(4 \, x\right) - 5 \, x^{2} \cos\left(2 \, x\right) - 5 i \, x^{2} \sin\left(2 \, x\right) + 2 \, x^{2}\right)} \sin\left(4 \, x\right) + 96 \, {\left(4 \, x^{2} \cos\left(2 \, x\right) - x^{2}\right)} \sin\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - {\left(32 i \, x^{3} + 12 \, x^{2} + {\left(32 i \, x^{3} + 24 \, x^{2} - 72 i \, x - 12\right)} \cos\left(4 \, x\right) + {\left(-64 i \, x^{3} + 78 \, x^{2} + 90 i \, x + 9\right)} \cos\left(2 \, x\right) - {\left(32 \, x^{3} - 24 i \, x^{2} - 72 \, x + 12 i\right)} \sin\left(4 \, x\right) + {\left(64 \, x^{3} + 78 i \, x^{2} - 90 \, x + 9 i\right)} \sin\left(2 \, x\right) - 12 i \, x - 6\right)} \cos\left(6 \, x\right) - {\left(-64 i \, x^{3} - 30 \, x^{2} + {\left(160 i \, x^{3} - 156 \, x^{2} - 276 i \, x - 18\right)} \cos\left(2 \, x\right) - {\left(160 \, x^{3} + 156 i \, x^{2} - 276 \, x + 18 i\right)} \sin\left(2 \, x\right) + 30 i \, x + 15\right)} \cos\left(4 \, x\right) - {\left(32 i \, x^{3} + 24 \, x^{2} - 24 i \, x - 12\right)} \cos\left(2 \, x\right) - {\left(-384 i \, x \cos\left(4 \, x\right)^{2} - 384 i \, x \cos\left(2 \, x\right)^{2} + 384 i \, x \sin\left(4 \, x\right)^{2} + 384 i \, x \sin\left(2 \, x\right)^{2} + {\left(192 i \, x \cos\left(4 \, x\right) - 384 i \, x \cos\left(2 \, x\right) - 192 \, x \sin\left(4 \, x\right) + 384 \, x \sin\left(2 \, x\right) + 192 i \, x\right)} \cos\left(6 \, x\right) + {\left(960 i \, x \cos\left(2 \, x\right) - 960 \, x \sin\left(2 \, x\right) - 384 i \, x\right)} \cos\left(4 \, x\right) + 192 i \, x \cos\left(2 \, x\right) - {\left(192 \, x \cos\left(4 \, x\right) - 384 \, x \cos\left(2 \, x\right) + 192 i \, x \sin\left(4 \, x\right) - 384 i \, x \sin\left(2 \, x\right) + 192 \, x\right)} \sin\left(6 \, x\right) + 192 \, {\left(4 \, x \cos\left(4 \, x\right) - 5 \, x \cos\left(2 \, x\right) - 5 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \sin\left(4 \, x\right) + 192 \, {\left(4 \, x \cos\left(2 \, x\right) - x\right)} \sin\left(2 \, x\right)\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - {\left(-384 i \, x \cos\left(4 \, x\right)^{2} - 384 i \, x \cos\left(2 \, x\right)^{2} + 384 i \, x \sin\left(4 \, x\right)^{2} + 384 i \, x \sin\left(2 \, x\right)^{2} + {\left(192 i \, x \cos\left(4 \, x\right) - 384 i \, x \cos\left(2 \, x\right) - 192 \, x \sin\left(4 \, x\right) + 384 \, x \sin\left(2 \, x\right) + 192 i \, x\right)} \cos\left(6 \, x\right) + {\left(960 i \, x \cos\left(2 \, x\right) - 960 \, x \sin\left(2 \, x\right) - 384 i \, x\right)} \cos\left(4 \, x\right) + 192 i \, x \cos\left(2 \, x\right) - {\left(192 \, x \cos\left(4 \, x\right) - 384 \, x \cos\left(2 \, x\right) + 192 i \, x \sin\left(4 \, x\right) - 384 i \, x \sin\left(2 \, x\right) + 192 \, x\right)} \sin\left(6 \, x\right) + 192 \, {\left(4 \, x \cos\left(4 \, x\right) - 5 \, x \cos\left(2 \, x\right) - 5 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \sin\left(4 \, x\right) + 192 \, {\left(4 \, x \cos\left(2 \, x\right) - x\right)} \sin\left(2 \, x\right)\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) - {\left(48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right)^{2} + 48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right)^{2} - 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right)^{2} - 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)^{2} - {\left(48 \, x^{2} + 24 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - {\left(-48 i \, x^{2} + 24 i\right)} \sin\left(4 \, x\right) - {\left(96 i \, x^{2} - 48 i\right)} \sin\left(2 \, x\right) - 24\right)} \cos\left(6 \, x\right) + {\left(96 \, x^{2} - 120 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(-240 i \, x^{2} + 120 i\right)} \sin\left(2 \, x\right) - 48\right)} \cos\left(4 \, x\right) - 24 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(-48 i \, x^{2} + {\left(-48 i \, x^{2} + 24 i\right)} \cos\left(4 \, x\right) + {\left(96 i \, x^{2} - 48 i\right)} \cos\left(2 \, x\right) + 24 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right) - 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) + 24 i\right)} \sin\left(6 \, x\right) + {\left(96 i \, x^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(4 \, x\right) + {\left(-240 i \, x^{2} + 120 i\right)} \cos\left(2 \, x\right) + 120 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) - 48 i\right)} \sin\left(4 \, x\right) + {\left(-48 i \, x^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(2 \, x\right) + 24 i\right)} \sin\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right)^{2} + 48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right)^{2} - 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right)^{2} - 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)^{2} - {\left(48 \, x^{2} + 24 \, {\left(2 \, x^{2} - 1\right)} \cos\left(4 \, x\right) - 48 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) - {\left(-48 i \, x^{2} + 24 i\right)} \sin\left(4 \, x\right) - {\left(96 i \, x^{2} - 48 i\right)} \sin\left(2 \, x\right) - 24\right)} \cos\left(6 \, x\right) + {\left(96 \, x^{2} - 120 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(-240 i \, x^{2} + 120 i\right)} \sin\left(2 \, x\right) - 48\right)} \cos\left(4 \, x\right) - 24 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + {\left(-48 i \, x^{2} + {\left(-48 i \, x^{2} + 24 i\right)} \cos\left(4 \, x\right) + {\left(96 i \, x^{2} - 48 i\right)} \cos\left(2 \, x\right) + 24 \, {\left(2 \, x^{2} - 1\right)} \sin\left(4 \, x\right) - 48 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) + 24 i\right)} \sin\left(6 \, x\right) + {\left(96 i \, x^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(4 \, x\right) + {\left(-240 i \, x^{2} + 120 i\right)} \cos\left(2 \, x\right) + 120 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right) - 48 i\right)} \sin\left(4 \, x\right) + {\left(-48 i \, x^{2} + {\left(192 i \, x^{2} - 96 i\right)} \cos\left(2 \, x\right) + 24 i\right)} \sin\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + {\left({\left(192 \, \cos\left(4 \, x\right) - 384 \, \cos\left(2 \, x\right) + 192 i \, \sin\left(4 \, x\right) - 384 i \, \sin\left(2 \, x\right) + 192\right)} \cos\left(6 \, x\right) + {\left(960 \, \cos\left(2 \, x\right) + 960 i \, \sin\left(2 \, x\right) - 384\right)} \cos\left(4 \, x\right) - 384 \, \cos\left(4 \, x\right)^{2} - 384 \, \cos\left(2 \, x\right)^{2} - {\left(-192 i \, \cos\left(4 \, x\right) + 384 i \, \cos\left(2 \, x\right) + 192 \, \sin\left(4 \, x\right) - 384 \, \sin\left(2 \, x\right) - 192 i\right)} \sin\left(6 \, x\right) - {\left(768 i \, \cos\left(4 \, x\right) - 960 i \, \cos\left(2 \, x\right) + 960 \, \sin\left(2 \, x\right) + 384 i\right)} \sin\left(4 \, x\right) + 384 \, \sin\left(4 \, x\right)^{2} - {\left(768 i \, \cos\left(2 \, x\right) - 192 i\right)} \sin\left(2 \, x\right) + 384 \, \sin\left(2 \, x\right)^{2} + 192 \, \cos\left(2 \, x\right)\right)} {\rm Li}_{3}(-e^{\left(i \, x\right)}) + {\left({\left(192 \, \cos\left(4 \, x\right) - 384 \, \cos\left(2 \, x\right) + 192 i \, \sin\left(4 \, x\right) - 384 i \, \sin\left(2 \, x\right) + 192\right)} \cos\left(6 \, x\right) + {\left(960 \, \cos\left(2 \, x\right) + 960 i \, \sin\left(2 \, x\right) - 384\right)} \cos\left(4 \, x\right) - 384 \, \cos\left(4 \, x\right)^{2} - 384 \, \cos\left(2 \, x\right)^{2} - {\left(-192 i \, \cos\left(4 \, x\right) + 384 i \, \cos\left(2 \, x\right) + 192 \, \sin\left(4 \, x\right) - 384 \, \sin\left(2 \, x\right) - 192 i\right)} \sin\left(6 \, x\right) - {\left(768 i \, \cos\left(4 \, x\right) - 960 i \, \cos\left(2 \, x\right) + 960 \, \sin\left(2 \, x\right) + 384 i\right)} \sin\left(4 \, x\right) + 384 \, \sin\left(4 \, x\right)^{2} - {\left(768 i \, \cos\left(2 \, x\right) - 192 i\right)} \sin\left(2 \, x\right) + 384 \, \sin\left(2 \, x\right)^{2} + 192 \, \cos\left(2 \, x\right)\right)} {\rm Li}_{3}(e^{\left(i \, x\right)}) + {\left(32 \, x^{3} - 12 i \, x^{2} - {\left(-12 i \, x^{2} + 12 \, x + 6 i\right)} \cos\left(6 \, x\right) + {\left(32 \, x^{3} - 24 i \, x^{2} - 72 \, x + 12 i\right)} \cos\left(4 \, x\right) - {\left(64 \, x^{3} + 78 i \, x^{2} - 90 \, x + 9 i\right)} \cos\left(2 \, x\right) - {\left(-32 i \, x^{3} - 24 \, x^{2} + 72 i \, x + 12\right)} \sin\left(4 \, x\right) - {\left(64 i \, x^{3} - 78 \, x^{2} - 90 i \, x - 9\right)} \sin\left(2 \, x\right) - 12 \, x + 6 i\right)} \sin\left(6 \, x\right) - {\left(64 \, x^{3} - 30 i \, x^{2} + {\left(128 \, x^{3} - 48 i \, x^{2} - 336 \, x + 24 i\right)} \cos\left(4 \, x\right) - {\left(160 \, x^{3} + 156 i \, x^{2} - 276 \, x + 18 i\right)} \cos\left(2 \, x\right) + {\left(-160 i \, x^{3} + 156 \, x^{2} + 276 i \, x + 18\right)} \sin\left(2 \, x\right) - 30 \, x + 15 i\right)} \sin\left(4 \, x\right) + {\left(32 \, x^{3} - 24 i \, x^{2} - {\left(128 \, x^{3} + 168 i \, x^{2} - 192 \, x + 12 i\right)} \cos\left(2 \, x\right) - 24 \, x + 12 i\right)} \sin\left(2 \, x\right) - 6 i \, x - 3}{{\left(48 \, \cos\left(4 \, x\right) - 96 \, \cos\left(2 \, x\right) + 48 i \, \sin\left(4 \, x\right) - 96 i \, \sin\left(2 \, x\right) + 48\right)} \cos\left(6 \, x\right) + {\left(240 \, \cos\left(2 \, x\right) + 240 i \, \sin\left(2 \, x\right) - 96\right)} \cos\left(4 \, x\right) - 96 \, \cos\left(4 \, x\right)^{2} - 96 \, \cos\left(2 \, x\right)^{2} - {\left(-48 i \, \cos\left(4 \, x\right) + 96 i \, \cos\left(2 \, x\right) + 48 \, \sin\left(4 \, x\right) - 96 \, \sin\left(2 \, x\right) - 48 i\right)} \sin\left(6 \, x\right) - {\left(192 i \, \cos\left(4 \, x\right) - 240 i \, \cos\left(2 \, x\right) + 240 \, \sin\left(2 \, x\right) + 96 i\right)} \sin\left(4 \, x\right) + 96 \, \sin\left(4 \, x\right)^{2} - {\left(192 i \, \cos\left(2 \, x\right) - 48 i\right)} \sin\left(2 \, x\right) + 96 \, \sin\left(2 \, x\right)^{2} + 48 \, \cos\left(2 \, x\right)}"," ",0,"-(3*(2*x^2 + 2*I*x - 1)*cos(6*x)^2 - (-64*I*x^3 - 24*x^2 + 168*I*x + 12)*cos(4*x)^2 - (-64*I*x^3 + 84*x^2 + 96*I*x + 6)*cos(2*x)^2 - 3*(2*x^2 + 2*I*x - 1)*sin(6*x)^2 - (64*I*x^3 + 24*x^2 - 168*I*x - 12)*sin(4*x)^2 - (64*I*x^3 - 84*x^2 - 96*I*x - 6)*sin(2*x)^2 + 6*x^2 - ((192*I*x^2 - 96*I)*cos(4*x)^2 + (192*I*x^2 - 96*I)*cos(2*x)^2 + (-192*I*x^2 + 96*I)*sin(4*x)^2 + (-192*I*x^2 + 96*I)*sin(2*x)^2 + (-96*I*x^2 + (-96*I*x^2 + 48*I)*cos(4*x) + (192*I*x^2 - 96*I)*cos(2*x) + 48*(2*x^2 - 1)*sin(4*x) - 96*(2*x^2 - 1)*sin(2*x) + 48*I)*cos(6*x) + (192*I*x^2 + (-480*I*x^2 + 240*I)*cos(2*x) + 240*(2*x^2 - 1)*sin(2*x) - 96*I)*cos(4*x) + (-96*I*x^2 + 48*I)*cos(2*x) + (96*x^2 + 48*(2*x^2 - 1)*cos(4*x) - 96*(2*x^2 - 1)*cos(2*x) + (96*I*x^2 - 48*I)*sin(4*x) + (-192*I*x^2 + 96*I)*sin(2*x) - 48)*sin(6*x) - (192*x^2 + 192*(2*x^2 - 1)*cos(4*x) - 240*(2*x^2 - 1)*cos(2*x) - (480*I*x^2 - 240*I)*sin(2*x) - 96)*sin(4*x) + 48*(2*x^2 - 4*(2*x^2 - 1)*cos(2*x) - 1)*sin(2*x))*arctan2(sin(x), cos(x) + 1) - ((48*I*cos(4*x) - 96*I*cos(2*x) - 48*sin(4*x) + 96*sin(2*x) + 48*I)*cos(6*x) + (240*I*cos(2*x) - 240*sin(2*x) - 96*I)*cos(4*x) - 96*I*cos(4*x)^2 - 96*I*cos(2*x)^2 - (48*cos(4*x) - 96*cos(2*x) + 48*I*sin(4*x) - 96*I*sin(2*x) + 48)*sin(6*x) + (192*cos(4*x) - 240*cos(2*x) - 240*I*sin(2*x) + 96)*sin(4*x) + 96*I*sin(4*x)^2 + 48*(4*cos(2*x) - 1)*sin(2*x) + 96*I*sin(2*x)^2 + 48*I*cos(2*x))*arctan2(sin(x), cos(x) - 1) - (-192*I*x^2*cos(4*x)^2 - 192*I*x^2*cos(2*x)^2 + 192*I*x^2*sin(4*x)^2 + 192*I*x^2*sin(2*x)^2 + 96*I*x^2*cos(2*x) + (96*I*x^2*cos(4*x) - 192*I*x^2*cos(2*x) - 96*x^2*sin(4*x) + 192*x^2*sin(2*x) + 96*I*x^2)*cos(6*x) + (480*I*x^2*cos(2*x) - 480*x^2*sin(2*x) - 192*I*x^2)*cos(4*x) - (96*x^2*cos(4*x) - 192*x^2*cos(2*x) + 96*I*x^2*sin(4*x) - 192*I*x^2*sin(2*x) + 96*x^2)*sin(6*x) + 96*(4*x^2*cos(4*x) - 5*x^2*cos(2*x) - 5*I*x^2*sin(2*x) + 2*x^2)*sin(4*x) + 96*(4*x^2*cos(2*x) - x^2)*sin(2*x))*arctan2(sin(x), -cos(x) + 1) - (32*I*x^3 + 12*x^2 + (32*I*x^3 + 24*x^2 - 72*I*x - 12)*cos(4*x) + (-64*I*x^3 + 78*x^2 + 90*I*x + 9)*cos(2*x) - (32*x^3 - 24*I*x^2 - 72*x + 12*I)*sin(4*x) + (64*x^3 + 78*I*x^2 - 90*x + 9*I)*sin(2*x) - 12*I*x - 6)*cos(6*x) - (-64*I*x^3 - 30*x^2 + (160*I*x^3 - 156*x^2 - 276*I*x - 18)*cos(2*x) - (160*x^3 + 156*I*x^2 - 276*x + 18*I)*sin(2*x) + 30*I*x + 15)*cos(4*x) - (32*I*x^3 + 24*x^2 - 24*I*x - 12)*cos(2*x) - (-384*I*x*cos(4*x)^2 - 384*I*x*cos(2*x)^2 + 384*I*x*sin(4*x)^2 + 384*I*x*sin(2*x)^2 + (192*I*x*cos(4*x) - 384*I*x*cos(2*x) - 192*x*sin(4*x) + 384*x*sin(2*x) + 192*I*x)*cos(6*x) + (960*I*x*cos(2*x) - 960*x*sin(2*x) - 384*I*x)*cos(4*x) + 192*I*x*cos(2*x) - (192*x*cos(4*x) - 384*x*cos(2*x) + 192*I*x*sin(4*x) - 384*I*x*sin(2*x) + 192*x)*sin(6*x) + 192*(4*x*cos(4*x) - 5*x*cos(2*x) - 5*I*x*sin(2*x) + 2*x)*sin(4*x) + 192*(4*x*cos(2*x) - x)*sin(2*x))*dilog(-e^(I*x)) - (-384*I*x*cos(4*x)^2 - 384*I*x*cos(2*x)^2 + 384*I*x*sin(4*x)^2 + 384*I*x*sin(2*x)^2 + (192*I*x*cos(4*x) - 384*I*x*cos(2*x) - 192*x*sin(4*x) + 384*x*sin(2*x) + 192*I*x)*cos(6*x) + (960*I*x*cos(2*x) - 960*x*sin(2*x) - 384*I*x)*cos(4*x) + 192*I*x*cos(2*x) - (192*x*cos(4*x) - 384*x*cos(2*x) + 192*I*x*sin(4*x) - 384*I*x*sin(2*x) + 192*x)*sin(6*x) + 192*(4*x*cos(4*x) - 5*x*cos(2*x) - 5*I*x*sin(2*x) + 2*x)*sin(4*x) + 192*(4*x*cos(2*x) - x)*sin(2*x))*dilog(e^(I*x)) - (48*(2*x^2 - 1)*cos(4*x)^2 + 48*(2*x^2 - 1)*cos(2*x)^2 - 48*(2*x^2 - 1)*sin(4*x)^2 - 48*(2*x^2 - 1)*sin(2*x)^2 - (48*x^2 + 24*(2*x^2 - 1)*cos(4*x) - 48*(2*x^2 - 1)*cos(2*x) - (-48*I*x^2 + 24*I)*sin(4*x) - (96*I*x^2 - 48*I)*sin(2*x) - 24)*cos(6*x) + (96*x^2 - 120*(2*x^2 - 1)*cos(2*x) + (-240*I*x^2 + 120*I)*sin(2*x) - 48)*cos(4*x) - 24*(2*x^2 - 1)*cos(2*x) + (-48*I*x^2 + (-48*I*x^2 + 24*I)*cos(4*x) + (96*I*x^2 - 48*I)*cos(2*x) + 24*(2*x^2 - 1)*sin(4*x) - 48*(2*x^2 - 1)*sin(2*x) + 24*I)*sin(6*x) + (96*I*x^2 + (192*I*x^2 - 96*I)*cos(4*x) + (-240*I*x^2 + 120*I)*cos(2*x) + 120*(2*x^2 - 1)*sin(2*x) - 48*I)*sin(4*x) + (-48*I*x^2 + (192*I*x^2 - 96*I)*cos(2*x) + 24*I)*sin(2*x))*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (48*(2*x^2 - 1)*cos(4*x)^2 + 48*(2*x^2 - 1)*cos(2*x)^2 - 48*(2*x^2 - 1)*sin(4*x)^2 - 48*(2*x^2 - 1)*sin(2*x)^2 - (48*x^2 + 24*(2*x^2 - 1)*cos(4*x) - 48*(2*x^2 - 1)*cos(2*x) - (-48*I*x^2 + 24*I)*sin(4*x) - (96*I*x^2 - 48*I)*sin(2*x) - 24)*cos(6*x) + (96*x^2 - 120*(2*x^2 - 1)*cos(2*x) + (-240*I*x^2 + 120*I)*sin(2*x) - 48)*cos(4*x) - 24*(2*x^2 - 1)*cos(2*x) + (-48*I*x^2 + (-48*I*x^2 + 24*I)*cos(4*x) + (96*I*x^2 - 48*I)*cos(2*x) + 24*(2*x^2 - 1)*sin(4*x) - 48*(2*x^2 - 1)*sin(2*x) + 24*I)*sin(6*x) + (96*I*x^2 + (192*I*x^2 - 96*I)*cos(4*x) + (-240*I*x^2 + 120*I)*cos(2*x) + 120*(2*x^2 - 1)*sin(2*x) - 48*I)*sin(4*x) + (-48*I*x^2 + (192*I*x^2 - 96*I)*cos(2*x) + 24*I)*sin(2*x))*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + ((192*cos(4*x) - 384*cos(2*x) + 192*I*sin(4*x) - 384*I*sin(2*x) + 192)*cos(6*x) + (960*cos(2*x) + 960*I*sin(2*x) - 384)*cos(4*x) - 384*cos(4*x)^2 - 384*cos(2*x)^2 - (-192*I*cos(4*x) + 384*I*cos(2*x) + 192*sin(4*x) - 384*sin(2*x) - 192*I)*sin(6*x) - (768*I*cos(4*x) - 960*I*cos(2*x) + 960*sin(2*x) + 384*I)*sin(4*x) + 384*sin(4*x)^2 - (768*I*cos(2*x) - 192*I)*sin(2*x) + 384*sin(2*x)^2 + 192*cos(2*x))*polylog(3, -e^(I*x)) + ((192*cos(4*x) - 384*cos(2*x) + 192*I*sin(4*x) - 384*I*sin(2*x) + 192)*cos(6*x) + (960*cos(2*x) + 960*I*sin(2*x) - 384)*cos(4*x) - 384*cos(4*x)^2 - 384*cos(2*x)^2 - (-192*I*cos(4*x) + 384*I*cos(2*x) + 192*sin(4*x) - 384*sin(2*x) - 192*I)*sin(6*x) - (768*I*cos(4*x) - 960*I*cos(2*x) + 960*sin(2*x) + 384*I)*sin(4*x) + 384*sin(4*x)^2 - (768*I*cos(2*x) - 192*I)*sin(2*x) + 384*sin(2*x)^2 + 192*cos(2*x))*polylog(3, e^(I*x)) + (32*x^3 - 12*I*x^2 - (-12*I*x^2 + 12*x + 6*I)*cos(6*x) + (32*x^3 - 24*I*x^2 - 72*x + 12*I)*cos(4*x) - (64*x^3 + 78*I*x^2 - 90*x + 9*I)*cos(2*x) - (-32*I*x^3 - 24*x^2 + 72*I*x + 12)*sin(4*x) - (64*I*x^3 - 78*x^2 - 90*I*x - 9)*sin(2*x) - 12*x + 6*I)*sin(6*x) - (64*x^3 - 30*I*x^2 + (128*x^3 - 48*I*x^2 - 336*x + 24*I)*cos(4*x) - (160*x^3 + 156*I*x^2 - 276*x + 18*I)*cos(2*x) + (-160*I*x^3 + 156*x^2 + 276*I*x + 18)*sin(2*x) - 30*x + 15*I)*sin(4*x) + (32*x^3 - 24*I*x^2 - (128*x^3 + 168*I*x^2 - 192*x + 12*I)*cos(2*x) - 24*x + 12*I)*sin(2*x) - 6*I*x - 3)/((48*cos(4*x) - 96*cos(2*x) + 48*I*sin(4*x) - 96*I*sin(2*x) + 48)*cos(6*x) + (240*cos(2*x) + 240*I*sin(2*x) - 96)*cos(4*x) - 96*cos(4*x)^2 - 96*cos(2*x)^2 - (-48*I*cos(4*x) + 96*I*cos(2*x) + 48*sin(4*x) - 96*sin(2*x) - 48*I)*sin(6*x) - (192*I*cos(4*x) - 240*I*cos(2*x) + 240*sin(2*x) + 96*I)*sin(4*x) + 96*sin(4*x)^2 - (192*I*cos(2*x) - 48*I)*sin(2*x) + 96*sin(2*x)^2 + 48*cos(2*x))","B",0
207,1,1739,0,0.588390," ","integrate(x*cos(x)^2*cot(x)^3,x, algorithm=""maxima"")","-\frac{{\left(2 \, x + i\right)} \cos\left(6 \, x\right)^{2} - {\left(-32 i \, x^{2} - 8 \, x - 4 i\right)} \cos\left(4 \, x\right)^{2} - {\left(-32 i \, x^{2} + 28 \, x - 16 i\right)} \cos\left(2 \, x\right)^{2} - {\left(2 \, x + i\right)} \sin\left(6 \, x\right)^{2} - {\left(32 i \, x^{2} + 8 \, x + 4 i\right)} \sin\left(4 \, x\right)^{2} - {\left(32 i \, x^{2} - 28 \, x + 16 i\right)} \sin\left(2 \, x\right)^{2} - {\left(64 i \, x \cos\left(4 \, x\right)^{2} + 64 i \, x \cos\left(2 \, x\right)^{2} - 64 i \, x \sin\left(4 \, x\right)^{2} - 64 i \, x \sin\left(2 \, x\right)^{2} + {\left(-32 i \, x \cos\left(4 \, x\right) + 64 i \, x \cos\left(2 \, x\right) + 32 \, x \sin\left(4 \, x\right) - 64 \, x \sin\left(2 \, x\right) - 32 i \, x\right)} \cos\left(6 \, x\right) + {\left(-160 i \, x \cos\left(2 \, x\right) + 160 \, x \sin\left(2 \, x\right) + 64 i \, x\right)} \cos\left(4 \, x\right) - 32 i \, x \cos\left(2 \, x\right) + {\left(32 \, x \cos\left(4 \, x\right) - 64 \, x \cos\left(2 \, x\right) + 32 i \, x \sin\left(4 \, x\right) - 64 i \, x \sin\left(2 \, x\right) + 32 \, x\right)} \sin\left(6 \, x\right) - 32 \, {\left(4 \, x \cos\left(4 \, x\right) - 5 \, x \cos\left(2 \, x\right) - 5 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \sin\left(4 \, x\right) - 32 \, {\left(4 \, x \cos\left(2 \, x\right) - x\right)} \sin\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), \cos\left(x\right) + 1\right) - {\left(-64 i \, x \cos\left(4 \, x\right)^{2} - 64 i \, x \cos\left(2 \, x\right)^{2} + 64 i \, x \sin\left(4 \, x\right)^{2} + 64 i \, x \sin\left(2 \, x\right)^{2} + {\left(32 i \, x \cos\left(4 \, x\right) - 64 i \, x \cos\left(2 \, x\right) - 32 \, x \sin\left(4 \, x\right) + 64 \, x \sin\left(2 \, x\right) + 32 i \, x\right)} \cos\left(6 \, x\right) + {\left(160 i \, x \cos\left(2 \, x\right) - 160 \, x \sin\left(2 \, x\right) - 64 i \, x\right)} \cos\left(4 \, x\right) + 32 i \, x \cos\left(2 \, x\right) - {\left(32 \, x \cos\left(4 \, x\right) - 64 \, x \cos\left(2 \, x\right) + 32 i \, x \sin\left(4 \, x\right) - 64 i \, x \sin\left(2 \, x\right) + 32 \, x\right)} \sin\left(6 \, x\right) + 32 \, {\left(4 \, x \cos\left(4 \, x\right) - 5 \, x \cos\left(2 \, x\right) - 5 i \, x \sin\left(2 \, x\right) + 2 \, x\right)} \sin\left(4 \, x\right) + 32 \, {\left(4 \, x \cos\left(2 \, x\right) - x\right)} \sin\left(2 \, x\right)\right)} \arctan\left(\sin\left(x\right), -\cos\left(x\right) + 1\right) - {\left(16 i \, x^{2} + {\left(16 i \, x^{2} + 8 \, x + 4 i\right)} \cos\left(4 \, x\right) + {\left(-32 i \, x^{2} + 26 \, x - 17 i\right)} \cos\left(2 \, x\right) - 4 \, {\left(4 \, x^{2} - 2 i \, x + 1\right)} \sin\left(4 \, x\right) + {\left(32 \, x^{2} + 26 i \, x + 17\right)} \sin\left(2 \, x\right) + 4 \, x + 14 i\right)} \cos\left(6 \, x\right) - {\left(-32 i \, x^{2} + {\left(80 i \, x^{2} - 52 \, x + 34 i\right)} \cos\left(2 \, x\right) - 2 \, {\left(40 \, x^{2} + 26 i \, x + 17\right)} \sin\left(2 \, x\right) - 10 \, x - 27 i\right)} \cos\left(4 \, x\right) - {\left(16 i \, x^{2} + 8 \, x + 12 i\right)} \cos\left(2 \, x\right) - {\left({\left(32 i \, \cos\left(4 \, x\right) - 64 i \, \cos\left(2 \, x\right) - 32 \, \sin\left(4 \, x\right) + 64 \, \sin\left(2 \, x\right) + 32 i\right)} \cos\left(6 \, x\right) + {\left(160 i \, \cos\left(2 \, x\right) - 160 \, \sin\left(2 \, x\right) - 64 i\right)} \cos\left(4 \, x\right) - 64 i \, \cos\left(4 \, x\right)^{2} - 64 i \, \cos\left(2 \, x\right)^{2} - {\left(32 \, \cos\left(4 \, x\right) - 64 \, \cos\left(2 \, x\right) + 32 i \, \sin\left(4 \, x\right) - 64 i \, \sin\left(2 \, x\right) + 32\right)} \sin\left(6 \, x\right) + {\left(128 \, \cos\left(4 \, x\right) - 160 \, \cos\left(2 \, x\right) - 160 i \, \sin\left(2 \, x\right) + 64\right)} \sin\left(4 \, x\right) + 64 i \, \sin\left(4 \, x\right)^{2} + 32 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right) + 64 i \, \sin\left(2 \, x\right)^{2} + 32 i \, \cos\left(2 \, x\right)\right)} {\rm Li}_2\left(-e^{\left(i \, x\right)}\right) - {\left({\left(32 i \, \cos\left(4 \, x\right) - 64 i \, \cos\left(2 \, x\right) - 32 \, \sin\left(4 \, x\right) + 64 \, \sin\left(2 \, x\right) + 32 i\right)} \cos\left(6 \, x\right) + {\left(160 i \, \cos\left(2 \, x\right) - 160 \, \sin\left(2 \, x\right) - 64 i\right)} \cos\left(4 \, x\right) - 64 i \, \cos\left(4 \, x\right)^{2} - 64 i \, \cos\left(2 \, x\right)^{2} - {\left(32 \, \cos\left(4 \, x\right) - 64 \, \cos\left(2 \, x\right) + 32 i \, \sin\left(4 \, x\right) - 64 i \, \sin\left(2 \, x\right) + 32\right)} \sin\left(6 \, x\right) + {\left(128 \, \cos\left(4 \, x\right) - 160 \, \cos\left(2 \, x\right) - 160 i \, \sin\left(2 \, x\right) + 64\right)} \sin\left(4 \, x\right) + 64 i \, \sin\left(4 \, x\right)^{2} + 32 \, {\left(4 \, \cos\left(2 \, x\right) - 1\right)} \sin\left(2 \, x\right) + 64 i \, \sin\left(2 \, x\right)^{2} + 32 i \, \cos\left(2 \, x\right)\right)} {\rm Li}_2\left(e^{\left(i \, x\right)}\right) - {\left(32 \, x \cos\left(4 \, x\right)^{2} + 32 \, x \cos\left(2 \, x\right)^{2} - 32 \, x \sin\left(4 \, x\right)^{2} - 32 \, x \sin\left(2 \, x\right)^{2} - {\left(16 \, x \cos\left(4 \, x\right) - 32 \, x \cos\left(2 \, x\right) + 16 i \, x \sin\left(4 \, x\right) - 32 i \, x \sin\left(2 \, x\right) + 16 \, x\right)} \cos\left(6 \, x\right) - 16 \, {\left(5 \, x \cos\left(2 \, x\right) + 5 i \, x \sin\left(2 \, x\right) - 2 \, x\right)} \cos\left(4 \, x\right) - 16 \, x \cos\left(2 \, x\right) + {\left(-16 i \, x \cos\left(4 \, x\right) + 32 i \, x \cos\left(2 \, x\right) + 16 \, x \sin\left(4 \, x\right) - 32 \, x \sin\left(2 \, x\right) - 16 i \, x\right)} \sin\left(6 \, x\right) + {\left(64 i \, x \cos\left(4 \, x\right) - 80 i \, x \cos\left(2 \, x\right) + 80 \, x \sin\left(2 \, x\right) + 32 i \, x\right)} \sin\left(4 \, x\right) + {\left(64 i \, x \cos\left(2 \, x\right) - 16 i \, x\right)} \sin\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} + 2 \, \cos\left(x\right) + 1\right) - {\left(32 \, x \cos\left(4 \, x\right)^{2} + 32 \, x \cos\left(2 \, x\right)^{2} - 32 \, x \sin\left(4 \, x\right)^{2} - 32 \, x \sin\left(2 \, x\right)^{2} - {\left(16 \, x \cos\left(4 \, x\right) - 32 \, x \cos\left(2 \, x\right) + 16 i \, x \sin\left(4 \, x\right) - 32 i \, x \sin\left(2 \, x\right) + 16 \, x\right)} \cos\left(6 \, x\right) - 16 \, {\left(5 \, x \cos\left(2 \, x\right) + 5 i \, x \sin\left(2 \, x\right) - 2 \, x\right)} \cos\left(4 \, x\right) - 16 \, x \cos\left(2 \, x\right) + {\left(-16 i \, x \cos\left(4 \, x\right) + 32 i \, x \cos\left(2 \, x\right) + 16 \, x \sin\left(4 \, x\right) - 32 \, x \sin\left(2 \, x\right) - 16 i \, x\right)} \sin\left(6 \, x\right) + {\left(64 i \, x \cos\left(4 \, x\right) - 80 i \, x \cos\left(2 \, x\right) + 80 \, x \sin\left(2 \, x\right) + 32 i \, x\right)} \sin\left(4 \, x\right) + {\left(64 i \, x \cos\left(2 \, x\right) - 16 i \, x\right)} \sin\left(2 \, x\right)\right)} \log\left(\cos\left(x\right)^{2} + \sin\left(x\right)^{2} - 2 \, \cos\left(x\right) + 1\right) + {\left(16 \, x^{2} + 2 \, {\left(2 i \, x - 1\right)} \cos\left(6 \, x\right) + 4 \, {\left(4 \, x^{2} - 2 i \, x + 1\right)} \cos\left(4 \, x\right) - {\left(32 \, x^{2} + 26 i \, x + 17\right)} \cos\left(2 \, x\right) - {\left(-16 i \, x^{2} - 8 \, x - 4 i\right)} \sin\left(4 \, x\right) - {\left(32 i \, x^{2} - 26 \, x + 17 i\right)} \sin\left(2 \, x\right) - 4 i \, x + 14\right)} \sin\left(6 \, x\right) - {\left(32 \, x^{2} + 8 \, {\left(8 \, x^{2} - 2 i \, x + 1\right)} \cos\left(4 \, x\right) - 2 \, {\left(40 \, x^{2} + 26 i \, x + 17\right)} \cos\left(2 \, x\right) + {\left(-80 i \, x^{2} + 52 \, x - 34 i\right)} \sin\left(2 \, x\right) - 10 i \, x + 27\right)} \sin\left(4 \, x\right) + 4 \, {\left(4 \, x^{2} - 2 \, {\left(8 \, x^{2} + 7 i \, x + 4\right)} \cos\left(2 \, x\right) - 2 i \, x + 3\right)} \sin\left(2 \, x\right) + 2 \, x - i}{{\left(16 \, \cos\left(4 \, x\right) - 32 \, \cos\left(2 \, x\right) + 16 i \, \sin\left(4 \, x\right) - 32 i \, \sin\left(2 \, x\right) + 16\right)} \cos\left(6 \, x\right) + {\left(80 \, \cos\left(2 \, x\right) + 80 i \, \sin\left(2 \, x\right) - 32\right)} \cos\left(4 \, x\right) - 32 \, \cos\left(4 \, x\right)^{2} - 32 \, \cos\left(2 \, x\right)^{2} - {\left(-16 i \, \cos\left(4 \, x\right) + 32 i \, \cos\left(2 \, x\right) + 16 \, \sin\left(4 \, x\right) - 32 \, \sin\left(2 \, x\right) - 16 i\right)} \sin\left(6 \, x\right) - {\left(64 i \, \cos\left(4 \, x\right) - 80 i \, \cos\left(2 \, x\right) + 80 \, \sin\left(2 \, x\right) + 32 i\right)} \sin\left(4 \, x\right) + 32 \, \sin\left(4 \, x\right)^{2} - {\left(64 i \, \cos\left(2 \, x\right) - 16 i\right)} \sin\left(2 \, x\right) + 32 \, \sin\left(2 \, x\right)^{2} + 16 \, \cos\left(2 \, x\right)}"," ",0,"-((2*x + I)*cos(6*x)^2 - (-32*I*x^2 - 8*x - 4*I)*cos(4*x)^2 - (-32*I*x^2 + 28*x - 16*I)*cos(2*x)^2 - (2*x + I)*sin(6*x)^2 - (32*I*x^2 + 8*x + 4*I)*sin(4*x)^2 - (32*I*x^2 - 28*x + 16*I)*sin(2*x)^2 - (64*I*x*cos(4*x)^2 + 64*I*x*cos(2*x)^2 - 64*I*x*sin(4*x)^2 - 64*I*x*sin(2*x)^2 + (-32*I*x*cos(4*x) + 64*I*x*cos(2*x) + 32*x*sin(4*x) - 64*x*sin(2*x) - 32*I*x)*cos(6*x) + (-160*I*x*cos(2*x) + 160*x*sin(2*x) + 64*I*x)*cos(4*x) - 32*I*x*cos(2*x) + (32*x*cos(4*x) - 64*x*cos(2*x) + 32*I*x*sin(4*x) - 64*I*x*sin(2*x) + 32*x)*sin(6*x) - 32*(4*x*cos(4*x) - 5*x*cos(2*x) - 5*I*x*sin(2*x) + 2*x)*sin(4*x) - 32*(4*x*cos(2*x) - x)*sin(2*x))*arctan2(sin(x), cos(x) + 1) - (-64*I*x*cos(4*x)^2 - 64*I*x*cos(2*x)^2 + 64*I*x*sin(4*x)^2 + 64*I*x*sin(2*x)^2 + (32*I*x*cos(4*x) - 64*I*x*cos(2*x) - 32*x*sin(4*x) + 64*x*sin(2*x) + 32*I*x)*cos(6*x) + (160*I*x*cos(2*x) - 160*x*sin(2*x) - 64*I*x)*cos(4*x) + 32*I*x*cos(2*x) - (32*x*cos(4*x) - 64*x*cos(2*x) + 32*I*x*sin(4*x) - 64*I*x*sin(2*x) + 32*x)*sin(6*x) + 32*(4*x*cos(4*x) - 5*x*cos(2*x) - 5*I*x*sin(2*x) + 2*x)*sin(4*x) + 32*(4*x*cos(2*x) - x)*sin(2*x))*arctan2(sin(x), -cos(x) + 1) - (16*I*x^2 + (16*I*x^2 + 8*x + 4*I)*cos(4*x) + (-32*I*x^2 + 26*x - 17*I)*cos(2*x) - 4*(4*x^2 - 2*I*x + 1)*sin(4*x) + (32*x^2 + 26*I*x + 17)*sin(2*x) + 4*x + 14*I)*cos(6*x) - (-32*I*x^2 + (80*I*x^2 - 52*x + 34*I)*cos(2*x) - 2*(40*x^2 + 26*I*x + 17)*sin(2*x) - 10*x - 27*I)*cos(4*x) - (16*I*x^2 + 8*x + 12*I)*cos(2*x) - ((32*I*cos(4*x) - 64*I*cos(2*x) - 32*sin(4*x) + 64*sin(2*x) + 32*I)*cos(6*x) + (160*I*cos(2*x) - 160*sin(2*x) - 64*I)*cos(4*x) - 64*I*cos(4*x)^2 - 64*I*cos(2*x)^2 - (32*cos(4*x) - 64*cos(2*x) + 32*I*sin(4*x) - 64*I*sin(2*x) + 32)*sin(6*x) + (128*cos(4*x) - 160*cos(2*x) - 160*I*sin(2*x) + 64)*sin(4*x) + 64*I*sin(4*x)^2 + 32*(4*cos(2*x) - 1)*sin(2*x) + 64*I*sin(2*x)^2 + 32*I*cos(2*x))*dilog(-e^(I*x)) - ((32*I*cos(4*x) - 64*I*cos(2*x) - 32*sin(4*x) + 64*sin(2*x) + 32*I)*cos(6*x) + (160*I*cos(2*x) - 160*sin(2*x) - 64*I)*cos(4*x) - 64*I*cos(4*x)^2 - 64*I*cos(2*x)^2 - (32*cos(4*x) - 64*cos(2*x) + 32*I*sin(4*x) - 64*I*sin(2*x) + 32)*sin(6*x) + (128*cos(4*x) - 160*cos(2*x) - 160*I*sin(2*x) + 64)*sin(4*x) + 64*I*sin(4*x)^2 + 32*(4*cos(2*x) - 1)*sin(2*x) + 64*I*sin(2*x)^2 + 32*I*cos(2*x))*dilog(e^(I*x)) - (32*x*cos(4*x)^2 + 32*x*cos(2*x)^2 - 32*x*sin(4*x)^2 - 32*x*sin(2*x)^2 - (16*x*cos(4*x) - 32*x*cos(2*x) + 16*I*x*sin(4*x) - 32*I*x*sin(2*x) + 16*x)*cos(6*x) - 16*(5*x*cos(2*x) + 5*I*x*sin(2*x) - 2*x)*cos(4*x) - 16*x*cos(2*x) + (-16*I*x*cos(4*x) + 32*I*x*cos(2*x) + 16*x*sin(4*x) - 32*x*sin(2*x) - 16*I*x)*sin(6*x) + (64*I*x*cos(4*x) - 80*I*x*cos(2*x) + 80*x*sin(2*x) + 32*I*x)*sin(4*x) + (64*I*x*cos(2*x) - 16*I*x)*sin(2*x))*log(cos(x)^2 + sin(x)^2 + 2*cos(x) + 1) - (32*x*cos(4*x)^2 + 32*x*cos(2*x)^2 - 32*x*sin(4*x)^2 - 32*x*sin(2*x)^2 - (16*x*cos(4*x) - 32*x*cos(2*x) + 16*I*x*sin(4*x) - 32*I*x*sin(2*x) + 16*x)*cos(6*x) - 16*(5*x*cos(2*x) + 5*I*x*sin(2*x) - 2*x)*cos(4*x) - 16*x*cos(2*x) + (-16*I*x*cos(4*x) + 32*I*x*cos(2*x) + 16*x*sin(4*x) - 32*x*sin(2*x) - 16*I*x)*sin(6*x) + (64*I*x*cos(4*x) - 80*I*x*cos(2*x) + 80*x*sin(2*x) + 32*I*x)*sin(4*x) + (64*I*x*cos(2*x) - 16*I*x)*sin(2*x))*log(cos(x)^2 + sin(x)^2 - 2*cos(x) + 1) + (16*x^2 + 2*(2*I*x - 1)*cos(6*x) + 4*(4*x^2 - 2*I*x + 1)*cos(4*x) - (32*x^2 + 26*I*x + 17)*cos(2*x) - (-16*I*x^2 - 8*x - 4*I)*sin(4*x) - (32*I*x^2 - 26*x + 17*I)*sin(2*x) - 4*I*x + 14)*sin(6*x) - (32*x^2 + 8*(8*x^2 - 2*I*x + 1)*cos(4*x) - 2*(40*x^2 + 26*I*x + 17)*cos(2*x) + (-80*I*x^2 + 52*x - 34*I)*sin(2*x) - 10*I*x + 27)*sin(4*x) + 4*(4*x^2 - 2*(8*x^2 + 7*I*x + 4)*cos(2*x) - 2*I*x + 3)*sin(2*x) + 2*x - I)/((16*cos(4*x) - 32*cos(2*x) + 16*I*sin(4*x) - 32*I*sin(2*x) + 16)*cos(6*x) + (80*cos(2*x) + 80*I*sin(2*x) - 32)*cos(4*x) - 32*cos(4*x)^2 - 32*cos(2*x)^2 - (-16*I*cos(4*x) + 32*I*cos(2*x) + 16*sin(4*x) - 32*sin(2*x) - 16*I)*sin(6*x) - (64*I*cos(4*x) - 80*I*cos(2*x) + 80*sin(2*x) + 32*I)*sin(4*x) + 32*sin(4*x)^2 - (64*I*cos(2*x) - 16*I)*sin(2*x) + 32*sin(2*x)^2 + 16*cos(2*x))","B",0
208,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right) \sin\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)*sin(b*x + a), x)","F",0
209,1,792,0,0.603798," ","integrate((d*x+c)^4*sec(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{15 \, c^{4} \log\left(-\sin\left(b x + a\right)^{2} + 1\right) - \frac{60 \, a c^{3} d \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b} + \frac{90 \, a^{2} c^{2} d^{2} \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b^{2}} - \frac{60 \, a^{3} c d^{3} \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b^{3}} + \frac{15 \, a^{4} d^{4} \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b^{4}} + \frac{2 \, {\left(-3 i \, {\left(b x + a\right)}^{5} d^{4} + {\left(-15 i \, b c d^{3} + 15 i \, a d^{4}\right)} {\left(b x + a\right)}^{4} - 45 \, d^{4} {\rm Li}_{5}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(-30 i \, b^{2} c^{2} d^{2} + 60 i \, a b c d^{3} - 30 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-30 i \, b^{3} c^{3} d + 90 i \, a b^{2} c^{2} d^{2} - 90 i \, a^{2} b c d^{3} + 30 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(30 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(80 i \, b c d^{3} - 80 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(90 i \, b^{2} c^{2} d^{2} - 180 i \, a b c d^{3} + 90 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(60 i \, b^{3} c^{3} d - 180 i \, a b^{2} c^{2} d^{2} + 180 i \, a^{2} b c d^{3} - 60 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-30 i \, b^{3} c^{3} d + 90 i \, a b^{2} c^{2} d^{2} - 90 i \, a^{2} b c d^{3} - 60 i \, {\left(b x + a\right)}^{3} d^{4} + 30 i \, a^{3} d^{4} + {\left(-120 i \, b c d^{3} + 120 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-90 i \, b^{2} c^{2} d^{2} + 180 i \, a b c d^{3} - 90 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 5 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 9 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \log\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) + {\left(60 i \, b c d^{3} + 90 i \, {\left(b x + a\right)} d^{4} - 60 i \, a d^{4}\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + 15 \, {\left(3 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + 6 \, {\left(b x + a\right)}^{2} d^{4} + 3 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)})\right)}}{b^{4}}}{30 \, b}"," ",0,"-1/30*(15*c^4*log(-sin(b*x + a)^2 + 1) - 60*a*c^3*d*log(-sin(b*x + a)^2 + 1)/b + 90*a^2*c^2*d^2*log(-sin(b*x + a)^2 + 1)/b^2 - 60*a^3*c*d^3*log(-sin(b*x + a)^2 + 1)/b^3 + 15*a^4*d^4*log(-sin(b*x + a)^2 + 1)/b^4 + 2*(-3*I*(b*x + a)^5*d^4 + (-15*I*b*c*d^3 + 15*I*a*d^4)*(b*x + a)^4 - 45*d^4*polylog(5, -e^(2*I*b*x + 2*I*a)) + (-30*I*b^2*c^2*d^2 + 60*I*a*b*c*d^3 - 30*I*a^2*d^4)*(b*x + a)^3 + (-30*I*b^3*c^3*d + 90*I*a*b^2*c^2*d^2 - 90*I*a^2*b*c*d^3 + 30*I*a^3*d^4)*(b*x + a)^2 + (30*I*(b*x + a)^4*d^4 + (80*I*b*c*d^3 - 80*I*a*d^4)*(b*x + a)^3 + (90*I*b^2*c^2*d^2 - 180*I*a*b*c*d^3 + 90*I*a^2*d^4)*(b*x + a)^2 + (60*I*b^3*c^3*d - 180*I*a*b^2*c^2*d^2 + 180*I*a^2*b*c*d^3 - 60*I*a^3*d^4)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (-30*I*b^3*c^3*d + 90*I*a*b^2*c^2*d^2 - 90*I*a^2*b*c*d^3 - 60*I*(b*x + a)^3*d^4 + 30*I*a^3*d^4 + (-120*I*b*c*d^3 + 120*I*a*d^4)*(b*x + a)^2 + (-90*I*b^2*c^2*d^2 + 180*I*a*b*c*d^3 - 90*I*a^2*d^4)*(b*x + a))*dilog(-e^(2*I*b*x + 2*I*a)) + 5*(3*(b*x + a)^4*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 9*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 6*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (60*I*b*c*d^3 + 90*I*(b*x + a)*d^4 - 60*I*a*d^4)*polylog(4, -e^(2*I*b*x + 2*I*a)) + 15*(3*b^2*c^2*d^2 - 6*a*b*c*d^3 + 6*(b*x + a)^2*d^4 + 3*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, -e^(2*I*b*x + 2*I*a)))/b^4)/b","B",0
210,1,490,0,0.572978," ","integrate((d*x+c)^3*sec(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{6 \, c^{3} \log\left(-\sin\left(b x + a\right)^{2} + 1\right) - \frac{18 \, a c^{2} d \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b} + \frac{18 \, a^{2} c d^{2} \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b^{2}} - \frac{6 \, a^{3} d^{3} \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b^{3}} + \frac{-3 i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + 12 i \, d^{3} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(16 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 24 i \, {\left(b x + a\right)}^{2} d^{3} - 18 i \, a^{2} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 2 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\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(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) + 6 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)})}{b^{3}}}{12 \, b}"," ",0,"-1/12*(6*c^3*log(-sin(b*x + a)^2 + 1) - 18*a*c^2*d*log(-sin(b*x + a)^2 + 1)/b + 18*a^2*c*d^2*log(-sin(b*x + a)^2 + 1)/b^2 - 6*a^3*d^3*log(-sin(b*x + a)^2 + 1)/b^3 + (-3*I*(b*x + a)^4*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a)^3 + 12*I*d^3*polylog(4, -e^(2*I*b*x + 2*I*a)) + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*a^2*d^3)*(b*x + a)^2 + (16*I*(b*x + a)^3*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*a^2*d^3)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 24*I*(b*x + a)^2*d^3 - 18*I*a^2*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*dilog(-e^(2*I*b*x + 2*I*a)) + 2*(4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 6*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*polylog(3, -e^(2*I*b*x + 2*I*a)))/b^3)/b","B",0
211,1,280,0,0.528906," ","integrate((d*x+c)^2*sec(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{3 \, c^{2} \log\left(-\sin\left(b x + a\right)^{2} + 1\right) - \frac{6 \, a c d \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b} + \frac{3 \, a^{2} d^{2} \log\left(-\sin\left(b x + a\right)^{2} + 1\right)}{b^{2}} + \frac{-2 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)}^{2} + 3 \, d^{2} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-6 i \, b c d - 6 i \, {\left(b x + a\right)} d^{2} + 6 i \, a d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 3 \, {\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(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}}}{6 \, b}"," ",0,"-1/6*(3*c^2*log(-sin(b*x + a)^2 + 1) - 6*a*c*d*log(-sin(b*x + a)^2 + 1)/b + 3*a^2*d^2*log(-sin(b*x + a)^2 + 1)/b^2 + (-2*I*(b*x + a)^3*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a)^2 + 3*d^2*polylog(3, -e^(2*I*b*x + 2*I*a)) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (-6*I*b*c*d - 6*I*(b*x + a)*d^2 + 6*I*a*d^2)*dilog(-e^(2*I*b*x + 2*I*a)) + 3*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1))/b^2)/b","B",0
212,1,114,0,0.525275," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a),x, algorithm=""maxima"")","-\frac{-i \, b^{2} d x^{2} - 2 i \, b^{2} c x + {\left(2 i \, b d x + 2 i \, b c\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - i \, d {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(b d x + b c\right)} \log\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)}{2 \, b^{2}}"," ",0,"-1/2*(-I*b^2*d*x^2 - 2*I*b^2*c*x + (2*I*b*d*x + 2*I*b*c)*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - I*d*dilog(-e^(2*I*b*x + 2*I*a)) + (b*d*x + b*c)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1))/b^2","B",0
213,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\sec\left(b x + a\right) \sin\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(sec(b*x + a)*sin(b*x + a)/(d*x + c), x)","F",0
214,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\int \frac{\sec\left(b x + a\right) \sin\left(b x + a\right)}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(sec(b*x + a)*sin(b*x + a)/(d*x + c)^2, x)","F",0
215,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right) \sin\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)*sin(b*x + a)^2, x)","F",0
216,1,924,0,0.673159," ","integrate((d*x+c)^3*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{3} {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)} - \frac{3 \, a c^{2} d {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)}}{b^{3}} + \frac{12 i \, d^{3} {\rm Li}_{4}(i \, e^{\left(i \, b x + i \, a\right)}) - 12 i \, d^{3} {\rm Li}_{4}(-i \, 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(\cos\left(b x + a\right), \sin\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(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\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(b x + 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} - 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(i \, 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(-i \, 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 \, \sin\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 \, \sin\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}(i \, 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}(-i \, e^{\left(i \, b x + i \, 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(b x + a\right)}{b^{3}}}{2 \, b}"," ",0,"1/2*(c^3*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a)) - 3*a*c^2*d*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a))/b + 3*a^2*c*d^2*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a))/b^2 - a^3*d^3*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a))/b^3 + (12*I*d^3*polylog(4, I*e^(I*b*x + I*a)) - 12*I*d^3*polylog(4, -I*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(cos(b*x + a), sin(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(cos(b*x + a), -sin(b*x + a) + 1) - 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(b*x + 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(I*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(-I*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*sin(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*sin(b*x + a) + 1) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, I*e^(I*b*x + I*a)) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, -I*e^(I*b*x + I*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(b*x + a))/b^3)/b","B",0
217,1,510,0,0.596851," ","integrate((d*x+c)^2*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{2} {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)} - \frac{2 \, a c d {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right) - 2 \, \sin\left(b x + a\right)\right)}}{b^{2}} + \frac{4 \, d^{2} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) - 4 \, d^{2} {\rm Li}_{3}(-i \, 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(\cos\left(b x + a\right), \sin\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(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(b x + a\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(i \, 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(-i \, 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 \, \sin\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 \, \sin\left(b x + a\right) + 1\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(b x + a\right)}{b^{2}}}{2 \, b}"," ",0,"1/2*(c^2*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a)) - 2*a*c*d*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a))/b + a^2*d^2*(log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1) - 2*sin(b*x + a))/b^2 + (4*d^2*polylog(3, I*e^(I*b*x + I*a)) - 4*d^2*polylog(3, -I*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(cos(b*x + a), sin(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(cos(b*x + a), -sin(b*x + a) + 1) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(b*x + a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*dilog(I*e^(I*b*x + I*a)) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*dilog(-I*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*sin(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*sin(b*x + a) + 1) - 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - 2*d^2)*sin(b*x + a))/b^2)/b","B",0
218,-1,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right) \sin\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)*sin(b*x + a)^3, x)","F",0
222,1,685,0,0.560654," ","integrate((d*x+c)^3*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{24 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} c^{3} - \frac{72 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} a c^{2} d}{b} + \frac{72 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{24 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} a^{3} d^{3}}{b^{3}} + \frac{-12 i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-48 i \, b c d^{2} + 48 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + 48 i \, d^{3} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(-72 i \, b^{2} c^{2} d + 144 i \, a b c d^{2} - 72 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(64 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(144 i \, b c d^{2} - 144 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(144 i \, b^{2} c^{2} d - 288 i \, a b c d^{2} + 144 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 6 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} - 3 \, b c d^{2} + 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-72 i \, b^{2} c^{2} d + 144 i \, a b c d^{2} - 96 i \, {\left(b x + a\right)}^{2} d^{3} - 72 i \, a^{2} d^{3} + {\left(-144 i \, b c d^{2} + 144 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 8 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\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(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) + 24 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + 9 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, {\left(b x + a\right)}^{2} d^{3} + {\left(2 \, a^{2} - 1\right)} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)}{b^{3}}}{48 \, b}"," ",0,"-1/48*(24*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*c^3 - 72*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*a*c^2*d/b + 72*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*a^2*c*d^2/b^2 - 24*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*a^3*d^3/b^3 + (-12*I*(b*x + a)^4*d^3 + (-48*I*b*c*d^2 + 48*I*a*d^3)*(b*x + a)^3 + 48*I*d^3*polylog(4, -e^(2*I*b*x + 2*I*a)) + (-72*I*b^2*c^2*d + 144*I*a*b*c*d^2 - 72*I*a^2*d^3)*(b*x + a)^2 + (64*I*(b*x + a)^3*d^3 + (144*I*b*c*d^2 - 144*I*a*d^3)*(b*x + a)^2 + (144*I*b^2*c^2*d - 288*I*a*b*c*d^2 + 144*I*a^2*d^3)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 6*(2*(b*x + a)^3*d^3 - 3*b*c*d^2 + 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 - 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-72*I*b^2*c^2*d + 144*I*a*b*c*d^2 - 96*I*(b*x + a)^2*d^3 - 72*I*a^2*d^3 + (-144*I*b*c*d^2 + 144*I*a*d^3)*(b*x + a))*dilog(-e^(2*I*b*x + 2*I*a)) + 8*(4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 24*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*polylog(3, -e^(2*I*b*x + 2*I*a)) + 9*(2*b^2*c^2*d - 4*a*b*c*d^2 + 2*(b*x + a)^2*d^3 + (2*a^2 - 1)*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))/b^3)/b","B",0
223,1,379,0,0.530945," ","integrate((d*x+c)^2*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{12 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} c^{2} - \frac{24 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} a c d}{b} + \frac{12 \, {\left(\sin\left(b x + a\right)^{2} + \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} a^{2} d^{2}}{b^{2}} + \frac{-8 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-24 i \, b c d + 24 i \, a d^{2}\right)} {\left(b x + a\right)}^{2} + 12 \, d^{2} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(24 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(48 i \, b c d - 48 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-24 i \, b c d - 24 i \, {\left(b x + a\right)} d^{2} + 24 i \, a d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 12 \, {\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(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) + 6 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)}{b^{2}}}{24 \, b}"," ",0,"-1/24*(12*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*c^2 - 24*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*a*c*d/b + 12*(sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1))*a^2*d^2/b^2 + (-8*I*(b*x + a)^3*d^2 + (-24*I*b*c*d + 24*I*a*d^2)*(b*x + a)^2 + 12*d^2*polylog(3, -e^(2*I*b*x + 2*I*a)) + (24*I*(b*x + a)^2*d^2 + (48*I*b*c*d - 48*I*a*d^2)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 3*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) - d^2)*cos(2*b*x + 2*a) + (-24*I*b*c*d - 24*I*(b*x + a)*d^2 + 24*I*a*d^2)*dilog(-e^(2*I*b*x + 2*I*a)) + 12*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 6*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(2*b*x + 2*a))/b^2)/b","B",0
224,1,145,0,0.515706," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""maxima"")","-\frac{-4 i \, b^{2} d x^{2} - 8 i \, b^{2} c x + {\left(8 i \, b d x + 8 i \, b c\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 i \, d {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 4 \, {\left(b d x + b c\right)} \log\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) + d \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{2}}"," ",0,"-1/8*(-4*I*b^2*d*x^2 - 8*I*b^2*c*x + (8*I*b*d*x + 8*I*b*c)*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 2*(b*d*x + b*c)*cos(2*b*x + 2*a) - 4*I*d*dilog(-e^(2*I*b*x + 2*I*a)) + 4*(b*d*x + b*c)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + d*sin(2*b*x + 2*a))/b^2","A",0
225,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{{\left(i \, E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 8 \, d \int \frac{\sin\left(2 \, b x + 2 \, a\right)}{{\left(d x + c\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)}}\,{d x} + {\left(E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, d}"," ",0,"1/4*((I*exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 8*d*integrate(sin(2*b*x + 2*a)/((d*x + c)*cos(2*b*x + 2*a)^2 + (d*x + c)*sin(2*b*x + 2*a)^2 + d*x + 2*(d*x + c)*cos(2*b*x + 2*a) + c), x) + (exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/d","F",0
226,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(i \, E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 8 \, {\left(d^{2} x + c d\right)} \int \frac{\sin\left(2 \, b x + 2 \, a\right)}{{\left(d x + c\right)}^{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)}}\,{d x} + {\left(E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{2} x + c d\right)}}"," ",0,"1/4*((I*exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 8*(d^2*x + c*d)*integrate(sin(2*b*x + 2*a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(2*b*x + 2*a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(2*b*x + 2*a)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(2*b*x + 2*a)), x) + (exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/(d^2*x + c*d)","F",0
227,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)*sec(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right) \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)*sec(b*x + a), x)","F",0
228,1,1779,0,0.713898," ","integrate((d*x+c)^4*csc(b*x+a)*sec(b*x+a),x, algorithm=""maxima"")","-\frac{3 \, c^{4} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{12 \, a c^{3} d {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{18 \, a^{2} c^{2} d^{2} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{12 \, a^{3} c d^{3} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} + \frac{3 \, a^{4} d^{4} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{4}} - \frac{18 \, d^{4} {\rm Li}_{5}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - 144 \, d^{4} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) - 144 \, d^{4} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) - {\left(12 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(32 i \, b c d^{3} - 32 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} - 24 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(-6 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} - 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{3} c^{3} d + 72 i \, a b^{2} c^{2} d^{2} - 72 i \, a^{2} b c d^{3} + 24 i \, a^{3} d^{4}\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 \, {\left(b x + a\right)}^{4} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} - 24 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - {\left(-12 i \, b^{3} c^{3} d + 36 i \, a b^{2} c^{2} d^{2} - 36 i \, a^{2} b c d^{3} - 24 i \, {\left(b x + a\right)}^{3} d^{4} + 12 i \, a^{3} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} - 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) - {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} + 24 i \, {\left(b x + a\right)}^{3} d^{4} - 24 i \, a^{3} d^{4} + {\left(72 i \, b c d^{3} - 72 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} + 24 i \, {\left(b x + a\right)}^{3} d^{4} - 24 i \, a^{3} d^{4} + {\left(72 i \, b c d^{3} - 72 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - 2 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 9 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \log\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) + 3 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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) + 3 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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(24 i \, b c d^{3} + 36 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4}\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(-144 i \, b c d^{3} - 144 i \, {\left(b x + a\right)} d^{4} + 144 i \, a d^{4}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-144 i \, b c d^{3} - 144 i \, {\left(b x + a\right)} d^{4} + 144 i \, a d^{4}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - 6 \, {\left(3 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + 6 \, {\left(b x + a\right)}^{2} d^{4} + 3 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + 72 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + 72 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)})}{b^{4}}}{6 \, b}"," ",0,"-1/6*(3*c^4*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 12*a*c^3*d*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + 18*a^2*c^2*d^2*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 - 12*a^3*c*d^3*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^3 + 3*a^4*d^4*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^4 - (18*d^4*polylog(5, -e^(2*I*b*x + 2*I*a)) - 144*d^4*polylog(5, -e^(I*b*x + I*a)) - 144*d^4*polylog(5, e^(I*b*x + I*a)) - (12*I*(b*x + a)^4*d^4 + (32*I*b*c*d^3 - 32*I*a*d^4)*(b*x + a)^3 + (36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + 36*I*a^2*d^4)*(b*x + a)^2 + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 - 24*I*a^3*d^4)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (-6*I*(b*x + a)^4*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^3 + (-36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 - 36*I*a^2*d^4)*(b*x + a)^2 + (-24*I*b^3*c^3*d + 72*I*a*b^2*c^2*d^2 - 72*I*a^2*b*c*d^3 + 24*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (6*I*(b*x + a)^4*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^3 + (36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + 36*I*a^2*d^4)*(b*x + a)^2 + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 - 24*I*a^3*d^4)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (-12*I*b^3*c^3*d + 36*I*a*b^2*c^2*d^2 - 36*I*a^2*b*c*d^3 - 24*I*(b*x + a)^3*d^4 + 12*I*a^3*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a)^2 + (-36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 - 36*I*a^2*d^4)*(b*x + a))*dilog(-e^(2*I*b*x + 2*I*a)) - (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 + 24*I*(b*x + a)^3*d^4 - 24*I*a^3*d^4 + (72*I*b*c*d^3 - 72*I*a*d^4)*(b*x + a)^2 + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*a^2*d^4)*(b*x + a))*dilog(-e^(I*b*x + I*a)) - (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 + 24*I*(b*x + a)^3*d^4 - 24*I*a^3*d^4 + (72*I*b*c*d^3 - 72*I*a*d^4)*(b*x + a)^2 + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*a^2*d^4)*(b*x + a))*dilog(e^(I*b*x + I*a)) - 2*(3*(b*x + a)^4*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 9*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 6*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 3*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + 3*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (24*I*b*c*d^3 + 36*I*(b*x + a)*d^4 - 24*I*a*d^4)*polylog(4, -e^(2*I*b*x + 2*I*a)) - (-144*I*b*c*d^3 - 144*I*(b*x + a)*d^4 + 144*I*a*d^4)*polylog(4, -e^(I*b*x + I*a)) - (-144*I*b*c*d^3 - 144*I*(b*x + a)*d^4 + 144*I*a*d^4)*polylog(4, e^(I*b*x + I*a)) - 6*(3*b^2*c^2*d^2 - 6*a*b*c*d^3 + 6*(b*x + a)^2*d^4 + 3*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, -e^(2*I*b*x + 2*I*a)) + 72*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, -e^(I*b*x + I*a)) + 72*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*polylog(3, e^(I*b*x + I*a)))/b^4)/b","B",0
229,1,1063,0,0.609631," ","integrate((d*x+c)^3*csc(b*x+a)*sec(b*x+a),x, algorithm=""maxima"")","-\frac{3 \, c^{3} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{9 \, a c^{2} d {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{9 \, a^{2} c d^{2} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{3 \, a^{3} d^{3} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} + \frac{6 i \, d^{3} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - 36 i \, d^{3} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - 36 i \, d^{3} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 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 \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 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(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 9 i \, a^{2} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + 18 i \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 36 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(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + 18 i \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 36 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(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\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(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) - 3 \, {\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) - 3 \, {\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) + 3 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - 36 \, {\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)}) - 36 \, {\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}}}{6 \, b}"," ",0,"-1/6*(3*c^3*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 9*a*c^2*d*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + 9*a^2*c*d^2*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 - 3*a^3*d^3*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^3 + (6*I*d^3*polylog(4, -e^(2*I*b*x + 2*I*a)) - 36*I*d^3*polylog(4, -e^(I*b*x + I*a)) - 36*I*d^3*polylog(4, e^(I*b*x + I*a)) + (8*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (-6*I*(b*x + a)^3*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*a^2*d^3)*(b*x + a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 - 12*I*(b*x + a)^2*d^3 - 9*I*a^2*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a))*dilog(-e^(2*I*b*x + 2*I*a)) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + 18*I*a^2*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*dilog(-e^(I*b*x + I*a)) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + 18*I*a^2*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*dilog(e^(I*b*x + I*a)) + (4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - 3*((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) - 3*((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) + 3*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*polylog(3, -e^(2*I*b*x + 2*I*a)) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*polylog(3, -e^(I*b*x + I*a)) - 36*(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
230,1,590,0,0.595735," ","integrate((d*x+c)^2*csc(b*x+a)*sec(b*x+a),x, algorithm=""maxima"")","-\frac{c^{2} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{2 \, a c d {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} + \frac{d^{2} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - 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(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, 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(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 \, b c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(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(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) - {\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*(c^2*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 2*a*c*d*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + a^2*d^2*(log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 + (d^2*polylog(3, -e^(2*I*b*x + 2*I*a)) - 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(2*b*x + 2*a), cos(2*b*x + 2*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) + (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*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2)*dilog(-e^(2*I*b*x + 2*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)) + (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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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*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
231,1,267,0,0.697098," ","integrate((d*x+c)*csc(b*x+a)*sec(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(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, 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) - i \, d {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\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(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) - {\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(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (-2*I*b*d*x - 2*I*b*c)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - I*d*dilog(-e^(2*I*b*x + 2*I*a)) + 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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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*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
232,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right) \sec\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(csc(b*x + a)*sec(b*x + a)/(d*x + c), x)","F",0
233,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\int \frac{\csc\left(b x + a\right) \sec\left(b x + a\right)}{{\left(d x + c\right)}^{2}}\,{d x}"," ",0,"integrate(csc(b*x + a)*sec(b*x + a)/(d*x + c)^2, x)","F",0
234,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^2*sec(b*x + a), x)","F",0
235,1,3240,0,1.411475," ","integrate((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{3}} - \frac{2 \, {\left({\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} + a^{2} 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} + a^{2} 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} - 6 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\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} + a^{2} 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} + a^{2} 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} - 6 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) + {\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 6 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, a^{2} 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} + a^{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 \, 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)} \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 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 6 \, a^{2} d^{3} - 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\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 \, a^{2} 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(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} + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} 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 \, a^{2} 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} + a^{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 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, 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 \, a^{2} 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} + a^{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 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, 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(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 \, b^{2} c^{2} d + 6 i \, a b c d^{2} - 3 i \, {\left(b x + a\right)}^{2} d^{3} - 3 i \, a^{2} d^{3} + {\left(-6 i \, b c d^{2} + 6 i \, a d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, b^{2} c^{2} d - 6 i \, a b c d^{2} + 3 i \, {\left(b x + a\right)}^{2} d^{3} + 3 i \, a^{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(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)} \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 \, b^{2} c^{2} d - 6 i \, a b c d^{2} + 3 i \, {\left(b x + a\right)}^{2} d^{3} + 3 i \, a^{2} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)} + {\left(-3 i \, b^{2} c^{2} d + 6 i \, a b c d^{2} - 3 i \, {\left(b x + a\right)}^{2} d^{3} - 3 i \, a^{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(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)} \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} + {\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} + 3 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(-i \, {\left(b x + a\right)}^{3} 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} - 3 i \, a^{2} 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} + 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)} \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 \, \sin\left(b x + a\right) + 1\right) + {\left(-i \, {\left(b x + a\right)}^{3} 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} - 3 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(i \, {\left(b x + a\right)}^{3} 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} + 3 i \, a^{2} 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} + 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)} \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 \, \sin\left(b x + a\right) + 1\right) + 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - d^{3}\right)} {\rm Li}_{4}(i \, e^{\left(i \, b x + i \, a\right)}) - 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - d^{3}\right)} {\rm Li}_{4}(-i \, 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(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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(i \, 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(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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-i \, 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(-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} + {\left(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + 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*(c^3*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1)) - 3*a*c^2*d*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1))/b + 3*a^2*c*d^2*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1))/b^2 - a^3*d^3*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1))/b^3 - 2*((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*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*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*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(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*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*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*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) + (6*b^2*c^2*d - 12*a*b*c*d^2 + 6*(b*x + a)^2*d^3 + 6*a^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*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*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^2*c^2*d - 12*a*b*c*d^2 + 6*a^2*d^3 - 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(2*b*x + 2*a) - (6*I*b^2*c^2*d - 12*I*a*b*c*d^2 + 6*I*a^2*d^3)*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 + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*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*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*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*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(I*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*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*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*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-I*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)) + (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^2*c^2*d + 6*I*a*b*c*d^2 - 3*I*(b*x + a)^2*d^3 - 3*I*a^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a) + (3*I*b^2*c^2*d - 6*I*a*b*c*d^2 + 3*I*(b*x + a)^2*d^3 + 3*I*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^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))*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^2*c^2*d - 6*I*a*b*c*d^2 + 3*I*(b*x + a)^2*d^3 + 3*I*a^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a) + (-3*I*b^2*c^2*d + 6*I*a*b*c*d^2 - 3*I*(b*x + a)^2*d^3 - 3*I*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^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))*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 + (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*d^3)*(b*x + a) + (-I*(b*x + a)^3*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*d^3)*(b*x + a))*cos(2*b*x + 2*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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) + (-I*(b*x + a)^3*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*d^3)*(b*x + a) + (I*(b*x + a)^3*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*d^3)*(b*x + a))*cos(2*b*x + 2*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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) - d^3)*polylog(4, I*e^(I*b*x + I*a)) - 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) - d^3)*polylog(4, -I*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(2*b*x + 2*a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*polylog(3, I*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(2*b*x + 2*a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*polylog(3, -I*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)) + (-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 + (-12*I*b^2*c^2*d + 24*I*a*b*c*d^2 - 12*I*a^2*d^3)*(b*x + a))*sin(b*x + 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
236,1,1632,0,0.773866," ","integrate((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)} - \frac{2 \, a c d {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{2}{\sin\left(b x + a\right)} - \log\left(\sin\left(b x + a\right) + 1\right) + \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{2 \, {\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)} - 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(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(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\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(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(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\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(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(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 \, b c d - 4 \, a d^{2} - 4 \, {\left(b c d - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(4 i \, b c d - 4 i \, a 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 \, {\left(b x + a\right)} d^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 i \, {\left(b x + a\right)} d^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b x + a\right)} d^{2}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\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(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(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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, 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(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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + 4 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - 4 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-2 i \, b c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2} + {\left(2 i \, b c d + 2 i \, {\left(b x + a\right)} d^{2} - 2 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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(2 i \, b c d + 2 i \, {\left(b x + a\right)} d^{2} - 2 i \, a d^{2} + {\left(-2 i \, b c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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)} + {\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)}\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)}\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 \, \sin\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)} + {\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)}\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)}\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 \, \sin\left(b x + a\right) + 1\right) + {\left(-4 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 4 i \, d^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) + {\left(4 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) - 4 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, d^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, 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(b x + a\right)\right)}}{-2 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 i \, b^{2}}}{2 \, b}"," ",0,"-1/2*(c^2*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1)) - 2*a*c*d*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1))/b + a^2*d^2*(2/sin(b*x + a) - log(sin(b*x + a) + 1) + log(sin(b*x + a) - 1))/b^2 - 2*((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(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(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(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(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(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) + (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(2*b*x + 2*a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (4*b*c*d - 4*a*d^2 - 4*(b*c*d - a*d^2)*cos(2*b*x + 2*a) - (4*I*b*c*d - 4*I*a*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (4*(b*x + a)*d^2*cos(2*b*x + 2*a) + 4*I*(b*x + a)*d^2*sin(2*b*x + 2*a) - 4*(b*x + a)*d^2)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 4*((b*x + a)^2*d^2 + 2*(b*c*d - a*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(2*b*x + 2*a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(2*b*x + 2*a))*dilog(I*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(2*b*x + 2*a) - (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-I*e^(I*b*x + I*a)) + 4*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) - d^2)*dilog(-e^(I*b*x + I*a)) - 4*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) - d^2)*dilog(e^(I*b*x + I*a)) + (-2*I*b*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2 + (2*I*b*c*d + 2*I*(b*x + a)*d^2 - 2*I*a*d^2)*cos(2*b*x + 2*a) - 2*(b*c*d + (b*x + a)*d^2 - a*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) + (2*I*b*c*d + 2*I*(b*x + a)*d^2 - 2*I*a*d^2 + (-2*I*b*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2)*cos(2*b*x + 2*a) + 2*(b*c*d + (b*x + a)*d^2 - a*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) + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a) + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a))*cos(2*b*x + 2*a) - ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + (-4*I*d^2*cos(2*b*x + 2*a) + 4*d^2*sin(2*b*x + 2*a) + 4*I*d^2)*polylog(3, I*e^(I*b*x + I*a)) + (4*I*d^2*cos(2*b*x + 2*a) - 4*d^2*sin(2*b*x + 2*a) - 4*I*d^2)*polylog(3, -I*e^(I*b*x + I*a)) + (-4*I*(b*x + a)^2*d^2 + (-8*I*b*c*d + 8*I*a*d^2)*(b*x + a))*sin(b*x + a))/(-2*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(2*b*x + 2*a) + 2*I*b^2))/b","B",0
237,-1,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
238,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sec(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
239,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sec(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
240,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^3*sec(b*x + a), x)","F",0
241,1,5140,0,2.136586," ","integrate((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} - \frac{2 \, {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, a^{2} d^{3} - {\left(8 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)} + 2 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-16 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 36 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(6 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, b c d^{2} - 18 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, 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} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, 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} + 1\right)} 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)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{3} d^{3} + 36 i \, b c d^{2} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + {\left(36 i \, a^{2} + 36 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(18 \, b c d^{2} - 18 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 36 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(36 i \, b c d^{2} - 36 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(6 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\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} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\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} + 1\right)} 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)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} + {\left(-36 i \, a^{2} - 36 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) - 18 \, {\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(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{3} d^{3} + 18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 18 \, {\left(2 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 36 \, {\left(2 i \, a + 1\right)} b c d^{2} + {\left(36 i \, a^{2} + 36 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(9 \, b^{2} c^{2} d - 18 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 9 \, a^{2} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 3 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 4 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, a^{2} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 4 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, a^{2} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 9 i \, a^{2} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 24 i \, {\left(b x + a\right)}^{2} d^{3} + 18 i \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 36 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(2 i \, b x + 2 i \, a\right)}\right) - {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, {\left(a^{2} + 1\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 1\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) - 36 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 1\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(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 18 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 36 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-36 i \, a^{2} - 36 i\right)} d^{3} + {\left(-72 i \, b c d^{2} + 72 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(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, {\left(a^{2} + 1\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 1\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) - 36 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + {\left(a^{2} + 1\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(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 18 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 36 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-36 i \, a^{2} - 36 i\right)} d^{3} + {\left(-72 i \, b c d^{2} + 72 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(-4 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} - 9 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} - 9 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 2 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) - {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, 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} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, 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} + 1\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(3 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, 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} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, 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} + 1\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(6 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 12 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 12 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 6 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 72 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 72 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 36 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + {\left(36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 72 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 72 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 36 \, d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-9 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 9 i \, a d^{3} + {\left(-9 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 9 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(18 i \, b c d^{2} + 24 i \, {\left(b x + a\right)} d^{3} - 18 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-72 i \, b c d^{2} - 72 i \, {\left(b x + a\right)} d^{3} + 72 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 72 \, {\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(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-72 i \, b c d^{2} - 72 i \, {\left(b x + a\right)} d^{3} + 72 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 72 \, {\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(18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, a^{2} d^{3} + {\left(36 \, b c d^{2} - {\left(36 \, a - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a - 36 i\right)} b c d^{2} + 36 \, {\left(a^{2} - i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-6 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + 12 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) - 12 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(c^3*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 3*a*c^2*d*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + 3*a^2*c*d^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 - a^3*d^3*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^3 - 2*(18*b^2*c^2*d - 36*a*b*c*d^2 + 18*a^2*d^3 - (8*(b*x + a)^3*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a) + 2*(4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 4*(4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (8*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-16*I*(b*x + a)^3*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 36*I*a^2*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (6*(b*x + a)^3*d^3 + 18*b*c*d^2 - 18*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a) + 6*((b*x + a)^3*d^3 + 3*b*c*d^2 - 3*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 + 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 12*((b*x + a)^3*d^3 + 3*b*c*d^2 - 3*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 + 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-6*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 18*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (12*I*(b*x + a)^3*d^3 + 36*I*b*c*d^2 - 36*I*a*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + (36*I*a^2 + 36*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (18*b*c*d^2 - 18*a*d^3 + 18*(b*c*d^2 - a*d^3)*cos(4*b*x + 4*a) - 36*(b*c*d^2 - a*d^3)*cos(2*b*x + 2*a) - (-18*I*b*c*d^2 + 18*I*a*d^3)*sin(4*b*x + 4*a) - (36*I*b*c*d^2 - 36*I*a*d^3)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*(b*x + a)^3*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a) + 6*((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 + 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 12*((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 + 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 18*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-12*I*(b*x + a)^3*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 + (-36*I*a^2 - 36*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 18*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - (12*I*(b*x + a)^3*d^3 + 18*b^2*c^2*d - 36*a*b*c*d^2 + 18*a^2*d^3 + (36*I*b*c*d^2 - 18*(2*I*a + 1)*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 36*(2*I*a + 1)*b*c*d^2 + (36*I*a^2 + 36*a)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (9*b^2*c^2*d - 18*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 9*a^2*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a) + 3*(3*b^2*c^2*d - 6*a*b*c*d^2 + 4*(b*x + a)^2*d^3 + 3*a^2*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 4*(b*x + a)^2*d^3 + 3*a^2*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 - 12*I*(b*x + a)^2*d^3 - 9*I*a^2*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 24*I*(b*x + a)^2*d^3 + 18*I*a^2*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*I*a)) - (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 18*(a^2 + 1)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 18*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 36*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 18*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 36*I*(b*x + a)^2*d^3 + (-36*I*a^2 - 36*I)*d^3 + (-72*I*b*c*d^2 + 72*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) - (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 18*(a^2 + 1)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 18*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 36*(b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + (a^2 + 1)*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 18*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 36*I*(b*x + a)^2*d^3 + (-36*I*a^2 - 36*I)*d^3 + (-72*I*b*c*d^2 + 72*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (-4*I*(b*x + a)^3*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 - 9*I*a^2*d^3)*(b*x + a) + (-4*I*(b*x + a)^3*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 - 9*I*a^2*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (8*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*sin(4*b*x + 4*a) - 2*(4*(b*x + a)^3*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - (3*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 9*I)*d^3)*(b*x + a) + (3*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 9*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-6*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 18*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 3*((b*x + a)^3*d^3 + 3*b*c*d^2 - 3*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 + 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 6*((b*x + a)^3*d^3 + 3*b*c*d^2 - 3*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 + 1)*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)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 9*I)*d^3)*(b*x + a) + (3*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 9*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-6*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 18*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 3*((b*x + a)^3*d^3 + 3*b*c*d^2 - 3*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 + 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 6*((b*x + a)^3*d^3 + 3*b*c*d^2 - 3*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 + 1)*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) - (6*d^3*cos(4*b*x + 4*a) - 12*d^3*cos(2*b*x + 2*a) + 6*I*d^3*sin(4*b*x + 4*a) - 12*I*d^3*sin(2*b*x + 2*a) + 6*d^3)*polylog(4, -e^(2*I*b*x + 2*I*a)) + (36*d^3*cos(4*b*x + 4*a) - 72*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(4*b*x + 4*a) - 72*I*d^3*sin(2*b*x + 2*a) + 36*d^3)*polylog(4, -e^(I*b*x + I*a)) + (36*d^3*cos(4*b*x + 4*a) - 72*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(4*b*x + 4*a) - 72*I*d^3*sin(2*b*x + 2*a) + 36*d^3)*polylog(4, e^(I*b*x + I*a)) - (-9*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 9*I*a*d^3 + (-9*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 9*I*a*d^3)*cos(4*b*x + 4*a) + (18*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 18*I*a*d^3)*cos(2*b*x + 2*a) + 3*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(4*b*x + 4*a) - 6*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(2*b*x + 2*a))*polylog(3, -e^(2*I*b*x + 2*I*a)) - (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3 + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + (-72*I*b*c*d^2 - 72*I*(b*x + a)*d^3 + 72*I*a*d^3)*cos(2*b*x + 2*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) + 72*(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)) - (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3 + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + (-72*I*b*c*d^2 - 72*I*(b*x + a)*d^3 + 72*I*a*d^3)*cos(2*b*x + 2*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) + 72*(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)) - (18*I*(b*x + a)^2*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (12*(b*x + a)^3*d^3 - 18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*a^2*d^3 + (36*b*c*d^2 - (36*a - 18*I)*d^3)*(b*x + a)^2 + (36*b^2*c^2*d - (72*a - 36*I)*b*c*d^2 + 36*(a^2 - I*a)*d^3)*(b*x + a))*sin(2*b*x + 2*a))/(-6*I*b^3*cos(4*b*x + 4*a) + 12*I*b^3*cos(2*b*x + 2*a) + 6*b^3*sin(4*b*x + 4*a) - 12*b^3*sin(2*b*x + 2*a) - 6*I*b^3))/b","B",0
242,1,2522,0,0.823264," ","integrate((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{2 \, a c d {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2}} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} + \frac{2 \, {\left(4 \, {\left(b x + a\right)} d^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, {\left(b x + a\right)} d^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b c d + 4 \, a d^{2} + {\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(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, 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 \, 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)} + 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)} + 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)} - 2 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)} + 4 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(2 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 4 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 2 \, 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} + 4 \, b c d - 4 \, a d^{2} + {\left(8 i \, b c d - 4 \, {\left(2 i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(2 \, b c d + 2 \, {\left(b x + a\right)} d^{2} - 2 \, a d^{2} + 2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-2 i \, b c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, 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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(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)} + {\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)}\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)}\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)}\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)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) + {\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)} + 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)} + 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)} - 2 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)} + 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)} + 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)} + 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)} + 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)} - 2 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)} + 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)} + 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 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 2 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + d^{2} \sin\left(4 \, b x + 4 \, a\right) - 2 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 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 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} - 4 i \, b c d + 4 i \, a d^{2} + {\left(8 \, b c d - {\left(8 \, a - 4 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}}{2 \, b}"," ",0,"-1/2*(c^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 2*a*c*d*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + a^2*d^2*(1/sin(b*x + a)^2 + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 + 2*(4*(b*x + a)*d^2*cos(4*b*x + 4*a) + 4*I*(b*x + a)*d^2*sin(4*b*x + 4*a) - 4*b*c*d + 4*a*d^2 + (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(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + 2*d^2 + 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 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) + 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) - 2*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) + 4*I*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*d^2*cos(4*b*x + 4*a) - 4*d^2*cos(2*b*x + 2*a) + 2*I*d^2*sin(4*b*x + 4*a) - 4*I*d^2*sin(2*b*x + 2*a) + 2*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 + 4*b*c*d - 4*a*d^2 + (8*I*b*c*d - 4*(2*I*a + 1)*d^2)*(b*x + a))*cos(2*b*x + 2*a) - (2*b*c*d + 2*(b*x + a)*d^2 - 2*a*d^2 + 2*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-2*I*b*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2)*sin(4*b*x + 4*a) - (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*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)) + (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) + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a))*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))*cos(2*b*x + 2*a) + ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(4*b*x + 4*a) - 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + I*d^2 + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + 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) - 2*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) + 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) + 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) + I*d^2 + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + 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) - 2*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) + 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) + 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*d^2*cos(4*b*x + 4*a) + 2*I*d^2*cos(2*b*x + 2*a) + d^2*sin(4*b*x + 4*a) - 2*d^2*sin(2*b*x + 2*a) - I*d^2)*polylog(3, -e^(2*I*b*x + 2*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*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 - 4*I*b*c*d + 4*I*a*d^2 + (8*b*c*d - (8*a - 4*I)*d^2)*(b*x + a))*sin(2*b*x + 2*a))/(-2*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2))/b","B",0
243,1,1035,0,0.624790," ","integrate((d*x+c)*csc(b*x+a)^3*sec(b*x+a),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(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\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 + 2 \, d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(d \cos\left(4 \, b x + 4 \, a\right) - 2 \, d \cos\left(2 \, b x + 2 \, a\right) + i \, d \sin\left(4 \, b x + 4 \, a\right) - 2 i \, d \sin\left(2 \, b x + 2 \, a\right) + d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(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(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) + {\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) - {\left(4 \, b d x + 4 \, b c - 2 i \, d\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 \, d}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 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(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (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 + 2*d)*cos(2*b*x + 2*a) - (d*cos(4*b*x + 4*a) - 2*d*cos(2*b*x + 2*a) + I*d*sin(4*b*x + 4*a) - 2*I*d*sin(2*b*x + 2*a) + d)*dilog(-e^(2*I*b*x + 2*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)) + (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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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) + (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 + 4*b*c - 2*I*d)*sin(2*b*x + 2*a) - 2*d)/(-2*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2)","B",0
244,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)*tan(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right) \tan\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)*tan(b*x + a), x)","F",0
247,1,2944,0,0.792210," ","integrate((d*x+c)^4*sec(b*x+a)*tan(b*x+a),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\right)\right)} c^{3} 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(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\right)\right)} a c^{2} 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{6 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\right)\right)} a^{2} c 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 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\right)\right)} a^{3} d^{4}}{{\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^{4}} + \frac{c^{4}}{\cos\left(b x + a\right)} - \frac{4 \, a c^{3} d}{b \cos\left(b x + a\right)} + \frac{6 \, a^{2} c^{2} d^{2}}{b^{2} \cos\left(b x + a\right)} - \frac{4 \, a^{3} c d^{3}}{b^{3} \cos\left(b x + a\right)} + \frac{a^{4} d^{4}}{b^{4} \cos\left(b x + a\right)} + \frac{{\left(4 \, {\left(b x + a\right)}^{3} d^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 4 \, {\left({\left(b x + a\right)}^{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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-4 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(4 \, {\left(b x + a\right)}^{3} d^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 4 \, {\left({\left(b x + a\right)}^{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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-4 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(b x + a\right) + {\left(12 \, b^{2} c^{2} d^{2} - 24 \, a b c d^{3} + 12 \, {\left(b x + a\right)}^{2} d^{4} + 12 \, a^{2} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, {\left(b x + a\right)}^{2} d^{4} - 12 i \, a^{2} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(12 \, b^{2} c^{2} d^{2} - 24 \, a b c d^{3} + 12 \, {\left(b x + a\right)}^{2} d^{4} + 12 \, a^{2} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, {\left(b x + a\right)}^{2} d^{4} + 12 i \, a^{2} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(-2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} - 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(-2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} - 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left({\left(b x + a\right)}^{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)} \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 \, \sin\left(b x + a\right) + 1\right) - {\left(2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(6 i \, b c d^{3} - 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(2 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(6 i \, b c d^{3} - 6 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left({\left(b x + a\right)}^{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)} \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 \, \sin\left(b x + a\right) + 1\right) - 24 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + d^{4}\right)} {\rm Li}_{4}(i \, e^{\left(i \, b x + i \, a\right)}) + 24 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + d^{4}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, b c d^{3} - 24 i \, {\left(b x + a\right)} d^{4} + 24 i \, a d^{4} + {\left(-24 i \, b c d^{3} - 24 i \, {\left(b x + a\right)} d^{4} + 24 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + 24 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) - {\left(24 i \, b c d^{3} + 24 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4} + {\left(24 i \, b c d^{3} + 24 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - 24 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, a\right)}) + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(b x + a\right)}{-i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + b^{4} \sin\left(2 \, b x + 2 \, a\right) - i \, b^{4}}}{b}"," ",0,"(2*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*c^3*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*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*a*c^2*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) + 6*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*a^2*c*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*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*a^3*d^4/((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*b^4) + c^4/cos(b*x + a) - 4*a*c^3*d/(b*cos(b*x + a)) + 6*a^2*c^2*d^2/(b^2*cos(b*x + a)) - 4*a^3*c*d^3/(b^3*cos(b*x + a)) + a^4*d^4/(b^4*cos(b*x + a)) + ((4*(b*x + a)^3*d^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 4*((b*x + 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))*cos(2*b*x + 2*a) - (-4*I*(b*x + a)^3*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2 + (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (4*(b*x + a)^3*d^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 4*((b*x + 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))*cos(2*b*x + 2*a) - (-4*I*(b*x + a)^3*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2 + (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) - (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a)^2)*cos(b*x + a) + (12*b^2*c^2*d^2 - 24*a*b*c*d^3 + 12*(b*x + a)^2*d^4 + 12*a^2*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a) + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*(b*x + a)^2*d^4 - 12*I*a^2*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(I*e^(I*b*x + I*a)) - (12*b^2*c^2*d^2 - 24*a*b*c*d^3 + 12*(b*x + a)^2*d^4 + 12*a^2*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a) + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*(b*x + a)^2*d^4 + 12*I*a^2*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-I*e^(I*b*x + I*a)) - (-2*I*(b*x + a)^3*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a)^2 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 - 6*I*a^2*d^4)*(b*x + a) + (-2*I*(b*x + a)^3*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a)^2 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 - 6*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 2*((b*x + 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (2*I*(b*x + a)^3*d^4 + (6*I*b*c*d^3 - 6*I*a*d^4)*(b*x + a)^2 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + 6*I*a^2*d^4)*(b*x + a) + (2*I*(b*x + a)^3*d^4 + (6*I*b*c*d^3 - 6*I*a*d^4)*(b*x + a)^2 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + 6*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 2*((b*x + 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - 24*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) + d^4)*polylog(4, I*e^(I*b*x + I*a)) + 24*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) + d^4)*polylog(4, -I*e^(I*b*x + I*a)) - (-24*I*b*c*d^3 - 24*I*(b*x + a)*d^4 + 24*I*a*d^4 + (-24*I*b*c*d^3 - 24*I*(b*x + a)*d^4 + 24*I*a*d^4)*cos(2*b*x + 2*a) + 24*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, I*e^(I*b*x + I*a)) - (24*I*b*c*d^3 + 24*I*(b*x + a)*d^4 - 24*I*a*d^4 + (24*I*b*c*d^3 + 24*I*(b*x + a)*d^4 - 24*I*a*d^4)*cos(2*b*x + 2*a) - 24*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, -I*e^(I*b*x + I*a)) + 2*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2)*sin(b*x + a))/(-I*b^4*cos(2*b*x + 2*a) + b^4*sin(2*b*x + 2*a) - I*b^4))/b","B",0
248,1,1774,0,0.621478," ","integrate((d*x+c)^3*sec(b*x+a)*tan(b*x+a),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\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(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\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(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\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}}{\cos\left(b x + a\right)} - \frac{6 \, a c^{2} d}{b \cos\left(b x + a\right)} + \frac{6 \, a^{2} c d^{2}}{b^{2} \cos\left(b x + a\right)} - \frac{2 \, a^{3} d^{3}}{b^{3} \cos\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(\cos\left(b x + a\right), \sin\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(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\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)} \cos\left(b x + 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(i \, 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(-i \, 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 \, \sin\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 \, \sin\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}(i \, 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}(-i \, e^{\left(i \, b x + i \, 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}\right)} \sin\left(b x + 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*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*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*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*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*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*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/cos(b*x + a) - 6*a*c^2*d/(b*cos(b*x + a)) + 6*a^2*c*d^2/(b^2*cos(b*x + a)) - 2*a^3*d^3/(b^3*cos(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(cos(b*x + a), sin(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(cos(b*x + a), -sin(b*x + a) + 1) - (4*I*(b*x + a)^3*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a)^2)*cos(b*x + 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(I*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(-I*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*sin(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*sin(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, I*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, -I*e^(I*b*x + I*a)) + 4*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*sin(b*x + 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
249,-1,0,0,0.000000," ","integrate((d*x+c)^2*sec(b*x+a)*tan(b*x+a),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,1,259,0,0.449408," ","integrate((d*x+c)*sec(b*x+a)*tan(b*x+a),x, algorithm=""maxima"")","\frac{\frac{{\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\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 \, \sin\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 \, \sin\left(b x + a\right) + 1\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}{\cos\left(b x + a\right)} - \frac{2 \, a d}{b \cos\left(b x + a\right)}}{2 \, b}"," ",0,"1/2*((4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + 4*(b*x + a)*cos(b*x + a) - (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*sin(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*sin(b*x + a) + 1))*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/cos(b*x + a) - 2*a*d/(b*cos(b*x + a)))/b","B",0
251,-1,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,-1,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
253,0,0,0,0.000000," ","integrate((d*x+c)^m*tan(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \tan\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*tan(b*x + a)^2, x)","F",0
254,1,1363,0,0.630444," ","integrate((d*x+c)^3*tan(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(b x + a - \tan\left(b x + a\right)\right)} c^{3} - \frac{6 \, {\left(b x + a - \tan\left(b x + a\right)\right)} a c^{2} d}{b} + \frac{6 \, {\left(b x + a - \tan\left(b x + a\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{2 \, {\left(b x + a - \tan\left(b x + a\right)\right)} a^{3} d^{3}}{b^{3}} + \frac{3 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \log\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) - 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(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \log\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) - 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(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \log\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) - 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 \, {\left(i \, {\left(b x + a\right)}^{4} d^{3} + {\left(4 i \, b c d^{2} - 4 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + {\left(12 \, {\left(b x + a\right)}^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 12 \, {\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(12 i \, {\left(b x + a\right)}^{2} 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)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(i \, {\left(b x + a\right)}^{4} d^{3} + {\left(4 i \, b c d^{2} - 4 \, {\left(i \, a + 2\right)} d^{3}\right)} {\left(b x + a\right)}^{3} - 24 \, {\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(2 i \, b x + 2 i \, a\right)}\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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) + {\left(-6 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left({\left(b x + a\right)}^{4} d^{3} + {\left(4 \, b c d^{2} - {\left(4 \, a - 8 i\right)} d^{3}\right)} {\left(b x + a\right)}^{3} - {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-4 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(2*(b*x + a - tan(b*x + a))*c^3 - 6*(b*x + a - tan(b*x + a))*a*c^2*d/b + 6*(b*x + a - tan(b*x + a))*a^2*c*d^2/b^2 - 2*(b*x + a - tan(b*x + a))*a^3*d^3/b^3 + 3*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 + 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 + 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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*((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 + 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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*(I*(b*x + a)^4*d^3 + (4*I*b*c*d^2 - 4*I*a*d^3)*(b*x + a)^3 + (12*(b*x + a)^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) + 12*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (12*I*(b*x + a)^2*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (I*(b*x + a)^4*d^3 + (4*I*b*c*d^2 - 4*(I*a + 2)*d^3)*(b*x + a)^3 - 24*(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^(2*I*b*x + 2*I*a)) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 6*((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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (-6*I*d^3*cos(2*b*x + 2*a) + 6*d^3*sin(2*b*x + 2*a) - 6*I*d^3)*polylog(3, -e^(2*I*b*x + 2*I*a)) - ((b*x + a)^4*d^3 + (4*b*c*d^2 - (4*a - 8*I)*d^3)*(b*x + a)^3 - (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-4*I*b^3*cos(2*b*x + 2*a) + 4*b^3*sin(2*b*x + 2*a) - 4*I*b^3))/b","B",0
255,1,417,0,0.602495," ","integrate((d*x+c)^2*tan(b*x+a)^2,x, algorithm=""maxima"")","\frac{i \, b^{3} d^{2} x^{3} + 3 i \, b^{3} c d x^{2} + 3 i \, b^{3} c^{2} x + 6 \, b^{2} c^{2} + {\left(6 \, b d^{2} x + 6 \, b c d + 6 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(i \, b^{3} d^{2} x^{3} + {\left(3 i \, b^{3} c d - 6 \, b^{2} d^{2}\right)} x^{2} - 3 \, {\left(-i \, b^{3} c^{2} + 4 \, b^{2} c d\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-3 i \, b d^{2} x - 3 i \, b c d + {\left(-3 i \, b d^{2} x - 3 i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) - {\left(b^{3} d^{2} x^{3} + 3 \, {\left(b^{3} c d + 2 i \, b^{2} d^{2}\right)} x^{2} + {\left(3 \, b^{3} c^{2} + 12 i \, b^{2} c d\right)} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{-3 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 3 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 3 i \, b^{3}}"," ",0,"(I*b^3*d^2*x^3 + 3*I*b^3*c*d*x^2 + 3*I*b^3*c^2*x + 6*b^2*c^2 + (6*b*d^2*x + 6*b*c*d + 6*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a) + (6*I*b*d^2*x + 6*I*b*c*d)*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (I*b^3*d^2*x^3 + (3*I*b^3*c*d - 6*b^2*d^2)*x^2 - 3*(-I*b^3*c^2 + 4*b^2*c*d)*x)*cos(2*b*x + 2*a) - 3*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) + d^2)*dilog(-e^(2*I*b*x + 2*I*a)) + (-3*I*b*d^2*x - 3*I*b*c*d + (-3*I*b*d^2*x - 3*I*b*c*d)*cos(2*b*x + 2*a) + 3*(b*d^2*x + b*c*d)*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - (b^3*d^2*x^3 + 3*(b^3*c*d + 2*I*b^2*d^2)*x^2 + (3*b^3*c^2 + 12*I*b^2*c*d)*x)*sin(2*b*x + 2*a))/(-3*I*b^3*cos(2*b*x + 2*a) + 3*b^3*sin(2*b*x + 2*a) - 3*I*b^3)","B",0
256,1,237,0,0.457007," ","integrate((d*x+c)*tan(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(b x + a - \tan\left(b x + a\right)\right)} c - \frac{2 \, {\left(b x + a - \tan\left(b x + a\right)\right)} a d}{b} + \frac{{\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)}^{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)} \log\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) - 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}}{2 \, b}"," ",0,"-1/2*(2*(b*x + a - tan(b*x + a))*c - 2*(b*x + a - tan(b*x + a))*a*d/b + ((b*x + a)^2*cos(2*b*x + 2*a)^2 + (b*x + a)^2*sin(2*b*x + 2*a)^2 + 2*(b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)^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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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))/b","B",0
257,0,0,0,0.000000," ","integrate(tan(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{-{\left(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)\right)} \log\left(d x + c\right) + 2 \, d \sin\left(2 \, b x + 2 \, a\right) + \frac{2 \, {\left(b d^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(b d^{3} x + b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \int \frac{\sin\left(2 \, b x + 2 \, a\right)}{{\left(d x + c\right)}^{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)}}\,{d x}}{b}}{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)}"," ",0,"(2*(b*d^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a)^2 + (b*d^3*x + b*c*d^2)*sin(2*b*x + 2*a)^2 + 2*(b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a))*integrate(sin(2*b*x + 2*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(2*b*x + 2*a)^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sin(2*b*x + 2*a)^2 + 2*(b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cos(2*b*x + 2*a)), x) - (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))*log(d*x + c) + 2*d*sin(2*b*x + 2*a))/(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))","F",0
258,-1,0,0,0.000000," ","integrate(tan(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate((d*x+c)^m*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sin\left(b x + a\right) \tan\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*sin(b*x + a)*tan(b*x + a)^2, x)","F",0
260,1,11054,0,2.377143," ","integrate((d*x+c)^3*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, c^{3} {\left(\frac{1}{\cos\left(b x + a\right)} + \cos\left(b x + a\right)\right)} - \frac{6 \, a c^{2} d {\left(\frac{1}{\cos\left(b x + a\right)} + \cos\left(b x + a\right)\right)}}{b} + \frac{6 \, a^{2} c d^{2} {\left(\frac{1}{\cos\left(b x + a\right)} + \cos\left(b x + a\right)\right)}}{b^{2}} - \frac{2 \, a^{3} d^{3} {\left(\frac{1}{\cos\left(b x + a\right)} + \cos\left(b x + a\right)\right)}}{b^{3}} + \frac{3 \, {\left({\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 2 \, \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \cos\left(b x + a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left({\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2} - 2\right)} \cos\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)^{2} - \cos\left(b x + a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(b x + a\right)^{2} - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + {\left(b x + a\right)} \sin\left(b x + a\right)^{3}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} c^{2} d}{{\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b} - \frac{6 \, {\left({\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 2 \, \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \cos\left(b x + a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left({\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2} - 2\right)} \cos\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)^{2} - \cos\left(b x + a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(b x + a\right)^{2} - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + {\left(b x + a\right)} \sin\left(b x + a\right)^{3}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} a c d^{2}}{{\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b^{2}} + \frac{3 \, {\left({\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 2 \, \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \cos\left(b x + a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left({\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2} - 2\right)} \cos\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)^{2} - \cos\left(b x + a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(b x + a\right)^{2} - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + {\left(b x + a\right)} \sin\left(b x + a\right)^{3}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} a^{2} d^{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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b^{3}} + \frac{2 \, {\left({\left(b x + a\right)}^{3} d^{3} - 6 \, b c d^{2} + {\left(6 \, a + 6 i\right)} d^{3} + {\left(3 \, b c d^{2} - {\left(3 \, a + 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left({\left(b x + a\right)}^{3} d^{3} - 6 \, b c d^{2} + {\left(6 \, a - 6 i\right)} d^{3} + {\left(3 \, b c d^{2} - {\left(3 \, a - 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b c d^{2} - 6 \, {\left(i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} - 2 \, b c d^{2} - 2 \, {\left(b x + a\right)} d^{3} + 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(b x + a\right)^{2} - {\left({\left(b x + a\right)}^{3} d^{3} - 6 \, b c d^{2} + {\left(6 \, a - 6 i\right)} d^{3} + {\left(3 \, b c d^{2} - {\left(3 \, a - 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(-6 i \, b c d^{2} - 6 \, {\left(-i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(12 i \, {\left(b x + a\right)}^{3} d^{3} - 24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} - 2 \, b c d^{2} - 2 \, {\left(b x + a\right)} d^{3} + 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(b x + a\right)^{2} - 6 \, {\left(i \, b c d^{2} + {\left(-i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)} + {\left({\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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\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)} \cos\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)} \sin\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)} \cos\left(b x + a\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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\left(b x + a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left({\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)} + {\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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\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)} \cos\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)} \sin\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)} \cos\left(b x + a\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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\left(b x + a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) + {\left({\left(7 \, {\left(b x + a\right)}^{3} d^{3} - 18 \, b c d^{2} + {\left(18 \, a - 6 i\right)} d^{3} + {\left(21 \, b c d^{2} - {\left(21 \, a - 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 i \, b c d^{2} - 6 \, {\left(i \, a + 3\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(7 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} - 6 \, {\left(-3 i \, a - 1\right)} d^{3} + {\left(21 i \, b c d^{2} - 3 \, {\left(7 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(6 \, b c d^{2} - {\left(6 \, a - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\left(b x + a\right)}^{3} d^{3} - 6 \, b c d^{2} + {\left(6 \, a + 6 i\right)} d^{3} + {\left(3 \, b c d^{2} - {\left(3 \, a + 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - 6 \, {\left(i \, b c d^{2} + {\left(-i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\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(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(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\left(12 i \, b c d^{2} + 12 i \, {\left(b x + a\right)} d^{3} - 12 i \, a d^{3}\right)} \cos\left(b x + a\right) - 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(b x + a\right)\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)} \cos\left(b x + 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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(b x + 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(b x + a\right)\right)} \sin\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(b x + a\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left({\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(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(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\left(-12 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 12 i \, a d^{3}\right)} \cos\left(b x + a\right) + 12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(b x + a\right)\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)} \cos\left(b x + 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)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(b x + 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(b x + a\right)\right)} \sin\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(b x + a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left({\left(3 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + 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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(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)} \cos\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)} \sin\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)} \cos\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)} + {\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)} \sin\left(3 \, b x + 3 \, a\right) - {\left({\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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left(3 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + 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)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(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)} \cos\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)} \sin\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)} \cos\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)} + {\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)} \sin\left(3 \, b x + 3 \, a\right) + {\left({\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(b x + 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(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, 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)} \sin\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) - {\left(12 \, d^{3} \cos\left(b x + a\right) + 12 i \, d^{3} \sin\left(b x + a\right) + 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + d^{3}\right)} \cos\left(3 \, b x + 3 \, a\right) + 12 \, {\left(d^{3} \cos\left(b x + a\right) + i \, d^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(3 \, b x + 3 \, a\right) - {\left(-12 i \, d^{3} \cos\left(b x + a\right) + 12 \, d^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) + {\left(12 \, d^{3} \cos\left(b x + a\right) + 12 i \, d^{3} \sin\left(b x + a\right) + 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + d^{3}\right)} \cos\left(3 \, b x + 3 \, a\right) + 12 \, {\left(d^{3} \cos\left(b x + a\right) + i \, d^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, 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)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 i \, d^{3} \cos\left(b x + a\right) - 12 \, d^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, a\right)}) + {\left({\left(2 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} - 12 \, {\left(-i \, a - 1\right)} d^{3} + {\left(6 i \, b c d^{2} - 6 \, {\left(i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(12 \, b c d^{2} - {\left(12 \, a - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(7 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} - 6 \, {\left(-3 i \, a - 1\right)} d^{3} + {\left(21 i \, b c d^{2} - 3 \, {\left(7 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(6 \, b c d^{2} - {\left(6 \, a - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) - {\left(7 \, {\left(b x + a\right)}^{3} d^{3} - 18 \, b c d^{2} + {\left(18 \, a - 6 i\right)} d^{3} + {\left(21 \, b c d^{2} - {\left(21 \, a - 3 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(-6 i \, b c d^{2} - 6 \, {\left(-i \, a - 3\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} - 6 \, {\left(-i \, a + 1\right)} d^{3} - 3 \, {\left(-i \, b c d^{2} + {\left(i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(6 \, b c d^{2} - {\left(6 \, a + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{2 \, b^{3} \cos\left(b x + a\right) + 2 i \, b^{3} \sin\left(b x + a\right) + {\left(2 \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 2 i \, b^{3} \sin\left(2 \, b x + 2 \, a\right) + 2 \, b^{3}\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{3} \cos\left(b x + a\right) + i \, b^{3} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-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}\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(-2 i \, b^{3} \cos\left(b x + a\right) + 2 \, b^{3} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)}}{2 \, b}"," ",0,"1/2*(2*c^3*(1/cos(b*x + a) + cos(b*x + a)) - 6*a*c^2*d*(1/cos(b*x + a) + cos(b*x + a))/b + 6*a^2*c*d^2*(1/cos(b*x + a) + cos(b*x + a))/b^2 - 2*a^3*d^3*(1/cos(b*x + a) + cos(b*x + a))/b^3 + 3*((b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)^3 + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + 2*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*cos(b*x + a) + (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + (b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + 6*(b*x + a)*cos(b*x + a) - 2*sin(b*x + a))*sin(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a)^2 + ((b*x + a)*cos(2*b*x + 2*a)^2 + 13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + (b*x + a)*sin(b*x + a)^2 + b*x + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a)^3 + 3*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + (b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + (b*x + a)*cos(b*x + a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + (((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a)^2 + 12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + 2*(((b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)*cos(b*x + a) + sin(b*x + a))*sin(2*b*x + 2*a) + (b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(3*b*x + 3*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2 - 2)*cos(2*b*x + 2*a) - cos(2*b*x + 2*a)^2 - cos(b*x + a)^2 + ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 - sin(b*x + a)^2 - 1)*sin(3*b*x + 3*a) + 6*((b*x + a)*cos(b*x + a)^2*sin(b*x + a) + (b*x + a)*sin(b*x + a)^3)*sin(2*b*x + 2*a) - sin(b*x + 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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b) - 6*((b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)^3 + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + 2*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*cos(b*x + a) + (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + (b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + 6*(b*x + a)*cos(b*x + a) - 2*sin(b*x + a))*sin(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a)^2 + ((b*x + a)*cos(2*b*x + 2*a)^2 + 13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + (b*x + a)*sin(b*x + a)^2 + b*x + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a)^3 + 3*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + (b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + (b*x + a)*cos(b*x + a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + (((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a)^2 + 12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + 2*(((b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)*cos(b*x + a) + sin(b*x + a))*sin(2*b*x + 2*a) + (b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(3*b*x + 3*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2 - 2)*cos(2*b*x + 2*a) - cos(2*b*x + 2*a)^2 - cos(b*x + a)^2 + ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 - sin(b*x + a)^2 - 1)*sin(3*b*x + 3*a) + 6*((b*x + a)*cos(b*x + a)^2*sin(b*x + a) + (b*x + a)*sin(b*x + a)^3)*sin(2*b*x + 2*a) - sin(b*x + 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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b^2) + 3*((b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)^3 + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + 2*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*cos(b*x + a) + (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + (b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + 6*(b*x + a)*cos(b*x + a) - 2*sin(b*x + a))*sin(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a)^2 + ((b*x + a)*cos(2*b*x + 2*a)^2 + 13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + (b*x + a)*sin(b*x + a)^2 + b*x + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a)^3 + 3*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + (b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + (b*x + a)*cos(b*x + a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + (((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a)^2 + 12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + 2*(((b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)*cos(b*x + a) + sin(b*x + a))*sin(2*b*x + 2*a) + (b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(3*b*x + 3*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2 - 2)*cos(2*b*x + 2*a) - cos(2*b*x + 2*a)^2 - cos(b*x + a)^2 + ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 - sin(b*x + a)^2 - 1)*sin(3*b*x + 3*a) + 6*((b*x + a)*cos(b*x + a)^2*sin(b*x + a) + (b*x + a)*sin(b*x + a)^3)*sin(2*b*x + 2*a) - sin(b*x + 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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b^3) + 2*((b*x + a)^3*d^3 - 6*b*c*d^2 + (6*a + 6*I)*d^3 + (3*b*c*d^2 - (3*a + 3*I)*d^3)*(b*x + a)^2 + ((b*x + a)^3*d^3 - 6*b*c*d^2 + (6*a - 6*I)*d^3 + (3*b*c*d^2 - (3*a - 3*I)*d^3)*(b*x + a)^2 + (6*I*b*c*d^2 - 6*(I*a + 1)*d^3)*(b*x + a))*cos(3*b*x + 3*a)^2 + 6*((b*x + a)^3*d^3 - 2*b*c*d^2 - 2*(b*x + a)*d^3 + 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*cos(b*x + a)^2 - ((b*x + a)^3*d^3 - 6*b*c*d^2 + (6*a - 6*I)*d^3 + (3*b*c*d^2 - (3*a - 3*I)*d^3)*(b*x + a)^2 - (-6*I*b*c*d^2 - 6*(-I*a - 1)*d^3)*(b*x + a))*sin(3*b*x + 3*a)^2 + (12*I*(b*x + a)^3*d^3 - 24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2)*cos(b*x + a)*sin(b*x + a) - 6*((b*x + a)^3*d^3 - 2*b*c*d^2 - 2*(b*x + a)*d^3 + 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*sin(b*x + a)^2 - 6*(I*b*c*d^2 + (-I*a + 1)*d^3)*(b*x + a) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a) + (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*cos(b*x + a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(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))*cos(b*x + a) - (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))*sin(3*b*x + 3*a) - (6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(b*x + a) - (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a) + (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*cos(b*x + a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(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))*cos(b*x + a) - (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))*sin(3*b*x + 3*a) - (6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(b*x + a) - (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) - 6*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) + ((7*(b*x + a)^3*d^3 - 18*b*c*d^2 + (18*a - 6*I)*d^3 + (21*b*c*d^2 - (21*a - 3*I)*d^3)*(b*x + a)^2 + (6*I*b*c*d^2 - 6*(I*a + 3)*d^3)*(b*x + a))*cos(b*x + a) + (7*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 - 6*(-3*I*a - 1)*d^3 + (21*I*b*c*d^2 - 3*(7*I*a + 1)*d^3)*(b*x + a)^2 - (6*b*c*d^2 - (6*a - 18*I)*d^3)*(b*x + a))*sin(b*x + a))*cos(3*b*x + 3*a) + ((b*x + a)^3*d^3 - 6*b*c*d^2 + (6*a + 6*I)*d^3 + (3*b*c*d^2 - (3*a + 3*I)*d^3)*(b*x + a)^2 - 6*(I*b*c*d^2 + (-I*a + 1)*d^3)*(b*x + a))*cos(2*b*x + 2*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(2*b*x + 2*a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*cos(b*x + a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*cos(2*b*x + 2*a) + (12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*cos(b*x + 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))*sin(3*b*x + 3*a) - (12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(b*x + a) - (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*sin(b*x + a))*sin(2*b*x + 2*a) - 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*dilog(I*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(2*b*x + 2*a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + ((-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*cos(b*x + a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*cos(2*b*x + 2*a) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*cos(b*x + 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))*sin(3*b*x + 3*a) + (12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(b*x + a) + (12*I*b*c*d^2 + 12*I*(b*x + a)*d^3 - 12*I*a*d^3)*sin(b*x + a))*sin(2*b*x + 2*a) + 12*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(b*x + a))*dilog(-I*e^(I*b*x + I*a)) - ((3*(b*x + a)^2*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + (3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(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))*sin(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))*cos(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) + (-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))*sin(3*b*x + 3*a) - ((-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*cos(b*x + a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) - (-3*I*(b*x + a)^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a))*sin(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) + ((3*(b*x + a)^2*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + (3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(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))*sin(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))*cos(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) + (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))*sin(3*b*x + 3*a) + ((3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a))*cos(b*x + a) - 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(b*x + a))*sin(2*b*x + 2*a) + (3*I*(b*x + a)^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a))*sin(b*x + a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (12*d^3*cos(b*x + a) + 12*I*d^3*sin(b*x + a) + 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) + d^3)*cos(3*b*x + 3*a) + 12*(d^3*cos(b*x + a) + I*d^3*sin(b*x + a))*cos(2*b*x + 2*a) - (-12*I*d^3*cos(2*b*x + 2*a) + 12*d^3*sin(2*b*x + 2*a) - 12*I*d^3)*sin(3*b*x + 3*a) - (-12*I*d^3*cos(b*x + a) + 12*d^3*sin(b*x + a))*sin(2*b*x + 2*a))*polylog(3, I*e^(I*b*x + I*a)) + (12*d^3*cos(b*x + a) + 12*I*d^3*sin(b*x + a) + 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) + d^3)*cos(3*b*x + 3*a) + 12*(d^3*cos(b*x + a) + I*d^3*sin(b*x + a))*cos(2*b*x + 2*a) + (12*I*d^3*cos(2*b*x + 2*a) - 12*d^3*sin(2*b*x + 2*a) + 12*I*d^3)*sin(3*b*x + 3*a) + (12*I*d^3*cos(b*x + a) - 12*d^3*sin(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -I*e^(I*b*x + I*a)) + ((2*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 - 12*(-I*a - 1)*d^3 + (6*I*b*c*d^2 - 6*(I*a + 1)*d^3)*(b*x + a)^2 - (12*b*c*d^2 - (12*a - 12*I)*d^3)*(b*x + a))*cos(3*b*x + 3*a) + (7*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 - 6*(-3*I*a - 1)*d^3 + (21*I*b*c*d^2 - 3*(7*I*a + 1)*d^3)*(b*x + a)^2 - (6*b*c*d^2 - (6*a - 18*I)*d^3)*(b*x + a))*cos(b*x + a) - (7*(b*x + a)^3*d^3 - 18*b*c*d^2 + (18*a - 6*I)*d^3 + (21*b*c*d^2 - (21*a - 3*I)*d^3)*(b*x + a)^2 - (-6*I*b*c*d^2 - 6*(-I*a - 3)*d^3)*(b*x + a))*sin(b*x + a))*sin(3*b*x + 3*a) + (I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 - 6*(-I*a + 1)*d^3 - 3*(-I*b*c*d^2 + (I*a - 1)*d^3)*(b*x + a)^2 + (6*b*c*d^2 - (6*a + 6*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))/(2*b^3*cos(b*x + a) + 2*I*b^3*sin(b*x + a) + (2*b^3*cos(2*b*x + 2*a) + 2*I*b^3*sin(2*b*x + 2*a) + 2*b^3)*cos(3*b*x + 3*a) + 2*(b^3*cos(b*x + a) + I*b^3*sin(b*x + a))*cos(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)*sin(3*b*x + 3*a) - (-2*I*b^3*cos(b*x + a) + 2*b^3*sin(b*x + a))*sin(2*b*x + 2*a)))/b","B",0
261,-1,0,0,0.000000," ","integrate((d*x+c)^2*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,1,2123,0,0.483186," ","integrate((d*x+c)*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, c {\left(\frac{1}{\cos\left(b x + a\right)} + \cos\left(b x + a\right)\right)} - \frac{2 \, a d {\left(\frac{1}{\cos\left(b x + a\right)} + \cos\left(b x + a\right)\right)}}{b} + \frac{{\left({\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + {\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(3 \, b x + 3 \, a\right)^{3} + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + 2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + 4 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left(3 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + {\left(8 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left(b x + {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + a + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(b x + a\right)} \cos\left(b x + a\right) - 2 \, \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + b x + {\left(13 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{2} + {\left(b x + a\right)} \sin\left(b x + a\right)^{2} + 2 \, b x + 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) + a\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)^{2} + {\left(b x + a\right)} \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \cos\left(b x + a\right) - {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left({\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left({\left({\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)} \cos\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(b x + a\right) - \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - \cos\left(b x + a\right)^{2} - \sin\left(b x + a\right)^{2} - 2\right)} \cos\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right)^{2} - \cos\left(b x + a\right)^{2} + {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} + 13 \, {\left(b x + a\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)^{2} - \sin\left(b x + a\right)^{2} - 1\right)} \sin\left(3 \, b x + 3 \, a\right) + 6 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + {\left(b x + a\right)} \sin\left(b x + a\right)^{3}\right)} \sin\left(2 \, b x + 2 \, a\right) - \sin\left(b x + a\right)\right)} d}{{\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)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)^{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)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + \cos\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + \sin\left(2 \, b x + 2 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)^{2}\right)} b}}{2 \, b}"," ",0,"1/2*(2*c*(1/cos(b*x + a) + cos(b*x + a)) - 2*a*d*(1/cos(b*x + a) + cos(b*x + a))/b + ((b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)^3 + ((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(3*b*x + 3*a)^3 + 6*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + 2*(4*(b*x + a)*cos(2*b*x + 2*a)*cos(b*x + a) + 4*(b*x + a)*cos(b*x + a) + (3*(b*x + a)*sin(b*x + a) + cos(b*x + a))*sin(2*b*x + 2*a))*cos(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a)^2 + (8*(b*x + a)*sin(2*b*x + 2*a)*sin(b*x + a) + (b*x + (b*x + a)*cos(2*b*x + 2*a) + a + sin(2*b*x + 2*a))*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + 6*(b*x + a)*cos(b*x + a) - 2*sin(b*x + a))*sin(3*b*x + 3*a)^2 + ((b*x + a)*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 2*a)^2 + ((b*x + a)*cos(2*b*x + 2*a)^2 + 13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(2*b*x + 2*a)^2 + (b*x + a)*sin(b*x + a)^2 + b*x + (13*(b*x + a)*cos(b*x + a)^2 + (b*x + a)*sin(b*x + a)^2 + 2*b*x + 2*a)*cos(2*b*x + 2*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a) + a)*cos(3*b*x + 3*a) + 2*(3*(b*x + a)*cos(b*x + a)^3 + 3*(b*x + a)*cos(b*x + a)*sin(b*x + a)^2 + (b*x + a)*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 2*a) + (b*x + a)*cos(b*x + a) - ((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(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)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + (((b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*cos(3*b*x + 3*a)^2 + 12*(b*x + a)*cos(b*x + a)*sin(b*x + a) + 2*(((b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)*cos(b*x + a) + sin(b*x + a))*sin(2*b*x + 2*a) + (b*x + a)*sin(b*x + a) - cos(b*x + a))*cos(3*b*x + 3*a) + (12*(b*x + a)*cos(b*x + a)*sin(b*x + a) - cos(b*x + a)^2 - sin(b*x + a)^2 - 2)*cos(2*b*x + 2*a) - cos(2*b*x + 2*a)^2 - cos(b*x + a)^2 + ((b*x + a)*cos(b*x + a)^2 + 13*(b*x + a)*sin(b*x + a)^2)*sin(2*b*x + 2*a) - sin(2*b*x + 2*a)^2 - sin(b*x + a)^2 - 1)*sin(3*b*x + 3*a) + 6*((b*x + a)*cos(b*x + a)^2*sin(b*x + a) + (b*x + a)*sin(b*x + a)^3)*sin(2*b*x + 2*a) - sin(b*x + a))*d/(((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a)^2 + (cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 2*a)^2 + 2*(cos(2*b*x + 2*a)^2*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a)*cos(b*x + a) + cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 2*a) + cos(b*x + a)^2 + 2*(cos(2*b*x + 2*a)^2*sin(b*x + a) + sin(2*b*x + 2*a)^2*sin(b*x + a) + 2*cos(2*b*x + 2*a)*sin(b*x + a) + sin(b*x + a))*sin(3*b*x + 3*a) + sin(b*x + a)^2)*b))/b","B",0
263,-1,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right) \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)*sec(b*x + a)^2, x)","F",0
266,1,5695,0,2.567891," ","integrate((d*x+c)^4*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{4} {\left(\frac{2}{\cos\left(b x + a\right)} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{4 \, a c^{3} d {\left(\frac{2}{\cos\left(b x + a\right)} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b} + \frac{6 \, a^{2} c^{2} d^{2} {\left(\frac{2}{\cos\left(b x + a\right)} - \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 \, a^{3} c d^{3} {\left(\frac{2}{\cos\left(b x + a\right)} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{3}} + \frac{a^{4} d^{4} {\left(\frac{2}{\cos\left(b x + a\right)} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{4}} + \frac{2 \, {\left({\left(8 \, b^{3} c^{3} d - 24 \, a b^{2} c^{2} d^{2} + 24 \, a^{2} b c d^{3} + 8 \, {\left(b x + a\right)}^{3} d^{4} - 8 \, a^{3} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 8 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-8 i \, b^{3} c^{3} d + 24 i \, a b^{2} c^{2} d^{2} - 24 i \, a^{2} b c d^{3} - 8 i \, {\left(b x + a\right)}^{3} d^{4} + 8 i \, a^{3} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(8 \, b^{3} c^{3} d - 24 \, a b^{2} c^{2} d^{2} + 24 \, a^{2} b c d^{3} + 8 \, {\left(b x + a\right)}^{3} d^{4} - 8 \, a^{3} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 8 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-8 i \, b^{3} c^{3} d + 24 i \, a b^{2} c^{2} d^{2} - 24 i \, a^{2} b c d^{3} - 8 i \, {\left(b x + a\right)}^{3} d^{4} + 8 i \, a^{3} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - {\left(2 \, {\left(b x + a\right)}^{4} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 24 i \, a^{2} b c d^{3} - 8 i \, a^{3} d^{4}\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(2 \, {\left(b x + a\right)}^{4} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 12 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 8 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)} + 2 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 8 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 24 i \, a^{2} b c d^{3} - 8 i \, a^{3} d^{4}\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)}^{4} d^{4} + {\left(16 i \, b c d^{3} - 16 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(16 i \, b^{3} c^{3} d - 48 i \, a b^{2} c^{2} d^{2} + 48 i \, a^{2} b c d^{3} - 16 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(24 \, b^{2} c^{2} d^{2} - 48 \, a b c d^{3} + 24 \, {\left(b x + a\right)}^{2} d^{4} + 24 \, a^{2} d^{4} + 48 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, {\left(b x + a\right)}^{2} d^{4} - 24 i \, a^{2} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(24 \, b^{2} c^{2} d^{2} - 48 \, a b c d^{3} + 24 \, {\left(b x + a\right)}^{2} d^{4} + 24 \, a^{2} d^{4} + 48 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, {\left(b x + a\right)}^{2} d^{4} + 24 i \, a^{2} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left(8 \, b^{3} c^{3} d - 24 \, a b^{2} c^{2} d^{2} + 24 \, a^{2} b c d^{3} + 8 \, {\left(b x + a\right)}^{3} d^{4} - 8 \, a^{3} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 8 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-8 i \, b^{3} c^{3} d + 24 i \, a b^{2} c^{2} d^{2} - 24 i \, a^{2} b c d^{3} - 8 i \, {\left(b x + a\right)}^{3} d^{4} + 8 i \, a^{3} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, a^{2} d^{4}\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(8 \, b^{3} c^{3} d - 24 \, a b^{2} c^{2} d^{2} + 24 \, a^{2} b c d^{3} + 8 \, {\left(b x + a\right)}^{3} d^{4} - 8 \, a^{3} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 8 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(8 i \, b^{3} c^{3} d - 24 i \, a b^{2} c^{2} d^{2} + 24 i \, a^{2} b c d^{3} + 8 i \, {\left(b x + a\right)}^{3} d^{4} - 8 i \, a^{3} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, a^{2} d^{4}\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)}^{4} d^{4} + {\left(-4 i \, b c d^{3} + 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} - 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-4 i \, b^{3} c^{3} d + 12 i \, a b^{2} c^{2} d^{2} - 12 i \, a^{2} b c d^{3} + 4 i \, a^{3} d^{4}\right)} {\left(b x + a\right)} + {\left(-i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-4 i \, b c d^{3} + 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-6 i \, b^{2} c^{2} d^{2} + 12 i \, a b c d^{3} - 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-4 i \, b^{3} c^{3} d + 12 i \, a b^{2} c^{2} d^{2} - 12 i \, a^{2} b c d^{3} + 4 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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)}^{4} d^{4} + {\left(4 i \, b c d^{3} - 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(4 i \, b^{3} c^{3} d - 12 i \, a b^{2} c^{2} d^{2} + 12 i \, a^{2} b c d^{3} - 4 i \, a^{3} d^{4}\right)} {\left(b x + a\right)} + {\left(i \, {\left(b x + a\right)}^{4} d^{4} + {\left(4 i \, b c d^{3} - 4 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(6 i \, b^{2} c^{2} d^{2} - 12 i \, a b c d^{3} + 6 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(4 i \, b^{3} c^{3} d - 12 i \, a b^{2} c^{2} d^{2} + 12 i \, a^{2} b c d^{3} - 4 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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(-4 i \, b^{3} c^{3} d + 12 i \, a b^{2} c^{2} d^{2} - 12 i \, a^{2} b c d^{3} - 4 i \, {\left(b x + a\right)}^{3} d^{4} + 4 i \, a^{3} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(-4 i \, b^{3} c^{3} d + 12 i \, a b^{2} c^{2} d^{2} - 12 i \, a^{2} b c d^{3} - 4 i \, {\left(b x + a\right)}^{3} d^{4} + 4 i \, a^{3} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{2} c^{2} d^{2} + 24 i \, a b c d^{3} - 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\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)} \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 \, \sin\left(b x + a\right) + 1\right) - {\left(4 i \, b^{3} c^{3} d - 12 i \, a b^{2} c^{2} d^{2} + 12 i \, a^{2} b c d^{3} + 4 i \, {\left(b x + a\right)}^{3} d^{4} - 4 i \, a^{3} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)} + {\left(4 i \, b^{3} c^{3} d - 12 i \, a b^{2} c^{2} d^{2} + 12 i \, a^{2} b c d^{3} + 4 i \, {\left(b x + a\right)}^{3} d^{4} - 4 i \, a^{3} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d^{2} - 24 i \, a b c d^{3} + 12 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\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)} \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 \, \sin\left(b x + a\right) + 1\right) - {\left(48 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) - 48 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + 48 i \, d^{4}\right)} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) - {\left(-48 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 48 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 48 i \, d^{4}\right)} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) - 48 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + d^{4}\right)} {\rm Li}_{4}(i \, e^{\left(i \, b x + i \, a\right)}) + 48 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + d^{4}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, b x + i \, a\right)}) - {\left(48 \, b c d^{3} + 48 \, {\left(b x + a\right)} d^{4} - 48 \, a d^{4} + 48 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(48 i \, b c d^{3} + 48 i \, {\left(b x + a\right)} d^{4} - 48 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + {\left(48 \, b c d^{3} + 48 \, {\left(b x + a\right)} d^{4} - 48 \, a d^{4} + 48 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-48 i \, b c d^{3} - 48 i \, {\left(b x + a\right)} d^{4} + 48 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-48 i \, b c d^{3} - 48 i \, {\left(b x + a\right)} d^{4} + 48 i \, a d^{4} + {\left(-48 i \, b c d^{3} - 48 i \, {\left(b x + a\right)} d^{4} + 48 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + 48 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) - {\left(48 i \, b c d^{3} + 48 i \, {\left(b x + a\right)} d^{4} - 48 i \, a d^{4} + {\left(48 i \, b c d^{3} + 48 i \, {\left(b x + a\right)} d^{4} - 48 i \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - 48 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, {\left(b x + a\right)}^{2} d^{4} - 24 i \, a^{2} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-24 i \, b^{2} c^{2} d^{2} + 48 i \, a b c d^{3} - 24 i \, {\left(b x + a\right)}^{2} d^{4} - 24 i \, a^{2} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, {\left(b x + a\right)}^{2} d^{4} + 24 i \, a^{2} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(24 i \, b^{2} c^{2} d^{2} - 48 i \, a b c d^{3} + 24 i \, {\left(b x + a\right)}^{2} d^{4} + 24 i \, a^{2} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 24 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + 4 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)}}{-2 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{4}}}{2 \, b}"," ",0,"1/2*(c^4*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 4*a*c^3*d*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + 6*a^2*c^2*d^2*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 - 4*a^3*c*d^3*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^3 + a^4*d^4*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^4 + 2*((8*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 24*a^2*b*c*d^3 + 8*(b*x + a)^3*d^4 - 8*a^3*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 8*(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))*cos(2*b*x + 2*a) - (-8*I*b^3*c^3*d + 24*I*a*b^2*c^2*d^2 - 24*I*a^2*b*c*d^3 - 8*I*(b*x + a)^3*d^4 + 8*I*a^3*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^2 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (8*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 24*a^2*b*c*d^3 + 8*(b*x + a)^3*d^4 - 8*a^3*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 8*(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))*cos(2*b*x + 2*a) - (-8*I*b^3*c^3*d + 24*I*a*b^2*c^2*d^2 - 24*I*a^2*b*c*d^3 - 8*I*(b*x + a)^3*d^4 + 8*I*a^3*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^2 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) - (2*(b*x + a)^4*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a) + 2*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 24*I*a^2*b*c*d^3 - 8*I*a^3*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*(b*x + a)^4*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 12*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 8*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a) + 2*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 8*I*a*d^4)*(b*x + a)^3 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a)^2 + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 24*I*a^2*b*c*d^3 - 8*I*a^3*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (4*I*(b*x + a)^4*d^4 + (16*I*b*c*d^3 - 16*I*a*d^4)*(b*x + a)^3 + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*a^2*d^4)*(b*x + a)^2 + (16*I*b^3*c^3*d - 48*I*a*b^2*c^2*d^2 + 48*I*a^2*b*c*d^3 - 16*I*a^3*d^4)*(b*x + a))*cos(b*x + a) + (24*b^2*c^2*d^2 - 48*a*b*c*d^3 + 24*(b*x + a)^2*d^4 + 24*a^2*d^4 + 48*(b*c*d^3 - a*d^4)*(b*x + a) + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*(b*x + a)^2*d^4 - 24*I*a^2*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(I*e^(I*b*x + I*a)) - (24*b^2*c^2*d^2 - 48*a*b*c*d^3 + 24*(b*x + a)^2*d^4 + 24*a^2*d^4 + 48*(b*c*d^3 - a*d^4)*(b*x + a) + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*(b*x + a)^2*d^4 + 24*I*a^2*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-I*e^(I*b*x + I*a)) + (8*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 24*a^2*b*c*d^3 + 8*(b*x + a)^3*d^4 - 8*a^3*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 8*(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))*cos(2*b*x + 2*a) - (-8*I*b^3*c^3*d + 24*I*a*b^2*c^2*d^2 - 24*I*a^2*b*c*d^3 - 8*I*(b*x + a)^3*d^4 + 8*I*a^3*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^2 + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) - (8*b^3*c^3*d - 24*a*b^2*c^2*d^2 + 24*a^2*b*c*d^3 + 8*(b*x + a)^3*d^4 - 8*a^3*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 8*(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))*cos(2*b*x + 2*a) + (8*I*b^3*c^3*d - 24*I*a*b^2*c^2*d^2 + 24*I*a^2*b*c*d^3 + 8*I*(b*x + a)^3*d^4 - 8*I*a^3*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^2 + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (-I*(b*x + a)^4*d^4 + (-4*I*b*c*d^3 + 4*I*a*d^4)*(b*x + a)^3 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 - 6*I*a^2*d^4)*(b*x + a)^2 + (-4*I*b^3*c^3*d + 12*I*a*b^2*c^2*d^2 - 12*I*a^2*b*c*d^3 + 4*I*a^3*d^4)*(b*x + a) + (-I*(b*x + a)^4*d^4 + (-4*I*b*c*d^3 + 4*I*a*d^4)*(b*x + a)^3 + (-6*I*b^2*c^2*d^2 + 12*I*a*b*c*d^3 - 6*I*a^2*d^4)*(b*x + a)^2 + (-4*I*b^3*c^3*d + 12*I*a*b^2*c^2*d^2 - 12*I*a^2*b*c*d^3 + 4*I*a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(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)^4*d^4 + (4*I*b*c*d^3 - 4*I*a*d^4)*(b*x + a)^3 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + 6*I*a^2*d^4)*(b*x + a)^2 + (4*I*b^3*c^3*d - 12*I*a*b^2*c^2*d^2 + 12*I*a^2*b*c*d^3 - 4*I*a^3*d^4)*(b*x + a) + (I*(b*x + a)^4*d^4 + (4*I*b*c*d^3 - 4*I*a*d^4)*(b*x + a)^3 + (6*I*b^2*c^2*d^2 - 12*I*a*b*c*d^3 + 6*I*a^2*d^4)*(b*x + a)^2 + (4*I*b^3*c^3*d - 12*I*a*b^2*c^2*d^2 + 12*I*a^2*b*c*d^3 - 4*I*a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) - ((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(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) - (-4*I*b^3*c^3*d + 12*I*a*b^2*c^2*d^2 - 12*I*a^2*b*c*d^3 - 4*I*(b*x + a)^3*d^4 + 4*I*a^3*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2 + (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*a^2*d^4)*(b*x + a) + (-4*I*b^3*c^3*d + 12*I*a*b^2*c^2*d^2 - 12*I*a^2*b*c*d^3 - 4*I*(b*x + a)^3*d^4 + 4*I*a^3*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2 + (-12*I*b^2*c^2*d^2 + 24*I*a*b*c*d^3 - 12*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (4*I*b^3*c^3*d - 12*I*a*b^2*c^2*d^2 + 12*I*a^2*b*c*d^3 + 4*I*(b*x + a)^3*d^4 - 4*I*a^3*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^2 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a) + (4*I*b^3*c^3*d - 12*I*a*b^2*c^2*d^2 + 12*I*a^2*b*c*d^3 + 4*I*(b*x + a)^3*d^4 - 4*I*a^3*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^2 + (12*I*b^2*c^2*d^2 - 24*I*a*b*c*d^3 + 12*I*a^2*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (48*I*d^4*cos(2*b*x + 2*a) - 48*d^4*sin(2*b*x + 2*a) + 48*I*d^4)*polylog(5, -e^(I*b*x + I*a)) - (-48*I*d^4*cos(2*b*x + 2*a) + 48*d^4*sin(2*b*x + 2*a) - 48*I*d^4)*polylog(5, e^(I*b*x + I*a)) - 48*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) + d^4)*polylog(4, I*e^(I*b*x + I*a)) + 48*(d^4*cos(2*b*x + 2*a) + I*d^4*sin(2*b*x + 2*a) + d^4)*polylog(4, -I*e^(I*b*x + I*a)) - (48*b*c*d^3 + 48*(b*x + a)*d^4 - 48*a*d^4 + 48*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) + (48*I*b*c*d^3 + 48*I*(b*x + a)*d^4 - 48*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, -e^(I*b*x + I*a)) + (48*b*c*d^3 + 48*(b*x + a)*d^4 - 48*a*d^4 + 48*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-48*I*b*c*d^3 - 48*I*(b*x + a)*d^4 + 48*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, e^(I*b*x + I*a)) - (-48*I*b*c*d^3 - 48*I*(b*x + a)*d^4 + 48*I*a*d^4 + (-48*I*b*c*d^3 - 48*I*(b*x + a)*d^4 + 48*I*a*d^4)*cos(2*b*x + 2*a) + 48*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, I*e^(I*b*x + I*a)) - (48*I*b*c*d^3 + 48*I*(b*x + a)*d^4 - 48*I*a*d^4 + (48*I*b*c*d^3 + 48*I*(b*x + a)*d^4 - 48*I*a*d^4)*cos(2*b*x + 2*a) - 48*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*sin(2*b*x + 2*a))*polylog(3, -I*e^(I*b*x + I*a)) - (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*(b*x + a)^2*d^4 - 24*I*a^2*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a) + (-24*I*b^2*c^2*d^2 + 48*I*a*b*c*d^3 - 24*I*(b*x + a)^2*d^4 - 24*I*a^2*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) - (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*(b*x + a)^2*d^4 + 24*I*a^2*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a) + (24*I*b^2*c^2*d^2 - 48*I*a*b*c*d^3 + 24*I*(b*x + a)^2*d^4 + 24*I*a^2*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 24*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) + 4*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*sin(b*x + a))/(-2*I*b^4*cos(2*b*x + 2*a) + 2*b^4*sin(2*b*x + 2*a) - 2*I*b^4))/b","B",0
267,1,3205,0,1.143076," ","integrate((d*x+c)^3*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{3} {\left(\frac{2}{\cos\left(b x + a\right)} - \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)} - \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)} - \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)} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{3}} + \frac{2 \, {\left({\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 6 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, a^{2} 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} + a^{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 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 6 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, a^{2} 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} + a^{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 \, 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)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\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} + a^{2} 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} + a^{2} 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} + 6 i \, a^{2} 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(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} + a^{2} 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} + a^{2} 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} + 6 i \, a^{2} 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} + {\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} + 12 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + 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(i \, 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(-i \, 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 \, a^{2} 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} + a^{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 \, 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)} \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 \, a^{2} 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} + a^{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 \, 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)} \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} + {\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} - 3 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(-i \, {\left(b x + a\right)}^{3} 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} - 3 i \, a^{2} 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} + 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)} \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} + {\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} + 3 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(i \, {\left(b x + a\right)}^{3} 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} + 3 i \, a^{2} 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} + 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)} \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 \, b^{2} c^{2} d + 6 i \, a b c d^{2} - 3 i \, {\left(b x + a\right)}^{2} d^{3} - 3 i \, a^{2} d^{3} + {\left(-6 i \, b c d^{2} + 6 i \, a d^{3}\right)} {\left(b x + a\right)} + {\left(-3 i \, b^{2} c^{2} d + 6 i \, a b c d^{2} - 3 i \, {\left(b x + a\right)}^{2} d^{3} - 3 i \, a^{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(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)} \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 \, \sin\left(b x + a\right) + 1\right) - {\left(3 i \, b^{2} c^{2} d - 6 i \, a b c d^{2} + 3 i \, {\left(b x + a\right)}^{2} d^{3} + 3 i \, a^{2} d^{3} + {\left(6 i \, b c d^{2} - 6 i \, a d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, b^{2} c^{2} d - 6 i \, a b c d^{2} + 3 i \, {\left(b x + a\right)}^{2} d^{3} + 3 i \, a^{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(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)} \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 \, \sin\left(b x + a\right) + 1\right) - 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + 12 \, {\left(d^{3} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + d^{3}\right)} {\rm Li}_{4}(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}(i \, 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}(-i \, 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(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(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(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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, 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} + a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + 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*(c^3*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 3*a*c^2*d*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + 3*a^2*c*d^2*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 - a^3*d^3*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^3 + 2*((6*b^2*c^2*d - 12*a*b*c*d^2 + 6*(b*x + a)^2*d^3 + 6*a^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*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*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (6*b^2*c^2*d - 12*a*b*c*d^2 + 6*(b*x + a)^2*d^3 + 6*a^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*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*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(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*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*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*d^3)*(b*x + a))*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*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*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*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*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*d^3)*(b*x + a))*cos(b*x + 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(I*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(-I*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*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*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*d^3 + (-12*I*b*c*d^2 + 12*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*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*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*d^3 + (12*I*b*c*d^2 - 12*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 + (-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*d^3)*(b*x + a) + (-I*(b*x + a)^3*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*d^3)*(b*x + a))*cos(2*b*x + 2*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))*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 + (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*d^3)*(b*x + a) + (I*(b*x + a)^3*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*d^3)*(b*x + a))*cos(2*b*x + 2*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))*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^2*c^2*d + 6*I*a*b*c*d^2 - 3*I*(b*x + a)^2*d^3 - 3*I*a^2*d^3 + (-6*I*b*c*d^2 + 6*I*a*d^3)*(b*x + a) + (-3*I*b^2*c^2*d + 6*I*a*b*c*d^2 - 3*I*(b*x + a)^2*d^3 - 3*I*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^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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (3*I*b^2*c^2*d - 6*I*a*b*c*d^2 + 3*I*(b*x + a)^2*d^3 + 3*I*a^2*d^3 + (6*I*b*c*d^2 - 6*I*a*d^3)*(b*x + a) + (3*I*b^2*c^2*d - 6*I*a*b*c*d^2 + 3*I*(b*x + a)^2*d^3 + 3*I*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^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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) + d^3)*polylog(4, -e^(I*b*x + I*a)) + 12*(d^3*cos(2*b*x + 2*a) + I*d^3*sin(2*b*x + 2*a) + d^3)*polylog(4, 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, I*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, -I*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(2*b*x + 2*a) + 12*(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(2*b*x + 2*a) - 12*(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 + 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))*sin(b*x + 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
268,1,1598,0,0.686646," ","integrate((d*x+c)^2*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{2} {\left(\frac{2}{\cos\left(b x + a\right)} - \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)} - \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)} - \log\left(\cos\left(b x + a\right) + 1\right) + \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{2}} + \frac{2 \, {\left({\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(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(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\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(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(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\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(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(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)}^{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(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(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} + {\left(8 i \, b c d - 8 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + 4 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + d^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - 4 \, {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) + i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + d^{2}\right)} {\rm Li}_2\left(-i \, 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(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(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(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(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)} + {\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)}\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)}\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)} + {\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)}\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)}\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 c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2} + {\left(-2 i \, b c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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 \, \sin\left(b x + a\right) + 1\right) - {\left(2 i \, b c d + 2 i \, {\left(b x + a\right)} d^{2} - 2 i \, a d^{2} + {\left(2 i \, b c d + 2 i \, {\left(b x + a\right)} d^{2} - 2 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - 2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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 \, \sin\left(b x + a\right) + 1\right) - {\left(-4 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, 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(2 \, b x + 2 \, a\right) - 4 \, 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)}) + 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)} \sin\left(b x + a\right)\right)}}{-2 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}}{2 \, b}"," ",0,"1/2*(c^2*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1)) - 2*a*c*d*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b + a^2*d^2*(2/cos(b*x + a) - log(cos(b*x + a) + 1) + log(cos(b*x + a) - 1))/b^2 + 2*((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(2*b*x + 2*a) - (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (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(2*b*x + 2*a) - (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(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(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(2*b*x + 2*a))*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(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(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (4*I*(b*x + a)^2*d^2 + (8*I*b*c*d - 8*I*a*d^2)*(b*x + a))*cos(b*x + a) + 4*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) + d^2)*dilog(I*e^(I*b*x + I*a)) - 4*(d^2*cos(2*b*x + 2*a) + I*d^2*sin(2*b*x + 2*a) + d^2)*dilog(-I*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(2*b*x + 2*a) - (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*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(2*b*x + 2*a) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*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) + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a))*cos(2*b*x + 2*a) + ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(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)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a))*cos(2*b*x + 2*a) - ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(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) - (-2*I*b*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2 + (-2*I*b*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2)*cos(2*b*x + 2*a) + 2*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (2*I*b*c*d + 2*I*(b*x + a)*d^2 - 2*I*a*d^2 + (2*I*b*c*d + 2*I*(b*x + a)*d^2 - 2*I*a*d^2)*cos(2*b*x + 2*a) - 2*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (-4*I*d^2*cos(2*b*x + 2*a) + 4*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(2*b*x + 2*a) - 4*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 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(b*x + a))/(-2*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(2*b*x + 2*a) - 2*I*b^2))/b","B",0
269,1,806,0,0.619001," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(d \cos\left(2 \, b x + 2 \, a\right) + i \, d \sin\left(2 \, b x + 2 \, a\right) + d\right)} \arctan\left(\frac{2 \, {\left(\cos\left(b x + 2 \, a\right) \cos\left(a\right) + \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}, \frac{\cos\left(b x + 2 \, a\right)^{2} - \cos\left(a\right)^{2} + \sin\left(b x + 2 \, a\right)^{2} - \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + {\left(2 \, b d x + 2 \, b c + 2 \, {\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(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(2 \, b x + 2 \, a\right) + 2 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(2 \, b x + 2 \, a\right) + 2 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\right)} \cos\left(b x + a\right) - 2 \, {\left(d \cos\left(2 \, b x + 2 \, a\right) + i \, d \sin\left(2 \, b x + 2 \, a\right) + d\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + 2 \, {\left(d \cos\left(2 \, b x + 2 \, a\right) + i \, d \sin\left(2 \, b x + 2 \, a\right) + 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(2 \, b x + 2 \, a\right) - {\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(2 \, b x + 2 \, a\right) + {\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 \, d \cos\left(2 \, b x + 2 \, a\right) + d \sin\left(2 \, b x + 2 \, a\right) - i \, d\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - 4 \, {\left(b d x + b c\right)} \sin\left(b x + a\right)}{-2 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}"," ",0,"-(2*(d*cos(2*b*x + 2*a) + I*d*sin(2*b*x + 2*a) + d)*arctan2(2*(cos(b*x + 2*a)*cos(a) + sin(b*x + 2*a)*sin(a))/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2), (cos(b*x + 2*a)^2 - cos(a)^2 + sin(b*x + 2*a)^2 - sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) + (2*b*d*x + 2*b*c + 2*(b*d*x + b*c)*cos(2*b*x + 2*a) - (-2*I*b*d*x - 2*I*b*c)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*b*c*cos(2*b*x + 2*a) + 2*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(2*b*x + 2*a) + 2*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)*cos(b*x + a) - 2*(d*cos(2*b*x + 2*a) + I*d*sin(2*b*x + 2*a) + d)*dilog(-e^(I*b*x + I*a)) + 2*(d*cos(2*b*x + 2*a) + I*d*sin(2*b*x + 2*a) + d)*dilog(e^(I*b*x + I*a)) - (I*b*d*x + I*b*c + (I*b*d*x + I*b*c)*cos(2*b*x + 2*a) - (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(2*b*x + 2*a) + (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*d*cos(2*b*x + 2*a) + d*sin(2*b*x + 2*a) - I*d)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - 4*(b*d*x + b*c)*sin(b*x + a))/(-2*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(2*b*x + 2*a) - 2*I*b^2)","B",0
270,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^2*sec(b*x + a)^2, x)","F",0
273,1,2355,0,0.744890," ","integrate((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c^{3} {\left(\frac{1}{\tan\left(b x + a\right)} - \tan\left(b x + a\right)\right)} - \frac{6 \, a c^{2} d {\left(\frac{1}{\tan\left(b x + a\right)} - \tan\left(b x + a\right)\right)}}{b} + \frac{6 \, a^{2} c d^{2} {\left(\frac{1}{\tan\left(b x + a\right)} - \tan\left(b x + a\right)\right)}}{b^{2}} - \frac{2 \, a^{3} d^{3} {\left(\frac{1}{\tan\left(b x + a\right)} - \tan\left(b x + a\right)\right)}}{b^{3}} - \frac{3 \, {\left({\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} \log\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) + {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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) - 8 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} c^{2} d}{{\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} b} + \frac{6 \, {\left({\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} \log\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) + {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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) - 8 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} a c d^{2}}{{\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} b^{2}} - \frac{3 \, {\left({\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} \log\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) + {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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) - 8 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} a^{2} d^{3}}{{\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} b^{3}} + \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(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 8 \, {\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(4 \, b x + 4 \, a\right) - {\left(6 \, b c d^{2} + 6 \, {\left(b x + a\right)} d^{3} - 6 \, a d^{3} - 6 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, b c d^{2} - 6 i \, {\left(b x + a\right)} d^{3} + 6 i \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)\right)} \log\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) - {\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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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(4 \, b x + 4 \, 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 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 3 \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 3 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(-12 i \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 12 \, d^{3} \sin\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right) + 12 \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 12 i \, d^{3}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)}}{-2 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + 2 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) + 2 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(2*c^3*(1/tan(b*x + a) - tan(b*x + a)) - 6*a*c^2*d*(1/tan(b*x + a) - tan(b*x + a))/b + 6*a^2*c*d^2*(1/tan(b*x + a) - tan(b*x + a))/b^2 - 2*a^3*d^3*(1/tan(b*x + a) - tan(b*x + a))/b^3 - 3*((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 8*(b*x + a)*sin(4*b*x + 4*a))*c^2*d/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*b) + 6*((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 8*(b*x + a)*sin(4*b*x + 4*a))*a*c*d^2/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*b^2) - 3*((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 8*(b*x + a)*sin(4*b*x + 4*a))*a^2*d^3/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*b^3) + 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(4*b*x + 4*a) - (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*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(4*b*x + 4*a) - (6*I*(b*x + a)^2*d^3 + (12*I*b*c*d^2 - 12*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*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(4*b*x + 4*a) + (-6*I*(b*x + a)^2*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 8*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*cos(4*b*x + 4*a) - (6*b*c*d^2 + 6*(b*x + a)*d^3 - 6*a*d^3 - 6*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(4*b*x + 4*a) + (-6*I*b*c*d^2 - 6*I*(b*x + a)*d^3 + 6*I*a*d^3)*sin(4*b*x + 4*a))*dilog(-e^(2*I*b*x + 2*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(4*b*x + 4*a) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*sin(4*b*x + 4*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(4*b*x + 4*a) + (-12*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 12*I*a*d^3)*sin(4*b*x + 4*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(4*b*x + 4*a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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(4*b*x + 4*a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(4*b*x + 4*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(4*b*x + 4*a) + 3*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-3*I*d^3*cos(4*b*x + 4*a) + 3*d^3*sin(4*b*x + 4*a) + 3*I*d^3)*polylog(3, -e^(2*I*b*x + 2*I*a)) - (-12*I*d^3*cos(4*b*x + 4*a) + 12*d^3*sin(4*b*x + 4*a) + 12*I*d^3)*polylog(3, -e^(I*b*x + I*a)) - (-12*I*d^3*cos(4*b*x + 4*a) + 12*d^3*sin(4*b*x + 4*a) + 12*I*d^3)*polylog(3, e^(I*b*x + I*a)) - (-8*I*(b*x + a)^3*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a)^2)*sin(4*b*x + 4*a))/(-2*I*b^3*cos(4*b*x + 4*a) + 2*b^3*sin(4*b*x + 4*a) + 2*I*b^3))/b","B",0
274,1,777,0,0.685600," ","integrate((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""maxima"")","-\frac{4 \, 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(4 \, b x + 4 \, a\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(2 \, b d^{2} x + 2 \, b c d - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sin\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right) + 2 i \, b c d \sin\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right) + 2 i \, b d^{2} x \sin\left(4 \, b x + 4 \, a\right) - 2 \, b d^{2} x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(d^{2} \cos\left(4 \, b x + 4 \, a\right) + i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - d^{2}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 2 \, {\left(d^{2} \cos\left(4 \, b x + 4 \, a\right) + i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + 2 \, {\left(d^{2} \cos\left(4 \, b x + 4 \, a\right) + i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 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(4 \, b x + 4 \, a\right) + {\left(b d^{2} x + b c d\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \log\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) - {\left(i \, b d^{2} x + i \, b c d + {\left(-i \, b d^{2} x - i \, b c d\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(b d^{2} x + b c d\right)} \sin\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right) + {\left(b d^{2} x + b c d\right)} \sin\left(4 \, b x + 4 \, 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 \, b^{2} d^{2} x^{2} - 8 i \, b^{2} c d x\right)} \sin\left(4 \, b x + 4 \, a\right)}{-i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + b^{3} \sin\left(4 \, b x + 4 \, a\right) + i \, b^{3}}"," ",0,"-(4*b^2*c^2 + (2*b*d^2*x + 2*b*c*d - 2*(b*d^2*x + b*c*d)*cos(4*b*x + 4*a) - (2*I*b*d^2*x + 2*I*b*c*d)*sin(4*b*x + 4*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (2*b*d^2*x + 2*b*c*d - 2*(b*d^2*x + b*c*d)*cos(4*b*x + 4*a) - (2*I*b*d^2*x + 2*I*b*c*d)*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*b*c*d*cos(4*b*x + 4*a) + 2*I*b*c*d*sin(4*b*x + 4*a) - 2*b*c*d)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*b*d^2*x*cos(4*b*x + 4*a) + 2*I*b*d^2*x*sin(4*b*x + 4*a) - 2*b*d^2*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x)*cos(4*b*x + 4*a) + (d^2*cos(4*b*x + 4*a) + I*d^2*sin(4*b*x + 4*a) - d^2)*dilog(-e^(2*I*b*x + 2*I*a)) + 2*(d^2*cos(4*b*x + 4*a) + I*d^2*sin(4*b*x + 4*a) - d^2)*dilog(-e^(I*b*x + I*a)) + 2*(d^2*cos(4*b*x + 4*a) + I*d^2*sin(4*b*x + 4*a) - 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(4*b*x + 4*a) + (b*d^2*x + b*c*d)*sin(4*b*x + 4*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - (I*b*d^2*x + I*b*c*d + (-I*b*d^2*x - I*b*c*d)*cos(4*b*x + 4*a) + (b*d^2*x + b*c*d)*sin(4*b*x + 4*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(4*b*x + 4*a) + (b*d^2*x + b*c*d)*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-4*I*b^2*d^2*x^2 - 8*I*b^2*c*d*x)*sin(4*b*x + 4*a))/(-I*b^3*cos(4*b*x + 4*a) + b^3*sin(4*b*x + 4*a) + I*b^3)","B",0
275,1,308,0,0.477177," ","integrate((d*x+c)*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""maxima"")","-\frac{2 \, c {\left(\frac{1}{\tan\left(b x + a\right)} - \tan\left(b x + a\right)\right)} - \frac{2 \, a d {\left(\frac{1}{\tan\left(b x + a\right)} - \tan\left(b x + a\right)\right)}}{b} - \frac{{\left({\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} \log\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) + {\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, 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) - 8 \, {\left(b x + a\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} d}{{\left(\cos\left(4 \, b x + 4 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} - 2 \, \cos\left(4 \, b x + 4 \, a\right) + 1\right)} b}}{2 \, b}"," ",0,"-1/2*(2*c*(1/tan(b*x + a) - tan(b*x + a)) - 2*a*d*(1/tan(b*x + a) - tan(b*x + a))/b - ((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - 8*(b*x + a)*sin(4*b*x + 4*a))*d/((cos(4*b*x + 4*a)^2 + sin(4*b*x + 4*a)^2 - 2*cos(4*b*x + 4*a) + 1)*b))/b","B",0
276,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^3*sec(b*x + a)^2, x)","F",0
279,1,8043,0,6.029812," ","integrate((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{3}} + \frac{4 \, {\left({\left(12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, a^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 12 \, {\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)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\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)} \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} + a^{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(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 12 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, 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} + 12 i \, a^{2} d^{3} + {\left(24 i \, b c d^{2} - 24 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} + 12 i \, a^{2} 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)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, a^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 12 \, {\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)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\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)} \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} + a^{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(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 12 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, 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} + 12 i \, a^{2} d^{3} + {\left(24 i \, b c d^{2} - 24 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} + 12 i \, a^{2} 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)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{3} d^{3} + 12 \, b c d^{2} - 12 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} 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)}^{3} d^{3} + 12 i \, b c d^{2} - 12 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 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(6 \, b x + 6 \, a\right) - 12 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\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(6 \, b x + 6 \, a\right) - {\left(12 i \, b c d^{2} - 12 i \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, b c d^{2} - 12 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(6 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\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} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\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} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\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} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} 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)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 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 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(-3 i \, b c d^{2} + {\left(3 i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 24 \, {\left(3 i \, a - 1\right)} b c d^{2} + {\left(36 i \, a^{2} - 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(5 \, b x + 5 \, a\right) - {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d + 48 i \, a b c d^{2} - 24 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(12 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(36 i \, b c d^{2} - 12 \, {\left(3 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 24 \, {\left(3 i \, a + 1\right)} b c d^{2} + {\left(36 i \, a^{2} + 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(24 \, b c d^{2} + 24 \, {\left(b x + a\right)} d^{3} - 24 \, a d^{3} + 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\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(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(24 i \, b c d^{2} + 24 i \, {\left(b x + a\right)} d^{3} - 24 i \, a d^{3}\right)} \sin\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)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(24 \, b c d^{2} + 24 \, {\left(b x + a\right)} d^{3} - 24 \, a d^{3} + 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 24 \, {\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(24 i \, b c d^{2} + 24 i \, {\left(b x + a\right)} d^{3} - 24 i \, a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \sin\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)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(3 \, a^{2} + 2\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 12 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 12 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 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(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(3 \, a^{2} + 2\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 12 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 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(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, 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(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, 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(-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)} + {\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)} \cos\left(6 \, b x + 6 \, 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} + 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)} \cos\left(4 \, b x + 4 \, 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} + 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)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\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)} \sin\left(6 \, b x + 6 \, a\right) - 6 \, {\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)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\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)} \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 \, \sin\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)} + {\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)} \cos\left(6 \, b x + 6 \, 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} - 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)} \cos\left(4 \, b x + 4 \, 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} - 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)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\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)} \sin\left(6 \, b x + 6 \, a\right) + 6 \, {\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)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\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)} \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 \, \sin\left(b x + a\right) + 1\right) - {\left(36 \, d^{3} \cos\left(6 \, b x + 6 \, a\right) - 36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 36 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(6 \, b x + 6 \, a\right) - 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 36 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 36 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + {\left(36 \, d^{3} \cos\left(6 \, b x + 6 \, a\right) - 36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 36 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(6 \, b x + 6 \, a\right) - 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 36 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 36 \, d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, d^{3} \cos\left(6 \, b x + 6 \, a\right) + 24 i \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 24 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 24 \, d^{3} \sin\left(6 \, b x + 6 \, a\right) - 24 \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 24 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - 24 i \, d^{3}\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) - {\left(24 i \, d^{3} \cos\left(6 \, b x + 6 \, a\right) - 24 i \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 24 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) - 24 \, d^{3} \sin\left(6 \, b x + 6 \, a\right) + 24 \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 24 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 24 i \, d^{3}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, a\right)}) - {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3} + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 36 \, {\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(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) + 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 36 \, {\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 \, {\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(36 \, b c d^{2} - {\left(36 \, a + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a + 24 i\right)} b c d^{2} + 12 \, {\left(3 \, a^{2} + 2 i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(5 \, b x + 5 \, a\right) - 8 \, {\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)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\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(36 \, b c d^{2} - {\left(36 \, a - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a - 24 i\right)} b c d^{2} + 12 \, {\left(3 \, 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(6 \, b x + 6 \, a\right) + 4 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} \sin\left(6 \, b x + 6 \, a\right) - 4 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{3}}}{4 \, b}"," ",0,"1/4*(c^3*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1)) - 3*a*c^2*d*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1))/b + 3*a^2*c*d^2*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1))/b^2 - a^3*d^3*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1))/b^3 + 4*((12*b^2*c^2*d - 24*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 12*a^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) + 12*(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))*cos(6*b*x + 6*a) - 12*(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))*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*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*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*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*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*d^3 + (24*I*b*c*d^2 - 24*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*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (12*b^2*c^2*d - 24*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 12*a^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) + 12*(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))*cos(6*b*x + 6*a) - 12*(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))*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*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*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*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*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*d^3 + (24*I*b*c*d^2 - 24*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*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) - (6*(b*x + a)^3*d^3 + 12*b*c*d^2 - 12*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a) + 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^3*d^3 + 12*I*b*c*d^2 - 12*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 12*I)*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*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(6*b*x + 6*a) - 12*(b*c*d^2 - a*d^3)*cos(4*b*x + 4*a) - 12*(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(6*b*x + 6*a) - (12*I*b*c*d^2 - 12*I*a*d^3)*sin(4*b*x + 4*a) - (12*I*b*c*d^2 - 12*I*a*d^3)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*(b*x + a)^3*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a) + 6*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 6*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 12*I)*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^3*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^3*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (12*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*(-3*I*b*c*d^2 + (3*I*a - 1)*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 24*(3*I*a - 1)*b*c*d^2 + (36*I*a^2 - 24*a)*d^3)*(b*x + a))*cos(5*b*x + 5*a) - (-8*I*(b*x + a)^3*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a)^2 + (-24*I*b^2*c^2*d + 48*I*a*b*c*d^2 - 24*I*a^2*d^3)*(b*x + a))*cos(3*b*x + 3*a) - (12*I*(b*x + a)^3*d^3 - 12*b^2*c^2*d + 24*a*b*c*d^2 - 12*a^2*d^3 + (36*I*b*c*d^2 - 12*(3*I*a + 1)*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 24*(3*I*a + 1)*b*c*d^2 + (36*I*a^2 + 24*a)*d^3)*(b*x + a))*cos(b*x + a) + (24*b*c*d^2 + 24*(b*x + a)*d^3 - 24*a*d^3 + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(6*b*x + 6*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(4*b*x + 4*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) - (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(6*b*x + 6*a) - (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*sin(4*b*x + 4*a) - (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*sin(2*b*x + 2*a))*dilog(I*e^(I*b*x + I*a)) - (24*b*c*d^2 + 24*(b*x + a)*d^3 - 24*a*d^3 + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(6*b*x + 6*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(4*b*x + 4*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) + (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*sin(6*b*x + 6*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(4*b*x + 4*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(2*b*x + 2*a))*dilog(-I*e^(I*b*x + I*a)) + (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 6*(3*a^2 + 2)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 12*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*a) - (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 12*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 12*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) - (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 6*(3*a^2 + 2)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 12*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 12*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 12*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(6*b*x + 6*a) + (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(6*b*x + 6*a) - 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*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) - (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a) + (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(6*b*x + 6*a) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(6*b*x + 6*a) + 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*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) - (-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) + (-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))*cos(6*b*x + 6*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))*cos(4*b*x + 4*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))*cos(2*b*x + 2*a) + 6*(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))*sin(6*b*x + 6*a) - 6*(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))*sin(4*b*x + 4*a) - 6*(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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(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) + (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))*cos(6*b*x + 6*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))*cos(4*b*x + 4*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))*cos(2*b*x + 2*a) - 6*(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))*sin(6*b*x + 6*a) + 6*(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))*sin(4*b*x + 4*a) + 6*(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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (36*d^3*cos(6*b*x + 6*a) - 36*d^3*cos(4*b*x + 4*a) - 36*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(6*b*x + 6*a) - 36*I*d^3*sin(4*b*x + 4*a) - 36*I*d^3*sin(2*b*x + 2*a) + 36*d^3)*polylog(4, -e^(I*b*x + I*a)) + (36*d^3*cos(6*b*x + 6*a) - 36*d^3*cos(4*b*x + 4*a) - 36*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(6*b*x + 6*a) - 36*I*d^3*sin(4*b*x + 4*a) - 36*I*d^3*sin(2*b*x + 2*a) + 36*d^3)*polylog(4, e^(I*b*x + I*a)) - (-24*I*d^3*cos(6*b*x + 6*a) + 24*I*d^3*cos(4*b*x + 4*a) + 24*I*d^3*cos(2*b*x + 2*a) + 24*d^3*sin(6*b*x + 6*a) - 24*d^3*sin(4*b*x + 4*a) - 24*d^3*sin(2*b*x + 2*a) - 24*I*d^3)*polylog(3, I*e^(I*b*x + I*a)) - (24*I*d^3*cos(6*b*x + 6*a) - 24*I*d^3*cos(4*b*x + 4*a) - 24*I*d^3*cos(2*b*x + 2*a) - 24*d^3*sin(6*b*x + 6*a) + 24*d^3*sin(4*b*x + 4*a) + 24*d^3*sin(2*b*x + 2*a) + 24*I*d^3)*polylog(3, -I*e^(I*b*x + I*a)) - (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3 + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(6*b*x + 6*a) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(2*b*x + 2*a) + 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(6*b*x + 6*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 36*(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)) - (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3 + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(6*b*x + 6*a) + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(4*b*x + 4*a) + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(2*b*x + 2*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(6*b*x + 6*a) + 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) + 36*(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*(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 + (36*b*c*d^2 - (36*a + 12*I)*d^3)*(b*x + a)^2 + (36*b^2*c^2*d - (72*a + 24*I)*b*c*d^2 + 12*(3*a^2 + 2*I*a)*d^3)*(b*x + a))*sin(5*b*x + 5*a) - 8*((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))*sin(3*b*x + 3*a) + (12*(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 + (36*b*c*d^2 - (36*a - 12*I)*d^3)*(b*x + a)^2 + (36*b^2*c^2*d - (72*a - 24*I)*b*c*d^2 + 12*(3*a^2 - 2*I*a)*d^3)*(b*x + a))*sin(b*x + a))/(-4*I*b^3*cos(6*b*x + 6*a) + 4*I*b^3*cos(4*b*x + 4*a) + 4*I*b^3*cos(2*b*x + 2*a) + 4*b^3*sin(6*b*x + 6*a) - 4*b^3*sin(4*b*x + 4*a) - 4*b^3*sin(2*b*x + 2*a) - 4*I*b^3))/b","B",0
280,1,3820,0,1.615746," ","integrate((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{c^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{2 \, a c d {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)}}{b^{2}} + \frac{4 \, {\left({\left(8 \, b c d + 8 \, {\left(b x + a\right)} d^{2} - 8 \, a d^{2} + 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 8 \, {\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(-8 i \, b c d - 8 i \, {\left(b x + a\right)} d^{2} + 8 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, 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(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)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(8 \, b c d + 8 \, {\left(b x + a\right)} d^{2} - 8 \, a d^{2} + 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 8 \, {\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(-8 i \, b c d - 8 i \, {\left(b x + a\right)} d^{2} + 8 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, 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(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)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{2} d^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 4 \, d^{2} + 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} + 4 i \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 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(6 \, b x + 6 \, a\right) - 4 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 4 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 i \, d^{2} \sin\left(6 \, b x + 6 \, a\right) - 4 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 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(6 \, {\left(b x + a\right)}^{2} d^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 6 \, {\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(6 \, b x + 6 \, a\right) - 6 \, {\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) - 6 \, {\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(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 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) + 4 \, {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} - 2 \, b c d + 2 \, a d^{2} + 2 \, {\left(-3 i \, b c d + {\left(3 i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(5 \, b x + 5 \, a\right) - {\left(-8 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-16 i \, b c d + 16 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} d^{2} - 8 \, b c d + 8 \, a d^{2} + {\left(24 i \, b c d - 8 \, {\left(3 i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(8 \, d^{2} \cos\left(6 \, b x + 6 \, a\right) - 8 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 8 i \, d^{2} \sin\left(6 \, b x + 6 \, a\right) - 8 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 8 \, d^{2}\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(8 \, d^{2} \cos\left(6 \, b x + 6 \, a\right) - 8 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 8 i \, d^{2} \sin\left(6 \, b x + 6 \, a\right) - 8 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 8 \, d^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left(12 \, b c d + 12 \, {\left(b x + a\right)} d^{2} - 12 \, a d^{2} + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(12 i \, b c d + 12 i \, {\left(b x + a\right)} d^{2} - 12 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, b c d + 12 i \, {\left(b x + a\right)} d^{2} - 12 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(12 \, b c d + 12 \, {\left(b x + a\right)} d^{2} - 12 \, a d^{2} + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 i \, b c d + 12 i \, {\left(b x + a\right)} d^{2} - 12 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 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(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) - {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2} + {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) + {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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 \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2} + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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 \, \sin\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} + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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 \, \sin\left(b x + a\right) + 1\right) - {\left(-12 i \, d^{2} \cos\left(6 \, b x + 6 \, a\right) + 12 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 12 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{2} \sin\left(6 \, b x + 6 \, a\right) - 12 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 12 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(12 i \, d^{2} \cos\left(6 \, b x + 6 \, a\right) - 12 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 12 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) - 12 \, d^{2} \sin\left(6 \, b x + 6 \, a\right) + 12 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 12 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 12 i \, d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(12 \, {\left(b x + a\right)}^{2} d^{2} - 8 i \, b c d + 8 i \, a d^{2} + {\left(24 \, b c d - {\left(24 \, a + 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(5 \, b x + 5 \, a\right) - 8 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)}^{2} d^{2} + 8 i \, b c d - 8 i \, a d^{2} + {\left(24 \, b c d - {\left(24 \, 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(6 \, b x + 6 \, a\right) + 4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} \sin\left(6 \, b x + 6 \, a\right) - 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{2}}}{4 \, b}"," ",0,"1/4*(c^2*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1)) - 2*a*c*d*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1))/b + a^2*d^2*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1))/b^2 + 4*((8*b*c*d + 8*(b*x + a)*d^2 - 8*a*d^2 + 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 8*(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) - (-8*I*b*c*d - 8*I*(b*x + a)*d^2 + 8*I*a*d^2)*sin(6*b*x + 6*a) - (8*I*b*c*d + 8*I*(b*x + a)*d^2 - 8*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))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (8*b*c*d + 8*(b*x + a)*d^2 - 8*a*d^2 + 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 8*(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) - (-8*I*b*c*d - 8*I*(b*x + a)*d^2 + 8*I*a*d^2)*sin(6*b*x + 6*a) - (8*I*b*c*d + 8*I*(b*x + a)*d^2 - 8*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))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) - (6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) + 4*d^2 + 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(6*b*x + 6*a) - 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(4*b*x + 4*a) - 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) + 4*I*d^2)*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (4*d^2*cos(6*b*x + 6*a) - 4*d^2*cos(4*b*x + 4*a) - 4*d^2*cos(2*b*x + 2*a) + 4*I*d^2*sin(6*b*x + 6*a) - 4*I*d^2*sin(4*b*x + 4*a) - 4*I*d^2*sin(2*b*x + 2*a) + 4*d^2)*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) + 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(6*b*x + 6*a) - 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(4*b*x + 4*a) - 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a))*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a))*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + 4*(-3*I*(b*x + a)^2*d^2 - 2*b*c*d + 2*a*d^2 + 2*(-3*I*b*c*d + (3*I*a - 1)*d^2)*(b*x + a))*cos(5*b*x + 5*a) - (-8*I*(b*x + a)^2*d^2 + (-16*I*b*c*d + 16*I*a*d^2)*(b*x + a))*cos(3*b*x + 3*a) - (12*I*(b*x + a)^2*d^2 - 8*b*c*d + 8*a*d^2 + (24*I*b*c*d - 8*(3*I*a + 1)*d^2)*(b*x + a))*cos(b*x + a) + (8*d^2*cos(6*b*x + 6*a) - 8*d^2*cos(4*b*x + 4*a) - 8*d^2*cos(2*b*x + 2*a) + 8*I*d^2*sin(6*b*x + 6*a) - 8*I*d^2*sin(4*b*x + 4*a) - 8*I*d^2*sin(2*b*x + 2*a) + 8*d^2)*dilog(I*e^(I*b*x + I*a)) - (8*d^2*cos(6*b*x + 6*a) - 8*d^2*cos(4*b*x + 4*a) - 8*d^2*cos(2*b*x + 2*a) + 8*I*d^2*sin(6*b*x + 6*a) - 8*I*d^2*sin(4*b*x + 4*a) - 8*I*d^2*sin(2*b*x + 2*a) + 8*d^2)*dilog(-I*e^(I*b*x + I*a)) + (12*b*c*d + 12*(b*x + a)*d^2 - 12*a*d^2 + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(6*b*x + 6*a) - (12*I*b*c*d + 12*I*(b*x + a)*d^2 - 12*I*a*d^2)*sin(4*b*x + 4*a) - (12*I*b*c*d + 12*I*(b*x + a)*d^2 - 12*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) - (12*b*c*d + 12*(b*x + a)*d^2 - 12*a*d^2 + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) + (12*I*b*c*d + 12*I*(b*x + a)*d^2 - 12*I*a*d^2)*sin(6*b*x + 6*a) + (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(4*b*x + 4*a) + (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) - (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2 + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(6*b*x + 6*a) + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(4*b*x + 4*a) + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(2*b*x + 2*a) + (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(6*b*x + 6*a) - (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(4*b*x + 4*a) - (3*(b*x + a)^2*d^2 + 6*(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) - (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2 + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(6*b*x + 6*a) + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(4*b*x + 4*a) + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(2*b*x + 2*a) - (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(6*b*x + 6*a) + (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(4*b*x + 4*a) + (3*(b*x + a)^2*d^2 + 6*(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*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2 + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*cos(6*b*x + 6*a) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*cos(4*b*x + 4*a) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*cos(2*b*x + 2*a) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(6*b*x + 6*a) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(4*b*x + 4*a) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2 + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*cos(6*b*x + 6*a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*cos(4*b*x + 4*a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*cos(2*b*x + 2*a) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(6*b*x + 6*a) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(4*b*x + 4*a) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (-12*I*d^2*cos(6*b*x + 6*a) + 12*I*d^2*cos(4*b*x + 4*a) + 12*I*d^2*cos(2*b*x + 2*a) + 12*d^2*sin(6*b*x + 6*a) - 12*d^2*sin(4*b*x + 4*a) - 12*d^2*sin(2*b*x + 2*a) - 12*I*d^2)*polylog(3, -e^(I*b*x + I*a)) - (12*I*d^2*cos(6*b*x + 6*a) - 12*I*d^2*cos(4*b*x + 4*a) - 12*I*d^2*cos(2*b*x + 2*a) - 12*d^2*sin(6*b*x + 6*a) + 12*d^2*sin(4*b*x + 4*a) + 12*d^2*sin(2*b*x + 2*a) + 12*I*d^2)*polylog(3, e^(I*b*x + I*a)) + (12*(b*x + a)^2*d^2 - 8*I*b*c*d + 8*I*a*d^2 + (24*b*c*d - (24*a + 8*I)*d^2)*(b*x + a))*sin(5*b*x + 5*a) - 8*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(3*b*x + 3*a) + (12*(b*x + a)^2*d^2 + 8*I*b*c*d - 8*I*a*d^2 + (24*b*c*d - (24*a - 8*I)*d^2)*(b*x + a))*sin(b*x + a))/(-4*I*b^2*cos(6*b*x + 6*a) + 4*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 4*b^2*sin(6*b*x + 6*a) - 4*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 4*I*b^2))/b","B",0
281,1,1503,0,0.899614," ","integrate((d*x+c)*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","-\frac{{\left(4 \, d \cos\left(6 \, b x + 6 \, a\right) - 4 \, d \cos\left(4 \, b x + 4 \, a\right) - 4 \, d \cos\left(2 \, b x + 2 \, a\right) + 4 i \, d \sin\left(6 \, b x + 6 \, a\right) - 4 i \, d \sin\left(4 \, b x + 4 \, a\right) - 4 i \, d \sin\left(2 \, b x + 2 \, a\right) + 4 \, d\right)} \arctan\left(\frac{2 \, {\left(\cos\left(b x + 2 \, a\right) \cos\left(a\right) + \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}, \frac{\cos\left(b x + 2 \, a\right)^{2} - \cos\left(a\right)^{2} + \sin\left(b x + 2 \, a\right)^{2} - \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + {\left(6 \, b d x + 6 \, b c + 6 \, {\left(b d x + b c\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(b d x + b c\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, b d x - 6 i \, b c\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(6 i \, b d x + 6 i \, b c\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(6 i \, b d x + 6 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(6 \, b c \cos\left(6 \, b x + 6 \, a\right) - 6 \, b c \cos\left(4 \, b x + 4 \, a\right) - 6 \, b c \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b c \sin\left(6 \, b x + 6 \, a\right) - 6 i \, b c \sin\left(4 \, b x + 4 \, a\right) - 6 i \, b c \sin\left(2 \, b x + 2 \, a\right) + 6 \, b c\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(6 \, b d x \cos\left(6 \, b x + 6 \, a\right) - 6 \, b d x \cos\left(4 \, b x + 4 \, a\right) - 6 \, b d x \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b d x \sin\left(6 \, b x + 6 \, a\right) - 6 i \, b d x \sin\left(4 \, b x + 4 \, a\right) - 6 i \, b d x \sin\left(2 \, b x + 2 \, a\right) + 6 \, b d x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - {\left(-12 i \, b d x - 12 i \, b c - 4 \, d\right)} \cos\left(5 \, b x + 5 \, a\right) - {\left(8 i \, b d x + 8 i \, b c\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(-12 i \, b d x - 12 i \, b c + 4 \, d\right)} \cos\left(b x + a\right) - {\left(6 \, d \cos\left(6 \, b x + 6 \, a\right) - 6 \, d \cos\left(4 \, b x + 4 \, a\right) - 6 \, d \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d \sin\left(6 \, b x + 6 \, a\right) - 6 i \, d \sin\left(4 \, b x + 4 \, a\right) - 6 i \, d \sin\left(2 \, b x + 2 \, a\right) + 6 \, d\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(6 \, d \cos\left(6 \, b x + 6 \, a\right) - 6 \, d \cos\left(4 \, b x + 4 \, a\right) - 6 \, d \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d \sin\left(6 \, b x + 6 \, a\right) - 6 i \, d \sin\left(4 \, b x + 4 \, a\right) - 6 i \, d \sin\left(2 \, b x + 2 \, a\right) + 6 \, d\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(3 i \, b d x + 3 i \, b c + {\left(3 i \, b d x + 3 i \, b c\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, b d x - 3 i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, b d x - 3 i \, b c\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left(b d x + b c\right)} \sin\left(6 \, b x + 6 \, a\right) + 3 \, {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, a\right) + 3 \, {\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(-3 i \, b d x - 3 i \, b c + {\left(-3 i \, b d x - 3 i \, b c\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, b d x + 3 i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, b d x + 3 i \, b c\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b d x + b c\right)} \sin\left(6 \, b x + 6 \, a\right) - 3 \, {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, a\right) - 3 \, {\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(-2 i \, d \cos\left(6 \, b x + 6 \, a\right) + 2 i \, d \cos\left(4 \, b x + 4 \, a\right) + 2 i \, d \cos\left(2 \, b x + 2 \, a\right) + 2 \, d \sin\left(6 \, b x + 6 \, a\right) - 2 \, d \sin\left(4 \, b x + 4 \, a\right) - 2 \, d \sin\left(2 \, b x + 2 \, a\right) - 2 i \, d\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - {\left(12 \, b d x + 12 \, b c - 4 i \, d\right)} \sin\left(5 \, b x + 5 \, a\right) + 8 \, {\left(b d x + b c\right)} \sin\left(3 \, b x + 3 \, a\right) - {\left(12 \, b d x + 12 \, b c + 4 i \, d\right)} \sin\left(b x + a\right)}{-4 i \, b^{2} \cos\left(6 \, b x + 6 \, a\right) + 4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} \sin\left(6 \, b x + 6 \, a\right) - 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{2}}"," ",0,"-((4*d*cos(6*b*x + 6*a) - 4*d*cos(4*b*x + 4*a) - 4*d*cos(2*b*x + 2*a) + 4*I*d*sin(6*b*x + 6*a) - 4*I*d*sin(4*b*x + 4*a) - 4*I*d*sin(2*b*x + 2*a) + 4*d)*arctan2(2*(cos(b*x + 2*a)*cos(a) + sin(b*x + 2*a)*sin(a))/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2), (cos(b*x + 2*a)^2 - cos(a)^2 + sin(b*x + 2*a)^2 - sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) + (6*b*d*x + 6*b*c + 6*(b*d*x + b*c)*cos(6*b*x + 6*a) - 6*(b*d*x + b*c)*cos(4*b*x + 4*a) - 6*(b*d*x + b*c)*cos(2*b*x + 2*a) - (-6*I*b*d*x - 6*I*b*c)*sin(6*b*x + 6*a) - (6*I*b*d*x + 6*I*b*c)*sin(4*b*x + 4*a) - (6*I*b*d*x + 6*I*b*c)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (6*b*c*cos(6*b*x + 6*a) - 6*b*c*cos(4*b*x + 4*a) - 6*b*c*cos(2*b*x + 2*a) + 6*I*b*c*sin(6*b*x + 6*a) - 6*I*b*c*sin(4*b*x + 4*a) - 6*I*b*c*sin(2*b*x + 2*a) + 6*b*c)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (6*b*d*x*cos(6*b*x + 6*a) - 6*b*d*x*cos(4*b*x + 4*a) - 6*b*d*x*cos(2*b*x + 2*a) + 6*I*b*d*x*sin(6*b*x + 6*a) - 6*I*b*d*x*sin(4*b*x + 4*a) - 6*I*b*d*x*sin(2*b*x + 2*a) + 6*b*d*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (-12*I*b*d*x - 12*I*b*c - 4*d)*cos(5*b*x + 5*a) - (8*I*b*d*x + 8*I*b*c)*cos(3*b*x + 3*a) - (-12*I*b*d*x - 12*I*b*c + 4*d)*cos(b*x + a) - (6*d*cos(6*b*x + 6*a) - 6*d*cos(4*b*x + 4*a) - 6*d*cos(2*b*x + 2*a) + 6*I*d*sin(6*b*x + 6*a) - 6*I*d*sin(4*b*x + 4*a) - 6*I*d*sin(2*b*x + 2*a) + 6*d)*dilog(-e^(I*b*x + I*a)) + (6*d*cos(6*b*x + 6*a) - 6*d*cos(4*b*x + 4*a) - 6*d*cos(2*b*x + 2*a) + 6*I*d*sin(6*b*x + 6*a) - 6*I*d*sin(4*b*x + 4*a) - 6*I*d*sin(2*b*x + 2*a) + 6*d)*dilog(e^(I*b*x + I*a)) - (3*I*b*d*x + 3*I*b*c + (3*I*b*d*x + 3*I*b*c)*cos(6*b*x + 6*a) + (-3*I*b*d*x - 3*I*b*c)*cos(4*b*x + 4*a) + (-3*I*b*d*x - 3*I*b*c)*cos(2*b*x + 2*a) - 3*(b*d*x + b*c)*sin(6*b*x + 6*a) + 3*(b*d*x + b*c)*sin(4*b*x + 4*a) + 3*(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) - (-3*I*b*d*x - 3*I*b*c + (-3*I*b*d*x - 3*I*b*c)*cos(6*b*x + 6*a) + (3*I*b*d*x + 3*I*b*c)*cos(4*b*x + 4*a) + (3*I*b*d*x + 3*I*b*c)*cos(2*b*x + 2*a) + 3*(b*d*x + b*c)*sin(6*b*x + 6*a) - 3*(b*d*x + b*c)*sin(4*b*x + 4*a) - 3*(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) - (-2*I*d*cos(6*b*x + 6*a) + 2*I*d*cos(4*b*x + 4*a) + 2*I*d*cos(2*b*x + 2*a) + 2*d*sin(6*b*x + 6*a) - 2*d*sin(4*b*x + 4*a) - 2*d*sin(2*b*x + 2*a) - 2*I*d)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - (12*b*d*x + 12*b*c - 4*I*d)*sin(5*b*x + 5*a) + 8*(b*d*x + b*c)*sin(3*b*x + 3*a) - (12*b*d*x + 12*b*c + 4*I*d)*sin(b*x + a))/(-4*I*b^2*cos(6*b*x + 6*a) + 4*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 4*b^2*sin(6*b*x + 6*a) - 4*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 4*I*b^2)","B",0
282,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,0,0,0,0.000000," ","integrate(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\int x^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^m*csc(b*x + a)^3*sec(b*x + a)^2, x)","F",0
285,1,3989,0,1.240943," ","integrate(x^3*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","-\frac{a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)} - \frac{4 \, {\left({\left(12 \, {\left(b x + a\right)}^{2} - 24 \, {\left(b x + a\right)} a + 12 \, a^{2} + 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a - 12 i \, a^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a + 12 i \, a^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a + 12 i \, a^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(12 \, {\left(b x + a\right)}^{2} - 24 \, {\left(b x + a\right)} a + 12 \, a^{2} + 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) - 12 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{2} + 24 i \, {\left(b x + a\right)} a - 12 i \, a^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a + 12 i \, a^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 24 i \, {\left(b x + a\right)} a + 12 i \, a^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{3} - 18 \, {\left(b x + a\right)}^{2} a + 6 \, {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + {\left(18 i \, a^{2} + 12 i\right)} {\left(b x + a\right)} - 12 i \, a\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a + {\left(-18 i \, a^{2} - 12 i\right)} {\left(b x + a\right)} + 12 i \, a\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a + {\left(-18 i \, a^{2} - 12 i\right)} {\left(b x + a\right)} + 12 i \, a\right)} \sin\left(2 \, b x + 2 \, a\right) - 12 \, a\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(12 \, a \cos\left(6 \, b x + 6 \, a\right) - 12 \, a \cos\left(4 \, b x + 4 \, a\right) - 12 \, a \cos\left(2 \, b x + 2 \, a\right) + 12 i \, a \sin\left(6 \, b x + 6 \, a\right) - 12 i \, a \sin\left(4 \, b x + 4 \, a\right) - 12 i \, a \sin\left(2 \, b x + 2 \, a\right) + 12 \, a\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) - {\left(6 \, {\left(b x + a\right)}^{3} - 18 \, {\left(b x + a\right)}^{2} a + 6 \, {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} - 18 i \, {\left(b x + a\right)}^{2} a + {\left(18 i \, a^{2} + 12 i\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a + {\left(-18 i \, a^{2} - 12 i\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} + 18 i \, {\left(b x + a\right)}^{2} a + {\left(-18 i \, a^{2} - 12 i\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 i \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)}^{2} {\left(3 i \, a - 1\right)} + {\left(36 i \, a^{2} - 24 \, a\right)} {\left(b x + a\right)} + 12 \, a^{2}\right)} \cos\left(5 \, b x + 5 \, a\right) - {\left(-8 i \, {\left(b x + a\right)}^{3} + 24 i \, {\left(b x + a\right)}^{2} a - 24 i \, {\left(b x + a\right)} a^{2}\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{3} - 12 \, {\left(b x + a\right)}^{2} {\left(3 i \, a + 1\right)} + {\left(36 i \, a^{2} + 24 \, a\right)} {\left(b x + a\right)} - 12 \, a^{2}\right)} \cos\left(b x + a\right) + {\left(24 \, b x \cos\left(6 \, b x + 6 \, a\right) - 24 \, b x \cos\left(4 \, b x + 4 \, a\right) - 24 \, b x \cos\left(2 \, b x + 2 \, a\right) + 24 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 24 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 24 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 24 \, b x\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(24 \, b x \cos\left(6 \, b x + 6 \, a\right) - 24 \, b x \cos\left(4 \, b x + 4 \, a\right) - 24 \, b x \cos\left(2 \, b x + 2 \, a\right) + 24 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 24 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 24 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 24 \, b x\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left(18 \, {\left(b x + a\right)}^{2} - 36 \, {\left(b x + a\right)} a + 18 \, a^{2} + 6 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 3 \, a^{2} + 2\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 3 \, a^{2} + 2\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 3 \, a^{2} + 2\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-18 i \, {\left(b x + a\right)}^{2} + 36 i \, {\left(b x + a\right)} a - 18 i \, a^{2} - 12 i\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(18 i \, {\left(b x + a\right)}^{2} - 36 i \, {\left(b x + a\right)} a + 18 i \, a^{2} + 12 i\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(18 i \, {\left(b x + a\right)}^{2} - 36 i \, {\left(b x + a\right)} a + 18 i \, a^{2} + 12 i\right)} \sin\left(2 \, b x + 2 \, a\right) + 12\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(18 \, {\left(b x + a\right)}^{2} - 36 \, {\left(b x + a\right)} a + 18 \, a^{2} + 6 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 3 \, a^{2} + 2\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 3 \, a^{2} + 2\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 3 \, a^{2} + 2\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(18 i \, {\left(b x + a\right)}^{2} - 36 i \, {\left(b x + a\right)} a + 18 i \, a^{2} + 12 i\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-18 i \, {\left(b x + a\right)}^{2} + 36 i \, {\left(b x + a\right)} a - 18 i \, a^{2} - 12 i\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-18 i \, {\left(b x + a\right)}^{2} + 36 i \, {\left(b x + a\right)} a - 18 i \, a^{2} - 12 i\right)} \sin\left(2 \, b x + 2 \, a\right) + 12\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(-3 i \, {\left(b x + a\right)}^{3} + 9 i \, {\left(b x + a\right)}^{2} a + {\left(-9 i \, a^{2} - 6 i\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{3} + 9 i \, {\left(b x + a\right)}^{2} a + {\left(-9 i \, a^{2} - 6 i\right)} {\left(b x + a\right)} + 6 i \, a\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{3} - 9 i \, {\left(b x + a\right)}^{2} a + {\left(9 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} - 6 i \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{3} - 9 i \, {\left(b x + a\right)}^{2} a + {\left(9 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} - 6 i \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \sin\left(6 \, b x + 6 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \sin\left(4 \, b x + 4 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \sin\left(2 \, b x + 2 \, a\right) + 6 i \, a\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)}^{3} - 9 i \, {\left(b x + a\right)}^{2} a + {\left(9 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} - 9 i \, {\left(b x + a\right)}^{2} a + {\left(9 i \, a^{2} + 6 i\right)} {\left(b x + a\right)} - 6 i \, a\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} + 9 i \, {\left(b x + a\right)}^{2} a + {\left(-9 i \, a^{2} - 6 i\right)} {\left(b x + a\right)} + 6 i \, a\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} + 9 i \, {\left(b x + a\right)}^{2} a + {\left(-9 i \, a^{2} - 6 i\right)} {\left(b x + a\right)} + 6 i \, a\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \sin\left(6 \, b x + 6 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \sin\left(4 \, b x + 4 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + {\left(3 \, a^{2} + 2\right)} {\left(b x + a\right)} - 2 \, a\right)} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, a\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(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a - 6 i \, a^{2} + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a - 6 i \, a^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + 6 i \, a^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + 6 i \, a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{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 \, \sin\left(b x + a\right) + 1\right) - {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + 6 i \, a^{2} + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + 6 i \, a^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a - 6 i \, a^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a - 6 i \, a^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a + a^{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 \, \sin\left(b x + a\right) + 1\right) - {\left(36 \, \cos\left(6 \, b x + 6 \, a\right) - 36 \, \cos\left(4 \, b x + 4 \, a\right) - 36 \, \cos\left(2 \, b x + 2 \, a\right) + 36 i \, \sin\left(6 \, b x + 6 \, a\right) - 36 i \, \sin\left(4 \, b x + 4 \, a\right) - 36 i \, \sin\left(2 \, b x + 2 \, a\right) + 36\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) + {\left(36 \, \cos\left(6 \, b x + 6 \, a\right) - 36 \, \cos\left(4 \, b x + 4 \, a\right) - 36 \, \cos\left(2 \, b x + 2 \, a\right) + 36 i \, \sin\left(6 \, b x + 6 \, a\right) - 36 i \, \sin\left(4 \, b x + 4 \, a\right) - 36 i \, \sin\left(2 \, b x + 2 \, a\right) + 36\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) - {\left(-24 i \, \cos\left(6 \, b x + 6 \, a\right) + 24 i \, \cos\left(4 \, b x + 4 \, a\right) + 24 i \, \cos\left(2 \, b x + 2 \, a\right) + 24 \, \sin\left(6 \, b x + 6 \, a\right) - 24 \, \sin\left(4 \, b x + 4 \, a\right) - 24 \, \sin\left(2 \, b x + 2 \, a\right) - 24 i\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) - {\left(24 i \, \cos\left(6 \, b x + 6 \, a\right) - 24 i \, \cos\left(4 \, b x + 4 \, a\right) - 24 i \, \cos\left(2 \, b x + 2 \, a\right) - 24 \, \sin\left(6 \, b x + 6 \, a\right) + 24 \, \sin\left(4 \, b x + 4 \, a\right) + 24 \, \sin\left(2 \, b x + 2 \, a\right) + 24 i\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, a\right)}) - {\left(-36 i \, b x \cos\left(6 \, b x + 6 \, a\right) + 36 i \, b x \cos\left(4 \, b x + 4 \, a\right) + 36 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 36 \, b x \sin\left(6 \, b x + 6 \, a\right) - 36 \, b x \sin\left(4 \, b x + 4 \, a\right) - 36 \, b x \sin\left(2 \, b x + 2 \, a\right) - 36 i \, b x\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(36 i \, b x \cos\left(6 \, b x + 6 \, a\right) - 36 i \, b x \cos\left(4 \, b x + 4 \, a\right) - 36 i \, b x \cos\left(2 \, b x + 2 \, a\right) - 36 \, b x \sin\left(6 \, b x + 6 \, a\right) + 36 \, b x \sin\left(4 \, b x + 4 \, a\right) + 36 \, b x \sin\left(2 \, b x + 2 \, a\right) + 36 i \, b x\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(12 \, {\left(b x + a\right)}^{3} - {\left(b x + a\right)}^{2} {\left(36 \, a + 12 i\right)} + 12 \, {\left(3 \, a^{2} + 2 i \, a\right)} {\left(b x + a\right)} - 12 i \, a^{2}\right)} \sin\left(5 \, b x + 5 \, a\right) - 8 \, {\left({\left(b x + a\right)}^{3} - 3 \, {\left(b x + a\right)}^{2} a + 3 \, {\left(b x + a\right)} a^{2}\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)}^{3} - {\left(b x + a\right)}^{2} {\left(36 \, a - 12 i\right)} + 12 \, {\left(3 \, a^{2} - 2 i \, a\right)} {\left(b x + a\right)} + 12 i \, a^{2}\right)} \sin\left(b x + a\right)\right)}}{-4 i \, \cos\left(6 \, b x + 6 \, a\right) + 4 i \, \cos\left(4 \, b x + 4 \, a\right) + 4 i \, \cos\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(4 \, b x + 4 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right) - 4 i}}{4 \, b^{4}}"," ",0,"-1/4*(a^3*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1)) - 4*((12*(b*x + a)^2 - 24*(b*x + a)*a + 12*a^2 + 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*cos(6*b*x + 6*a) - 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*cos(4*b*x + 4*a) - 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*cos(2*b*x + 2*a) - (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a - 12*I*a^2)*sin(6*b*x + 6*a) - (12*I*(b*x + a)^2 - 24*I*(b*x + a)*a + 12*I*a^2)*sin(4*b*x + 4*a) - (12*I*(b*x + a)^2 - 24*I*(b*x + a)*a + 12*I*a^2)*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (12*(b*x + a)^2 - 24*(b*x + a)*a + 12*a^2 + 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*cos(6*b*x + 6*a) - 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*cos(4*b*x + 4*a) - 12*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*cos(2*b*x + 2*a) - (-12*I*(b*x + a)^2 + 24*I*(b*x + a)*a - 12*I*a^2)*sin(6*b*x + 6*a) - (12*I*(b*x + a)^2 - 24*I*(b*x + a)*a + 12*I*a^2)*sin(4*b*x + 4*a) - (12*I*(b*x + a)^2 - 24*I*(b*x + a)*a + 12*I*a^2)*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) - (6*(b*x + a)^3 - 18*(b*x + a)^2*a + 6*(3*a^2 + 2)*(b*x + a) + 6*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*cos(6*b*x + 6*a) - 6*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*cos(4*b*x + 4*a) - 6*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + (18*I*a^2 + 12*I)*(b*x + a) - 12*I*a)*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a + (-18*I*a^2 - 12*I)*(b*x + a) + 12*I*a)*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a + (-18*I*a^2 - 12*I)*(b*x + a) + 12*I*a)*sin(2*b*x + 2*a) - 12*a)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (12*a*cos(6*b*x + 6*a) - 12*a*cos(4*b*x + 4*a) - 12*a*cos(2*b*x + 2*a) + 12*I*a*sin(6*b*x + 6*a) - 12*I*a*sin(4*b*x + 4*a) - 12*I*a*sin(2*b*x + 2*a) + 12*a)*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*(b*x + a)^3 - 18*(b*x + a)^2*a + 6*(3*a^2 + 2)*(b*x + a) + 6*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a))*cos(6*b*x + 6*a) - 6*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a))*cos(4*b*x + 4*a) - 6*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^3 - 18*I*(b*x + a)^2*a + (18*I*a^2 + 12*I)*(b*x + a))*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a + (-18*I*a^2 - 12*I)*(b*x + a))*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^3 + 18*I*(b*x + a)^2*a + (-18*I*a^2 - 12*I)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (12*I*(b*x + a)^3 - 12*(b*x + a)^2*(3*I*a - 1) + (36*I*a^2 - 24*a)*(b*x + a) + 12*a^2)*cos(5*b*x + 5*a) - (-8*I*(b*x + a)^3 + 24*I*(b*x + a)^2*a - 24*I*(b*x + a)*a^2)*cos(3*b*x + 3*a) - (12*I*(b*x + a)^3 - 12*(b*x + a)^2*(3*I*a + 1) + (36*I*a^2 + 24*a)*(b*x + a) - 12*a^2)*cos(b*x + a) + (24*b*x*cos(6*b*x + 6*a) - 24*b*x*cos(4*b*x + 4*a) - 24*b*x*cos(2*b*x + 2*a) + 24*I*b*x*sin(6*b*x + 6*a) - 24*I*b*x*sin(4*b*x + 4*a) - 24*I*b*x*sin(2*b*x + 2*a) + 24*b*x)*dilog(I*e^(I*b*x + I*a)) - (24*b*x*cos(6*b*x + 6*a) - 24*b*x*cos(4*b*x + 4*a) - 24*b*x*cos(2*b*x + 2*a) + 24*I*b*x*sin(6*b*x + 6*a) - 24*I*b*x*sin(4*b*x + 4*a) - 24*I*b*x*sin(2*b*x + 2*a) + 24*b*x)*dilog(-I*e^(I*b*x + I*a)) + (18*(b*x + a)^2 - 36*(b*x + a)*a + 18*a^2 + 6*(3*(b*x + a)^2 - 6*(b*x + a)*a + 3*a^2 + 2)*cos(6*b*x + 6*a) - 6*(3*(b*x + a)^2 - 6*(b*x + a)*a + 3*a^2 + 2)*cos(4*b*x + 4*a) - 6*(3*(b*x + a)^2 - 6*(b*x + a)*a + 3*a^2 + 2)*cos(2*b*x + 2*a) - (-18*I*(b*x + a)^2 + 36*I*(b*x + a)*a - 18*I*a^2 - 12*I)*sin(6*b*x + 6*a) - (18*I*(b*x + a)^2 - 36*I*(b*x + a)*a + 18*I*a^2 + 12*I)*sin(4*b*x + 4*a) - (18*I*(b*x + a)^2 - 36*I*(b*x + a)*a + 18*I*a^2 + 12*I)*sin(2*b*x + 2*a) + 12)*dilog(-e^(I*b*x + I*a)) - (18*(b*x + a)^2 - 36*(b*x + a)*a + 18*a^2 + 6*(3*(b*x + a)^2 - 6*(b*x + a)*a + 3*a^2 + 2)*cos(6*b*x + 6*a) - 6*(3*(b*x + a)^2 - 6*(b*x + a)*a + 3*a^2 + 2)*cos(4*b*x + 4*a) - 6*(3*(b*x + a)^2 - 6*(b*x + a)*a + 3*a^2 + 2)*cos(2*b*x + 2*a) + (18*I*(b*x + a)^2 - 36*I*(b*x + a)*a + 18*I*a^2 + 12*I)*sin(6*b*x + 6*a) + (-18*I*(b*x + a)^2 + 36*I*(b*x + a)*a - 18*I*a^2 - 12*I)*sin(4*b*x + 4*a) + (-18*I*(b*x + a)^2 + 36*I*(b*x + a)*a - 18*I*a^2 - 12*I)*sin(2*b*x + 2*a) + 12)*dilog(e^(I*b*x + I*a)) - (-3*I*(b*x + a)^3 + 9*I*(b*x + a)^2*a + (-9*I*a^2 - 6*I)*(b*x + a) + (-3*I*(b*x + a)^3 + 9*I*(b*x + a)^2*a + (-9*I*a^2 - 6*I)*(b*x + a) + 6*I*a)*cos(6*b*x + 6*a) + (3*I*(b*x + a)^3 - 9*I*(b*x + a)^2*a + (9*I*a^2 + 6*I)*(b*x + a) - 6*I*a)*cos(4*b*x + 4*a) + (3*I*(b*x + a)^3 - 9*I*(b*x + a)^2*a + (9*I*a^2 + 6*I)*(b*x + a) - 6*I*a)*cos(2*b*x + 2*a) + 3*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*sin(6*b*x + 6*a) - 3*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*sin(4*b*x + 4*a) - 3*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*sin(2*b*x + 2*a) + 6*I*a)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (3*I*(b*x + a)^3 - 9*I*(b*x + a)^2*a + (9*I*a^2 + 6*I)*(b*x + a) + (3*I*(b*x + a)^3 - 9*I*(b*x + a)^2*a + (9*I*a^2 + 6*I)*(b*x + a) - 6*I*a)*cos(6*b*x + 6*a) + (-3*I*(b*x + a)^3 + 9*I*(b*x + a)^2*a + (-9*I*a^2 - 6*I)*(b*x + a) + 6*I*a)*cos(4*b*x + 4*a) + (-3*I*(b*x + a)^3 + 9*I*(b*x + a)^2*a + (-9*I*a^2 - 6*I)*(b*x + a) + 6*I*a)*cos(2*b*x + 2*a) - 3*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*sin(6*b*x + 6*a) + 3*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*sin(4*b*x + 4*a) + 3*((b*x + a)^3 - 3*(b*x + a)^2*a + (3*a^2 + 2)*(b*x + a) - 2*a)*sin(2*b*x + 2*a) - 6*I*a)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a - 6*I*a^2 + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a - 6*I*a^2)*cos(6*b*x + 6*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + 6*I*a^2)*cos(4*b*x + 4*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + 6*I*a^2)*cos(2*b*x + 2*a) + 6*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*sin(6*b*x + 6*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*sin(4*b*x + 4*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + 6*I*a^2 + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + 6*I*a^2)*cos(6*b*x + 6*a) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a - 6*I*a^2)*cos(4*b*x + 4*a) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a - 6*I*a^2)*cos(2*b*x + 2*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*sin(6*b*x + 6*a) + 6*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*sin(4*b*x + 4*a) + 6*((b*x + a)^2 - 2*(b*x + a)*a + a^2)*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (36*cos(6*b*x + 6*a) - 36*cos(4*b*x + 4*a) - 36*cos(2*b*x + 2*a) + 36*I*sin(6*b*x + 6*a) - 36*I*sin(4*b*x + 4*a) - 36*I*sin(2*b*x + 2*a) + 36)*polylog(4, -e^(I*b*x + I*a)) + (36*cos(6*b*x + 6*a) - 36*cos(4*b*x + 4*a) - 36*cos(2*b*x + 2*a) + 36*I*sin(6*b*x + 6*a) - 36*I*sin(4*b*x + 4*a) - 36*I*sin(2*b*x + 2*a) + 36)*polylog(4, e^(I*b*x + I*a)) - (-24*I*cos(6*b*x + 6*a) + 24*I*cos(4*b*x + 4*a) + 24*I*cos(2*b*x + 2*a) + 24*sin(6*b*x + 6*a) - 24*sin(4*b*x + 4*a) - 24*sin(2*b*x + 2*a) - 24*I)*polylog(3, I*e^(I*b*x + I*a)) - (24*I*cos(6*b*x + 6*a) - 24*I*cos(4*b*x + 4*a) - 24*I*cos(2*b*x + 2*a) - 24*sin(6*b*x + 6*a) + 24*sin(4*b*x + 4*a) + 24*sin(2*b*x + 2*a) + 24*I)*polylog(3, -I*e^(I*b*x + I*a)) - (-36*I*b*x*cos(6*b*x + 6*a) + 36*I*b*x*cos(4*b*x + 4*a) + 36*I*b*x*cos(2*b*x + 2*a) + 36*b*x*sin(6*b*x + 6*a) - 36*b*x*sin(4*b*x + 4*a) - 36*b*x*sin(2*b*x + 2*a) - 36*I*b*x)*polylog(3, -e^(I*b*x + I*a)) - (36*I*b*x*cos(6*b*x + 6*a) - 36*I*b*x*cos(4*b*x + 4*a) - 36*I*b*x*cos(2*b*x + 2*a) - 36*b*x*sin(6*b*x + 6*a) + 36*b*x*sin(4*b*x + 4*a) + 36*b*x*sin(2*b*x + 2*a) + 36*I*b*x)*polylog(3, e^(I*b*x + I*a)) + (12*(b*x + a)^3 - (b*x + a)^2*(36*a + 12*I) + 12*(3*a^2 + 2*I*a)*(b*x + a) - 12*I*a^2)*sin(5*b*x + 5*a) - 8*((b*x + a)^3 - 3*(b*x + a)^2*a + 3*(b*x + a)*a^2)*sin(3*b*x + 3*a) + (12*(b*x + a)^3 - (b*x + a)^2*(36*a - 12*I) + 12*(3*a^2 - 2*I*a)*(b*x + a) + 12*I*a^2)*sin(b*x + a))/(-4*I*cos(6*b*x + 6*a) + 4*I*cos(4*b*x + 4*a) + 4*I*cos(2*b*x + 2*a) + 4*sin(6*b*x + 6*a) - 4*sin(4*b*x + 4*a) - 4*sin(2*b*x + 2*a) - 4*I))/b^4","B",0
286,1,2219,0,0.743425," ","integrate(x^2*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(b x + a\right)^{2} - 2\right)}}{\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)} - 3 \, \log\left(\cos\left(b x + a\right) + 1\right) + 3 \, \log\left(\cos\left(b x + a\right) - 1\right)\right)} + \frac{4 \, {\left({\left(8 \, b x \cos\left(6 \, b x + 6 \, a\right) - 8 \, b x \cos\left(4 \, b x + 4 \, a\right) - 8 \, b x \cos\left(2 \, b x + 2 \, a\right) + 8 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 8 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 8 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 8 \, b x\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(8 \, b x \cos\left(6 \, b x + 6 \, a\right) - 8 \, b x \cos\left(4 \, b x + 4 \, a\right) - 8 \, b x \cos\left(2 \, b x + 2 \, a\right) + 8 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 8 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 8 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 8 \, b x\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{2} - 12 \, {\left(b x + a\right)} a + 2 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \cos\left(4 \, b x + 4 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a + 4 i\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a - 4 i\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a - 4 i\right)} \sin\left(2 \, b x + 2 \, a\right) + 4\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) + 4 i \, \sin\left(6 \, b x + 6 \, a\right) - 4 i \, \sin\left(4 \, b x + 4 \, a\right) - 4 i \, \sin\left(2 \, b x + 2 \, a\right) + 4\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} - 12 \, {\left(b x + a\right)} a + 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} - 12 i \, {\left(b x + a\right)} a\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} a\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 i \, {\left(b x + a\right)}^{2} - 8 \, {\left(b x + a\right)} {\left(3 i \, a - 1\right)} - 8 \, a\right)} \cos\left(5 \, b x + 5 \, a\right) - {\left(-8 i \, {\left(b x + a\right)}^{2} + 16 i \, {\left(b x + a\right)} a\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(12 i \, {\left(b x + a\right)}^{2} - 8 \, {\left(b x + a\right)} {\left(3 i \, a + 1\right)} + 8 \, a\right)} \cos\left(b x + a\right) + {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 8 \, \cos\left(4 \, b x + 4 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right) + 8 i \, \sin\left(6 \, b x + 6 \, a\right) - 8 i \, \sin\left(4 \, b x + 4 \, a\right) - 8 i \, \sin\left(2 \, b x + 2 \, a\right) + 8\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(8 \, \cos\left(6 \, b x + 6 \, a\right) - 8 \, \cos\left(4 \, b x + 4 \, a\right) - 8 \, \cos\left(2 \, b x + 2 \, a\right) + 8 i \, \sin\left(6 \, b x + 6 \, a\right) - 8 i \, \sin\left(4 \, b x + 4 \, a\right) - 8 i \, \sin\left(2 \, b x + 2 \, a\right) + 8\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left(12 \, b x \cos\left(6 \, b x + 6 \, a\right) - 12 \, b x \cos\left(4 \, b x + 4 \, a\right) - 12 \, b x \cos\left(2 \, b x + 2 \, a\right) + 12 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 12 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 12 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 12 \, b x\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(12 \, b x \cos\left(6 \, b x + 6 \, a\right) - 12 \, b x \cos\left(4 \, b x + 4 \, a\right) - 12 \, b x \cos\left(2 \, b x + 2 \, a\right) + 12 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 12 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 12 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 12 \, b x\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) - {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a + {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a - 2 i\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{2} - 6 i \, {\left(b x + a\right)} a + 2 i\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{2} - 6 i \, {\left(b x + a\right)} a + 2 i\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \sin\left(2 \, b x + 2 \, a\right) - 2 i\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} - 6 i \, {\left(b x + a\right)} a + {\left(3 i \, {\left(b x + a\right)}^{2} - 6 i \, {\left(b x + a\right)} a + 2 i\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a - 2 i\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} + 6 i \, {\left(b x + a\right)} a - 2 i\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} a + 2\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 i\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 \, b x \cos\left(6 \, b x + 6 \, a\right) + 4 i \, b x \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 4 \, b x \sin\left(6 \, b x + 6 \, a\right) - 4 \, b x \sin\left(4 \, b x + 4 \, a\right) - 4 \, b x \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b x\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) - {\left(4 i \, b x \cos\left(6 \, b x + 6 \, a\right) - 4 i \, b x \cos\left(4 \, b x + 4 \, a\right) - 4 i \, b x \cos\left(2 \, b x + 2 \, a\right) - 4 \, b x \sin\left(6 \, b x + 6 \, a\right) + 4 \, b x \sin\left(4 \, b x + 4 \, a\right) + 4 \, b x \sin\left(2 \, b x + 2 \, a\right) + 4 i \, b x\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) - {\left(-12 i \, \cos\left(6 \, b x + 6 \, a\right) + 12 i \, \cos\left(4 \, b x + 4 \, a\right) + 12 i \, \cos\left(2 \, b x + 2 \, a\right) + 12 \, \sin\left(6 \, b x + 6 \, a\right) - 12 \, \sin\left(4 \, b x + 4 \, a\right) - 12 \, \sin\left(2 \, b x + 2 \, a\right) - 12 i\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - {\left(12 i \, \cos\left(6 \, b x + 6 \, a\right) - 12 i \, \cos\left(4 \, b x + 4 \, a\right) - 12 i \, \cos\left(2 \, b x + 2 \, a\right) - 12 \, \sin\left(6 \, b x + 6 \, a\right) + 12 \, \sin\left(4 \, b x + 4 \, a\right) + 12 \, \sin\left(2 \, b x + 2 \, a\right) + 12 i\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(12 \, {\left(b x + a\right)}^{2} - {\left(b x + a\right)} {\left(24 \, a + 8 i\right)} + 8 i \, a\right)} \sin\left(5 \, b x + 5 \, a\right) - 8 \, {\left({\left(b x + a\right)}^{2} - 2 \, {\left(b x + a\right)} a\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(12 \, {\left(b x + a\right)}^{2} - {\left(b x + a\right)} {\left(24 \, a - 8 i\right)} - 8 i \, a\right)} \sin\left(b x + a\right)\right)}}{-4 i \, \cos\left(6 \, b x + 6 \, a\right) + 4 i \, \cos\left(4 \, b x + 4 \, a\right) + 4 i \, \cos\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(6 \, b x + 6 \, a\right) - 4 \, \sin\left(4 \, b x + 4 \, a\right) - 4 \, \sin\left(2 \, b x + 2 \, a\right) - 4 i}}{4 \, b^{3}}"," ",0,"1/4*(a^2*(2*(3*cos(b*x + a)^2 - 2)/(cos(b*x + a)^3 - cos(b*x + a)) - 3*log(cos(b*x + a) + 1) + 3*log(cos(b*x + a) - 1)) + 4*((8*b*x*cos(6*b*x + 6*a) - 8*b*x*cos(4*b*x + 4*a) - 8*b*x*cos(2*b*x + 2*a) + 8*I*b*x*sin(6*b*x + 6*a) - 8*I*b*x*sin(4*b*x + 4*a) - 8*I*b*x*sin(2*b*x + 2*a) + 8*b*x)*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (8*b*x*cos(6*b*x + 6*a) - 8*b*x*cos(4*b*x + 4*a) - 8*b*x*cos(2*b*x + 2*a) + 8*I*b*x*sin(6*b*x + 6*a) - 8*I*b*x*sin(4*b*x + 4*a) - 8*I*b*x*sin(2*b*x + 2*a) + 8*b*x)*arctan2(cos(b*x + a), -sin(b*x + a) + 1) - (6*(b*x + a)^2 - 12*(b*x + a)*a + 2*(3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*cos(6*b*x + 6*a) - 2*(3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*cos(4*b*x + 4*a) - 2*(3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a + 4*I)*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a - 4*I)*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a - 4*I)*sin(2*b*x + 2*a) + 4)*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (4*cos(6*b*x + 6*a) - 4*cos(4*b*x + 4*a) - 4*cos(2*b*x + 2*a) + 4*I*sin(6*b*x + 6*a) - 4*I*sin(4*b*x + 4*a) - 4*I*sin(2*b*x + 2*a) + 4)*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (6*(b*x + a)^2 - 12*(b*x + a)*a + 6*((b*x + a)^2 - 2*(b*x + a)*a)*cos(6*b*x + 6*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a)*cos(4*b*x + 4*a) - 6*((b*x + a)^2 - 2*(b*x + a)*a)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2 - 12*I*(b*x + a)*a)*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*sin(4*b*x + 4*a) + (-6*I*(b*x + a)^2 + 12*I*(b*x + a)*a)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (12*I*(b*x + a)^2 - 8*(b*x + a)*(3*I*a - 1) - 8*a)*cos(5*b*x + 5*a) - (-8*I*(b*x + a)^2 + 16*I*(b*x + a)*a)*cos(3*b*x + 3*a) - (12*I*(b*x + a)^2 - 8*(b*x + a)*(3*I*a + 1) + 8*a)*cos(b*x + a) + (8*cos(6*b*x + 6*a) - 8*cos(4*b*x + 4*a) - 8*cos(2*b*x + 2*a) + 8*I*sin(6*b*x + 6*a) - 8*I*sin(4*b*x + 4*a) - 8*I*sin(2*b*x + 2*a) + 8)*dilog(I*e^(I*b*x + I*a)) - (8*cos(6*b*x + 6*a) - 8*cos(4*b*x + 4*a) - 8*cos(2*b*x + 2*a) + 8*I*sin(6*b*x + 6*a) - 8*I*sin(4*b*x + 4*a) - 8*I*sin(2*b*x + 2*a) + 8)*dilog(-I*e^(I*b*x + I*a)) + (12*b*x*cos(6*b*x + 6*a) - 12*b*x*cos(4*b*x + 4*a) - 12*b*x*cos(2*b*x + 2*a) + 12*I*b*x*sin(6*b*x + 6*a) - 12*I*b*x*sin(4*b*x + 4*a) - 12*I*b*x*sin(2*b*x + 2*a) + 12*b*x)*dilog(-e^(I*b*x + I*a)) - (12*b*x*cos(6*b*x + 6*a) - 12*b*x*cos(4*b*x + 4*a) - 12*b*x*cos(2*b*x + 2*a) + 12*I*b*x*sin(6*b*x + 6*a) - 12*I*b*x*sin(4*b*x + 4*a) - 12*I*b*x*sin(2*b*x + 2*a) + 12*b*x)*dilog(e^(I*b*x + I*a)) - (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a + (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a - 2*I)*cos(6*b*x + 6*a) + (3*I*(b*x + a)^2 - 6*I*(b*x + a)*a + 2*I)*cos(4*b*x + 4*a) + (3*I*(b*x + a)^2 - 6*I*(b*x + a)*a + 2*I)*cos(2*b*x + 2*a) + (3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*sin(6*b*x + 6*a) - (3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*sin(4*b*x + 4*a) - (3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*sin(2*b*x + 2*a) - 2*I)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - (3*I*(b*x + a)^2 - 6*I*(b*x + a)*a + (3*I*(b*x + a)^2 - 6*I*(b*x + a)*a + 2*I)*cos(6*b*x + 6*a) + (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a - 2*I)*cos(4*b*x + 4*a) + (-3*I*(b*x + a)^2 + 6*I*(b*x + a)*a - 2*I)*cos(2*b*x + 2*a) - (3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*sin(6*b*x + 6*a) + (3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*sin(4*b*x + 4*a) + (3*(b*x + a)^2 - 6*(b*x + a)*a + 2)*sin(2*b*x + 2*a) + 2*I)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (-4*I*b*x*cos(6*b*x + 6*a) + 4*I*b*x*cos(4*b*x + 4*a) + 4*I*b*x*cos(2*b*x + 2*a) + 4*b*x*sin(6*b*x + 6*a) - 4*b*x*sin(4*b*x + 4*a) - 4*b*x*sin(2*b*x + 2*a) - 4*I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) - (4*I*b*x*cos(6*b*x + 6*a) - 4*I*b*x*cos(4*b*x + 4*a) - 4*I*b*x*cos(2*b*x + 2*a) - 4*b*x*sin(6*b*x + 6*a) + 4*b*x*sin(4*b*x + 4*a) + 4*b*x*sin(2*b*x + 2*a) + 4*I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) - (-12*I*cos(6*b*x + 6*a) + 12*I*cos(4*b*x + 4*a) + 12*I*cos(2*b*x + 2*a) + 12*sin(6*b*x + 6*a) - 12*sin(4*b*x + 4*a) - 12*sin(2*b*x + 2*a) - 12*I)*polylog(3, -e^(I*b*x + I*a)) - (12*I*cos(6*b*x + 6*a) - 12*I*cos(4*b*x + 4*a) - 12*I*cos(2*b*x + 2*a) - 12*sin(6*b*x + 6*a) + 12*sin(4*b*x + 4*a) + 12*sin(2*b*x + 2*a) + 12*I)*polylog(3, e^(I*b*x + I*a)) + (12*(b*x + a)^2 - (b*x + a)*(24*a + 8*I) + 8*I*a)*sin(5*b*x + 5*a) - 8*((b*x + a)^2 - 2*(b*x + a)*a)*sin(3*b*x + 3*a) + (12*(b*x + a)^2 - (b*x + a)*(24*a - 8*I) - 8*I*a)*sin(b*x + a))/(-4*I*cos(6*b*x + 6*a) + 4*I*cos(4*b*x + 4*a) + 4*I*cos(2*b*x + 2*a) + 4*sin(6*b*x + 6*a) - 4*sin(4*b*x + 4*a) - 4*sin(2*b*x + 2*a) - 4*I))/b^3","B",0
287,1,1184,0,0.685429," ","integrate(x*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{8 i \, b x \cos\left(3 \, b x + 3 \, a\right) - 8 \, b x \sin\left(3 \, b x + 3 \, a\right) - {\left(4 \, \cos\left(6 \, b x + 6 \, a\right) - 4 \, \cos\left(4 \, b x + 4 \, a\right) - 4 \, \cos\left(2 \, b x + 2 \, a\right) + 4 i \, \sin\left(6 \, b x + 6 \, a\right) - 4 i \, \sin\left(4 \, b x + 4 \, a\right) - 4 i \, \sin\left(2 \, b x + 2 \, a\right) + 4\right)} \arctan\left(\frac{2 \, {\left(\cos\left(b x + 2 \, a\right) \cos\left(a\right) + \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}, \frac{\cos\left(b x + 2 \, a\right)^{2} - \cos\left(a\right)^{2} + \sin\left(b x + 2 \, a\right)^{2} - \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) - {\left(6 \, b x \cos\left(6 \, b x + 6 \, a\right) - 6 \, b x \cos\left(4 \, b x + 4 \, a\right) - 6 \, b x \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 6 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 6 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 6 \, b x\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(6 \, b x \cos\left(6 \, b x + 6 \, a\right) - 6 \, b x \cos\left(4 \, b x + 4 \, a\right) - 6 \, b x \cos\left(2 \, b x + 2 \, a\right) + 6 i \, b x \sin\left(6 \, b x + 6 \, a\right) - 6 i \, b x \sin\left(4 \, b x + 4 \, a\right) - 6 i \, b x \sin\left(2 \, b x + 2 \, a\right) + 6 \, b x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 4 \, {\left(3 i \, b x + 1\right)} \cos\left(5 \, b x + 5 \, a\right) - 4 \, {\left(3 i \, b x - 1\right)} \cos\left(b x + a\right) + {\left(6 \, \cos\left(6 \, b x + 6 \, a\right) - 6 \, \cos\left(4 \, b x + 4 \, a\right) - 6 \, \cos\left(2 \, b x + 2 \, a\right) + 6 i \, \sin\left(6 \, b x + 6 \, a\right) - 6 i \, \sin\left(4 \, b x + 4 \, a\right) - 6 i \, \sin\left(2 \, b x + 2 \, a\right) + 6\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(6 \, \cos\left(6 \, b x + 6 \, a\right) - 6 \, \cos\left(4 \, b x + 4 \, a\right) - 6 \, \cos\left(2 \, b x + 2 \, a\right) + 6 i \, \sin\left(6 \, b x + 6 \, a\right) - 6 i \, \sin\left(4 \, b x + 4 \, a\right) - 6 i \, \sin\left(2 \, b x + 2 \, a\right) + 6\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(3 i \, b x \cos\left(6 \, b x + 6 \, a\right) - 3 i \, b x \cos\left(4 \, b x + 4 \, a\right) - 3 i \, b x \cos\left(2 \, b x + 2 \, a\right) - 3 \, b x \sin\left(6 \, b x + 6 \, a\right) + 3 \, b x \sin\left(4 \, b x + 4 \, a\right) + 3 \, b x \sin\left(2 \, b x + 2 \, a\right) + 3 i \, b x\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 \, b x \cos\left(6 \, b x + 6 \, a\right) + 3 i \, b x \cos\left(4 \, b x + 4 \, a\right) + 3 i \, b x \cos\left(2 \, b x + 2 \, a\right) + 3 \, b x \sin\left(6 \, b x + 6 \, a\right) - 3 \, b x \sin\left(4 \, b x + 4 \, a\right) - 3 \, b x \sin\left(2 \, b x + 2 \, a\right) - 3 i \, b x\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 \, \cos\left(6 \, b x + 6 \, a\right) + 2 i \, \cos\left(4 \, b x + 4 \, a\right) + 2 i \, \cos\left(2 \, b x + 2 \, a\right) + 2 \, \sin\left(6 \, b x + 6 \, a\right) - 2 \, \sin\left(4 \, b x + 4 \, a\right) - 2 \, \sin\left(2 \, b x + 2 \, a\right) - 2 i\right)} \log\left(\frac{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} - 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} + 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}{\cos\left(b x + 2 \, a\right)^{2} + \cos\left(a\right)^{2} + 2 \, \cos\left(a\right) \sin\left(b x + 2 \, a\right) + \sin\left(b x + 2 \, a\right)^{2} - 2 \, \cos\left(b x + 2 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}}\right) + {\left(12 \, b x - 4 i\right)} \sin\left(5 \, b x + 5 \, a\right) + {\left(12 \, b x + 4 i\right)} \sin\left(b x + a\right)}{-4 i \, b^{2} \cos\left(6 \, b x + 6 \, a\right) + 4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} \sin\left(6 \, b x + 6 \, a\right) - 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 4 i \, b^{2}}"," ",0,"(8*I*b*x*cos(3*b*x + 3*a) - 8*b*x*sin(3*b*x + 3*a) - (4*cos(6*b*x + 6*a) - 4*cos(4*b*x + 4*a) - 4*cos(2*b*x + 2*a) + 4*I*sin(6*b*x + 6*a) - 4*I*sin(4*b*x + 4*a) - 4*I*sin(2*b*x + 2*a) + 4)*arctan2(2*(cos(b*x + 2*a)*cos(a) + sin(b*x + 2*a)*sin(a))/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2), (cos(b*x + 2*a)^2 - cos(a)^2 + sin(b*x + 2*a)^2 - sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) - (6*b*x*cos(6*b*x + 6*a) - 6*b*x*cos(4*b*x + 4*a) - 6*b*x*cos(2*b*x + 2*a) + 6*I*b*x*sin(6*b*x + 6*a) - 6*I*b*x*sin(4*b*x + 4*a) - 6*I*b*x*sin(2*b*x + 2*a) + 6*b*x)*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (6*b*x*cos(6*b*x + 6*a) - 6*b*x*cos(4*b*x + 4*a) - 6*b*x*cos(2*b*x + 2*a) + 6*I*b*x*sin(6*b*x + 6*a) - 6*I*b*x*sin(4*b*x + 4*a) - 6*I*b*x*sin(2*b*x + 2*a) + 6*b*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 4*(3*I*b*x + 1)*cos(5*b*x + 5*a) - 4*(3*I*b*x - 1)*cos(b*x + a) + (6*cos(6*b*x + 6*a) - 6*cos(4*b*x + 4*a) - 6*cos(2*b*x + 2*a) + 6*I*sin(6*b*x + 6*a) - 6*I*sin(4*b*x + 4*a) - 6*I*sin(2*b*x + 2*a) + 6)*dilog(-e^(I*b*x + I*a)) - (6*cos(6*b*x + 6*a) - 6*cos(4*b*x + 4*a) - 6*cos(2*b*x + 2*a) + 6*I*sin(6*b*x + 6*a) - 6*I*sin(4*b*x + 4*a) - 6*I*sin(2*b*x + 2*a) + 6)*dilog(e^(I*b*x + I*a)) + (3*I*b*x*cos(6*b*x + 6*a) - 3*I*b*x*cos(4*b*x + 4*a) - 3*I*b*x*cos(2*b*x + 2*a) - 3*b*x*sin(6*b*x + 6*a) + 3*b*x*sin(4*b*x + 4*a) + 3*b*x*sin(2*b*x + 2*a) + 3*I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (-3*I*b*x*cos(6*b*x + 6*a) + 3*I*b*x*cos(4*b*x + 4*a) + 3*I*b*x*cos(2*b*x + 2*a) + 3*b*x*sin(6*b*x + 6*a) - 3*b*x*sin(4*b*x + 4*a) - 3*b*x*sin(2*b*x + 2*a) - 3*I*b*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (-2*I*cos(6*b*x + 6*a) + 2*I*cos(4*b*x + 4*a) + 2*I*cos(2*b*x + 2*a) + 2*sin(6*b*x + 6*a) - 2*sin(4*b*x + 4*a) - 2*sin(2*b*x + 2*a) - 2*I)*log((cos(b*x + 2*a)^2 + cos(a)^2 - 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 + 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)/(cos(b*x + 2*a)^2 + cos(a)^2 + 2*cos(a)*sin(b*x + 2*a) + sin(b*x + 2*a)^2 - 2*cos(b*x + 2*a)*sin(a) + sin(a)^2)) + (12*b*x - 4*I)*sin(5*b*x + 5*a) + (12*b*x + 4*I)*sin(b*x + a))/(-4*I*b^2*cos(6*b*x + 6*a) + 4*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 4*b^2*sin(6*b*x + 6*a) - 4*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) - 4*I*b^2)","B",0
288,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/x,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/x^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right)^{2} \tan\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)^2*tan(b*x + a), x)","F",0
291,1,3438,0,0.684440," ","integrate((d*x+c)^4*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""maxima"")","\frac{c^{4} \tan\left(b x + a\right)^{2} - \frac{4 \, a c^{3} d \tan\left(b x + a\right)^{2}}{b} + \frac{6 \, a^{2} c^{2} d^{2} \tan\left(b x + a\right)^{2}}{b^{2}} - \frac{4 \, a^{3} c d^{3} \tan\left(b x + a\right)^{2}}{b^{3}} + \frac{a^{4} d^{4} \tan\left(b x + a\right)^{2}}{b^{4}} + \frac{8 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b} - \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{2}} + \frac{24 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{3}} - \frac{8 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{4}} + \frac{6 \, {\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\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) + 4 \, {\left({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) - b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - a\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{2}} - \frac{12 \, {\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\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) + 4 \, {\left({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) - b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - a\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{3}} + \frac{6 \, {\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\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) + 4 \, {\left({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) - b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - a\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{4}} - \frac{2 \, {\left({\left(6 \, {\left(b x + a\right)}^{2} d^{4} + 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\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^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 4 \, {\left({\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 i \, b c d^{3} - 4 \, {\left(2 i \, a + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{3} - 12 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(6 \, b c d^{3} + 6 \, {\left(b x + a\right)} d^{4} - 6 \, a d^{4} + 6 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, b c d^{3} - 6 i \, {\left(b x + a\right)} d^{4} + 6 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-12 i \, b c d^{3} - 12 i \, {\left(b x + a\right)} d^{4} + 12 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-6 i \, b c d^{3} + 6 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) + {\left(-3 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) - 6 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 3 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) + 6 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 3 i \, d^{4}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(b x + a\right)}^{4} d^{4} + {\left(8 \, b c d^{3} - {\left(8 \, a - 4 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} - {\left(-12 i \, b c d^{3} + 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) - 2 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + b^{4} \sin\left(4 \, b x + 4 \, a\right) + 2 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - i \, b^{4}}}{2 \, b}"," ",0,"1/2*(c^4*tan(b*x + a)^2 - 4*a*c^3*d*tan(b*x + a)^2/b + 6*a^2*c^2*d^2*tan(b*x + a)^2/b^2 - 4*a^3*c*d^3*tan(b*x + a)^2/b^3 + a^4*d^4*tan(b*x + a)^2/b^4 + 8*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*c^3*d/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b) - 24*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*a*c^2*d^2/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^2) + 24*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*a^2*c*d^3/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^3) - 8*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*a^3*d^4/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^4) + 6*(8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 + 4*(b*x + a)^2*cos(2*b*x + 2*a) + 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 4*((b*x + a)^2*sin(2*b*x + 2*a) - b*x - (b*x + a)*cos(2*b*x + 2*a) - a)*sin(4*b*x + 4*a) - 4*(b*x + a)*sin(2*b*x + 2*a))*c^2*d^2/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^2) - 12*(8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 + 4*(b*x + a)^2*cos(2*b*x + 2*a) + 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 4*((b*x + a)^2*sin(2*b*x + 2*a) - b*x - (b*x + a)*cos(2*b*x + 2*a) - a)*sin(4*b*x + 4*a) - 4*(b*x + a)*sin(2*b*x + 2*a))*a*c*d^3/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^3) + 6*(8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 + 4*(b*x + a)^2*cos(2*b*x + 2*a) + 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 4*((b*x + a)^2*sin(2*b*x + 2*a) - b*x - (b*x + a)*cos(2*b*x + 2*a) - a)*sin(4*b*x + 4*a) - 4*(b*x + a)*sin(2*b*x + 2*a))*a^2*d^4/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^4) - 2*((6*(b*x + a)^2*d^4 + 12*(b*c*d^3 - a*d^4)*(b*x + a) + 6*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + 12*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (12*I*(b*x + a)^2*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 4*((b*x + a)^3*d^4 + 3*(b*c*d^3 - a*d^4)*(b*x + a)^2)*cos(4*b*x + 4*a) + (2*I*(b*x + a)^4*d^4 + (8*I*b*c*d^3 - 4*(2*I*a + 1)*d^4)*(b*x + a)^3 - 12*(b*c*d^3 - a*d^4)*(b*x + a)^2)*cos(2*b*x + 2*a) - (6*b*c*d^3 + 6*(b*x + a)*d^4 - 6*a*d^4 + 6*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) + 12*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-6*I*b*c*d^3 - 6*I*(b*x + a)*d^4 + 6*I*a*d^4)*sin(4*b*x + 4*a) - (-12*I*b*c*d^3 - 12*I*(b*x + a)*d^4 + 12*I*a*d^4)*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*I*a)) + (-3*I*(b*x + a)^2*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a) + (-3*I*(b*x + a)^2*d^4 + (-6*I*b*c*d^3 + 6*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (-6*I*(b*x + a)^2*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) + 6*((b*x + a)^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (-3*I*d^4*cos(4*b*x + 4*a) - 6*I*d^4*cos(2*b*x + 2*a) + 3*d^4*sin(4*b*x + 4*a) + 6*d^4*sin(2*b*x + 2*a) - 3*I*d^4)*polylog(3, -e^(2*I*b*x + 2*I*a)) + (-4*I*(b*x + a)^3*d^4 + (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2)*sin(4*b*x + 4*a) - (2*(b*x + a)^4*d^4 + (8*b*c*d^3 - (8*a - 4*I)*d^4)*(b*x + a)^3 - (-12*I*b*c*d^3 + 12*I*a*d^4)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-I*b^4*cos(4*b*x + 4*a) - 2*I*b^4*cos(2*b*x + 2*a) + b^4*sin(4*b*x + 4*a) + 2*b^4*sin(2*b*x + 2*a) - I*b^4))/b","B",0
292,1,667,0,0.629343," ","integrate((d*x+c)^3*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""maxima"")","-\frac{6 \, b^{2} c^{2} d + {\left(6 \, b d^{3} x + 6 \, b c d^{2} + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, b^{3} d^{3} x^{3} + 4 i \, b^{3} c^{3} + 6 \, b^{2} c^{2} d + {\left(12 i \, b^{3} c d^{2} - 6 \, b^{2} d^{3}\right)} x^{2} + {\left(12 i \, b^{3} c^{2} d - 12 \, b^{2} c d^{2}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(3 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 6 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 3 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 6 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 3 \, d^{3}\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(-3 i \, b d^{3} x - 3 i \, b c d^{2} + {\left(-3 i \, b d^{3} x - 3 i \, b c d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(b d^{3} x + b c d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(4 \, b^{3} d^{3} x^{3} + 4 \, b^{3} c^{3} - 6 i \, b^{2} c^{2} d + 6 \, {\left(2 \, b^{3} c d^{2} + i \, b^{2} d^{3}\right)} x^{2} + 12 \, {\left(b^{3} c^{2} d + i \, b^{2} c d^{2}\right)} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{-2 i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) - 4 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{4} \sin\left(4 \, b x + 4 \, a\right) + 4 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{4}}"," ",0,"-(6*b^2*c^2*d + (6*b*d^3*x + 6*b*c*d^2 + 6*(b*d^3*x + b*c*d^2)*cos(4*b*x + 4*a) + 12*(b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*sin(4*b*x + 4*a) + (12*I*b*d^3*x + 12*I*b*c*d^2)*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x)*cos(4*b*x + 4*a) + (4*I*b^3*d^3*x^3 + 4*I*b^3*c^3 + 6*b^2*c^2*d + (12*I*b^3*c*d^2 - 6*b^2*d^3)*x^2 + (12*I*b^3*c^2*d - 12*b^2*c*d^2)*x)*cos(2*b*x + 2*a) - (3*d^3*cos(4*b*x + 4*a) + 6*d^3*cos(2*b*x + 2*a) + 3*I*d^3*sin(4*b*x + 4*a) + 6*I*d^3*sin(2*b*x + 2*a) + 3*d^3)*dilog(-e^(2*I*b*x + 2*I*a)) + (-3*I*b*d^3*x - 3*I*b*c*d^2 + (-3*I*b*d^3*x - 3*I*b*c*d^2)*cos(4*b*x + 4*a) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(2*b*x + 2*a) + 3*(b*d^3*x + b*c*d^2)*sin(4*b*x + 4*a) + 6*(b*d^3*x + b*c*d^2)*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x)*sin(4*b*x + 4*a) - (4*b^3*d^3*x^3 + 4*b^3*c^3 - 6*I*b^2*c^2*d + 6*(2*b^3*c*d^2 + I*b^2*d^3)*x^2 + 12*(b^3*c^2*d + I*b^2*c*d^2)*x)*sin(2*b*x + 2*a))/(-2*I*b^4*cos(4*b*x + 4*a) - 4*I*b^4*cos(2*b*x + 2*a) + 2*b^4*sin(4*b*x + 4*a) + 4*b^4*sin(2*b*x + 2*a) - 2*I*b^4)","B",0
293,1,988,0,0.522584," ","integrate((d*x+c)^2*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""maxima"")","\frac{c^{2} \tan\left(b x + a\right)^{2} - \frac{2 \, a c d \tan\left(b x + a\right)^{2}}{b} + \frac{a^{2} d^{2} \tan\left(b x + a\right)^{2}}{b^{2}} + \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} c d}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b} - \frac{4 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{2}} + \frac{{\left(8 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right)^{2} + 8 \, {\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left({\left(b x + a\right)}^{2} \cos\left(2 \, b x + 2 \, a\right) + {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\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) + 4 \, {\left({\left(b x + a\right)}^{2} \sin\left(2 \, b x + 2 \, a\right) - b x - {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) - a\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b^{2}}}{2 \, b}"," ",0,"1/2*(c^2*tan(b*x + a)^2 - 2*a*c*d*tan(b*x + a)^2/b + a^2*d^2*tan(b*x + a)^2/b^2 + 4*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*c*d/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b) - 4*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*a*d^2/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^2) + (8*(b*x + a)^2*cos(2*b*x + 2*a)^2 + 8*(b*x + a)^2*sin(2*b*x + 2*a)^2 + 4*(b*x + a)^2*cos(2*b*x + 2*a) + 4*((b*x + a)^2*cos(2*b*x + 2*a) + (b*x + a)*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) - (2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 4*((b*x + a)^2*sin(2*b*x + 2*a) - b*x - (b*x + a)*cos(2*b*x + 2*a) - a)*sin(4*b*x + 4*a) - 4*(b*x + a)*sin(2*b*x + 2*a))*d^2/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b^2))/b","B",0
294,1,283,0,0.351358," ","integrate((d*x+c)*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""maxima"")","\frac{c \tan\left(b x + a\right)^{2} - \frac{a d \tan\left(b x + a\right)^{2}}{b} + \frac{2 \, {\left(4 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) - \cos\left(2 \, b x + 2 \, a\right) - 1\right)} \sin\left(4 \, b x + 4 \, a\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} d}{{\left(2 \, {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(4 \, b x + 4 \, a\right) + \cos\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(4 \, b x + 4 \, a\right)^{2} + 4 \, \sin\left(4 \, b x + 4 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, \sin\left(2 \, b x + 2 \, a\right)^{2} + 4 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} b}}{2 \, b}"," ",0,"1/2*(c*tan(b*x + a)^2 - a*d*tan(b*x + a)^2/b + 2*(4*(b*x + a)*cos(2*b*x + 2*a)^2 + 4*(b*x + a)*sin(2*b*x + 2*a)^2 + (2*(b*x + a)*cos(2*b*x + 2*a) + sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*x + a)*cos(2*b*x + 2*a) + (2*(b*x + a)*sin(2*b*x + 2*a) - cos(2*b*x + 2*a) - 1)*sin(4*b*x + 4*a) - sin(2*b*x + 2*a))*d/((2*(2*cos(2*b*x + 2*a) + 1)*cos(4*b*x + 4*a) + cos(4*b*x + 4*a)^2 + 4*cos(2*b*x + 2*a)^2 + sin(4*b*x + 4*a)^2 + 4*sin(4*b*x + 4*a)*sin(2*b*x + 2*a) + 4*sin(2*b*x + 2*a)^2 + 4*cos(2*b*x + 2*a) + 1)*b))/b","B",0
295,-1,0,0,0.000000," ","integrate(sec(b*x+a)^2*tan(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate(sec(b*x+a)^2*tan(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right) \tan\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)*tan(b*x + a)^2, x)","F",0
298,1,3828,0,2.009069," ","integrate((d*x+c)^3*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\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(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\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(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\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)} \cos\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)} \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(i \, 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(-i \, 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 \, \sin\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 \, \sin\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}(i \, 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}(-i \, 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}(i \, 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}(-i \, e^{\left(i \, b x + i \, 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)} \sin\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} + {\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)} \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*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1)) - 3*a*c^2*d*(2*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1))/b + 3*a^2*c*d^2*(2*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1))/b^2 - a^3*d^3*(2*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(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(cos(b*x + a), sin(b*x + a) + 1) + (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(cos(b*x + a), -sin(b*x + a) + 1) - (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))*cos(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))*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(I*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(-I*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*sin(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*sin(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, I*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, -I*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, I*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, -I*e^(I*b*x + I*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))*sin(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 - 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))*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
299,1,1893,0,0.851041," ","integrate((d*x+c)^2*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right)\right)} - \frac{2 \, a c d {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{2 \, \sin\left(b x + a\right)}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right) + 1\right) - \log\left(\sin\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(\cos\left(b x + a\right), \sin\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)} - 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(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\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)} \cos\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)} \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(i \, 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(-i \, 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 \, \sin\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 \, \sin\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}(i \, 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}(-i \, e^{\left(i \, b x + i \, a\right)}) + 4 \, {\left(-i \, {\left(b x + a\right)}^{2} d^{2} - 2 \, b c d + 2 \, a d^{2} + 2 \, {\left(-i \, b c d + {\left(i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\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} + {\left(-8 i \, b c d - 8 \, {\left(-i \, a - 1\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*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1)) - 2*a*c*d*(2*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(b*x + a) - 1))/b + a^2*d^2*(2*sin(b*x + a)/(sin(b*x + a)^2 - 1) + log(sin(b*x + a) + 1) - log(sin(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(cos(b*x + a), sin(b*x + a) + 1) + (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(cos(b*x + a), -sin(b*x + a) + 1) - (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))*cos(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))*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(I*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(-I*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*sin(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*sin(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, I*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, -I*e^(I*b*x + I*a)) + 4*(-I*(b*x + a)^2*d^2 - 2*b*c*d + 2*a*d^2 + 2*(-I*b*c*d + (I*a - 1)*d^2)*(b*x + a))*sin(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 - 8*(-I*a - 1)*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
300,-1,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
301,-1,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
302,-1,0,0,0.000000," ","integrate(sec(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,0,0,0,0.000000," ","integrate((d*x+c)^m*tan(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \tan\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*tan(b*x + a)^3, x)","F",0
304,1,2405,0,1.185872," ","integrate((d*x+c)^3*tan(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)}}{b^{3}} + \frac{2 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{3} + 36 \, b^{2} c^{2} d - 72 \, a b c d^{2} + 36 \, a^{2} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{3} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(16 \, {\left(b x + a\right)}^{3} d^{3} - 36 \, b c d^{2} + 36 \, a d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 36 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)} + 4 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} - 9 \, b c d^{2} + 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 8 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} - 9 \, b c d^{2} + 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(16 i \, {\left(b x + a\right)}^{3} d^{3} - 36 i \, b c d^{2} + 36 i \, a d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + {\left(36 i \, a^{2} - 36 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(32 i \, {\left(b x + a\right)}^{3} d^{3} - 72 i \, b c d^{2} + 72 i \, a d^{3} + {\left(72 i \, b c d^{2} - 72 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d - 144 i \, a b c d^{2} + {\left(72 i \, a^{2} - 72 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)}^{4} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{3} + 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} - 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 \, {\left(b x + a\right)}^{4} d^{3} + 36 \, b^{2} c^{2} d - 72 \, a b c d^{2} + 36 \, a^{2} d^{3} + {\left(24 \, b c d^{2} - {\left(24 \, a - 24 i\right)} d^{3}\right)} {\left(b x + a\right)}^{3} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a - 72 i\right)} b c d^{2} + 36 \, {\left(a^{2} - 2 i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} - {\left(-72 i \, b^{2} c^{2} d - 72 \, {\left(-2 i \, a - 1\right)} b c d^{2} + {\left(-72 i \, a^{2} - 72 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 24 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, {\left(a^{2} - 1\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 4 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, {\left(a^{2} - 1\right)} d^{3} + 6 \, {\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(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 4 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, {\left(a^{2} - 1\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 24 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} + 18 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 48 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-36 i \, a^{2} + 36 i\right)} d^{3} + {\left(-72 i \, b c d^{2} + 72 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(2 i \, b x + 2 i \, a\right)}\right) - {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} + 18 i \, b c d^{2} - 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} + 18 i \, b c d^{2} - 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-16 i \, {\left(b x + a\right)}^{3} d^{3} + 36 i \, b c d^{2} - 36 i \, a d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} + {\left(-36 i \, a^{2} + 36 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} - 9 \, b c d^{2} + 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} - 9 \, b c d^{2} + 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} - 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) - {\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(2 i \, b x + 2 i \, a\right)}) - {\left(-18 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 18 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-36 i \, b c d^{2} - 48 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 12 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(-3 i \, {\left(b x + a\right)}^{4} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}^{3} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} + 36 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b c d^{2} - 72 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-6 i \, {\left(b x + a\right)}^{4} d^{3} - 36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 36 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} - 24 \, {\left(-i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{3} + {\left(-36 i \, b^{2} c^{2} d - 72 \, {\left(-i \, a - 1\right)} b c d^{2} + {\left(-36 i \, a^{2} - 72 \, a + 36 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 \, b^{2} c^{2} d - {\left(144 \, a - 72 i\right)} b c d^{2} + 72 \, {\left(a^{2} - i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-12 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) - 24 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 12 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) + 24 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(c^3*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1)) - 3*a*c^2*d*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1))/b + 3*a^2*c*d^2*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1))/b^2 - a^3*d^3*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1))/b^3 + 2*(3*(b*x + a)^4*d^3 + 36*b^2*c^2*d - 72*a*b*c*d^2 + 36*a^2*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a)^3 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a)^2 - (16*(b*x + a)^3*d^3 - 36*b*c*d^2 + 36*a*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 36*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + a) + 4*(4*(b*x + a)^3*d^3 - 9*b*c*d^2 + 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 8*(4*(b*x + a)^3*d^3 - 9*b*c*d^2 + 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (16*I*(b*x + a)^3*d^3 - 36*I*b*c*d^2 + 36*I*a*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + (36*I*a^2 - 36*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (32*I*(b*x + a)^3*d^3 - 72*I*b*c*d^2 + 72*I*a*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a)^2 + (72*I*b^2*c^2*d - 144*I*a*b*c*d^2 + (72*I*a^2 - 72*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + 3*((b*x + a)^4*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a)^3 + 6*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 2)*d^3)*(b*x + a)^2 - 24*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (6*(b*x + a)^4*d^3 + 36*b^2*c^2*d - 72*a*b*c*d^2 + 36*a^2*d^3 + (24*b*c*d^2 - (24*a - 24*I)*d^3)*(b*x + a)^3 + (36*b^2*c^2*d - (72*a - 72*I)*b*c*d^2 + 36*(a^2 - 2*I*a - 1)*d^3)*(b*x + a)^2 - (-72*I*b^2*c^2*d - 72*(-2*I*a - 1)*b*c*d^2 + (-72*I*a^2 - 72*a)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (18*b^2*c^2*d - 36*a*b*c*d^2 + 24*(b*x + a)^2*d^3 + 18*(a^2 - 1)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 4*(b*x + a)^2*d^3 + 3*(a^2 - 1)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 12*(3*b^2*c^2*d - 6*a*b*c*d^2 + 4*(b*x + a)^2*d^3 + 3*(a^2 - 1)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 24*I*(b*x + a)^2*d^3 + (-18*I*a^2 + 18*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 48*I*(b*x + a)^2*d^3 + (-36*I*a^2 + 36*I)*d^3 + (-72*I*b*c*d^2 + 72*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*I*a)) - (-8*I*(b*x + a)^3*d^3 + 18*I*b*c*d^2 - 18*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 + 18*I)*d^3)*(b*x + a) + (-8*I*(b*x + a)^3*d^3 + 18*I*b*c*d^2 - 18*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 + 18*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-16*I*(b*x + a)^3*d^3 + 36*I*b*c*d^2 - 36*I*a*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 + (-36*I*a^2 + 36*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 2*(4*(b*x + a)^3*d^3 - 9*b*c*d^2 + 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 4*(4*(b*x + a)^3*d^3 - 9*b*c*d^2 + 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 - 1)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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^(2*I*b*x + 2*I*a)) - (-18*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 18*I*a*d^3 + (-18*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 18*I*a*d^3)*cos(4*b*x + 4*a) + (-36*I*b*c*d^2 - 48*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(2*b*x + 2*a) + 6*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(4*b*x + 4*a) + 12*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(2*b*x + 2*a))*polylog(3, -e^(2*I*b*x + 2*I*a)) - (-3*I*(b*x + a)^4*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a)^3 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 + 36*I)*d^3)*(b*x + a)^2 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (-6*I*(b*x + a)^4*d^3 - 36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 36*I*a^2*d^3 + (-24*I*b*c*d^2 - 24*(-I*a - 1)*d^3)*(b*x + a)^3 + (-36*I*b^2*c^2*d - 72*(-I*a - 1)*b*c*d^2 + (-36*I*a^2 - 72*a + 36*I)*d^3)*(b*x + a)^2 + (72*b^2*c^2*d - (144*a - 72*I)*b*c*d^2 + 72*(a^2 - I*a)*d^3)*(b*x + a))*sin(2*b*x + 2*a))/(-12*I*b^3*cos(4*b*x + 4*a) - 24*I*b^3*cos(2*b*x + 2*a) + 12*b^3*sin(4*b*x + 4*a) + 24*b^3*sin(2*b*x + 2*a) - 12*I*b^3))/b","B",0
305,1,1226,0,0.673167," ","integrate((d*x+c)^2*tan(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)} - \frac{2 \, a c d {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} - \log\left(\sin\left(b x + a\right)^{2} - 1\right)\right)}}{b^{2}} + \frac{2 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}^{2} + 12 \, b c d - 12 \, a d^{2} - {\left(6 \, {\left(b x + a\right)}^{2} d^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - 6 \, d^{2} + 6 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 6 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(24 i \, b c d - 24 i \, a d^{2}\right)} {\left(b x + a\right)} - 12 i \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left({\left(b x + a\right)}^{3} d^{2} + 3 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)}^{2} - 6 \, {\left(b x + a\right)} d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 \, {\left(b x + a\right)}^{3} d^{2} + {\left(12 \, b c d - {\left(12 \, a - 12 i\right)} d^{2}\right)} {\left(b x + a\right)}^{2} + 12 \, b c d - 12 \, a d^{2} - {\left(-24 i \, b c d - 12 \, {\left(-2 i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 \, b c d + 6 \, {\left(b x + a\right)} d^{2} - 6 \, a d^{2} + 6 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, b c d - 6 i \, {\left(b x + a\right)} d^{2} + 6 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) - {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 3 i \, d^{2} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 3 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} + 6 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{2} d^{2} + 2 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} - d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) - {\left(-3 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 6 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 3 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 6 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 3 i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(-2 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)}^{2} + 12 i \, {\left(b x + a\right)} d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-4 i \, {\left(b x + a\right)}^{3} d^{2} + {\left(-12 i \, b c d - 12 \, {\left(-i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}^{2} - 12 i \, b c d + 12 i \, a d^{2} + {\left(24 \, b c d - {\left(24 \, a - 12 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-6 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) - 12 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 6 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) + 12 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, b^{2}}}{2 \, b}"," ",0,"-1/2*(c^2*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1)) - 2*a*c*d*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1))/b + a^2*d^2*(1/(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2 - 1))/b^2 + 2*(2*(b*x + a)^3*d^2 + 6*(b*c*d - a*d^2)*(b*x + a)^2 + 12*b*c*d - 12*a*d^2 - (6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) - 6*d^2 + 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*cos(4*b*x + 4*a) + 12*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*cos(2*b*x + 2*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) - 6*I*d^2)*sin(4*b*x + 4*a) + (12*I*(b*x + a)^2*d^2 + (24*I*b*c*d - 24*I*a*d^2)*(b*x + a) - 12*I*d^2)*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + 2*((b*x + a)^3*d^2 + 3*(b*c*d - a*d^2)*(b*x + a)^2 - 6*(b*x + a)*d^2)*cos(4*b*x + 4*a) + (4*(b*x + a)^3*d^2 + (12*b*c*d - (12*a - 12*I)*d^2)*(b*x + a)^2 + 12*b*c*d - 12*a*d^2 - (-24*I*b*c*d - 12*(-2*I*a - 1)*d^2)*(b*x + a))*cos(2*b*x + 2*a) + (6*b*c*d + 6*(b*x + a)*d^2 - 6*a*d^2 + 6*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-6*I*b*c*d - 6*I*(b*x + a)*d^2 + 6*I*a*d^2)*sin(4*b*x + 4*a) - (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*I*a)) - (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) + 3*I*d^2 + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) + 3*I*d^2)*cos(4*b*x + 4*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) + 6*I*d^2)*cos(2*b*x + 2*a) + 3*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*sin(4*b*x + 4*a) + 6*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) - d^2)*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - (-3*I*d^2*cos(4*b*x + 4*a) - 6*I*d^2*cos(2*b*x + 2*a) + 3*d^2*sin(4*b*x + 4*a) + 6*d^2*sin(2*b*x + 2*a) - 3*I*d^2)*polylog(3, -e^(2*I*b*x + 2*I*a)) - (-2*I*(b*x + a)^3*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a)^2 + 12*I*(b*x + a)*d^2)*sin(4*b*x + 4*a) - (-4*I*(b*x + a)^3*d^2 + (-12*I*b*c*d - 12*(-I*a - 1)*d^2)*(b*x + a)^2 - 12*I*b*c*d + 12*I*a*d^2 + (24*b*c*d - (24*a - 12*I)*d^2)*(b*x + a))*sin(2*b*x + 2*a))/(-6*I*b^2*cos(4*b*x + 4*a) - 12*I*b^2*cos(2*b*x + 2*a) + 6*b^2*sin(4*b*x + 4*a) + 12*b^2*sin(2*b*x + 2*a) - 6*I*b^2))/b","B",0
306,1,519,0,0.582666," ","integrate((d*x+c)*tan(b*x+a)^3,x, algorithm=""maxima"")","-\frac{b^{2} d x^{2} + 2 \, b^{2} c x - {\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(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(b^{2} d x^{2} + 2 \, b^{2} c x\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 \, b^{2} d x^{2} + 4 i \, b c + {\left(4 \, b^{2} c + 4 i \, b d\right)} x + 2 \, d\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(d \cos\left(4 \, b x + 4 \, a\right) + 2 \, d \cos\left(2 \, b x + 2 \, a\right) + i \, d \sin\left(4 \, b x + 4 \, a\right) + 2 i \, d \sin\left(2 \, b x + 2 \, a\right) + d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(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) - {\left(-i \, b^{2} d x^{2} - 2 i \, b^{2} c x\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-2 i \, b^{2} d x^{2} + 4 \, b c - 4 \, {\left(i \, b^{2} c - b d\right)} x - 2 i \, d\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) - 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) + 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}"," ",0,"-(b^2*d*x^2 + 2*b^2*c*x - (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(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) + (b^2*d*x^2 + 2*b^2*c*x)*cos(4*b*x + 4*a) + (2*b^2*d*x^2 + 4*I*b*c + (4*b^2*c + 4*I*b*d)*x + 2*d)*cos(2*b*x + 2*a) + (d*cos(4*b*x + 4*a) + 2*d*cos(2*b*x + 2*a) + I*d*sin(4*b*x + 4*a) + 2*I*d*sin(2*b*x + 2*a) + d)*dilog(-e^(2*I*b*x + 2*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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - (-I*b^2*d*x^2 - 2*I*b^2*c*x)*sin(4*b*x + 4*a) - (-2*I*b^2*d*x^2 + 4*b*c - 4*(I*b^2*c - b*d)*x - 2*I*d)*sin(2*b*x + 2*a) + 2*d)/(-2*I*b^2*cos(4*b*x + 4*a) - 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) + 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2)","B",0
307,0,0,0,0.000000," ","integrate(tan(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - d \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b d x + b c\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} + {\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} - d^{2}\right)} \sin\left(2 \, b x + 2 \, 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(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(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}\right)} \cos\left(2 \, b x + 2 \, a\right)}\,{d x} + {\left(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(4 \, b x + 4 \, a\right) + d \sin\left(2 \, b x + 2 \, 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,"(4*(b*d*x + b*c)*cos(2*b*x + 2*a)^2 + 4*(b*d*x + b*c)*sin(2*b*x + 2*a)^2 + (2*(b*d*x + b*c)*cos(2*b*x + 2*a) - d*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*d*x + b*c)*cos(2*b*x + 2*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(2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - d^2)*sin(2*b*x + 2*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(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(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)*cos(2*b*x + 2*a)), x) + (d*cos(2*b*x + 2*a) + 2*(b*d*x + b*c)*sin(2*b*x + 2*a) + d)*sin(4*b*x + 4*a) + d*sin(2*b*x + 2*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
308,0,0,0,0.000000," ","integrate(tan(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left({\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - d \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b d x + b c\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} + {\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} - 3 \, d^{2}\right)} \sin\left(2 \, b x + 2 \, 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(2 \, b x + 2 \, 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(2 \, b x + 2 \, 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(2 \, b x + 2 \, a\right)}\,{d x} + 2 \, {\left(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(4 \, b x + 4 \, a\right) + 2 \, d \sin\left(2 \, b x + 2 \, 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,"(4*(b*d*x + b*c)*cos(2*b*x + 2*a)^2 + 4*(b*d*x + b*c)*sin(2*b*x + 2*a)^2 + 2*((b*d*x + b*c)*cos(2*b*x + 2*a) - d*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*d*x + b*c)*cos(2*b*x + 2*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(2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 3*d^2)*sin(2*b*x + 2*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(2*b*x + 2*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(2*b*x + 2*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(2*b*x + 2*a)), x) + 2*(d*cos(2*b*x + 2*a) + (b*d*x + b*c)*sin(2*b*x + 2*a) + d)*sin(4*b*x + 4*a) + 2*d*sin(2*b*x + 2*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
309,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right) \sec\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)*sec(b*x + a)^3, x)","F",0
310,1,8770,0,6.051145," ","integrate((d*x+c)^4*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{4} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{4 \, a c^{3} d {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{6 \, a^{2} c^{2} d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{4 \, a^{3} c d^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} + \frac{a^{4} d^{4} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{4}} + \frac{2 \, {\left(24 \, b^{3} c^{3} d - 72 \, a b^{2} c^{2} d^{2} + 72 \, a^{2} b c d^{3} - 24 \, a^{3} d^{4} + {\left(12 \, {\left(b x + a\right)}^{4} d^{4} + 36 \, b^{2} c^{2} d^{2} - 72 \, a b c d^{3} + 36 \, a^{2} d^{4} + 32 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 36 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)} + 4 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{4} + 9 \, b^{2} c^{2} d^{2} - 18 \, a b c d^{3} + 9 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 9 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 8 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{4} + 9 \, b^{2} c^{2} d^{2} - 18 \, a b c d^{3} + 9 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 9 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{4} d^{4} + 36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + 36 i \, a^{2} d^{4} + {\left(32 i \, b c d^{3} - 32 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + {\left(36 i \, a^{2} + 36 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + {\left(72 i \, a^{2} + 72 i\right)} b c d^{3} + {\left(-24 i \, a^{3} - 72 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(24 i \, {\left(b x + a\right)}^{4} d^{4} + 72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, a^{2} d^{4} + {\left(64 i \, b c d^{3} - 64 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + {\left(72 i \, a^{2} + 72 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(48 i \, b^{3} c^{3} d - 144 i \, a b^{2} c^{2} d^{2} + {\left(144 i \, a^{2} + 144 i\right)} b c d^{3} + {\left(-48 i \, a^{3} - 144 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{4} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 36 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-24 i \, b c d^{3} + 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} - 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{3} c^{3} d + 72 i \, a b^{2} c^{2} d^{2} - 72 i \, a^{2} b c d^{3} + 24 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-72 i \, b^{2} c^{2} d^{2} + 144 i \, a b c d^{3} - 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-48 i \, b^{3} c^{3} d + 144 i \, a b^{2} c^{2} d^{2} - 144 i \, a^{2} b c d^{3} + 48 i \, a^{3} d^{4}\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)}^{4} d^{4} + 24 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 36 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 24 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)} + 6 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} - 24 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(48 i \, b c d^{3} - 48 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(48 i \, b^{3} c^{3} d - 144 i \, a b^{2} c^{2} d^{2} + 144 i \, a^{2} b c d^{3} - 48 i \, a^{3} d^{4}\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) - 24 \, {\left({\left(b x + a\right)}^{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)} \cos\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{4} d^{4} + 24 \, b^{3} c^{3} d - 72 \, a b^{2} c^{2} d^{2} + 72 \, a^{2} b c d^{3} - 24 \, a^{3} d^{4} + {\left(48 i \, b c d^{3} - 24 \, {\left(2 i \, a + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(72 i \, b^{2} c^{2} d^{2} - 72 \, {\left(2 i \, a + 1\right)} b c d^{3} + {\left(72 i \, a^{2} + 72 \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(48 i \, b^{3} c^{3} d - 72 \, {\left(2 i \, a + 1\right)} b^{2} c^{2} d^{2} + {\left(144 i \, a^{2} + 144 \, a\right)} b c d^{3} + {\left(-48 i \, a^{3} - 72 \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 \, b^{3} c^{3} d - 36 \, a b^{2} c^{2} d^{2} + 24 \, {\left(b x + a\right)}^{3} d^{4} + 36 \, {\left(a^{2} + 1\right)} b c d^{3} - 12 \, {\left(a^{3} + 3 \, a\right)} d^{4} + 48 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 36 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)} + 12 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 2 \, {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4} + 4 \, {\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} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 24 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 2 \, {\left(b x + a\right)}^{3} d^{4} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4} + 4 \, {\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} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-12 i \, b^{3} c^{3} d + 36 i \, a b^{2} c^{2} d^{2} - 24 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-36 i \, a^{2} - 36 i\right)} b c d^{3} + {\left(12 i \, a^{3} + 36 i \, a\right)} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} + {\left(-36 i \, a^{2} - 36 i\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-24 i \, b^{3} c^{3} d + 72 i \, a b^{2} c^{2} d^{2} - 48 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-72 i \, a^{2} - 72 i\right)} b c d^{3} + {\left(24 i \, a^{3} + 72 i \, a\right)} d^{4} + {\left(-96 i \, b c d^{3} + 96 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-72 i \, b^{2} c^{2} d^{2} + 144 i \, a b c d^{3} + {\left(-72 i \, a^{2} - 72 i\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(24 \, b^{3} c^{3} d - 72 \, a b^{2} c^{2} d^{2} + 72 \, a^{2} b c d^{3} + 24 \, {\left(b x + a\right)}^{3} d^{4} - 24 \, a^{3} d^{4} + 72 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 72 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 24 \, {\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)} \cos\left(4 \, b x + 4 \, a\right) + 48 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} + 24 i \, {\left(b x + a\right)}^{3} d^{4} - 24 i \, a^{3} d^{4} + {\left(72 i \, b c d^{3} - 72 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(48 i \, b^{3} c^{3} d - 144 i \, a b^{2} c^{2} d^{2} + 144 i \, a^{2} b c d^{3} + 48 i \, {\left(b x + a\right)}^{3} d^{4} - 48 i \, a^{3} d^{4} + {\left(144 i \, b c d^{3} - 144 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(144 i \, b^{2} c^{2} d^{2} - 288 i \, a b c d^{3} + 144 i \, a^{2} d^{4}\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(24 \, b^{3} c^{3} d - 72 \, a b^{2} c^{2} d^{2} + 72 \, a^{2} b c d^{3} + 24 \, {\left(b x + a\right)}^{3} d^{4} - 24 \, a^{3} d^{4} + 72 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{2} + 72 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)} + 24 \, {\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)} \cos\left(4 \, b x + 4 \, a\right) + 48 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} + 24 i \, {\left(b x + a\right)}^{3} d^{4} - 24 i \, a^{3} d^{4} + {\left(72 i \, b c d^{3} - 72 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(48 i \, b^{3} c^{3} d - 144 i \, a b^{2} c^{2} d^{2} + 144 i \, a^{2} b c d^{3} + 48 i \, {\left(b x + a\right)}^{3} d^{4} - 48 i \, a^{3} d^{4} + {\left(144 i \, b c d^{3} - 144 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(144 i \, b^{2} c^{2} d^{2} - 288 i \, a b c d^{3} + 144 i \, a^{2} d^{4}\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 i \, {\left(b x + a\right)}^{4} d^{4} - 18 i \, b^{2} c^{2} d^{2} + 36 i \, a b c d^{3} - 18 i \, a^{2} d^{4} + {\left(-16 i \, b c d^{3} + 16 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-18 i \, b^{2} c^{2} d^{2} + 36 i \, a b c d^{3} + {\left(-18 i \, a^{2} - 18 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{3} c^{3} d + 36 i \, a b^{2} c^{2} d^{2} + {\left(-36 i \, a^{2} - 36 i\right)} b c d^{3} + {\left(12 i \, a^{3} + 36 i \, a\right)} d^{4}\right)} {\left(b x + a\right)} + {\left(-6 i \, {\left(b x + a\right)}^{4} d^{4} - 18 i \, b^{2} c^{2} d^{2} + 36 i \, a b c d^{3} - 18 i \, a^{2} d^{4} + {\left(-16 i \, b c d^{3} + 16 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-18 i \, b^{2} c^{2} d^{2} + 36 i \, a b c d^{3} + {\left(-18 i \, a^{2} - 18 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-12 i \, b^{3} c^{3} d + 36 i \, a b^{2} c^{2} d^{2} + {\left(-36 i \, a^{2} - 36 i\right)} b c d^{3} + {\left(12 i \, a^{3} + 36 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{4} d^{4} - 36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} - 36 i \, a^{2} d^{4} + {\left(-32 i \, b c d^{3} + 32 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(-36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} + {\left(-36 i \, a^{2} - 36 i\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{3} c^{3} d + 72 i \, a b^{2} c^{2} d^{2} + {\left(-72 i \, a^{2} - 72 i\right)} b c d^{3} + {\left(24 i \, a^{3} + 72 i \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{4} + 9 \, b^{2} c^{2} d^{2} - 18 \, a b c d^{3} + 9 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 9 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(3 \, {\left(b x + a\right)}^{4} d^{4} + 9 \, b^{2} c^{2} d^{2} - 18 \, a b c d^{3} + 9 \, a^{2} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 9 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(a^{2} + 1\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, {\left(a^{2} + 1\right)} b c d^{3} - {\left(a^{3} + 3 \, a\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) + {\left(3 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(18 i \, b^{2} c^{2} d^{2} - 36 i \, a b c d^{3} + 18 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{3} c^{3} d - 36 i \, a b^{2} c^{2} d^{2} + 36 i \, a^{2} b c d^{3} - 12 i \, a^{3} d^{4}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(18 i \, b^{2} c^{2} d^{2} - 36 i \, a b c d^{3} + 18 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{3} c^{3} d - 36 i \, a b^{2} c^{2} d^{2} + 36 i \, a^{2} b c d^{3} - 12 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} - 24 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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)}^{4} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(18 i \, b^{2} c^{2} d^{2} - 36 i \, a b c d^{3} + 18 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{3} c^{3} d - 36 i \, a b^{2} c^{2} d^{2} + 36 i \, a^{2} b c d^{3} - 12 i \, a^{3} d^{4}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(12 i \, b c d^{3} - 12 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(18 i \, b^{2} c^{2} d^{2} - 36 i \, a b c d^{3} + 18 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{3} c^{3} d - 36 i \, a b^{2} c^{2} d^{2} + 36 i \, a^{2} b c d^{3} - 12 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{4} d^{4} + {\left(24 i \, b c d^{3} - 24 i \, a d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(36 i \, b^{2} c^{2} d^{2} - 72 i \, a b c d^{3} + 36 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(24 i \, b^{3} c^{3} d - 72 i \, a b^{2} c^{2} d^{2} + 72 i \, a^{2} b c d^{3} - 24 i \, a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{4} d^{4} + 4 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}^{3} + 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} {\left(b x + a\right)}^{2} + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\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(18 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) + 36 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) - 18 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) - 36 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) + 18 i \, d^{4}\right)} {\rm Li}_{5}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(-144 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) - 288 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 144 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) + 288 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 144 i \, d^{4}\right)} {\rm Li}_{5}(-e^{\left(i \, b x + i \, a\right)}) + {\left(-144 i \, d^{4} \cos\left(4 \, b x + 4 \, a\right) - 288 i \, d^{4} \cos\left(2 \, b x + 2 \, a\right) + 144 \, d^{4} \sin\left(4 \, b x + 4 \, a\right) + 288 \, d^{4} \sin\left(2 \, b x + 2 \, a\right) - 144 i \, d^{4}\right)} {\rm Li}_{5}(e^{\left(i \, b x + i \, a\right)}) + {\left(24 \, b c d^{3} + 36 \, {\left(b x + a\right)} d^{4} - 24 \, a d^{4} + 12 \, {\left(2 \, b c d^{3} + 3 \, {\left(b x + a\right)} d^{4} - 2 \, a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) + 24 \, {\left(2 \, b c d^{3} + 3 \, {\left(b x + a\right)} d^{4} - 2 \, a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(24 i \, b c d^{3} + 36 i \, {\left(b x + a\right)} d^{4} - 24 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(48 i \, b c d^{3} + 72 i \, {\left(b x + a\right)} d^{4} - 48 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(144 \, b c d^{3} + 144 \, {\left(b x + a\right)} d^{4} - 144 \, a d^{4} + 144 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) + 288 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-144 i \, b c d^{3} - 144 i \, {\left(b x + a\right)} d^{4} + 144 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-288 i \, b c d^{3} - 288 i \, {\left(b x + a\right)} d^{4} + 288 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(144 \, b c d^{3} + 144 \, {\left(b x + a\right)} d^{4} - 144 \, a d^{4} + 144 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(4 \, b x + 4 \, a\right) + 288 \, {\left(b c d^{3} + {\left(b x + a\right)} d^{4} - a d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-144 i \, b c d^{3} - 144 i \, {\left(b x + a\right)} d^{4} + 144 i \, a d^{4}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-288 i \, b c d^{3} - 288 i \, {\left(b x + a\right)} d^{4} + 288 i \, a d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(-18 i \, b^{2} c^{2} d^{2} + 36 i \, a b c d^{3} - 36 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-18 i \, a^{2} - 18 i\right)} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(-18 i \, b^{2} c^{2} d^{2} + 36 i \, a b c d^{3} - 36 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-18 i \, a^{2} - 18 i\right)} d^{4} + {\left(-48 i \, b c d^{3} + 48 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-36 i \, b^{2} c^{2} d^{2} + 72 i \, a b c d^{3} - 72 i \, {\left(b x + a\right)}^{2} d^{4} + {\left(-36 i \, a^{2} - 36 i\right)} d^{4} + {\left(-96 i \, b c d^{3} + 96 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\left(3 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + 6 \, {\left(b x + a\right)}^{2} d^{4} + 3 \, {\left(a^{2} + 1\right)} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 12 \, {\left(3 \, b^{2} c^{2} d^{2} - 6 \, a b c d^{3} + 6 \, {\left(b x + a\right)}^{2} d^{4} + 3 \, {\left(a^{2} + 1\right)} d^{4} + 8 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, {\left(b x + a\right)}^{2} d^{4} + 72 i \, a^{2} d^{4} + {\left(144 i \, b c d^{3} - 144 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, {\left(b x + a\right)}^{2} d^{4} + 72 i \, a^{2} d^{4} + {\left(144 i \, b c d^{3} - 144 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(144 i \, b^{2} c^{2} d^{2} - 288 i \, a b c d^{3} + 144 i \, {\left(b x + a\right)}^{2} d^{4} + 144 i \, a^{2} d^{4} + {\left(288 i \, b c d^{3} - 288 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 72 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 144 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, {\left(b x + a\right)}^{2} d^{4} + 72 i \, a^{2} d^{4} + {\left(144 i \, b c d^{3} - 144 i \, a d^{4}\right)} {\left(b x + a\right)} + {\left(72 i \, b^{2} c^{2} d^{2} - 144 i \, a b c d^{3} + 72 i \, {\left(b x + a\right)}^{2} d^{4} + 72 i \, a^{2} d^{4} + {\left(144 i \, b c d^{3} - 144 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(144 i \, b^{2} c^{2} d^{2} - 288 i \, a b c d^{3} + 144 i \, {\left(b x + a\right)}^{2} d^{4} + 144 i \, a^{2} d^{4} + {\left(288 i \, b c d^{3} - 288 i \, a d^{4}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 72 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 144 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + {\left(b x + a\right)}^{2} d^{4} + a^{2} d^{4} + 2 \, {\left(b c d^{3} - a d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(-24 i \, {\left(b x + a\right)}^{3} d^{4} + {\left(-72 i \, b c d^{3} + 72 i \, a d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(-72 i \, b^{2} c^{2} d^{2} + 144 i \, a b c d^{3} - 72 i \, a^{2} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 \, {\left(b x + a\right)}^{4} d^{4} - 24 i \, b^{3} c^{3} d + 72 i \, a b^{2} c^{2} d^{2} - 72 i \, a^{2} b c d^{3} + 24 i \, a^{3} d^{4} + {\left(48 \, b c d^{3} - {\left(48 \, a - 24 i\right)} d^{4}\right)} {\left(b x + a\right)}^{3} + {\left(72 \, b^{2} c^{2} d^{2} - {\left(144 \, a - 72 i\right)} b c d^{3} + 72 \, {\left(a^{2} - i \, a\right)} d^{4}\right)} {\left(b x + a\right)}^{2} + {\left(48 \, b^{3} c^{3} d - {\left(144 \, a - 72 i\right)} b^{2} c^{2} d^{2} + 144 \, {\left(a^{2} - i \, a\right)} b c d^{3} - 24 \, {\left(2 \, a^{3} - 3 i \, a^{2}\right)} d^{4}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-6 i \, b^{4} \cos\left(4 \, b x + 4 \, a\right) - 12 i \, b^{4} \cos\left(2 \, b x + 2 \, a\right) + 6 \, b^{4} \sin\left(4 \, b x + 4 \, a\right) + 12 \, b^{4} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, b^{4}}}{2 \, b}"," ",0,"-1/2*(c^4*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 4*a*c^3*d*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + 6*a^2*c^2*d^2*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 - 4*a^3*c*d^3*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^3 + a^4*d^4*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^4 + 2*(24*b^3*c^3*d - 72*a*b^2*c^2*d^2 + 72*a^2*b*c*d^3 - 24*a^3*d^4 + (12*(b*x + a)^4*d^4 + 36*b^2*c^2*d^2 - 72*a*b*c*d^3 + 36*a^2*d^4 + 32*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 36*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 + 1)*d^4)*(b*x + a)^2 + 24*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4)*(b*x + a) + 4*(3*(b*x + a)^4*d^4 + 9*b^2*c^2*d^2 - 18*a*b*c*d^3 + 9*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 9*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 + 1)*d^4)*(b*x + a)^2 + 6*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + 8*(3*(b*x + a)^4*d^4 + 9*b^2*c^2*d^2 - 18*a*b*c*d^3 + 9*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 9*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 + 1)*d^4)*(b*x + a)^2 + 6*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (12*I*(b*x + a)^4*d^4 + 36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + 36*I*a^2*d^4 + (32*I*b*c*d^3 - 32*I*a*d^4)*(b*x + a)^3 + (36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + (36*I*a^2 + 36*I)*d^4)*(b*x + a)^2 + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + (72*I*a^2 + 72*I)*b*c*d^3 + (-24*I*a^3 - 72*I*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (24*I*(b*x + a)^4*d^4 + 72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*a^2*d^4 + (64*I*b*c*d^3 - 64*I*a*d^4)*(b*x + a)^3 + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + (72*I*a^2 + 72*I)*d^4)*(b*x + a)^2 + (48*I*b^3*c^3*d - 144*I*a*b^2*c^2*d^2 + (144*I*a^2 + 144*I)*b*c*d^3 + (-48*I*a^3 - 144*I*a)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (6*(b*x + a)^4*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 36*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 24*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a) + 6*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*cos(4*b*x + 4*a) + 12*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-6*I*(b*x + a)^4*d^4 + (-24*I*b*c*d^3 + 24*I*a*d^4)*(b*x + a)^3 + (-36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 - 36*I*a^2*d^4)*(b*x + a)^2 + (-24*I*b^3*c^3*d + 72*I*a*b^2*c^2*d^2 - 72*I*a^2*b*c*d^3 + 24*I*a^3*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (-12*I*(b*x + a)^4*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a)^3 + (-72*I*b^2*c^2*d^2 + 144*I*a*b*c*d^3 - 72*I*a^2*d^4)*(b*x + a)^2 + (-48*I*b^3*c^3*d + 144*I*a*b^2*c^2*d^2 - 144*I*a^2*b*c*d^3 + 48*I*a^3*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*(b*x + a)^4*d^4 + 24*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 36*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 24*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a) + 6*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*cos(4*b*x + 4*a) + 12*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^4*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^3 + (36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + 36*I*a^2*d^4)*(b*x + a)^2 + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 - 24*I*a^3*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (12*I*(b*x + a)^4*d^4 + (48*I*b*c*d^3 - 48*I*a*d^4)*(b*x + a)^3 + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*a^2*d^4)*(b*x + a)^2 + (48*I*b^3*c^3*d - 144*I*a*b^2*c^2*d^2 + 144*I*a^2*b*c*d^3 - 48*I*a^3*d^4)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 24*((b*x + 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))*cos(4*b*x + 4*a) + (12*I*(b*x + a)^4*d^4 + 24*b^3*c^3*d - 72*a*b^2*c^2*d^2 + 72*a^2*b*c*d^3 - 24*a^3*d^4 + (48*I*b*c*d^3 - 24*(2*I*a + 1)*d^4)*(b*x + a)^3 + (72*I*b^2*c^2*d^2 - 72*(2*I*a + 1)*b*c*d^3 + (72*I*a^2 + 72*a)*d^4)*(b*x + a)^2 + (48*I*b^3*c^3*d - 72*(2*I*a + 1)*b^2*c^2*d^2 + (144*I*a^2 + 144*a)*b*c*d^3 + (-48*I*a^3 - 72*a^2)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (12*b^3*c^3*d - 36*a*b^2*c^2*d^2 + 24*(b*x + a)^3*d^4 + 36*(a^2 + 1)*b*c*d^3 - 12*(a^3 + 3*a)*d^4 + 48*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 36*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 + 1)*d^4)*(b*x + a) + 12*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 2*(b*x + a)^3*d^4 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4 + 4*(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 + 1)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + 24*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 2*(b*x + a)^3*d^4 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4 + 4*(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 + 1)*d^4)*(b*x + a))*cos(2*b*x + 2*a) - (-12*I*b^3*c^3*d + 36*I*a*b^2*c^2*d^2 - 24*I*(b*x + a)^3*d^4 + (-36*I*a^2 - 36*I)*b*c*d^3 + (12*I*a^3 + 36*I*a)*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a)^2 + (-36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 + (-36*I*a^2 - 36*I)*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (-24*I*b^3*c^3*d + 72*I*a*b^2*c^2*d^2 - 48*I*(b*x + a)^3*d^4 + (-72*I*a^2 - 72*I)*b*c*d^3 + (24*I*a^3 + 72*I*a)*d^4 + (-96*I*b*c*d^3 + 96*I*a*d^4)*(b*x + a)^2 + (-72*I*b^2*c^2*d^2 + 144*I*a*b*c*d^3 + (-72*I*a^2 - 72*I)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*I*a)) + (24*b^3*c^3*d - 72*a*b^2*c^2*d^2 + 72*a^2*b*c*d^3 + 24*(b*x + a)^3*d^4 - 24*a^3*d^4 + 72*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 72*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 24*(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))*cos(4*b*x + 4*a) + 48*(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))*cos(2*b*x + 2*a) + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 + 24*I*(b*x + a)^3*d^4 - 24*I*a^3*d^4 + (72*I*b*c*d^3 - 72*I*a*d^4)*(b*x + a)^2 + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*a^2*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (48*I*b^3*c^3*d - 144*I*a*b^2*c^2*d^2 + 144*I*a^2*b*c*d^3 + 48*I*(b*x + a)^3*d^4 - 48*I*a^3*d^4 + (144*I*b*c*d^3 - 144*I*a*d^4)*(b*x + a)^2 + (144*I*b^2*c^2*d^2 - 288*I*a*b*c*d^3 + 144*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (24*b^3*c^3*d - 72*a*b^2*c^2*d^2 + 72*a^2*b*c*d^3 + 24*(b*x + a)^3*d^4 - 24*a^3*d^4 + 72*(b*c*d^3 - a*d^4)*(b*x + a)^2 + 72*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a) + 24*(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))*cos(4*b*x + 4*a) + 48*(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))*cos(2*b*x + 2*a) + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 + 24*I*(b*x + a)^3*d^4 - 24*I*a^3*d^4 + (72*I*b*c*d^3 - 72*I*a*d^4)*(b*x + a)^2 + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*a^2*d^4)*(b*x + a))*sin(4*b*x + 4*a) + (48*I*b^3*c^3*d - 144*I*a*b^2*c^2*d^2 + 144*I*a^2*b*c*d^3 + 48*I*(b*x + a)^3*d^4 - 48*I*a^3*d^4 + (144*I*b*c*d^3 - 144*I*a*d^4)*(b*x + a)^2 + (144*I*b^2*c^2*d^2 - 288*I*a*b*c*d^3 + 144*I*a^2*d^4)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (-6*I*(b*x + a)^4*d^4 - 18*I*b^2*c^2*d^2 + 36*I*a*b*c*d^3 - 18*I*a^2*d^4 + (-16*I*b*c*d^3 + 16*I*a*d^4)*(b*x + a)^3 + (-18*I*b^2*c^2*d^2 + 36*I*a*b*c*d^3 + (-18*I*a^2 - 18*I)*d^4)*(b*x + a)^2 + (-12*I*b^3*c^3*d + 36*I*a*b^2*c^2*d^2 + (-36*I*a^2 - 36*I)*b*c*d^3 + (12*I*a^3 + 36*I*a)*d^4)*(b*x + a) + (-6*I*(b*x + a)^4*d^4 - 18*I*b^2*c^2*d^2 + 36*I*a*b*c*d^3 - 18*I*a^2*d^4 + (-16*I*b*c*d^3 + 16*I*a*d^4)*(b*x + a)^3 + (-18*I*b^2*c^2*d^2 + 36*I*a*b*c*d^3 + (-18*I*a^2 - 18*I)*d^4)*(b*x + a)^2 + (-12*I*b^3*c^3*d + 36*I*a*b^2*c^2*d^2 + (-36*I*a^2 - 36*I)*b*c*d^3 + (12*I*a^3 + 36*I*a)*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (-12*I*(b*x + a)^4*d^4 - 36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 - 36*I*a^2*d^4 + (-32*I*b*c*d^3 + 32*I*a*d^4)*(b*x + a)^3 + (-36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 + (-36*I*a^2 - 36*I)*d^4)*(b*x + a)^2 + (-24*I*b^3*c^3*d + 72*I*a*b^2*c^2*d^2 + (-72*I*a^2 - 72*I)*b*c*d^3 + (24*I*a^3 + 72*I*a)*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 2*(3*(b*x + a)^4*d^4 + 9*b^2*c^2*d^2 - 18*a*b*c*d^3 + 9*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 9*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 + 1)*d^4)*(b*x + a)^2 + 6*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4)*(b*x + a))*sin(4*b*x + 4*a) + 4*(3*(b*x + a)^4*d^4 + 9*b^2*c^2*d^2 - 18*a*b*c*d^3 + 9*a^2*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 9*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (a^2 + 1)*d^4)*(b*x + a)^2 + 6*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*(a^2 + 1)*b*c*d^3 - (a^3 + 3*a)*d^4)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (3*I*(b*x + a)^4*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^3 + (18*I*b^2*c^2*d^2 - 36*I*a*b*c*d^3 + 18*I*a^2*d^4)*(b*x + a)^2 + (12*I*b^3*c^3*d - 36*I*a*b^2*c^2*d^2 + 36*I*a^2*b*c*d^3 - 12*I*a^3*d^4)*(b*x + a) + (3*I*(b*x + a)^4*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^3 + (18*I*b^2*c^2*d^2 - 36*I*a*b*c*d^3 + 18*I*a^2*d^4)*(b*x + a)^2 + (12*I*b^3*c^3*d - 36*I*a*b^2*c^2*d^2 + 36*I*a^2*b*c*d^3 - 12*I*a^3*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (6*I*(b*x + a)^4*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^3 + (36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + 36*I*a^2*d^4)*(b*x + a)^2 + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 - 24*I*a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 3*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 6*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(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)^4*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^3 + (18*I*b^2*c^2*d^2 - 36*I*a*b*c*d^3 + 18*I*a^2*d^4)*(b*x + a)^2 + (12*I*b^3*c^3*d - 36*I*a*b^2*c^2*d^2 + 36*I*a^2*b*c*d^3 - 12*I*a^3*d^4)*(b*x + a) + (3*I*(b*x + a)^4*d^4 + (12*I*b*c*d^3 - 12*I*a*d^4)*(b*x + a)^3 + (18*I*b^2*c^2*d^2 - 36*I*a*b*c*d^3 + 18*I*a^2*d^4)*(b*x + a)^2 + (12*I*b^3*c^3*d - 36*I*a*b^2*c^2*d^2 + 36*I*a^2*b*c*d^3 - 12*I*a^3*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (6*I*(b*x + a)^4*d^4 + (24*I*b*c*d^3 - 24*I*a*d^4)*(b*x + a)^3 + (36*I*b^2*c^2*d^2 - 72*I*a*b*c*d^3 + 36*I*a^2*d^4)*(b*x + a)^2 + (24*I*b^3*c^3*d - 72*I*a*b^2*c^2*d^2 + 72*I*a^2*b*c*d^3 - 24*I*a^3*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 3*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 6*((b*x + a)^4*d^4 + 4*(b*c*d^3 - a*d^4)*(b*x + a)^3 + 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*(b*x + a)^2 + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*(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) + (18*I*d^4*cos(4*b*x + 4*a) + 36*I*d^4*cos(2*b*x + 2*a) - 18*d^4*sin(4*b*x + 4*a) - 36*d^4*sin(2*b*x + 2*a) + 18*I*d^4)*polylog(5, -e^(2*I*b*x + 2*I*a)) + (-144*I*d^4*cos(4*b*x + 4*a) - 288*I*d^4*cos(2*b*x + 2*a) + 144*d^4*sin(4*b*x + 4*a) + 288*d^4*sin(2*b*x + 2*a) - 144*I*d^4)*polylog(5, -e^(I*b*x + I*a)) + (-144*I*d^4*cos(4*b*x + 4*a) - 288*I*d^4*cos(2*b*x + 2*a) + 144*d^4*sin(4*b*x + 4*a) + 288*d^4*sin(2*b*x + 2*a) - 144*I*d^4)*polylog(5, e^(I*b*x + I*a)) + (24*b*c*d^3 + 36*(b*x + a)*d^4 - 24*a*d^4 + 12*(2*b*c*d^3 + 3*(b*x + a)*d^4 - 2*a*d^4)*cos(4*b*x + 4*a) + 24*(2*b*c*d^3 + 3*(b*x + a)*d^4 - 2*a*d^4)*cos(2*b*x + 2*a) + (24*I*b*c*d^3 + 36*I*(b*x + a)*d^4 - 24*I*a*d^4)*sin(4*b*x + 4*a) + (48*I*b*c*d^3 + 72*I*(b*x + a)*d^4 - 48*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, -e^(2*I*b*x + 2*I*a)) - (144*b*c*d^3 + 144*(b*x + a)*d^4 - 144*a*d^4 + 144*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) + 288*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-144*I*b*c*d^3 - 144*I*(b*x + a)*d^4 + 144*I*a*d^4)*sin(4*b*x + 4*a) - (-288*I*b*c*d^3 - 288*I*(b*x + a)*d^4 + 288*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, -e^(I*b*x + I*a)) - (144*b*c*d^3 + 144*(b*x + a)*d^4 - 144*a*d^4 + 144*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(4*b*x + 4*a) + 288*(b*c*d^3 + (b*x + a)*d^4 - a*d^4)*cos(2*b*x + 2*a) - (-144*I*b*c*d^3 - 144*I*(b*x + a)*d^4 + 144*I*a*d^4)*sin(4*b*x + 4*a) - (-288*I*b*c*d^3 - 288*I*(b*x + a)*d^4 + 288*I*a*d^4)*sin(2*b*x + 2*a))*polylog(4, e^(I*b*x + I*a)) + (-18*I*b^2*c^2*d^2 + 36*I*a*b*c*d^3 - 36*I*(b*x + a)^2*d^4 + (-18*I*a^2 - 18*I)*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a) + (-18*I*b^2*c^2*d^2 + 36*I*a*b*c*d^3 - 36*I*(b*x + a)^2*d^4 + (-18*I*a^2 - 18*I)*d^4 + (-48*I*b*c*d^3 + 48*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (-36*I*b^2*c^2*d^2 + 72*I*a*b*c*d^3 - 72*I*(b*x + a)^2*d^4 + (-36*I*a^2 - 36*I)*d^4 + (-96*I*b*c*d^3 + 96*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) + 6*(3*b^2*c^2*d^2 - 6*a*b*c*d^3 + 6*(b*x + a)^2*d^4 + 3*(a^2 + 1)*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) + 12*(3*b^2*c^2*d^2 - 6*a*b*c*d^3 + 6*(b*x + a)^2*d^4 + 3*(a^2 + 1)*d^4 + 8*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -e^(2*I*b*x + 2*I*a)) + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*(b*x + a)^2*d^4 + 72*I*a^2*d^4 + (144*I*b*c*d^3 - 144*I*a*d^4)*(b*x + a) + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*(b*x + a)^2*d^4 + 72*I*a^2*d^4 + (144*I*b*c*d^3 - 144*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (144*I*b^2*c^2*d^2 - 288*I*a*b*c*d^3 + 144*I*(b*x + a)^2*d^4 + 144*I*a^2*d^4 + (288*I*b*c*d^3 - 288*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 72*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 144*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, -e^(I*b*x + I*a)) + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*(b*x + a)^2*d^4 + 72*I*a^2*d^4 + (144*I*b*c*d^3 - 144*I*a*d^4)*(b*x + a) + (72*I*b^2*c^2*d^2 - 144*I*a*b*c*d^3 + 72*I*(b*x + a)^2*d^4 + 72*I*a^2*d^4 + (144*I*b*c*d^3 - 144*I*a*d^4)*(b*x + a))*cos(4*b*x + 4*a) + (144*I*b^2*c^2*d^2 - 288*I*a*b*c*d^3 + 144*I*(b*x + a)^2*d^4 + 144*I*a^2*d^4 + (288*I*b*c*d^3 - 288*I*a*d^4)*(b*x + a))*cos(2*b*x + 2*a) - 72*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(4*b*x + 4*a) - 144*(b^2*c^2*d^2 - 2*a*b*c*d^3 + (b*x + a)^2*d^4 + a^2*d^4 + 2*(b*c*d^3 - a*d^4)*(b*x + a))*sin(2*b*x + 2*a))*polylog(3, e^(I*b*x + I*a)) + (-24*I*(b*x + a)^3*d^4 + (-72*I*b*c*d^3 + 72*I*a*d^4)*(b*x + a)^2 + (-72*I*b^2*c^2*d^2 + 144*I*a*b*c*d^3 - 72*I*a^2*d^4)*(b*x + a))*sin(4*b*x + 4*a) - (12*(b*x + a)^4*d^4 - 24*I*b^3*c^3*d + 72*I*a*b^2*c^2*d^2 - 72*I*a^2*b*c*d^3 + 24*I*a^3*d^4 + (48*b*c*d^3 - (48*a - 24*I)*d^4)*(b*x + a)^3 + (72*b^2*c^2*d^2 - (144*a - 72*I)*b*c*d^3 + 72*(a^2 - I*a)*d^4)*(b*x + a)^2 + (48*b^3*c^3*d - (144*a - 72*I)*b^2*c^2*d^2 + 144*(a^2 - I*a)*b*c*d^3 - 24*(2*a^3 - 3*I*a^2)*d^4)*(b*x + a))*sin(2*b*x + 2*a))/(-6*I*b^4*cos(4*b*x + 4*a) - 12*I*b^4*cos(2*b*x + 2*a) + 6*b^4*sin(4*b*x + 4*a) + 12*b^4*sin(2*b*x + 2*a) - 6*I*b^4))/b","B",0
311,1,4918,0,2.018579," ","integrate((d*x+c)^3*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} + \frac{2 \, {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, a^{2} d^{3} + {\left(8 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, b c d^{2} - 18 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)} + 2 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(8 i \, {\left(b x + a\right)}^{3} d^{3} + 18 i \, b c d^{2} - 18 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(16 i \, {\left(b x + a\right)}^{3} d^{3} + 36 i \, b c d^{2} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + {\left(36 i \, a^{2} + 36 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(6 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\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)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 36 i \, a^{2} 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)}^{3} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\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)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, a^{2} 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) - 18 \, {\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(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{3} d^{3} + 18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 18 \, {\left(2 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 36 \, {\left(2 i \, a + 1\right)} b c d^{2} + {\left(36 i \, a^{2} + 36 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(9 \, b^{2} c^{2} d - 18 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 9 \, {\left(a^{2} + 1\right)} d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 3 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 4 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, {\left(a^{2} + 1\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 4 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, {\left(a^{2} + 1\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-9 i \, a^{2} - 9 i\right)} d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 24 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 18 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 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(2 i \, b x + 2 i \, a\right)}\right) + {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, a^{2} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 18 \, {\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)} \cos\left(4 \, b x + 4 \, a\right) + 36 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + 18 i \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, {\left(b x + a\right)}^{2} d^{3} + 36 i \, a^{2} d^{3} + {\left(72 i \, b c d^{2} - 72 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(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, a^{2} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 18 \, {\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)} \cos\left(4 \, b x + 4 \, a\right) + 36 \, {\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)} \cos\left(2 \, b x + 2 \, a\right) + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + 18 i \, a^{2} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, {\left(b x + a\right)}^{2} d^{3} + 36 i \, a^{2} d^{3} + {\left(72 i \, b c d^{2} - 72 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(-4 i \, {\left(b x + a\right)}^{3} d^{3} - 9 i \, b c d^{2} + 9 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 9 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{3} - 9 i \, b c d^{2} + 9 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 9 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 2 \, {\left(4 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 9 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + 9 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + 9 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\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)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\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)} \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)}^{3} d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + 9 i \, a^{2} d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + 9 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\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)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\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)} \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(6 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 12 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 12 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 6 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 72 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 72 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 36 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 72 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 72 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 36 \, d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(-9 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 9 i \, a d^{3} + {\left(-9 i \, b c d^{2} - 12 i \, {\left(b x + a\right)} d^{3} + 9 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-18 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 18 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(72 i \, b c d^{2} + 72 i \, {\left(b x + a\right)} d^{3} - 72 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 72 \, {\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(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3} + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(72 i \, b c d^{2} + 72 i \, {\left(b x + a\right)} d^{3} - 72 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 72 \, {\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(-18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(12 \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, a^{2} d^{3} + {\left(36 \, b c d^{2} - {\left(36 \, a - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a - 36 i\right)} b c d^{2} + 36 \, {\left(a^{2} - i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-6 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) - 12 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 6 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) + 12 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 6 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(c^3*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 3*a*c^2*d*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + 3*a^2*c*d^2*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 - a^3*d^3*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^3 + 2*(18*b^2*c^2*d - 36*a*b*c*d^2 + 18*a^2*d^3 + (8*(b*x + a)^3*d^3 + 18*b*c*d^2 - 18*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a) + 2*(4*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 4*(4*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (8*I*(b*x + a)^3*d^3 + 18*I*b*c*d^2 - 18*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 18*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (16*I*(b*x + a)^3*d^3 + 36*I*b*c*d^2 - 36*I*a*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + (36*I*a^2 + 36*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (6*(b*x + a)^3*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a) + 6*((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))*cos(4*b*x + 4*a) + 12*((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))*cos(2*b*x + 2*a) - (-6*I*(b*x + a)^3*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*a^2*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (-12*I*(b*x + a)^3*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 36*I*a^2*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)^3*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*(b*x + a) + 6*((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))*cos(4*b*x + 4*a) + 12*((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))*cos(2*b*x + 2*a) + (6*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (12*I*(b*x + a)^3*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*a^2*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 18*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (12*I*(b*x + a)^3*d^3 + 18*b^2*c^2*d - 36*a*b*c*d^2 + 18*a^2*d^3 + (36*I*b*c*d^2 - 18*(2*I*a + 1)*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 36*(2*I*a + 1)*b*c*d^2 + (36*I*a^2 + 36*a)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (9*b^2*c^2*d - 18*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 9*(a^2 + 1)*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a) + 3*(3*b^2*c^2*d - 6*a*b*c*d^2 + 4*(b*x + a)^2*d^3 + 3*(a^2 + 1)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 4*(b*x + a)^2*d^3 + 3*(a^2 + 1)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 - 12*I*(b*x + a)^2*d^3 + (-9*I*a^2 - 9*I)*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 24*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 18*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*I*a)) + (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 18*a^2*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 18*(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))*cos(4*b*x + 4*a) + 36*(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))*cos(2*b*x + 2*a) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + 18*I*a^2*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*(b*x + a)^2*d^3 + 36*I*a^2*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 18*a^2*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 18*(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))*cos(4*b*x + 4*a) + 36*(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))*cos(2*b*x + 2*a) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + 18*I*a^2*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*(b*x + a)^2*d^3 + 36*I*a^2*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(e^(I*b*x + I*a)) + (-4*I*(b*x + a)^3*d^3 - 9*I*b*c*d^2 + 9*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 9*I)*d^3)*(b*x + a) + (-4*I*(b*x + a)^3*d^3 - 9*I*b*c*d^2 + 9*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 9*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-8*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 18*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (4*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 2*(4*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 9*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(b^2*c^2*d - 2*a*b*c*d^2 + (a^2 + 1)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (3*I*(b*x + a)^3*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + 9*I*a^2*d^3)*(b*x + a) + (3*I*(b*x + a)^3*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + 9*I*a^2*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (6*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 3*((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))*sin(4*b*x + 4*a) - 6*((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))*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)^3*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + 9*I*a^2*d^3)*(b*x + a) + (3*I*(b*x + a)^3*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + 9*I*a^2*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (6*I*(b*x + a)^3*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*a^2*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 3*((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))*sin(4*b*x + 4*a) - 6*((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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (6*d^3*cos(4*b*x + 4*a) + 12*d^3*cos(2*b*x + 2*a) + 6*I*d^3*sin(4*b*x + 4*a) + 12*I*d^3*sin(2*b*x + 2*a) + 6*d^3)*polylog(4, -e^(2*I*b*x + 2*I*a)) - (36*d^3*cos(4*b*x + 4*a) + 72*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(4*b*x + 4*a) + 72*I*d^3*sin(2*b*x + 2*a) + 36*d^3)*polylog(4, -e^(I*b*x + I*a)) - (36*d^3*cos(4*b*x + 4*a) + 72*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(4*b*x + 4*a) + 72*I*d^3*sin(2*b*x + 2*a) + 36*d^3)*polylog(4, e^(I*b*x + I*a)) + (-9*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 9*I*a*d^3 + (-9*I*b*c*d^2 - 12*I*(b*x + a)*d^3 + 9*I*a*d^3)*cos(4*b*x + 4*a) + (-18*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 18*I*a*d^3)*cos(2*b*x + 2*a) + 3*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(4*b*x + 4*a) + 6*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(2*b*x + 2*a))*polylog(3, -e^(2*I*b*x + 2*I*a)) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3 + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + (72*I*b*c*d^2 + 72*I*(b*x + a)*d^3 - 72*I*a*d^3)*cos(2*b*x + 2*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 72*(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)) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3 + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + (72*I*b*c*d^2 + 72*I*(b*x + a)*d^3 - 72*I*a*d^3)*cos(2*b*x + 2*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 72*(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)) + (-18*I*(b*x + a)^2*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (12*(b*x + a)^3*d^3 - 18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*a^2*d^3 + (36*b*c*d^2 - (36*a - 18*I)*d^3)*(b*x + a)^2 + (36*b^2*c^2*d - (72*a - 36*I)*b*c*d^2 + 36*(a^2 - I*a)*d^3)*(b*x + a))*sin(2*b*x + 2*a))/(-6*I*b^3*cos(4*b*x + 4*a) - 12*I*b^3*cos(2*b*x + 2*a) + 6*b^3*sin(4*b*x + 4*a) + 12*b^3*sin(2*b*x + 2*a) - 6*I*b^3))/b","B",0
312,1,2442,0,0.814955," ","integrate((d*x+c)^2*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{2 \, a c d {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{1}{\sin\left(b x + a\right)^{2} - 1} + \log\left(\sin\left(b x + a\right)^{2} - 1\right) - \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{2 \, {\left(4 \, {\left(b x + a\right)} d^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, {\left(b x + a\right)} d^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b c d + 4 \, a d^{2} - {\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 \, 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)} + 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)} + 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)} + 2 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)} + 4 i \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, 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(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} + 4 \, b c d - 4 \, a d^{2} + {\left(8 i \, b c d - 4 \, {\left(2 i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 \, b c d + 2 \, {\left(b x + a\right)} d^{2} - 2 \, a d^{2} + 2 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(-2 i \, b c d - 2 i \, {\left(b x + a\right)} d^{2} + 2 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, 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(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(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)} - 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)} - 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)} - 2 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)} + 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)} + d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \log\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) - {\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)} + {\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)}\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)}\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)}\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)}\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)} + {\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)}\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)}\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)}\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)}\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 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 2 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + d^{2} \sin\left(4 \, b x + 4 \, a\right) + 2 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 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 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} - 4 i \, b c d + 4 i \, a d^{2} + {\left(8 \, b c d - {\left(8 \, a - 4 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) - 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) + 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{2}}}{2 \, b}"," ",0,"-1/2*(c^2*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2)) - 2*a*c*d*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b + a^2*d^2*(1/(sin(b*x + a)^2 - 1) + log(sin(b*x + a)^2 - 1) - log(sin(b*x + a)^2))/b^2 - 2*(4*(b*x + a)*d^2*cos(4*b*x + 4*a) + 4*I*(b*x + a)*d^2*sin(4*b*x + 4*a) - 4*b*c*d + 4*a*d^2 - (2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + 2*d^2 + 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a) + 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) + 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) + 2*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) + 4*I*d^2)*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*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) - (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 + 4*b*c*d - 4*a*d^2 + (8*I*b*c*d - 4*(2*I*a + 1)*d^2)*(b*x + a))*cos(2*b*x + 2*a) + (2*b*c*d + 2*(b*x + a)*d^2 - 2*a*d^2 + 2*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (-2*I*b*c*d - 2*I*(b*x + a)*d^2 + 2*I*a*d^2)*sin(4*b*x + 4*a) - (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*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)) - (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) - I*d^2 + (-I*(b*x + a)^2*d^2 + (-2*I*b*c*d + 2*I*a*d^2)*(b*x + a) - 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) - 2*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) + 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) + d^2)*sin(2*b*x + 2*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) - (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a))*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))*cos(2*b*x + 2*a) - ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(4*b*x + 4*a) - 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(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)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a) + (I*(b*x + a)^2*d^2 + (2*I*b*c*d - 2*I*a*d^2)*(b*x + a))*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))*cos(2*b*x + 2*a) - ((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*sin(4*b*x + 4*a) - 2*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(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*d^2*cos(4*b*x + 4*a) - 2*I*d^2*cos(2*b*x + 2*a) + d^2*sin(4*b*x + 4*a) + 2*d^2*sin(2*b*x + 2*a) - I*d^2)*polylog(3, -e^(2*I*b*x + 2*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*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 - 4*I*b*c*d + 4*I*a*d^2 + (8*b*c*d - (8*a - 4*I)*d^2)*(b*x + a))*sin(2*b*x + 2*a))/(-2*I*b^2*cos(4*b*x + 4*a) - 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) + 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2))/b","B",0
313,1,1035,0,0.632952," ","integrate((d*x+c)*csc(b*x+a)*sec(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(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\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 + 2 \, d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(d \cos\left(4 \, b x + 4 \, a\right) + 2 \, d \cos\left(2 \, b x + 2 \, a\right) + i \, d \sin\left(4 \, b x + 4 \, a\right) + 2 i \, d \sin\left(2 \, b x + 2 \, a\right) + d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 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(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(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) + {\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) - {\left(4 \, b d x + 4 \, b c - 2 i \, d\right)} \sin\left(2 \, b x + 2 \, a\right) + 2 \, d}{-2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) - 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) + 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) - 2 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(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (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 + 2*d)*cos(2*b*x + 2*a) - (d*cos(4*b*x + 4*a) + 2*d*cos(2*b*x + 2*a) + I*d*sin(4*b*x + 4*a) + 2*I*d*sin(2*b*x + 2*a) + d)*dilog(-e^(2*I*b*x + 2*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)) + (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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*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) + (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 + 4*b*c - 2*I*d)*sin(2*b*x + 2*a) + 2*d)/(-2*I*b^2*cos(4*b*x + 4*a) - 4*I*b^2*cos(2*b*x + 2*a) + 2*b^2*sin(4*b*x + 4*a) + 4*b^2*sin(2*b*x + 2*a) - 2*I*b^2)","B",0
314,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\frac{4 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + {\left(2 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - d \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b d x + b c\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} + {\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} + d^{2}\right)} \sin\left(2 \, b x + 2 \, 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(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(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}\right)} \cos\left(2 \, b x + 2 \, a\right)}\,{d x} - {\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{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} + {\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{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} + {\left(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(4 \, b x + 4 \, a\right) + d \sin\left(2 \, b x + 2 \, 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,"(4*(b*d*x + b*c)*cos(2*b*x + 2*a)^2 + 4*(b*d*x + b*c)*sin(2*b*x + 2*a)^2 + (2*(b*d*x + b*c)*cos(2*b*x + 2*a) - d*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*d*x + b*c)*cos(2*b*x + 2*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(2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + d^2)*sin(2*b*x + 2*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(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(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)*cos(2*b*x + 2*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(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x + 2*(d*x + c)*cos(b*x + a) + c), 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(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x - 2*(d*x + c)*cos(b*x + a) + c), x) + (d*cos(2*b*x + 2*a) + 2*(b*d*x + b*c)*sin(2*b*x + 2*a) + d)*sin(4*b*x + 4*a) + d*sin(2*b*x + 2*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
315,0,0,0,0.000000," ","integrate(csc(b*x+a)*sec(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right)^{2} + 4 \, {\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, {\left({\left(b d x + b c\right)} \cos\left(2 \, b x + 2 \, a\right) - d \sin\left(2 \, b x + 2 \, a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + 2 \, {\left(b d x + b c\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} + {\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} + 3 \, d^{2}\right)} \sin\left(2 \, b x + 2 \, 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(2 \, b x + 2 \, 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(2 \, b x + 2 \, 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(2 \, b x + 2 \, a\right)}\,{d x} - {\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{\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} + {\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{\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} + 2 \, {\left(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(4 \, b x + 4 \, a\right) + 2 \, d \sin\left(2 \, b x + 2 \, 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,"(4*(b*d*x + b*c)*cos(2*b*x + 2*a)^2 + 4*(b*d*x + b*c)*sin(2*b*x + 2*a)^2 + 2*((b*d*x + b*c)*cos(2*b*x + 2*a) - d*sin(2*b*x + 2*a))*cos(4*b*x + 4*a) + 2*(b*d*x + b*c)*cos(2*b*x + 2*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(2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 3*d^2)*sin(2*b*x + 2*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(2*b*x + 2*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(2*b*x + 2*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(2*b*x + 2*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(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*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(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 - 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) + 2*(d*cos(2*b*x + 2*a) + (b*d*x + b*c)*sin(2*b*x + 2*a) + d)*sin(4*b*x + 4*a) + 2*d*sin(2*b*x + 2*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
316,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^2*sec(b*x + a)^3, x)","F",0
317,1,8032,0,6.458751," ","integrate((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{3}} - \frac{4 \, {\left({\left(6 \, {\left(b x + a\right)}^{3} d^{3} + 12 \, b c d^{2} - 12 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)} - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} 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)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + 12 i \, b c d^{2} - 12 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(6 \, {\left(b x + a\right)}^{3} d^{3} + 12 \, b c d^{2} - 12 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)} - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} 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)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{3} d^{3} - 12 i \, b c d^{2} + 12 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + 12 i \, b c d^{2} - 12 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) + {\left(12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, {\left(b x + a\right)}^{2} d^{3} + 12 \, a^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 12 \, {\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)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\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)} \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} + a^{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(-12 i \, b^{2} c^{2} d + 24 i \, a b c d^{2} - 12 i \, {\left(b x + a\right)}^{2} d^{3} - 12 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, 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} - 12 i \, a^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 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} + 12 i \, a^{2} 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)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(12 \, b^{2} c^{2} d - 24 \, a b c d^{2} + 12 \, a^{2} d^{3} - 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 i \, b^{2} c^{2} d - 24 i \, a b c d^{2} + 12 i \, a^{2} d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(12 i \, b^{2} c^{2} d - 24 i \, a b c d^{2} + 12 i \, a^{2} d^{3}\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 \, a^{2} 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(12 \, {\left(b x + a\right)}^{2} d^{3} + 24 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 12 \, {\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(6 \, b x + 6 \, a\right) - 12 \, {\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(4 \, b x + 4 \, a\right) + 12 \, {\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(-12 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{2} 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)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - {\left(12 \, {\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(36 \, b c d^{2} - {\left(36 \, a + 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a + 24 i\right)} b c d^{2} + 12 \, {\left(3 \, a^{2} + 2 i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(5 \, b x + 5 \, a\right) - 8 \, {\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)} \cos\left(3 \, b x + 3 \, a\right) - {\left(12 \, {\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(36 \, b c d^{2} - {\left(36 \, a - 12 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 \, b^{2} c^{2} d - {\left(72 \, a - 24 i\right)} b c d^{2} + 12 \, {\left(3 \, a^{2} - 2 i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(3 \, a^{2} + 2\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 12 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 18 \, {\left(b x + a\right)}^{2} d^{3} + 6 \, {\left(3 \, a^{2} + 2\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) - 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + 3 \, {\left(b x + a\right)}^{2} d^{3} + {\left(3 \, a^{2} + 2\right)} d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 12 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(18 i \, a^{2} + 12 i\right)} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 18 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 12 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(24 \, b c d^{2} + 24 \, {\left(b x + a\right)} d^{3} - 24 \, a d^{3} - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + 24 \, {\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(24 i \, b c d^{2} + 24 i \, {\left(b x + a\right)} d^{3} - 24 i \, a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(24 i \, b c d^{2} + 24 i \, {\left(b x + a\right)} d^{3} - 24 i \, a d^{3}\right)} \sin\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)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(24 \, b c d^{2} + 24 \, {\left(b x + a\right)} d^{3} - 24 \, a d^{3} - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) - 24 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + 24 \, {\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(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-24 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 24 i \, a d^{3}\right)} \sin\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)} \sin\left(2 \, b x + 2 \, 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)} + {\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)} \cos\left(6 \, b x + 6 \, 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} + 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)} \cos\left(4 \, b x + 4 \, 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} - 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)} \cos\left(2 \, b x + 2 \, a\right) - 6 \, {\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)} \sin\left(6 \, b x + 6 \, a\right) - 6 \, {\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)} \sin\left(4 \, b x + 4 \, a\right) + 6 \, {\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)} \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(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)} + {\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)} \cos\left(6 \, b x + 6 \, 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} - 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)} \cos\left(4 \, b x + 4 \, 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} + 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)} \cos\left(2 \, b x + 2 \, a\right) + 6 \, {\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)} \sin\left(6 \, b x + 6 \, a\right) + 6 \, {\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)} \sin\left(4 \, b x + 4 \, a\right) - 6 \, {\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)} \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)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, 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 \, \sin\left(b x + a\right) + 1\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{3} d^{3} + 6 i \, b c d^{2} - 6 i \, a d^{3} + {\left(9 i \, b c d^{2} - 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(9 i \, b^{2} c^{2} d - 18 i \, a b c d^{2} + {\left(9 i \, a^{2} + 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{3} d^{3} - 6 i \, b c d^{2} + 6 i \, a d^{3} + {\left(-9 i \, b c d^{2} + 9 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-9 i \, b^{2} c^{2} d + 18 i \, a b c d^{2} + {\left(-9 i \, a^{2} - 6 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) - 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, a^{2} + 2\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right) + 3 \, {\left({\left(b x + a\right)}^{3} d^{3} + 2 \, b c d^{2} - 2 \, a d^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(3 \, b^{2} c^{2} d - 6 \, a b c d^{2} + {\left(3 \, 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 \, \sin\left(b x + a\right) + 1\right) + {\left(36 \, d^{3} \cos\left(6 \, b x + 6 \, a\right) + 36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 36 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(6 \, b x + 6 \, a\right) + 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 36 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - 36 \, d^{3}\right)} {\rm Li}_{4}(i \, e^{\left(i \, b x + i \, a\right)}) - {\left(36 \, d^{3} \cos\left(6 \, b x + 6 \, a\right) + 36 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 36 \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 36 i \, d^{3} \sin\left(6 \, b x + 6 \, a\right) + 36 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 36 i \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - 36 \, d^{3}\right)} {\rm Li}_{4}(-i \, e^{\left(i \, b x + i \, a\right)}) + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3} + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) + 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) - 36 \, {\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}(i \, e^{\left(i \, b x + i \, a\right)}) + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3} + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(36 i \, b c d^{2} + 36 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-36 i \, b c d^{2} - 36 i \, {\left(b x + a\right)} d^{3} + 36 i \, a d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(6 \, b x + 6 \, a\right) - 36 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right) + 36 \, {\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}(-i \, e^{\left(i \, b x + i \, a\right)}) + {\left(24 i \, d^{3} \cos\left(6 \, b x + 6 \, a\right) + 24 i \, d^{3} \cos\left(4 \, b x + 4 \, a\right) - 24 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) - 24 \, d^{3} \sin\left(6 \, b x + 6 \, a\right) - 24 \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 24 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - 24 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(-24 i \, d^{3} \cos\left(6 \, b x + 6 \, a\right) - 24 i \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 24 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 24 \, d^{3} \sin\left(6 \, b x + 6 \, a\right) + 24 \, d^{3} \sin\left(4 \, b x + 4 \, a\right) - 24 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) + 24 i \, d^{3}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(-12 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(3 i \, b c d^{2} + {\left(-3 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d - 24 \, {\left(-3 i \, a + 1\right)} b c d^{2} + {\left(-36 i \, a^{2} + 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(5 \, b x + 5 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-24 i \, b c d^{2} + 24 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-24 i \, b^{2} c^{2} d + 48 i \, a b c d^{2} - 24 i \, a^{2} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(-12 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(-36 i \, b c d^{2} - 12 \, {\left(-3 i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d - 24 \, {\left(-3 i \, a - 1\right)} b c d^{2} + {\left(-36 i \, a^{2} - 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)}}{-4 i \, b^{3} \cos\left(6 \, b x + 6 \, a\right) - 4 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{3} \sin\left(6 \, b x + 6 \, a\right) + 4 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) + 4 i \, b^{3}}}{4 \, b}"," ",0,"-1/4*(c^3*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1)) - 3*a*c^2*d*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1))/b + 3*a^2*c*d^2*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1))/b^2 - a^3*d^3*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1))/b^3 - 4*((6*(b*x + a)^3*d^3 + 12*b*c*d^2 - 12*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a) - 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (6*I*(b*x + a)^3*d^3 + 12*I*b*c*d^2 - 12*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 12*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (6*(b*x + a)^3*d^3 + 12*b*c*d^2 - 12*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a) - 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 6*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^3*d^3 - 12*I*b*c*d^2 + 12*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 12*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (6*I*(b*x + a)^3*d^3 + 12*I*b*c*d^2 - 12*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 12*I)*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) + (12*b^2*c^2*d - 24*a*b*c*d^2 + 12*(b*x + a)^2*d^3 + 12*a^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) - 12*(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))*cos(6*b*x + 6*a) - 12*(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))*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*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*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*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*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*d^3 + (-24*I*b*c*d^2 + 24*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*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (12*b^2*c^2*d - 24*a*b*c*d^2 + 12*a^2*d^3 - 12*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(6*b*x + 6*a) - 12*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(4*b*x + 4*a) + 12*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(2*b*x + 2*a) - (12*I*b^2*c^2*d - 24*I*a*b*c*d^2 + 12*I*a^2*d^3)*sin(6*b*x + 6*a) - (12*I*b^2*c^2*d - 24*I*a*b*c*d^2 + 12*I*a^2*d^3)*sin(4*b*x + 4*a) - (-12*I*b^2*c^2*d + 24*I*a*b*c*d^2 - 12*I*a^2*d^3)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (12*(b*x + a)^2*d^3 + 24*(b*c*d^2 - a*d^3)*(b*x + a) - 12*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 12*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 12*((b*x + a)^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-12*I*(b*x + a)^2*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-12*I*(b*x + a)^2*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (12*I*(b*x + a)^2*d^3 + (24*I*b*c*d^2 - 24*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (12*(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 + (36*b*c*d^2 - (36*a + 12*I)*d^3)*(b*x + a)^2 + (36*b^2*c^2*d - (72*a + 24*I)*b*c*d^2 + 12*(3*a^2 + 2*I*a)*d^3)*(b*x + a))*cos(5*b*x + 5*a) - 8*((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))*cos(3*b*x + 3*a) - (12*(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 + (36*b*c*d^2 - (36*a - 12*I)*d^3)*(b*x + a)^2 + (36*b^2*c^2*d - (72*a - 24*I)*b*c*d^2 + 12*(3*a^2 - 2*I*a)*d^3)*(b*x + a))*cos(b*x + a) + (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 6*(3*a^2 + 2)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 12*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*a) + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 12*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 12*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(I*e^(I*b*x + I*a)) - (18*b^2*c^2*d - 36*a*b*c*d^2 + 18*(b*x + a)^2*d^3 + 6*(3*a^2 + 2)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(6*b*x + 6*a) - 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + 6*(3*b^2*c^2*d - 6*a*b*c*d^2 + 3*(b*x + a)^2*d^3 + (3*a^2 + 2)*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 12*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(6*b*x + 6*a) - (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + 18*I*(b*x + a)^2*d^3 + (18*I*a^2 + 12*I)*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a) - (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 18*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 12*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(2*b*x + 2*a))*dilog(-I*e^(I*b*x + I*a)) - (24*b*c*d^2 + 24*(b*x + a)*d^3 - 24*a*d^3 - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(6*b*x + 6*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(4*b*x + 4*a) + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) - (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*sin(6*b*x + 6*a) - (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*sin(4*b*x + 4*a) - (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(2*b*x + 2*a))*dilog(-e^(I*b*x + I*a)) + (24*b*c*d^2 + 24*(b*x + a)*d^3 - 24*a*d^3 - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(6*b*x + 6*a) - 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(4*b*x + 4*a) + 24*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*cos(2*b*x + 2*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(6*b*x + 6*a) + (-24*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 24*I*a*d^3)*sin(4*b*x + 4*a) + (24*I*b*c*d^2 + 24*I*(b*x + a)*d^3 - 24*I*a*d^3)*sin(2*b*x + 2*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) + (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))*cos(6*b*x + 6*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))*cos(4*b*x + 4*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))*cos(2*b*x + 2*a) - 6*(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))*sin(6*b*x + 6*a) - 6*(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))*sin(4*b*x + 4*a) + 6*(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))*sin(2*b*x + 2*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*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) + (-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))*cos(6*b*x + 6*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))*cos(4*b*x + 4*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))*cos(2*b*x + 2*a) + 6*(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))*sin(6*b*x + 6*a) + 6*(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))*sin(4*b*x + 4*a) - 6*(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))*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)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(6*b*x + 6*a) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) + 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(6*b*x + 6*a) + 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(4*b*x + 4*a) - 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*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*sin(b*x + a) + 1) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a) + (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(6*b*x + 6*a) + (3*I*(b*x + a)^3*d^3 + 6*I*b*c*d^2 - 6*I*a*d^3 + (9*I*b*c*d^2 - 9*I*a*d^3)*(b*x + a)^2 + (9*I*b^2*c^2*d - 18*I*a*b*c*d^2 + (9*I*a^2 + 6*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (-3*I*(b*x + a)^3*d^3 - 6*I*b*c*d^2 + 6*I*a*d^3 + (-9*I*b*c*d^2 + 9*I*a*d^3)*(b*x + a)^2 + (-9*I*b^2*c^2*d + 18*I*a*b*c*d^2 + (-9*I*a^2 - 6*I)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(6*b*x + 6*a) - 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*a^2 + 2)*d^3)*(b*x + a))*sin(4*b*x + 4*a) + 3*((b*x + a)^3*d^3 + 2*b*c*d^2 - 2*a*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2 + (3*b^2*c^2*d - 6*a*b*c*d^2 + (3*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*sin(b*x + a) + 1) + (36*d^3*cos(6*b*x + 6*a) + 36*d^3*cos(4*b*x + 4*a) - 36*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(6*b*x + 6*a) + 36*I*d^3*sin(4*b*x + 4*a) - 36*I*d^3*sin(2*b*x + 2*a) - 36*d^3)*polylog(4, I*e^(I*b*x + I*a)) - (36*d^3*cos(6*b*x + 6*a) + 36*d^3*cos(4*b*x + 4*a) - 36*d^3*cos(2*b*x + 2*a) + 36*I*d^3*sin(6*b*x + 6*a) + 36*I*d^3*sin(4*b*x + 4*a) - 36*I*d^3*sin(2*b*x + 2*a) - 36*d^3)*polylog(4, -I*e^(I*b*x + I*a)) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3 + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(6*b*x + 6*a) + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(4*b*x + 4*a) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(2*b*x + 2*a) + 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(6*b*x + 6*a) + 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*polylog(3, I*e^(I*b*x + I*a)) + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3 + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(6*b*x + 6*a) + (36*I*b*c*d^2 + 36*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + (-36*I*b*c*d^2 - 36*I*(b*x + a)*d^3 + 36*I*a*d^3)*cos(2*b*x + 2*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(6*b*x + 6*a) - 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a) + 36*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(2*b*x + 2*a))*polylog(3, -I*e^(I*b*x + I*a)) + (24*I*d^3*cos(6*b*x + 6*a) + 24*I*d^3*cos(4*b*x + 4*a) - 24*I*d^3*cos(2*b*x + 2*a) - 24*d^3*sin(6*b*x + 6*a) - 24*d^3*sin(4*b*x + 4*a) + 24*d^3*sin(2*b*x + 2*a) - 24*I*d^3)*polylog(3, -e^(I*b*x + I*a)) + (-24*I*d^3*cos(6*b*x + 6*a) - 24*I*d^3*cos(4*b*x + 4*a) + 24*I*d^3*cos(2*b*x + 2*a) + 24*d^3*sin(6*b*x + 6*a) + 24*d^3*sin(4*b*x + 4*a) - 24*d^3*sin(2*b*x + 2*a) + 24*I*d^3)*polylog(3, e^(I*b*x + I*a)) + (-12*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*(3*I*b*c*d^2 + (-3*I*a + 1)*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d - 24*(-3*I*a + 1)*b*c*d^2 + (-36*I*a^2 + 24*a)*d^3)*(b*x + a))*sin(5*b*x + 5*a) + (-8*I*(b*x + a)^3*d^3 + (-24*I*b*c*d^2 + 24*I*a*d^3)*(b*x + a)^2 + (-24*I*b^2*c^2*d + 48*I*a*b*c*d^2 - 24*I*a^2*d^3)*(b*x + a))*sin(3*b*x + 3*a) + (-12*I*(b*x + a)^3*d^3 + 12*b^2*c^2*d - 24*a*b*c*d^2 + 12*a^2*d^3 + (-36*I*b*c*d^2 - 12*(-3*I*a - 1)*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d - 24*(-3*I*a - 1)*b*c*d^2 + (-36*I*a^2 - 24*a)*d^3)*(b*x + a))*sin(b*x + a))/(-4*I*b^3*cos(6*b*x + 6*a) - 4*I*b^3*cos(4*b*x + 4*a) + 4*I*b^3*cos(2*b*x + 2*a) + 4*b^3*sin(6*b*x + 6*a) + 4*b^3*sin(4*b*x + 4*a) - 4*b^3*sin(2*b*x + 2*a) + 4*I*b^3))/b","B",0
318,1,3819,0,1.621598," ","integrate((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)} - \frac{2 \, a c d {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{2 \, {\left(3 \, \sin\left(b x + a\right)^{2} - 2\right)}}{\sin\left(b x + a\right)^{3} - \sin\left(b x + a\right)} - 3 \, \log\left(\sin\left(b x + a\right) + 1\right) + 3 \, \log\left(\sin\left(b x + a\right) - 1\right)\right)}}{b^{2}} - \frac{4 \, {\left({\left(6 \, {\left(b x + a\right)}^{2} d^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 4 \, d^{2} - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) + 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} + 4 i \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), \sin\left(b x + a\right) + 1\right) + {\left(6 \, {\left(b x + a\right)}^{2} d^{2} + 12 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 4 \, d^{2} - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) + 2 \, {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-12 i \, b c d + 12 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(6 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(12 i \, b c d - 12 i \, a d^{2}\right)} {\left(b x + a\right)} + 4 i \, d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\cos\left(b x + a\right), -\sin\left(b x + a\right) + 1\right) + {\left(8 \, b c d + 8 \, {\left(b x + a\right)} d^{2} - 8 \, a d^{2} - 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 8 \, {\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(-8 i \, b c d - 8 i \, {\left(b x + a\right)} d^{2} + 8 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, 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(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)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(8 \, b c d - 8 \, a d^{2} - 8 \, {\left(b c d - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 8 \, {\left(b c d - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 8 \, {\left(b c d - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(8 i \, b c d - 8 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(8 i \, b c d - 8 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-8 i \, b c d + 8 i \, a 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(8 \, {\left(b x + a\right)} d^{2} \cos\left(6 \, b x + 6 \, a\right) + 8 \, {\left(b x + a\right)} d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, {\left(b x + a\right)} d^{2} \cos\left(2 \, b x + 2 \, a\right) + 8 i \, {\left(b x + a\right)} d^{2} \sin\left(6 \, b x + 6 \, a\right) + 8 i \, {\left(b x + a\right)} d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 i \, {\left(b x + a\right)} d^{2} \sin\left(2 \, b x + 2 \, a\right) - 8 \, {\left(b x + a\right)} d^{2}\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - {\left(12 \, {\left(b x + a\right)}^{2} d^{2} - 8 i \, b c d + 8 i \, a d^{2} + {\left(24 \, b c d - {\left(24 \, a + 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(5 \, b x + 5 \, a\right) - 8 \, {\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(3 \, b x + 3 \, a\right) - {\left(12 \, {\left(b x + a\right)}^{2} d^{2} + 8 i \, b c d - 8 i \, a d^{2} + {\left(24 \, b c d - {\left(24 \, a - 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(b x + a\right) + {\left(12 \, b c d + 12 \, {\left(b x + a\right)} d^{2} - 12 \, a d^{2} - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + {\left(12 i \, b c d + 12 i \, {\left(b x + a\right)} d^{2} - 12 i \, a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(i \, e^{\left(i \, b x + i \, a\right)}\right) - {\left(12 \, b c d + 12 \, {\left(b x + a\right)} d^{2} - 12 \, a d^{2} - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) - 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + 12 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(12 i \, b c d + 12 i \, {\left(b x + a\right)} d^{2} - 12 i \, a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(12 i \, b c d + 12 i \, {\left(b x + a\right)} d^{2} - 12 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - {\left(-12 i \, b c d - 12 i \, {\left(b x + a\right)} d^{2} + 12 i \, a d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(-i \, e^{\left(i \, b x + i \, a\right)}\right) + {\left(8 \, d^{2} \cos\left(6 \, b x + 6 \, a\right) + 8 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 8 i \, d^{2} \sin\left(6 \, b x + 6 \, a\right) + 8 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 8 \, d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) - {\left(8 \, d^{2} \cos\left(6 \, b x + 6 \, a\right) + 8 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 8 i \, d^{2} \sin\left(6 \, b x + 6 \, a\right) + 8 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 8 i \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 8 \, 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} + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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 \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2} + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-4 i \, b c d - 4 i \, {\left(b x + a\right)} d^{2} + 4 i \, a d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(4 i \, b c d + 4 i \, {\left(b x + a\right)} d^{2} - 4 i \, a d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right) - 4 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a 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(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2} + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) + {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) - {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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 \, \sin\left(b x + a\right) + 1\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2} + {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(6 i \, b c d - 6 i \, a d^{2}\right)} {\left(b x + a\right)} + 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(-3 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-6 i \, b c d + 6 i \, a d^{2}\right)} {\left(b x + a\right)} - 2 i \, d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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) + {\left(3 \, {\left(b x + a\right)}^{2} d^{2} + 6 \, {\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 \, \sin\left(b x + a\right) + 1\right) + {\left(-12 i \, d^{2} \cos\left(6 \, b x + 6 \, a\right) - 12 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 12 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) + 12 \, d^{2} \sin\left(6 \, b x + 6 \, a\right) + 12 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 12 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) + 12 i \, d^{2}\right)} {\rm Li}_{3}(i \, e^{\left(i \, b x + i \, a\right)}) + {\left(12 i \, d^{2} \cos\left(6 \, b x + 6 \, a\right) + 12 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 12 i \, d^{2} \cos\left(2 \, b x + 2 \, a\right) - 12 \, d^{2} \sin\left(6 \, b x + 6 \, a\right) - 12 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 12 \, d^{2} \sin\left(2 \, b x + 2 \, a\right) - 12 i \, d^{2}\right)} {\rm Li}_{3}(-i \, e^{\left(i \, b x + i \, a\right)}) - 4 \, {\left(3 i \, {\left(b x + a\right)}^{2} d^{2} + 2 \, b c d - 2 \, a d^{2} + 2 \, {\left(3 i \, b c d + {\left(-3 i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(5 \, b x + 5 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-16 i \, b c d + 16 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{2} d^{2} + 8 \, b c d - 8 \, a d^{2} + {\left(-24 i \, b c d - 8 \, {\left(-3 i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(b x + a\right)\right)}}{-4 i \, b^{2} \cos\left(6 \, b x + 6 \, a\right) - 4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 4 i \, b^{2} \cos\left(2 \, b x + 2 \, a\right) + 4 \, b^{2} \sin\left(6 \, b x + 6 \, a\right) + 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 4 \, b^{2} \sin\left(2 \, b x + 2 \, a\right) + 4 i \, b^{2}}}{4 \, b}"," ",0,"-1/4*(c^2*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1)) - 2*a*c*d*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1))/b + a^2*d^2*(2*(3*sin(b*x + a)^2 - 2)/(sin(b*x + a)^3 - sin(b*x + a)) - 3*log(sin(b*x + a) + 1) + 3*log(sin(b*x + a) - 1))/b^2 - 4*((6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) + 4*d^2 - 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(6*b*x + 6*a) - 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(4*b*x + 4*a) + 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(2*b*x + 2*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(4*b*x + 4*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) + 4*I*d^2)*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), sin(b*x + a) + 1) + (6*(b*x + a)^2*d^2 + 12*(b*c*d - a*d^2)*(b*x + a) + 4*d^2 - 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(6*b*x + 6*a) - 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(4*b*x + 4*a) + 2*(3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*cos(2*b*x + 2*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(6*b*x + 6*a) + (-6*I*(b*x + a)^2*d^2 + (-12*I*b*c*d + 12*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(4*b*x + 4*a) + (6*I*(b*x + a)^2*d^2 + (12*I*b*c*d - 12*I*a*d^2)*(b*x + a) + 4*I*d^2)*sin(2*b*x + 2*a))*arctan2(cos(b*x + a), -sin(b*x + a) + 1) + (8*b*c*d + 8*(b*x + a)*d^2 - 8*a*d^2 - 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 8*(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) + (-8*I*b*c*d - 8*I*(b*x + a)*d^2 + 8*I*a*d^2)*sin(6*b*x + 6*a) + (-8*I*b*c*d - 8*I*(b*x + a)*d^2 + 8*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))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (8*b*c*d - 8*a*d^2 - 8*(b*c*d - a*d^2)*cos(6*b*x + 6*a) - 8*(b*c*d - a*d^2)*cos(4*b*x + 4*a) + 8*(b*c*d - a*d^2)*cos(2*b*x + 2*a) - (8*I*b*c*d - 8*I*a*d^2)*sin(6*b*x + 6*a) - (8*I*b*c*d - 8*I*a*d^2)*sin(4*b*x + 4*a) - (-8*I*b*c*d + 8*I*a*d^2)*sin(2*b*x + 2*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) - (8*(b*x + a)*d^2*cos(6*b*x + 6*a) + 8*(b*x + a)*d^2*cos(4*b*x + 4*a) - 8*(b*x + a)*d^2*cos(2*b*x + 2*a) + 8*I*(b*x + a)*d^2*sin(6*b*x + 6*a) + 8*I*(b*x + a)*d^2*sin(4*b*x + 4*a) - 8*I*(b*x + a)*d^2*sin(2*b*x + 2*a) - 8*(b*x + a)*d^2)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - (12*(b*x + a)^2*d^2 - 8*I*b*c*d + 8*I*a*d^2 + (24*b*c*d - (24*a + 8*I)*d^2)*(b*x + a))*cos(5*b*x + 5*a) - 8*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(3*b*x + 3*a) - (12*(b*x + a)^2*d^2 + 8*I*b*c*d - 8*I*a*d^2 + (24*b*c*d - (24*a - 8*I)*d^2)*(b*x + a))*cos(b*x + a) + (12*b*c*d + 12*(b*x + a)*d^2 - 12*a*d^2 - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) + (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(6*b*x + 6*a) + (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(4*b*x + 4*a) + (12*I*b*c*d + 12*I*(b*x + a)*d^2 - 12*I*a*d^2)*sin(2*b*x + 2*a))*dilog(I*e^(I*b*x + I*a)) - (12*b*c*d + 12*(b*x + a)*d^2 - 12*a*d^2 - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(6*b*x + 6*a) - 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) + 12*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(2*b*x + 2*a) - (12*I*b*c*d + 12*I*(b*x + a)*d^2 - 12*I*a*d^2)*sin(6*b*x + 6*a) - (12*I*b*c*d + 12*I*(b*x + a)*d^2 - 12*I*a*d^2)*sin(4*b*x + 4*a) - (-12*I*b*c*d - 12*I*(b*x + a)*d^2 + 12*I*a*d^2)*sin(2*b*x + 2*a))*dilog(-I*e^(I*b*x + I*a)) + (8*d^2*cos(6*b*x + 6*a) + 8*d^2*cos(4*b*x + 4*a) - 8*d^2*cos(2*b*x + 2*a) + 8*I*d^2*sin(6*b*x + 6*a) + 8*I*d^2*sin(4*b*x + 4*a) - 8*I*d^2*sin(2*b*x + 2*a) - 8*d^2)*dilog(-e^(I*b*x + I*a)) - (8*d^2*cos(6*b*x + 6*a) + 8*d^2*cos(4*b*x + 4*a) - 8*d^2*cos(2*b*x + 2*a) + 8*I*d^2*sin(6*b*x + 6*a) + 8*I*d^2*sin(4*b*x + 4*a) - 8*I*d^2*sin(2*b*x + 2*a) - 8*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 + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*cos(6*b*x + 6*a) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*cos(4*b*x + 4*a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*cos(2*b*x + 2*a) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(6*b*x + 6*a) - 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(4*b*x + 4*a) + 4*(b*c*d + (b*x + a)*d^2 - a*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*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2 + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*cos(6*b*x + 6*a) + (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*cos(4*b*x + 4*a) + (4*I*b*c*d + 4*I*(b*x + a)*d^2 - 4*I*a*d^2)*cos(2*b*x + 2*a) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(6*b*x + 6*a) + 4*(b*c*d + (b*x + a)*d^2 - a*d^2)*sin(4*b*x + 4*a) - 4*(b*c*d + (b*x + a)*d^2 - a*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) + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2 + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(6*b*x + 6*a) + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(4*b*x + 4*a) + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(2*b*x + 2*a) + (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(6*b*x + 6*a) + (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(4*b*x + 4*a) - (3*(b*x + a)^2*d^2 + 6*(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*sin(b*x + a) + 1) + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2 + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(6*b*x + 6*a) + (3*I*(b*x + a)^2*d^2 + (6*I*b*c*d - 6*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(4*b*x + 4*a) + (-3*I*(b*x + a)^2*d^2 + (-6*I*b*c*d + 6*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(2*b*x + 2*a) - (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(6*b*x + 6*a) - (3*(b*x + a)^2*d^2 + 6*(b*c*d - a*d^2)*(b*x + a) + 2*d^2)*sin(4*b*x + 4*a) + (3*(b*x + a)^2*d^2 + 6*(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*sin(b*x + a) + 1) + (-12*I*d^2*cos(6*b*x + 6*a) - 12*I*d^2*cos(4*b*x + 4*a) + 12*I*d^2*cos(2*b*x + 2*a) + 12*d^2*sin(6*b*x + 6*a) + 12*d^2*sin(4*b*x + 4*a) - 12*d^2*sin(2*b*x + 2*a) + 12*I*d^2)*polylog(3, I*e^(I*b*x + I*a)) + (12*I*d^2*cos(6*b*x + 6*a) + 12*I*d^2*cos(4*b*x + 4*a) - 12*I*d^2*cos(2*b*x + 2*a) - 12*d^2*sin(6*b*x + 6*a) - 12*d^2*sin(4*b*x + 4*a) + 12*d^2*sin(2*b*x + 2*a) - 12*I*d^2)*polylog(3, -I*e^(I*b*x + I*a)) - 4*(3*I*(b*x + a)^2*d^2 + 2*b*c*d - 2*a*d^2 + 2*(3*I*b*c*d + (-3*I*a + 1)*d^2)*(b*x + a))*sin(5*b*x + 5*a) + (-8*I*(b*x + a)^2*d^2 + (-16*I*b*c*d + 16*I*a*d^2)*(b*x + a))*sin(3*b*x + 3*a) + (-12*I*(b*x + a)^2*d^2 + 8*b*c*d - 8*a*d^2 + (-24*I*b*c*d - 8*(-3*I*a - 1)*d^2)*(b*x + a))*sin(b*x + a))/(-4*I*b^2*cos(6*b*x + 6*a) - 4*I*b^2*cos(4*b*x + 4*a) + 4*I*b^2*cos(2*b*x + 2*a) + 4*b^2*sin(6*b*x + 6*a) + 4*b^2*sin(4*b*x + 4*a) - 4*b^2*sin(2*b*x + 2*a) + 4*I*b^2))/b","B",0
319,-1,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
322,0,0,0,0.000000," ","integrate((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*csc(b*x + a)^3*sec(b*x + a)^3, x)","F",0
323,1,5610,0,3.733883," ","integrate((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{3} {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{3 \, a c^{2} d {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{3 \, a^{2} c d^{2} {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} - \frac{a^{3} d^{3} {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{3}} + \frac{2 \, {\left({\left(16 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, b c d^{2} - 18 \, a d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)} + 2 \, {\left(8 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(8 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(16 i \, {\left(b x + a\right)}^{3} d^{3} + 18 i \, b c d^{2} - 18 i \, a d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + {\left(36 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) + {\left(-32 i \, {\left(b x + a\right)}^{3} d^{3} - 36 i \, b c d^{2} + 36 i \, a d^{3} + {\left(-72 i \, b c d^{2} + 72 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-72 i \, b^{2} c^{2} d + 144 i \, a b c d^{2} + {\left(-72 i \, a^{2} - 36 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(12 \, {\left(b x + a\right)}^{3} d^{3} + 18 \, b c d^{2} - 18 \, a d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) - 12 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(-12 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} + {\left(-36 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) - {\left(24 i \, {\left(b x + a\right)}^{3} d^{3} + 36 i \, b c d^{2} - 36 i \, a d^{3} + {\left(72 i \, b c d^{2} - 72 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d - 144 i \, a b c d^{2} + {\left(72 i \, a^{2} + 36 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(18 \, b c d^{2} - 18 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(8 \, b x + 8 \, a\right) - 36 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} \sin\left(8 \, b x + 8 \, a\right) - {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(12 \, {\left(b x + a\right)}^{3} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 18 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)} + 6 \, {\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} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) - 12 \, {\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} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(12 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + {\left(36 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) + {\left(-24 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-72 i \, b c d^{2} + 72 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-72 i \, b^{2} c^{2} d + 144 i \, a b c d^{2} + {\left(-72 i \, a^{2} - 36 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) + {\left(24 i \, {\left(b x + a\right)}^{3} d^{3} + 36 \, b^{2} c^{2} d - 72 \, a b c d^{2} + 36 \, a^{2} d^{3} - 36 \, {\left(-2 i \, b c d^{2} + {\left(2 i \, a - 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d - 72 \, {\left(2 i \, a - 1\right)} b c d^{2} + {\left(72 i \, a^{2} - 72 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(24 i \, {\left(b x + a\right)}^{3} d^{3} - 36 \, b^{2} c^{2} d + 72 \, a b c d^{2} - 36 \, a^{2} d^{3} + {\left(72 i \, b c d^{2} - 36 \, {\left(2 i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 i \, b^{2} c^{2} d - 72 \, {\left(2 i \, a + 1\right)} b c d^{2} + {\left(72 i \, a^{2} + 72 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(18 \, b^{2} c^{2} d - 36 \, a b c d^{2} + 24 \, {\left(b x + a\right)}^{2} d^{3} + 9 \, {\left(2 \, a^{2} + 1\right)} d^{3} + 36 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 3 \, {\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 8 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, {\left(2 \, a^{2} + 1\right)} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) - 6 \, {\left(6 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 8 \, {\left(b x + a\right)}^{2} d^{3} + 3 \, {\left(2 \, a^{2} + 1\right)} d^{3} + 12 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} - 24 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-18 i \, a^{2} - 9 i\right)} d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) - {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 48 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(36 i \, a^{2} + 18 i\right)} d^{3} + {\left(72 i \, b c d^{2} - 72 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(36 \, b^{2} c^{2} d - 72 \, a b c d^{2} + 36 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, {\left(2 \, a^{2} + 1\right)} d^{3} + 72 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 18 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, {\left(b x + a\right)}^{2} d^{3} + {\left(2 \, a^{2} + 1\right)} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) - 36 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, {\left(b x + a\right)}^{2} d^{3} + {\left(2 \, a^{2} + 1\right)} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(36 i \, a^{2} + 18 i\right)} d^{3} + {\left(72 i \, b c d^{2} - 72 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) + {\left(-72 i \, b^{2} c^{2} d + 144 i \, a b c d^{2} - 72 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-72 i \, a^{2} - 36 i\right)} d^{3} + {\left(-144 i \, b c d^{2} + 144 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(36 \, b^{2} c^{2} d - 72 \, a b c d^{2} + 36 \, {\left(b x + a\right)}^{2} d^{3} + 18 \, {\left(2 \, a^{2} + 1\right)} d^{3} + 72 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)} + 18 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, {\left(b x + a\right)}^{2} d^{3} + {\left(2 \, a^{2} + 1\right)} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) - 36 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + 2 \, {\left(b x + a\right)}^{2} d^{3} + {\left(2 \, a^{2} + 1\right)} d^{3} + 4 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(36 i \, a^{2} + 18 i\right)} d^{3} + {\left(72 i \, b c d^{2} - 72 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) + {\left(-72 i \, b^{2} c^{2} d + 144 i \, a b c d^{2} - 72 i \, {\left(b x + a\right)}^{2} d^{3} + {\left(-72 i \, a^{2} - 36 i\right)} d^{3} + {\left(-144 i \, b c d^{2} + 144 i \, a d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} - 9 i \, b c d^{2} + 9 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 9 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(-8 i \, {\left(b x + a\right)}^{3} d^{3} - 9 i \, b c d^{2} + 9 i \, a d^{3} + {\left(-18 i \, b c d^{2} + 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-18 i \, b^{2} c^{2} d + 36 i \, a b c d^{2} + {\left(-18 i \, a^{2} - 9 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(16 i \, {\left(b x + a\right)}^{3} d^{3} + 18 i \, b c d^{2} - 18 i \, a d^{3} + {\left(36 i \, b c d^{2} - 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + {\left(36 i \, a^{2} + 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(8 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) - 2 \, {\left(8 \, {\left(b x + a\right)}^{3} d^{3} + 9 \, b c d^{2} - 9 \, a d^{3} + 18 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 9 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \log\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) + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} + {\left(-36 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) + 6 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, 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(6 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)} + {\left(6 i \, {\left(b x + a\right)}^{3} d^{3} + 9 i \, b c d^{2} - 9 i \, a d^{3} + {\left(18 i \, b c d^{2} - 18 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(18 i \, b^{2} c^{2} d - 36 i \, a b c d^{2} + {\left(18 i \, a^{2} + 9 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(-12 i \, {\left(b x + a\right)}^{3} d^{3} - 18 i \, b c d^{2} + 18 i \, a d^{3} + {\left(-36 i \, b c d^{2} + 36 i \, a d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(-36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} + {\left(-36 i \, a^{2} - 18 i\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \cos\left(4 \, b x + 4 \, a\right) - 3 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(8 \, b x + 8 \, a\right) + 6 \, {\left(2 \, {\left(b x + a\right)}^{3} d^{3} + 3 \, b c d^{2} - 3 \, a d^{3} + 6 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2} + 3 \, {\left(2 \, b^{2} c^{2} d - 4 \, a b c d^{2} + {\left(2 \, a^{2} + 1\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, 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(8 \, b x + 8 \, a\right) - 24 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 12 i \, d^{3} \sin\left(8 \, b x + 8 \, a\right) - 24 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 12 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) - {\left(72 \, d^{3} \cos\left(8 \, b x + 8 \, a\right) - 144 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 72 i \, d^{3} \sin\left(8 \, b x + 8 \, a\right) - 144 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 72 \, d^{3}\right)} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - {\left(72 \, d^{3} \cos\left(8 \, b x + 8 \, a\right) - 144 \, d^{3} \cos\left(4 \, b x + 4 \, a\right) + 72 i \, d^{3} \sin\left(8 \, b x + 8 \, a\right) - 144 i \, d^{3} \sin\left(4 \, b x + 4 \, a\right) + 72 \, d^{3}\right)} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(-18 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 18 i \, a d^{3} + {\left(-18 i \, b c d^{2} - 24 i \, {\left(b x + a\right)} d^{3} + 18 i \, a d^{3}\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(36 i \, b c d^{2} + 48 i \, {\left(b x + a\right)} d^{3} - 36 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) + 6 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(8 \, b x + 8 \, a\right) - 12 \, {\left(3 \, b c d^{2} + 4 \, {\left(b x + a\right)} d^{3} - 3 \, a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(72 i \, b c d^{2} + 72 i \, {\left(b x + a\right)} d^{3} - 72 i \, a d^{3} + {\left(72 i \, b c d^{2} + 72 i \, {\left(b x + a\right)} d^{3} - 72 i \, a d^{3}\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(-144 i \, b c d^{2} - 144 i \, {\left(b x + a\right)} d^{3} + 144 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 72 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(8 \, b x + 8 \, a\right) + 144 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(72 i \, b c d^{2} + 72 i \, {\left(b x + a\right)} d^{3} - 72 i \, a d^{3} + {\left(72 i \, b c d^{2} + 72 i \, {\left(b x + a\right)} d^{3} - 72 i \, a d^{3}\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(-144 i \, b c d^{2} - 144 i \, {\left(b x + a\right)} d^{3} + 144 i \, a d^{3}\right)} \cos\left(4 \, b x + 4 \, a\right) - 72 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(8 \, b x + 8 \, a\right) + 144 \, {\left(b c d^{2} + {\left(b x + a\right)} d^{3} - a d^{3}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(24 \, {\left(b x + a\right)}^{3} d^{3} - 36 i \, b^{2} c^{2} d + 72 i \, a b c d^{2} - 36 i \, a^{2} d^{3} + {\left(72 \, b c d^{2} - {\left(72 \, a + 36 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 \, b^{2} c^{2} d - {\left(144 \, a + 72 i\right)} b c d^{2} + 72 \, {\left(a^{2} + i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(24 \, {\left(b x + a\right)}^{3} d^{3} + 36 i \, b^{2} c^{2} d - 72 i \, a b c d^{2} + 36 i \, a^{2} d^{3} + {\left(72 \, b c d^{2} - {\left(72 \, a - 36 i\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(72 \, b^{2} c^{2} d - {\left(144 \, a - 72 i\right)} b c d^{2} + 72 \, {\left(a^{2} - i \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-6 i \, b^{3} \cos\left(8 \, b x + 8 \, a\right) + 12 i \, b^{3} \cos\left(4 \, b x + 4 \, a\right) + 6 \, b^{3} \sin\left(8 \, b x + 8 \, a\right) - 12 \, b^{3} \sin\left(4 \, b x + 4 \, a\right) - 6 i \, b^{3}}}{2 \, b}"," ",0,"-1/2*(c^3*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2)) - 3*a*c^2*d*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2))/b + 3*a^2*c*d^2*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2))/b^2 - a^3*d^3*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2))/b^3 + 2*((16*(b*x + a)^3*d^3 + 18*b*c*d^2 - 18*a*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a) + 2*(8*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*cos(8*b*x + 8*a) - 4*(8*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (16*I*(b*x + a)^3*d^3 + 18*I*b*c*d^2 - 18*I*a*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + (36*I*a^2 + 18*I)*d^3)*(b*x + a))*sin(8*b*x + 8*a) + (-32*I*(b*x + a)^3*d^3 - 36*I*b*c*d^2 + 36*I*a*d^3 + (-72*I*b*c*d^2 + 72*I*a*d^3)*(b*x + a)^2 + (-72*I*b^2*c^2*d + 144*I*a*b*c*d^2 + (-72*I*a^2 - 36*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (12*(b*x + a)^3*d^3 + 18*b*c*d^2 - 18*a*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a) + 6*(2*(b*x + a)^3*d^3 + 3*b*c*d^2 - 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*cos(8*b*x + 8*a) - 12*(2*(b*x + a)^3*d^3 + 3*b*c*d^2 - 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - (-12*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 + (-36*I*a^2 - 18*I)*d^3)*(b*x + a))*sin(8*b*x + 8*a) - (24*I*(b*x + a)^3*d^3 + 36*I*b*c*d^2 - 36*I*a*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a)^2 + (72*I*b^2*c^2*d - 144*I*a*b*c*d^2 + (72*I*a^2 + 36*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (18*b*c*d^2 - 18*a*d^3 + 18*(b*c*d^2 - a*d^3)*cos(8*b*x + 8*a) - 36*(b*c*d^2 - a*d^3)*cos(4*b*x + 4*a) - (-18*I*b*c*d^2 + 18*I*a*d^3)*sin(8*b*x + 8*a) - (36*I*b*c*d^2 - 36*I*a*d^3)*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (12*(b*x + a)^3*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 18*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a) + 6*(2*(b*x + a)^3*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*cos(8*b*x + 8*a) - 12*(2*(b*x + a)^3*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (12*I*(b*x + a)^3*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + (36*I*a^2 + 18*I)*d^3)*(b*x + a))*sin(8*b*x + 8*a) + (-24*I*(b*x + a)^3*d^3 + (-72*I*b*c*d^2 + 72*I*a*d^3)*(b*x + a)^2 + (-72*I*b^2*c^2*d + 144*I*a*b*c*d^2 + (-72*I*a^2 - 36*I)*d^3)*(b*x + a))*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (24*I*(b*x + a)^3*d^3 + 36*b^2*c^2*d - 72*a*b*c*d^2 + 36*a^2*d^3 - 36*(-2*I*b*c*d^2 + (2*I*a - 1)*d^3)*(b*x + a)^2 + (72*I*b^2*c^2*d - 72*(2*I*a - 1)*b*c*d^2 + (72*I*a^2 - 72*a)*d^3)*(b*x + a))*cos(6*b*x + 6*a) + (24*I*(b*x + a)^3*d^3 - 36*b^2*c^2*d + 72*a*b*c*d^2 - 36*a^2*d^3 + (72*I*b*c*d^2 - 36*(2*I*a + 1)*d^3)*(b*x + a)^2 + (72*I*b^2*c^2*d - 72*(2*I*a + 1)*b*c*d^2 + (72*I*a^2 + 72*a)*d^3)*(b*x + a))*cos(2*b*x + 2*a) - (18*b^2*c^2*d - 36*a*b*c*d^2 + 24*(b*x + a)^2*d^3 + 9*(2*a^2 + 1)*d^3 + 36*(b*c*d^2 - a*d^3)*(b*x + a) + 3*(6*b^2*c^2*d - 12*a*b*c*d^2 + 8*(b*x + a)^2*d^3 + 3*(2*a^2 + 1)*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a))*cos(8*b*x + 8*a) - 6*(6*b^2*c^2*d - 12*a*b*c*d^2 + 8*(b*x + a)^2*d^3 + 3*(2*a^2 + 1)*d^3 + 12*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) - (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 - 24*I*(b*x + a)^2*d^3 + (-18*I*a^2 - 9*I)*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a))*sin(8*b*x + 8*a) - (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 48*I*(b*x + a)^2*d^3 + (36*I*a^2 + 18*I)*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*dilog(-e^(2*I*b*x + 2*I*a)) + (36*b^2*c^2*d - 72*a*b*c*d^2 + 36*(b*x + a)^2*d^3 + 18*(2*a^2 + 1)*d^3 + 72*(b*c*d^2 - a*d^3)*(b*x + a) + 18*(2*b^2*c^2*d - 4*a*b*c*d^2 + 2*(b*x + a)^2*d^3 + (2*a^2 + 1)*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a))*cos(8*b*x + 8*a) - 36*(2*b^2*c^2*d - 4*a*b*c*d^2 + 2*(b*x + a)^2*d^3 + (2*a^2 + 1)*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*(b*x + a)^2*d^3 + (36*I*a^2 + 18*I)*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a))*sin(8*b*x + 8*a) + (-72*I*b^2*c^2*d + 144*I*a*b*c*d^2 - 72*I*(b*x + a)^2*d^3 + (-72*I*a^2 - 36*I)*d^3 + (-144*I*b*c*d^2 + 144*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*dilog(-e^(I*b*x + I*a)) + (36*b^2*c^2*d - 72*a*b*c*d^2 + 36*(b*x + a)^2*d^3 + 18*(2*a^2 + 1)*d^3 + 72*(b*c*d^2 - a*d^3)*(b*x + a) + 18*(2*b^2*c^2*d - 4*a*b*c*d^2 + 2*(b*x + a)^2*d^3 + (2*a^2 + 1)*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a))*cos(8*b*x + 8*a) - 36*(2*b^2*c^2*d - 4*a*b*c*d^2 + 2*(b*x + a)^2*d^3 + (2*a^2 + 1)*d^3 + 4*(b*c*d^2 - a*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*(b*x + a)^2*d^3 + (36*I*a^2 + 18*I)*d^3 + (72*I*b*c*d^2 - 72*I*a*d^3)*(b*x + a))*sin(8*b*x + 8*a) + (-72*I*b^2*c^2*d + 144*I*a*b*c*d^2 - 72*I*(b*x + a)^2*d^3 + (-72*I*a^2 - 36*I)*d^3 + (-144*I*b*c*d^2 + 144*I*a*d^3)*(b*x + a))*sin(4*b*x + 4*a))*dilog(e^(I*b*x + I*a)) + (-8*I*(b*x + a)^3*d^3 - 9*I*b*c*d^2 + 9*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 9*I)*d^3)*(b*x + a) + (-8*I*(b*x + a)^3*d^3 - 9*I*b*c*d^2 + 9*I*a*d^3 + (-18*I*b*c*d^2 + 18*I*a*d^3)*(b*x + a)^2 + (-18*I*b^2*c^2*d + 36*I*a*b*c*d^2 + (-18*I*a^2 - 9*I)*d^3)*(b*x + a))*cos(8*b*x + 8*a) + (16*I*(b*x + a)^3*d^3 + 18*I*b*c*d^2 - 18*I*a*d^3 + (36*I*b*c*d^2 - 36*I*a*d^3)*(b*x + a)^2 + (36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + (36*I*a^2 + 18*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) + (8*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*sin(8*b*x + 8*a) - 2*(8*(b*x + a)^3*d^3 + 9*b*c*d^2 - 9*a*d^3 + 18*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 9*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (6*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 9*I)*d^3)*(b*x + a) + (6*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 9*I)*d^3)*(b*x + a))*cos(8*b*x + 8*a) + (-12*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 + (-36*I*a^2 - 18*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 3*(2*(b*x + a)^3*d^3 + 3*b*c*d^2 - 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*sin(8*b*x + 8*a) + 6*(2*(b*x + a)^3*d^3 + 3*b*c*d^2 - 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) + (6*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 9*I)*d^3)*(b*x + a) + (6*I*(b*x + a)^3*d^3 + 9*I*b*c*d^2 - 9*I*a*d^3 + (18*I*b*c*d^2 - 18*I*a*d^3)*(b*x + a)^2 + (18*I*b^2*c^2*d - 36*I*a*b*c*d^2 + (18*I*a^2 + 9*I)*d^3)*(b*x + a))*cos(8*b*x + 8*a) + (-12*I*(b*x + a)^3*d^3 - 18*I*b*c*d^2 + 18*I*a*d^3 + (-36*I*b*c*d^2 + 36*I*a*d^3)*(b*x + a)^2 + (-36*I*b^2*c^2*d + 72*I*a*b*c*d^2 + (-36*I*a^2 - 18*I)*d^3)*(b*x + a))*cos(4*b*x + 4*a) - 3*(2*(b*x + a)^3*d^3 + 3*b*c*d^2 - 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*sin(8*b*x + 8*a) + 6*(2*(b*x + a)^3*d^3 + 3*b*c*d^2 - 3*a*d^3 + 6*(b*c*d^2 - a*d^3)*(b*x + a)^2 + 3*(2*b^2*c^2*d - 4*a*b*c*d^2 + (2*a^2 + 1)*d^3)*(b*x + a))*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (12*d^3*cos(8*b*x + 8*a) - 24*d^3*cos(4*b*x + 4*a) + 12*I*d^3*sin(8*b*x + 8*a) - 24*I*d^3*sin(4*b*x + 4*a) + 12*d^3)*polylog(4, -e^(2*I*b*x + 2*I*a)) - (72*d^3*cos(8*b*x + 8*a) - 144*d^3*cos(4*b*x + 4*a) + 72*I*d^3*sin(8*b*x + 8*a) - 144*I*d^3*sin(4*b*x + 4*a) + 72*d^3)*polylog(4, -e^(I*b*x + I*a)) - (72*d^3*cos(8*b*x + 8*a) - 144*d^3*cos(4*b*x + 4*a) + 72*I*d^3*sin(8*b*x + 8*a) - 144*I*d^3*sin(4*b*x + 4*a) + 72*d^3)*polylog(4, e^(I*b*x + I*a)) + (-18*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 18*I*a*d^3 + (-18*I*b*c*d^2 - 24*I*(b*x + a)*d^3 + 18*I*a*d^3)*cos(8*b*x + 8*a) + (36*I*b*c*d^2 + 48*I*(b*x + a)*d^3 - 36*I*a*d^3)*cos(4*b*x + 4*a) + 6*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(8*b*x + 8*a) - 12*(3*b*c*d^2 + 4*(b*x + a)*d^3 - 3*a*d^3)*sin(4*b*x + 4*a))*polylog(3, -e^(2*I*b*x + 2*I*a)) + (72*I*b*c*d^2 + 72*I*(b*x + a)*d^3 - 72*I*a*d^3 + (72*I*b*c*d^2 + 72*I*(b*x + a)*d^3 - 72*I*a*d^3)*cos(8*b*x + 8*a) + (-144*I*b*c*d^2 - 144*I*(b*x + a)*d^3 + 144*I*a*d^3)*cos(4*b*x + 4*a) - 72*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(8*b*x + 8*a) + 144*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a))*polylog(3, -e^(I*b*x + I*a)) + (72*I*b*c*d^2 + 72*I*(b*x + a)*d^3 - 72*I*a*d^3 + (72*I*b*c*d^2 + 72*I*(b*x + a)*d^3 - 72*I*a*d^3)*cos(8*b*x + 8*a) + (-144*I*b*c*d^2 - 144*I*(b*x + a)*d^3 + 144*I*a*d^3)*cos(4*b*x + 4*a) - 72*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(8*b*x + 8*a) + 144*(b*c*d^2 + (b*x + a)*d^3 - a*d^3)*sin(4*b*x + 4*a))*polylog(3, e^(I*b*x + I*a)) - (24*(b*x + a)^3*d^3 - 36*I*b^2*c^2*d + 72*I*a*b*c*d^2 - 36*I*a^2*d^3 + (72*b*c*d^2 - (72*a + 36*I)*d^3)*(b*x + a)^2 + (72*b^2*c^2*d - (144*a + 72*I)*b*c*d^2 + 72*(a^2 + I*a)*d^3)*(b*x + a))*sin(6*b*x + 6*a) - (24*(b*x + a)^3*d^3 + 36*I*b^2*c^2*d - 72*I*a*b*c*d^2 + 36*I*a^2*d^3 + (72*b*c*d^2 - (72*a - 36*I)*d^3)*(b*x + a)^2 + (72*b^2*c^2*d - (144*a - 72*I)*b*c*d^2 + 72*(a^2 - I*a)*d^3)*(b*x + a))*sin(2*b*x + 2*a))/(-6*I*b^3*cos(8*b*x + 8*a) + 12*I*b^3*cos(4*b*x + 4*a) + 6*b^3*sin(8*b*x + 8*a) - 12*b^3*sin(4*b*x + 4*a) - 6*I*b^3))/b","B",0
324,1,2722,0,1.101577," ","integrate((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""maxima"")","-\frac{c^{2} {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)} - \frac{2 \, a c d {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b} + \frac{a^{2} d^{2} {\left(\frac{2 \, \sin\left(b x + a\right)^{2} - 1}{\sin\left(b x + a\right)^{4} - \sin\left(b x + a\right)^{2}} + 2 \, \log\left(\sin\left(b x + a\right)^{2} - 1\right) - 2 \, \log\left(\sin\left(b x + a\right)^{2}\right)\right)}}{b^{2}} + \frac{2 \, {\left({\left(4 \, {\left(b x + a\right)}^{2} d^{2} + 8 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2} + 2 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \cos\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)} + 2 i \, d^{2}\right)} \sin\left(8 \, b x + 8 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-16 i \, b c d + 16 i \, a d^{2}\right)} {\left(b x + a\right)} - 4 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(4 \, {\left(b x + a\right)}^{2} d^{2} + 8 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + 2 \, d^{2} + 2 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \cos\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)} - 2 i \, d^{2}\right)} \sin\left(8 \, b x + 8 \, a\right) - {\left(8 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(16 i \, b c d - 16 i \, a d^{2}\right)} {\left(b x + a\right)} + 4 i \, d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) - {\left(2 \, d^{2} \cos\left(8 \, b x + 8 \, a\right) - 4 \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 2 i \, d^{2} \sin\left(8 \, b x + 8 \, a\right) - 4 i \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 2 \, d^{2}\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) - 1\right) + {\left(4 \, {\left(b x + a\right)}^{2} d^{2} + 8 \, {\left(b c d - a d^{2}\right)} {\left(b x + 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(8 \, b x + 8 \, a\right) - 8 \, {\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) + {\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(8 \, b x + 8 \, a\right) + {\left(-8 i \, {\left(b x + a\right)}^{2} d^{2} + {\left(-16 i \, b c d + 16 i \, a d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 8 \, {\left(-i \, {\left(b x + a\right)}^{2} d^{2} - b c d + a d^{2} + {\left(-2 i \, b c d + {\left(2 i \, a - 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(8 i \, {\left(b x + a\right)}^{2} d^{2} - 8 \, b c d + 8 \, a d^{2} + {\left(16 i \, b c d - 8 \, {\left(2 i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \cos\left(2 \, b x + 2 \, 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(8 \, b x + 8 \, a\right) - 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(4 \, b x + 4 \, 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(8 \, b x + 8 \, 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(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(8 \, b c d + 8 \, {\left(b x + a\right)} d^{2} - 8 \, a d^{2} + 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(8 \, b x + 8 \, a\right) - 16 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\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(8 \, b x + 8 \, a\right) + {\left(-16 i \, b c d - 16 i \, {\left(b x + a\right)} d^{2} + 16 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(8 \, b c d + 8 \, {\left(b x + a\right)} d^{2} - 8 \, a d^{2} + 8 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\left(8 \, b x + 8 \, a\right) - 16 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} \cos\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(8 \, b x + 8 \, a\right) + {\left(-16 i \, b c d - 16 i \, {\left(b x + a\right)} d^{2} + 16 i \, a d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\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)} - i \, d^{2} + {\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)} - i \, d^{2}\right)} \cos\left(8 \, b x + 8 \, 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)} + 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\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)} + d^{2}\right)} \sin\left(8 \, b x + 8 \, a\right) - 2 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \log\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) + {\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)} + i \, d^{2} + {\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)} + i \, d^{2}\right)} \cos\left(8 \, b x + 8 \, 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)} - 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\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)} + d^{2}\right)} \sin\left(8 \, b x + 8 \, a\right) + 2 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \sin\left(4 \, b x + 4 \, 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 \, {\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)} + i \, d^{2} + {\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)} + i \, d^{2}\right)} \cos\left(8 \, b x + 8 \, 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)} - 2 i \, d^{2}\right)} \cos\left(4 \, b x + 4 \, a\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)} + d^{2}\right)} \sin\left(8 \, b x + 8 \, a\right) + 2 \, {\left(2 \, {\left(b x + a\right)}^{2} d^{2} + 4 \, {\left(b c d - a d^{2}\right)} {\left(b x + a\right)} + d^{2}\right)} \sin\left(4 \, b x + 4 \, 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 \, d^{2} \cos\left(8 \, b x + 8 \, a\right) + 4 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) + 2 \, d^{2} \sin\left(8 \, b x + 8 \, a\right) - 4 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) - 2 i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(8 i \, d^{2} \cos\left(8 \, b x + 8 \, a\right) - 16 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \sin\left(8 \, b x + 8 \, a\right) + 16 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 8 i \, d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) + {\left(8 i \, d^{2} \cos\left(8 \, b x + 8 \, a\right) - 16 i \, d^{2} \cos\left(4 \, b x + 4 \, a\right) - 8 \, d^{2} \sin\left(8 \, b x + 8 \, a\right) + 16 \, d^{2} \sin\left(4 \, b x + 4 \, a\right) + 8 i \, d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) - {\left(8 \, {\left(b x + a\right)}^{2} d^{2} - 8 i \, b c d + 8 i \, a d^{2} + {\left(16 \, b c d - {\left(16 \, a + 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(8 \, {\left(b x + a\right)}^{2} d^{2} + 8 i \, b c d - 8 i \, a d^{2} + {\left(16 \, b c d - {\left(16 \, a - 8 i\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-2 i \, b^{2} \cos\left(8 \, b x + 8 \, a\right) + 4 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + 2 \, b^{2} \sin\left(8 \, b x + 8 \, a\right) - 4 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - 2 i \, b^{2}}}{2 \, b}"," ",0,"-1/2*(c^2*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2)) - 2*a*c*d*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2))/b + a^2*d^2*((2*sin(b*x + a)^2 - 1)/(sin(b*x + a)^4 - sin(b*x + a)^2) + 2*log(sin(b*x + a)^2 - 1) - 2*log(sin(b*x + a)^2))/b^2 + 2*((4*(b*x + a)^2*d^2 + 8*(b*c*d - a*d^2)*(b*x + a) + 2*d^2 + 2*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*cos(8*b*x + 8*a) - 4*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*cos(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) + 2*I*d^2)*sin(8*b*x + 8*a) + (-8*I*(b*x + a)^2*d^2 + (-16*I*b*c*d + 16*I*a*d^2)*(b*x + a) - 4*I*d^2)*sin(4*b*x + 4*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (4*(b*x + a)^2*d^2 + 8*(b*c*d - a*d^2)*(b*x + a) + 2*d^2 + 2*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*cos(8*b*x + 8*a) - 4*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*cos(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) - 2*I*d^2)*sin(8*b*x + 8*a) - (8*I*(b*x + a)^2*d^2 + (16*I*b*c*d - 16*I*a*d^2)*(b*x + a) + 4*I*d^2)*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*d^2*cos(8*b*x + 8*a) - 4*d^2*cos(4*b*x + 4*a) + 2*I*d^2*sin(8*b*x + 8*a) - 4*I*d^2*sin(4*b*x + 4*a) + 2*d^2)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (4*(b*x + a)^2*d^2 + 8*(b*c*d - a*d^2)*(b*x + a) + 4*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(8*b*x + 8*a) - 8*((b*x + a)^2*d^2 + 2*(b*c*d - a*d^2)*(b*x + a))*cos(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(8*b*x + 8*a) + (-8*I*(b*x + a)^2*d^2 + (-16*I*b*c*d + 16*I*a*d^2)*(b*x + a))*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 8*(-I*(b*x + a)^2*d^2 - b*c*d + a*d^2 + (-2*I*b*c*d + (2*I*a - 1)*d^2)*(b*x + a))*cos(6*b*x + 6*a) + (8*I*(b*x + a)^2*d^2 - 8*b*c*d + 8*a*d^2 + (16*I*b*c*d - 8*(2*I*a + 1)*d^2)*(b*x + a))*cos(2*b*x + 2*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(8*b*x + 8*a) - 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) - (-4*I*b*c*d - 4*I*(b*x + a)*d^2 + 4*I*a*d^2)*sin(8*b*x + 8*a) - (8*I*b*c*d + 8*I*(b*x + a)*d^2 - 8*I*a*d^2)*sin(4*b*x + 4*a))*dilog(-e^(2*I*b*x + 2*I*a)) + (8*b*c*d + 8*(b*x + a)*d^2 - 8*a*d^2 + 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(8*b*x + 8*a) - 16*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) + (8*I*b*c*d + 8*I*(b*x + a)*d^2 - 8*I*a*d^2)*sin(8*b*x + 8*a) + (-16*I*b*c*d - 16*I*(b*x + a)*d^2 + 16*I*a*d^2)*sin(4*b*x + 4*a))*dilog(-e^(I*b*x + I*a)) + (8*b*c*d + 8*(b*x + a)*d^2 - 8*a*d^2 + 8*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(8*b*x + 8*a) - 16*(b*c*d + (b*x + a)*d^2 - a*d^2)*cos(4*b*x + 4*a) + (8*I*b*c*d + 8*I*(b*x + a)*d^2 - 8*I*a*d^2)*sin(8*b*x + 8*a) + (-16*I*b*c*d - 16*I*(b*x + a)*d^2 + 16*I*a*d^2)*sin(4*b*x + 4*a))*dilog(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) - I*d^2 + (-2*I*(b*x + a)^2*d^2 + (-4*I*b*c*d + 4*I*a*d^2)*(b*x + a) - I*d^2)*cos(8*b*x + 8*a) + (4*I*(b*x + a)^2*d^2 + (8*I*b*c*d - 8*I*a*d^2)*(b*x + a) + 2*I*d^2)*cos(4*b*x + 4*a) + (2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*sin(8*b*x + 8*a) - 2*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*sin(4*b*x + 4*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a) + I*d^2 + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a) + I*d^2)*cos(8*b*x + 8*a) + (-4*I*(b*x + a)^2*d^2 + (-8*I*b*c*d + 8*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(4*b*x + 4*a) - (2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*sin(8*b*x + 8*a) + 2*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*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) + I*d^2 + (2*I*(b*x + a)^2*d^2 + (4*I*b*c*d - 4*I*a*d^2)*(b*x + a) + I*d^2)*cos(8*b*x + 8*a) + (-4*I*(b*x + a)^2*d^2 + (-8*I*b*c*d + 8*I*a*d^2)*(b*x + a) - 2*I*d^2)*cos(4*b*x + 4*a) - (2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*sin(8*b*x + 8*a) + 2*(2*(b*x + a)^2*d^2 + 4*(b*c*d - a*d^2)*(b*x + a) + d^2)*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + (-2*I*d^2*cos(8*b*x + 8*a) + 4*I*d^2*cos(4*b*x + 4*a) + 2*d^2*sin(8*b*x + 8*a) - 4*d^2*sin(4*b*x + 4*a) - 2*I*d^2)*polylog(3, -e^(2*I*b*x + 2*I*a)) + (8*I*d^2*cos(8*b*x + 8*a) - 16*I*d^2*cos(4*b*x + 4*a) - 8*d^2*sin(8*b*x + 8*a) + 16*d^2*sin(4*b*x + 4*a) + 8*I*d^2)*polylog(3, -e^(I*b*x + I*a)) + (8*I*d^2*cos(8*b*x + 8*a) - 16*I*d^2*cos(4*b*x + 4*a) - 8*d^2*sin(8*b*x + 8*a) + 16*d^2*sin(4*b*x + 4*a) + 8*I*d^2)*polylog(3, e^(I*b*x + I*a)) - (8*(b*x + a)^2*d^2 - 8*I*b*c*d + 8*I*a*d^2 + (16*b*c*d - (16*a + 8*I)*d^2)*(b*x + a))*sin(6*b*x + 6*a) - (8*(b*x + a)^2*d^2 + 8*I*b*c*d - 8*I*a*d^2 + (16*b*c*d - (16*a - 8*I)*d^2)*(b*x + a))*sin(2*b*x + 2*a))/(-2*I*b^2*cos(8*b*x + 8*a) + 4*I*b^2*cos(4*b*x + 4*a) + 2*b^2*sin(8*b*x + 8*a) - 4*b^2*sin(4*b*x + 4*a) - 2*I*b^2))/b","B",0
325,1,1078,0,0.748036," ","integrate((d*x+c)*csc(b*x+a)^3*sec(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(8 \, b x + 8 \, a\right) - 4 \, {\left(b d x + b c\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(2 i \, b d x + 2 i \, b c\right)} \sin\left(8 \, b x + 8 \, a\right) + {\left(-4 i \, b d x - 4 i \, b c\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(2 \, b d x + 2 \, b c + 2 \, {\left(b d x + b c\right)} \cos\left(8 \, b x + 8 \, a\right) - 4 \, {\left(b d x + b c\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(-2 i \, b d x - 2 i \, b c\right)} \sin\left(8 \, b x + 8 \, a\right) - {\left(4 i \, b d x + 4 i \, b c\right)} \sin\left(4 \, b x + 4 \, 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(8 \, b x + 8 \, a\right) - 4 \, b c \cos\left(4 \, b x + 4 \, a\right) + 2 i \, b c \sin\left(8 \, b x + 8 \, a\right) - 4 i \, b c \sin\left(4 \, b x + 4 \, 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(8 \, b x + 8 \, a\right) - 4 \, b d x \cos\left(4 \, b x + 4 \, a\right) + 2 i \, b d x \sin\left(8 \, b x + 8 \, a\right) - 4 i \, b d x \sin\left(4 \, b x + 4 \, 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 + 2 \, d\right)} \cos\left(6 \, b x + 6 \, a\right) + {\left(4 i \, b d x + 4 i \, b c - 2 \, d\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(d \cos\left(8 \, b x + 8 \, a\right) - 2 \, d \cos\left(4 \, b x + 4 \, a\right) + i \, d \sin\left(8 \, b x + 8 \, a\right) - 2 i \, d \sin\left(4 \, b x + 4 \, a\right) + d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + {\left(2 \, d \cos\left(8 \, b x + 8 \, a\right) - 4 \, d \cos\left(4 \, b x + 4 \, a\right) + 2 i \, d \sin\left(8 \, b x + 8 \, a\right) - 4 i \, d \sin\left(4 \, b x + 4 \, a\right) + 2 \, d\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(2 \, d \cos\left(8 \, b x + 8 \, a\right) - 4 \, d \cos\left(4 \, b x + 4 \, a\right) + 2 i \, d \sin\left(8 \, b x + 8 \, a\right) - 4 i \, d \sin\left(4 \, b x + 4 \, 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(8 \, b x + 8 \, a\right) + {\left(2 i \, b d x + 2 i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(b d x + b c\right)} \sin\left(8 \, b x + 8 \, a\right) - 2 \, {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, a\right)\right)} \log\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) + {\left(i \, b d x + i \, b c + {\left(i \, b d x + i \, b c\right)} \cos\left(8 \, b x + 8 \, a\right) + {\left(-2 i \, b d x - 2 i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(b d x + b c\right)} \sin\left(8 \, b x + 8 \, a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, 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(8 \, b x + 8 \, a\right) + {\left(-2 i \, b d x - 2 i \, b c\right)} \cos\left(4 \, b x + 4 \, a\right) - {\left(b d x + b c\right)} \sin\left(8 \, b x + 8 \, a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(4 \, b x + 4 \, 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 \, b d x + 4 \, b c - 2 i \, d\right)} \sin\left(6 \, b x + 6 \, a\right) - {\left(4 \, b d x + 4 \, b c + 2 i \, d\right)} \sin\left(2 \, b x + 2 \, a\right)}{-i \, b^{2} \cos\left(8 \, b x + 8 \, a\right) + 2 i \, b^{2} \cos\left(4 \, b x + 4 \, a\right) + b^{2} \sin\left(8 \, b x + 8 \, a\right) - 2 \, b^{2} \sin\left(4 \, b x + 4 \, a\right) - i \, b^{2}}"," ",0,"-((2*b*d*x + 2*b*c + 2*(b*d*x + b*c)*cos(8*b*x + 8*a) - 4*(b*d*x + b*c)*cos(4*b*x + 4*a) + (2*I*b*d*x + 2*I*b*c)*sin(8*b*x + 8*a) + (-4*I*b*d*x - 4*I*b*c)*sin(4*b*x + 4*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - (2*b*d*x + 2*b*c + 2*(b*d*x + b*c)*cos(8*b*x + 8*a) - 4*(b*d*x + b*c)*cos(4*b*x + 4*a) - (-2*I*b*d*x - 2*I*b*c)*sin(8*b*x + 8*a) - (4*I*b*d*x + 4*I*b*c)*sin(4*b*x + 4*a))*arctan2(sin(b*x + a), cos(b*x + a) + 1) - (2*b*c*cos(8*b*x + 8*a) - 4*b*c*cos(4*b*x + 4*a) + 2*I*b*c*sin(8*b*x + 8*a) - 4*I*b*c*sin(4*b*x + 4*a) + 2*b*c)*arctan2(sin(b*x + a), cos(b*x + a) - 1) + (2*b*d*x*cos(8*b*x + 8*a) - 4*b*d*x*cos(4*b*x + 4*a) + 2*I*b*d*x*sin(8*b*x + 8*a) - 4*I*b*d*x*sin(4*b*x + 4*a) + 2*b*d*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) + (4*I*b*d*x + 4*I*b*c + 2*d)*cos(6*b*x + 6*a) + (4*I*b*d*x + 4*I*b*c - 2*d)*cos(2*b*x + 2*a) - (d*cos(8*b*x + 8*a) - 2*d*cos(4*b*x + 4*a) + I*d*sin(8*b*x + 8*a) - 2*I*d*sin(4*b*x + 4*a) + d)*dilog(-e^(2*I*b*x + 2*I*a)) + (2*d*cos(8*b*x + 8*a) - 4*d*cos(4*b*x + 4*a) + 2*I*d*sin(8*b*x + 8*a) - 4*I*d*sin(4*b*x + 4*a) + 2*d)*dilog(-e^(I*b*x + I*a)) + (2*d*cos(8*b*x + 8*a) - 4*d*cos(4*b*x + 4*a) + 2*I*d*sin(8*b*x + 8*a) - 4*I*d*sin(4*b*x + 4*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(8*b*x + 8*a) + (2*I*b*d*x + 2*I*b*c)*cos(4*b*x + 4*a) + (b*d*x + b*c)*sin(8*b*x + 8*a) - 2*(b*d*x + b*c)*sin(4*b*x + 4*a))*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (I*b*d*x + I*b*c + (I*b*d*x + I*b*c)*cos(8*b*x + 8*a) + (-2*I*b*d*x - 2*I*b*c)*cos(4*b*x + 4*a) - (b*d*x + b*c)*sin(8*b*x + 8*a) + 2*(b*d*x + b*c)*sin(4*b*x + 4*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(8*b*x + 8*a) + (-2*I*b*d*x - 2*I*b*c)*cos(4*b*x + 4*a) - (b*d*x + b*c)*sin(8*b*x + 8*a) + 2*(b*d*x + b*c)*sin(4*b*x + 4*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) - (4*b*d*x + 4*b*c - 2*I*d)*sin(6*b*x + 6*a) - (4*b*d*x + 4*b*c + 2*I*d)*sin(2*b*x + 2*a))/(-I*b^2*cos(8*b*x + 8*a) + 2*I*b^2*cos(4*b*x + 4*a) + b^2*sin(8*b*x + 8*a) - 2*b^2*sin(4*b*x + 4*a) - I*b^2)","B",0
326,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(5/2)*sin(b*x+a),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right)^{\frac{5}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*cos(b*x + a)^(5/2)*sin(b*x + a), x)","F",0
329,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2)*sin(b*x+a),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right)^{\frac{3}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*cos(b*x + a)^(3/2)*sin(b*x + a), x)","F",0
330,0,0,0,0.000000," ","integrate(x*sin(b*x+a)*cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\cos\left(b x + a\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*sqrt(cos(b*x + a))*sin(b*x + a), x)","F",0
331,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/sqrt(cos(b*x + a)), x)","F",0
332,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/cos(b*x + a)^(3/2), x)","F",0
333,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/cos(b*x + a)^(5/2), x)","F",0
334,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/cos(b*x + a)^(7/2), x)","F",0
335,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(9/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\cos\left(b x + a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/cos(b*x + a)^(9/2), x)","F",0
336,0,0,0,0.000000," ","integrate(x*sec(b*x+a)^(9/2)*sin(b*x+a),x, algorithm=""maxima"")","\int x \sec\left(b x + a\right)^{\frac{9}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*sec(b*x + a)^(9/2)*sin(b*x + a), x)","F",0
337,0,0,0,0.000000," ","integrate(x*sec(b*x+a)^(7/2)*sin(b*x+a),x, algorithm=""maxima"")","\int x \sec\left(b x + a\right)^{\frac{7}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*sec(b*x + a)^(7/2)*sin(b*x + a), x)","F",0
338,0,0,0,0.000000," ","integrate(x*sec(b*x+a)^(5/2)*sin(b*x+a),x, algorithm=""maxima"")","\int x \sec\left(b x + a\right)^{\frac{5}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*sec(b*x + a)^(5/2)*sin(b*x + a), x)","F",0
339,0,0,0,0.000000," ","integrate(x*sec(b*x+a)^(3/2)*sin(b*x+a),x, algorithm=""maxima"")","\int x \sec\left(b x + a\right)^{\frac{3}{2}} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*sec(b*x + a)^(3/2)*sin(b*x + a), x)","F",0
340,0,0,0,0.000000," ","integrate(x*sin(b*x+a)*sec(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\sec\left(b x + a\right)} \sin\left(b x + a\right)\,{d x}"," ",0,"integrate(x*sqrt(sec(b*x + a))*sin(b*x + a), x)","F",0
341,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\sqrt{\sec\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/sqrt(sec(b*x + a)), x)","F",0
342,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\sec\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/sec(b*x + a)^(3/2), x)","F",0
343,0,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{x \sin\left(b x + a\right)}{\sec\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*sin(b*x + a)/sec(b*x + a)^(5/2), x)","F",0
344,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)^(5/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \sin\left(b x + a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*sin(b*x + a)^(5/2), x)","F",0
345,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)^(3/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \sin\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*sin(b*x + a)^(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \sqrt{\sin\left(b x + a\right)}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*sqrt(sin(b*x + a)), x)","F",0
347,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\sqrt{\sin\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/sqrt(sin(b*x + a)), x)","F",0
348,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\sin\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/sin(b*x + a)^(3/2), x)","F",0
349,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\sin\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/sin(b*x + a)^(5/2), x)","F",0
350,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(7/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\sin\left(b x + a\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/sin(b*x + a)^(7/2), x)","F",0
351,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(9/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\sin\left(b x + a\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/sin(b*x + a)^(9/2), x)","F",0
352,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(9/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \csc\left(b x + a\right)^{\frac{9}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*csc(b*x + a)^(9/2), x)","F",0
353,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(7/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \csc\left(b x + a\right)^{\frac{7}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*csc(b*x + a)^(7/2), x)","F",0
354,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(5/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \csc\left(b x + a\right)^{\frac{5}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*csc(b*x + a)^(5/2), x)","F",0
355,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(3/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \csc\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*csc(b*x + a)^(3/2), x)","F",0
356,0,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right) \sqrt{\csc\left(b x + a\right)}\,{d x}"," ",0,"integrate(x*cos(b*x + a)*sqrt(csc(b*x + a)), x)","F",0
357,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\sqrt{\csc\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/sqrt(csc(b*x + a)), x)","F",0
358,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\csc\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/csc(b*x + a)^(3/2), x)","F",0
359,0,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)^(5/2),x, algorithm=""maxima"")","\int \frac{x \cos\left(b x + a\right)}{\csc\left(b x + a\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)/csc(b*x + a)^(5/2), x)","F",0
360,1,18,0,0.317660," ","integrate(x*csc(x)*sin(3*x),x, algorithm=""maxima"")","\frac{1}{2} \, x^{2} + x \sin\left(2 \, x\right) + \frac{1}{2} \, \cos\left(2 \, x\right)"," ",0,"1/2*x^2 + x*sin(2*x) + 1/2*cos(2*x)","A",0
361,1,146,0,0.346184," ","integrate((d*x+c)^4*csc(x)*sin(3*x),x, algorithm=""maxima"")","2 \, {\left(x^{2} + 2 \, x \sin\left(2 \, x\right) + \cos\left(2 \, x\right)\right)} c^{3} d + {\left(2 \, x^{3} + 6 \, x \cos\left(2 \, x\right) + 3 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)\right)} c^{2} d^{2} + {\left(x^{4} + 3 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + 2 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right)\right)} c d^{3} + \frac{1}{10} \, {\left(2 \, x^{5} + 10 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(2 \, x\right) + 5 \, {\left(2 \, x^{4} - 6 \, x^{2} + 3\right)} \sin\left(2 \, x\right)\right)} d^{4} + c^{4} {\left(x + \sin\left(2 \, x\right)\right)}"," ",0,"2*(x^2 + 2*x*sin(2*x) + cos(2*x))*c^3*d + (2*x^3 + 6*x*cos(2*x) + 3*(2*x^2 - 1)*sin(2*x))*c^2*d^2 + (x^4 + 3*(2*x^2 - 1)*cos(2*x) + 2*(2*x^3 - 3*x)*sin(2*x))*c*d^3 + 1/10*(2*x^5 + 10*(2*x^3 - 3*x)*cos(2*x) + 5*(2*x^4 - 6*x^2 + 3)*sin(2*x))*d^4 + c^4*(x + sin(2*x))","A",0
362,1,101,0,0.338393," ","integrate((d*x+c)^3*csc(x)*sin(3*x),x, algorithm=""maxima"")","\frac{3}{2} \, {\left(x^{2} + 2 \, x \sin\left(2 \, x\right) + \cos\left(2 \, x\right)\right)} c^{2} d + \frac{1}{2} \, {\left(2 \, x^{3} + 6 \, x \cos\left(2 \, x\right) + 3 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)\right)} c d^{2} + \frac{1}{4} \, {\left(x^{4} + 3 \, {\left(2 \, x^{2} - 1\right)} \cos\left(2 \, x\right) + 2 \, {\left(2 \, x^{3} - 3 \, x\right)} \sin\left(2 \, x\right)\right)} d^{3} + c^{3} {\left(x + \sin\left(2 \, x\right)\right)}"," ",0,"3/2*(x^2 + 2*x*sin(2*x) + cos(2*x))*c^2*d + 1/2*(2*x^3 + 6*x*cos(2*x) + 3*(2*x^2 - 1)*sin(2*x))*c*d^2 + 1/4*(x^4 + 3*(2*x^2 - 1)*cos(2*x) + 2*(2*x^3 - 3*x)*sin(2*x))*d^3 + c^3*(x + sin(2*x))","A",0
363,1,60,0,0.333487," ","integrate((d*x+c)^2*csc(x)*sin(3*x),x, algorithm=""maxima"")","{\left(x^{2} + 2 \, x \sin\left(2 \, x\right) + \cos\left(2 \, x\right)\right)} c d + \frac{1}{6} \, {\left(2 \, x^{3} + 6 \, x \cos\left(2 \, x\right) + 3 \, {\left(2 \, x^{2} - 1\right)} \sin\left(2 \, x\right)\right)} d^{2} + c^{2} {\left(x + \sin\left(2 \, x\right)\right)}"," ",0,"(x^2 + 2*x*sin(2*x) + cos(2*x))*c*d + 1/6*(2*x^3 + 6*x*cos(2*x) + 3*(2*x^2 - 1)*sin(2*x))*d^2 + c^2*(x + sin(2*x))","A",0
364,1,27,0,0.342240," ","integrate((d*x+c)*csc(x)*sin(3*x),x, algorithm=""maxima"")","\frac{1}{2} \, {\left(x^{2} + 2 \, x \sin\left(2 \, x\right) + \cos\left(2 \, x\right)\right)} d + c {\left(x + \sin\left(2 \, x\right)\right)}"," ",0,"1/2*(x^2 + 2*x*sin(2*x) + cos(2*x))*d + c*(x + sin(2*x))","A",0
365,1,95,0,0.381656," ","integrate(csc(x)*sin(3*x)/(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(E_{1}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{1}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right) - {\left(-i \, E_{1}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + i \, E_{1}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \sin\left(\frac{2 \, c}{d}\right) - \log\left(d x + c\right)}{d}"," ",0,"-((exp_integral_e(1, (2*I*d*x + 2*I*c)/d) + exp_integral_e(1, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d) - (-I*exp_integral_e(1, (2*I*d*x + 2*I*c)/d) + I*exp_integral_e(1, -(2*I*d*x + 2*I*c)/d))*sin(2*c/d) - log(d*x + c))/d","C",0
366,1,324,0,0.401341," ","integrate(csc(x)*sin(3*x)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(E_{2}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{2}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right)^{3} + {\left(i \, E_{2}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) - i \, E_{2}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \sin\left(\frac{2 \, c}{d}\right)^{3} + {\left({\left(E_{2}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{2}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right) + 2\right)} \sin\left(\frac{2 \, c}{d}\right)^{2} + {\left(E_{2}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{2}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right) + 2 \, \cos\left(\frac{2 \, c}{d}\right)^{2} + {\left({\left(i \, E_{2}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) - i \, E_{2}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right)^{2} + i \, E_{2}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) - i \, E_{2}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \sin\left(\frac{2 \, c}{d}\right)}{2 \, {\left({\left(\cos\left(\frac{2 \, c}{d}\right)^{2} + \sin\left(\frac{2 \, c}{d}\right)^{2}\right)} d^{2} x + {\left(c \cos\left(\frac{2 \, c}{d}\right)^{2} + c \sin\left(\frac{2 \, c}{d}\right)^{2}\right)} d\right)}}"," ",0,"-1/2*((exp_integral_e(2, (2*I*d*x + 2*I*c)/d) + exp_integral_e(2, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d)^3 + (I*exp_integral_e(2, (2*I*d*x + 2*I*c)/d) - I*exp_integral_e(2, -(2*I*d*x + 2*I*c)/d))*sin(2*c/d)^3 + ((exp_integral_e(2, (2*I*d*x + 2*I*c)/d) + exp_integral_e(2, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d) + 2)*sin(2*c/d)^2 + (exp_integral_e(2, (2*I*d*x + 2*I*c)/d) + exp_integral_e(2, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d) + 2*cos(2*c/d)^2 + ((I*exp_integral_e(2, (2*I*d*x + 2*I*c)/d) - I*exp_integral_e(2, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d)^2 + I*exp_integral_e(2, (2*I*d*x + 2*I*c)/d) - I*exp_integral_e(2, -(2*I*d*x + 2*I*c)/d))*sin(2*c/d))/((cos(2*c/d)^2 + sin(2*c/d)^2)*d^2*x + (c*cos(2*c/d)^2 + c*sin(2*c/d)^2)*d)","C",0
367,1,362,0,0.421883," ","integrate(csc(x)*sin(3*x)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(E_{3}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{3}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right)^{3} + {\left(2 i \, E_{3}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) - 2 i \, E_{3}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \sin\left(\frac{2 \, c}{d}\right)^{3} + 2 \, {\left({\left(E_{3}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{3}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right) + 1\right)} \sin\left(\frac{2 \, c}{d}\right)^{2} + 2 \, {\left(E_{3}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) + E_{3}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right) + 2 \, \cos\left(\frac{2 \, c}{d}\right)^{2} + {\left({\left(2 i \, E_{3}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) - 2 i \, E_{3}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right)^{2} + 2 i \, E_{3}\left(\frac{2 i \, d x + 2 i \, c}{d}\right) - 2 i \, E_{3}\left(-\frac{2 i \, d x + 2 i \, c}{d}\right)\right)} \sin\left(\frac{2 \, c}{d}\right)}{4 \, {\left({\left(\cos\left(\frac{2 \, c}{d}\right)^{2} + \sin\left(\frac{2 \, c}{d}\right)^{2}\right)} d^{3} x^{2} + 2 \, {\left(c \cos\left(\frac{2 \, c}{d}\right)^{2} + c \sin\left(\frac{2 \, c}{d}\right)^{2}\right)} d^{2} x + {\left(c^{2} \cos\left(\frac{2 \, c}{d}\right)^{2} + c^{2} \sin\left(\frac{2 \, c}{d}\right)^{2}\right)} d\right)}}"," ",0,"-1/4*(2*(exp_integral_e(3, (2*I*d*x + 2*I*c)/d) + exp_integral_e(3, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d)^3 + (2*I*exp_integral_e(3, (2*I*d*x + 2*I*c)/d) - 2*I*exp_integral_e(3, -(2*I*d*x + 2*I*c)/d))*sin(2*c/d)^3 + 2*((exp_integral_e(3, (2*I*d*x + 2*I*c)/d) + exp_integral_e(3, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d) + 1)*sin(2*c/d)^2 + 2*(exp_integral_e(3, (2*I*d*x + 2*I*c)/d) + exp_integral_e(3, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d) + 2*cos(2*c/d)^2 + ((2*I*exp_integral_e(3, (2*I*d*x + 2*I*c)/d) - 2*I*exp_integral_e(3, -(2*I*d*x + 2*I*c)/d))*cos(2*c/d)^2 + 2*I*exp_integral_e(3, (2*I*d*x + 2*I*c)/d) - 2*I*exp_integral_e(3, -(2*I*d*x + 2*I*c)/d))*sin(2*c/d))/((cos(2*c/d)^2 + sin(2*c/d)^2)*d^3*x^2 + 2*(c*cos(2*c/d)^2 + c*sin(2*c/d)^2)*d^2*x + (c^2*cos(2*c/d)^2 + c^2*sin(2*c/d)^2)*d)","C",0
368,1,244,0,0.401329," ","integrate((d*x+c)^4*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{{\left(b x + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{4}}{b} + \frac{2 \, {\left(b^{2} x^{2} + 2 \, b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b^{2}} + \frac{{\left(2 \, b^{3} x^{3} + 6 \, b x \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{3}} + \frac{{\left(b^{4} x^{4} + 3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(2 \, b^{3} x^{3} - 3 \, b x\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{3}}{b^{4}} + \frac{{\left(2 \, b^{5} x^{5} + 10 \, {\left(2 \, b^{3} x^{3} - 3 \, b x\right)} \cos\left(2 \, b x + 2 \, a\right) + 5 \, {\left(2 \, b^{4} x^{4} - 6 \, b^{2} x^{2} + 3\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{4}}{10 \, b^{5}}"," ",0,"(b*x + sin(2*b*x + 2*a))*c^4/b + 2*(b^2*x^2 + 2*b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*c^3*d/b^2 + (2*b^3*x^3 + 6*b*x*cos(2*b*x + 2*a) + 3*(2*b^2*x^2 - 1)*sin(2*b*x + 2*a))*c^2*d^2/b^3 + (b^4*x^4 + 3*(2*b^2*x^2 - 1)*cos(2*b*x + 2*a) + 2*(2*b^3*x^3 - 3*b*x)*sin(2*b*x + 2*a))*c*d^3/b^4 + 1/10*(2*b^5*x^5 + 10*(2*b^3*x^3 - 3*b*x)*cos(2*b*x + 2*a) + 5*(2*b^4*x^4 - 6*b^2*x^2 + 3)*sin(2*b*x + 2*a))*d^4/b^5","A",0
369,1,173,0,0.371550," ","integrate((d*x+c)^3*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{{\left(b x + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3}}{b} + \frac{3 \, {\left(b^{2} x^{2} + 2 \, b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{2 \, b^{2}} + \frac{{\left(2 \, b^{3} x^{3} + 6 \, b x \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{2 \, b^{3}} + \frac{{\left(b^{4} x^{4} + 3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(2 \, b^{3} x^{3} - 3 \, b x\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{3}}{4 \, b^{4}}"," ",0,"(b*x + sin(2*b*x + 2*a))*c^3/b + 3/2*(b^2*x^2 + 2*b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*c^2*d/b^2 + 1/2*(2*b^3*x^3 + 6*b*x*cos(2*b*x + 2*a) + 3*(2*b^2*x^2 - 1)*sin(2*b*x + 2*a))*c*d^2/b^3 + 1/4*(b^4*x^4 + 3*(2*b^2*x^2 - 1)*cos(2*b*x + 2*a) + 2*(2*b^3*x^3 - 3*b*x)*sin(2*b*x + 2*a))*d^3/b^4","A",0
370,1,108,0,0.353146," ","integrate((d*x+c)^2*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{{\left(b x + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2}}{b} + \frac{{\left(b^{2} x^{2} + 2 \, b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} c d}{b^{2}} + \frac{{\left(2 \, b^{3} x^{3} + 6 \, b x \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{6 \, b^{3}}"," ",0,"(b*x + sin(2*b*x + 2*a))*c^2/b + (b^2*x^2 + 2*b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*c*d/b^2 + 1/6*(2*b^3*x^3 + 6*b*x*cos(2*b*x + 2*a) + 3*(2*b^2*x^2 - 1)*sin(2*b*x + 2*a))*d^2/b^3","A",0
371,1,55,0,0.344974," ","integrate((d*x+c)*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{{\left(b x + \sin\left(2 \, b x + 2 \, a\right)\right)} c}{b} + \frac{{\left(b^{2} x^{2} + 2 \, b x \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} d}{2 \, b^{2}}"," ",0,"(b*x + sin(2*b*x + 2*a))*c/b + 1/2*(b^2*x^2 + 2*b*x*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*d/b^2","A",0
372,1,117,0,0.406284," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(i \, E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \log\left(d x + c\right)}{d}"," ",0,"-((exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) - (I*exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d) - log(d*x + c))/d","C",0
373,1,118,0,0.420711," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(i \, E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 1}{d^{2} x + c d}"," ",0,"-((exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) - (I*exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d) + 1)/(d^2*x + c*d)","C",0
374,1,130,0,0.430017," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(E_{3}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{3}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(2 i \, E_{3}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - 2 i \, E_{3}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 1}{2 \, {\left(d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d\right)}}"," ",0,"-1/2*(2*(exp_integral_e(3, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(3, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) - (2*I*exp_integral_e(3, (2*I*b*d*x + 2*I*b*c)/d) - 2*I*exp_integral_e(3, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d) + 1)/(d^3*x^2 + 2*c*d^2*x + c^2*d)","C",0
375,1,141,0,0.446551," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{3 \, {\left(E_{4}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{4}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(3 i \, E_{4}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - 3 i \, E_{4}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 1}{3 \, {\left(d^{4} x^{3} + 3 \, c d^{3} x^{2} + 3 \, c^{2} d^{2} x + c^{3} d\right)}}"," ",0,"-1/3*(3*(exp_integral_e(4, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(4, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) - (3*I*exp_integral_e(4, (2*I*b*d*x + 2*I*b*c)/d) - 3*I*exp_integral_e(4, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d) + 1)/(d^4*x^3 + 3*c*d^3*x^2 + 3*c^2*d^2*x + c^3*d)","C",0
376,1,602,0,0.542935," ","integrate((d*x+c)^3*csc(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{c^{3} {\left(8 \, \cos\left(b x + a\right) - 3 \, \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 3 \, \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)\right)}}{2 \, b} - \frac{36 i \, d^{3} {\rm Li}_{4}(-e^{\left(i \, b x + i \, a\right)}) - 36 i \, d^{3} {\rm Li}_{4}(e^{\left(i \, b x + i \, a\right)}) + {\left(6 i \, b^{3} d^{3} x^{3} + 18 i \, b^{3} c d^{2} x^{2} + 18 i \, b^{3} c^{2} d x\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(6 i \, b^{3} d^{3} x^{3} + 18 i \, b^{3} c d^{2} x^{2} + 18 i \, b^{3} c^{2} d x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 8 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right) + {\left(-18 i \, b^{2} d^{3} x^{2} - 36 i \, b^{2} c d^{2} x - 18 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(18 i \, b^{2} d^{3} x^{2} + 36 i \, b^{2} c d^{2} x + 18 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x\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) - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x\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) + 36 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - 36 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + 24 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \sin\left(b x + a\right)}{2 \, b^{4}}"," ",0,"1/2*c^3*(8*cos(b*x + a) - 3*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + 3*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b - 1/2*(36*I*d^3*polylog(4, -e^(I*b*x + I*a)) - 36*I*d^3*polylog(4, e^(I*b*x + I*a)) + (6*I*b^3*d^3*x^3 + 18*I*b^3*c*d^2*x^2 + 18*I*b^3*c^2*d*x)*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*I*b^3*d^3*x^3 + 18*I*b^3*c*d^2*x^2 + 18*I*b^3*c^2*d*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 8*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a) + (-18*I*b^2*d^3*x^2 - 36*I*b^2*c*d^2*x - 18*I*b^2*c^2*d)*dilog(-e^(I*b*x + I*a)) + (18*I*b^2*d^3*x^2 + 36*I*b^2*c*d^2*x + 18*I*b^2*c^2*d)*dilog(e^(I*b*x + I*a)) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 36*(b*d^3*x + b*c*d^2)*polylog(3, -e^(I*b*x + I*a)) - 36*(b*d^3*x + b*c*d^2)*polylog(3, e^(I*b*x + I*a)) + 24*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*sin(b*x + a))/b^4","B",0
377,1,409,0,0.491490," ","integrate((d*x+c)^2*csc(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{c^{2} {\left(8 \, \cos\left(b x + a\right) - 3 \, \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 3 \, \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)\right)}}{2 \, b} - \frac{12 \, d^{2} {\rm Li}_{3}(-e^{\left(i \, b x + i \, a\right)}) - 12 \, d^{2} {\rm Li}_{3}(e^{\left(i \, b x + i \, a\right)}) + {\left(6 i \, b^{2} d^{2} x^{2} + 12 i \, b^{2} c d x\right)} \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + {\left(6 i \, b^{2} d^{2} x^{2} + 12 i \, b^{2} c d x\right)} \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 8 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x - 2 \, d^{2}\right)} \cos\left(b x + a\right) + {\left(-12 i \, b d^{2} x - 12 i \, b c d\right)} {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + {\left(12 i \, b d^{2} x + 12 i \, b c d\right)} {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x\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) - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x\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) + 16 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*c^2*(8*cos(b*x + a) - 3*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + 3*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b - 1/2*(12*d^2*polylog(3, -e^(I*b*x + I*a)) - 12*d^2*polylog(3, e^(I*b*x + I*a)) + (6*I*b^2*d^2*x^2 + 12*I*b^2*c*d*x)*arctan2(sin(b*x + a), cos(b*x + a) + 1) + (6*I*b^2*d^2*x^2 + 12*I*b^2*c*d*x)*arctan2(sin(b*x + a), -cos(b*x + a) + 1) - 8*(b^2*d^2*x^2 + 2*b^2*c*d*x - 2*d^2)*cos(b*x + a) + (-12*I*b*d^2*x - 12*I*b*c*d)*dilog(-e^(I*b*x + I*a)) + (12*I*b*d^2*x + 12*I*b*c*d)*dilog(e^(I*b*x + I*a)) + 3*(b^2*d^2*x^2 + 2*b^2*c*d*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1) - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x)*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1) + 16*(b*d^2*x + b*c*d)*sin(b*x + a))/b^3","B",0
378,0,0,0,0.000000," ","integrate((d*x+c)*csc(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""maxima"")","\frac{c {\left(8 \, \cos\left(b x + a\right) - 3 \, \log\left(\cos\left(b x\right)^{2} + 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} - 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right) + 3 \, \log\left(\cos\left(b x\right)^{2} - 2 \, \cos\left(b x\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(b x\right)^{2} + 2 \, \sin\left(b x\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)\right)}}{2 \, b} + \frac{-\frac{1}{2} \, {\left(6 i \, b x \arctan\left(\sin\left(b x + a\right), \cos\left(b x + a\right) + 1\right) + 6 i \, b x \arctan\left(\sin\left(b x + a\right), -\cos\left(b x + a\right) + 1\right) - 8 \, b x \cos\left(b x + a\right) + 3 \, b x \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) - 3 \, b x \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) - 6 i \, {\rm Li}_2\left(-e^{\left(i \, b x + i \, a\right)}\right) + 6 i \, {\rm Li}_2\left(e^{\left(i \, b x + i \, a\right)}\right) + 8 \, \sin\left(b x + a\right)\right)} d}{b^{2}}"," ",0,"1/2*c*(8*cos(b*x + a) - 3*log(cos(b*x)^2 + 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 - 2*sin(b*x)*sin(a) + sin(a)^2) + 3*log(cos(b*x)^2 - 2*cos(b*x)*cos(a) + cos(a)^2 + sin(b*x)^2 + 2*sin(b*x)*sin(a) + sin(a)^2))/b + (4*b*x*cos(b*x + a) + 3*b^2*integrate(x*sin(b*x + a)/(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*cos(b*x + a) + 1), x) + 3*b^2*integrate(x*sin(b*x + a)/(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*cos(b*x + a) + 1), x) - 4*sin(b*x + a))*d/b^2","F",0
379,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""maxima"")","\frac{{\left(2 i \, E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) - 2 i \, E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 3 \, d \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} + 3 \, d \int \frac{\sin\left(b x + a\right)}{{\left(d x + c\right)} {\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} + 2 \, {\left(E_{1}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{1}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{d}"," ",0,"((2*I*exp_integral_e(1, (I*b*d*x + I*b*c)/d) - 2*I*exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) + 3*d*integrate(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x + 2*(d*x + c)*cos(b*x + a) + c), x) + 3*d*integrate(sin(b*x + a)/((d*x + c)*cos(b*x + a)^2 + (d*x + c)*sin(b*x + a)^2 + d*x - 2*(d*x + c)*cos(b*x + a) + c), x) + 2*(exp_integral_e(1, (I*b*d*x + I*b*c)/d) + exp_integral_e(1, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))/d","F",0
380,0,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""maxima"")","\frac{{\left(2 i \, E_{2}\left(\frac{i \, b d x + i \, b c}{d}\right) - 2 i \, E_{2}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 3 \, {\left(d^{2} x + c d\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} + 3 \, {\left(d^{2} x + c d\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} + 2 \, {\left(E_{2}\left(\frac{i \, b d x + i \, b c}{d}\right) + E_{2}\left(-\frac{i \, b d x + i \, b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{d^{2} x + c d}"," ",0,"((2*I*exp_integral_e(2, (I*b*d*x + I*b*c)/d) - 2*I*exp_integral_e(2, -(I*b*d*x + I*b*c)/d))*cos(-(b*c - a*d)/d) + 3*(d^2*x + c*d)*integrate(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) + 3*(d^2*x + c*d)*integrate(sin(b*x + a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(b*x + a)^2 + c^2 - 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(b*x + a)), x) + 2*(exp_integral_e(2, (I*b*d*x + I*b*c)/d) + exp_integral_e(2, -(I*b*d*x + I*b*c)/d))*sin(-(b*c - a*d)/d))/(d^2*x + c*d)","F",0
381,-1,0,0,0.000000," ","integrate(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
382,1,607,0,0.517454," ","integrate((d*x+c)^4*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","-\frac{c^{4} {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right)\right)}}{2 \, b} + \frac{-6 i \, b^{5} d^{4} x^{5} - 30 i \, b^{5} c d^{3} x^{4} - 60 i \, b^{5} c^{2} d^{2} x^{3} - 60 i \, b^{5} c^{3} d x^{2} - 90 \, d^{4} {\rm Li}_{5}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(60 i \, b^{4} d^{4} x^{4} + 160 i \, b^{4} c d^{3} x^{3} + 180 i \, b^{4} c^{2} d^{2} x^{2} + 120 i \, b^{4} c^{3} d x\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 15 \, {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} - 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-120 i \, b^{3} d^{4} x^{3} - 240 i \, b^{3} c d^{3} x^{2} - 180 i \, b^{3} c^{2} d^{2} x - 60 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 10 \, {\left(3 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 9 \, b^{4} c^{2} d^{2} x^{2} + 6 \, b^{4} c^{3} d x\right)} \log\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) + {\left(180 i \, b d^{4} x + 120 i \, b c d^{3}\right)} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + 30 \, {\left(6 \, b^{2} d^{4} x^{2} + 8 \, b^{2} c d^{3} x + 3 \, b^{2} c^{2} d^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + 30 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{30 \, b^{5}}"," ",0,"-1/2*c^4*(2*cos(2*b*x + 2*a) - log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2))/b + 1/30*(-6*I*b^5*d^4*x^5 - 30*I*b^5*c*d^3*x^4 - 60*I*b^5*c^2*d^2*x^3 - 60*I*b^5*c^3*d*x^2 - 90*d^4*polylog(5, -e^(2*I*b*x + 2*I*a)) + (60*I*b^4*d^4*x^4 + 160*I*b^4*c*d^3*x^3 + 180*I*b^4*c^2*d^2*x^2 + 120*I*b^4*c^3*d*x)*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 15*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 - 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(2*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(2*b*x + 2*a) + (-120*I*b^3*d^4*x^3 - 240*I*b^3*c*d^3*x^2 - 180*I*b^3*c^2*d^2*x - 60*I*b^3*c^3*d)*dilog(-e^(2*I*b*x + 2*I*a)) + 10*(3*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 9*b^4*c^2*d^2*x^2 + 6*b^4*c^3*d*x)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (180*I*b*d^4*x + 120*I*b*c*d^3)*polylog(4, -e^(2*I*b*x + 2*I*a)) + 30*(6*b^2*d^4*x^2 + 8*b^2*c*d^3*x + 3*b^2*c^2*d^2)*polylog(3, -e^(2*I*b*x + 2*I*a)) + 30*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d - 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 - b*d^4)*x)*sin(2*b*x + 2*a))/b^5","B",0
383,1,442,0,0.479889," ","integrate((d*x+c)^3*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","-\frac{c^{3} {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right)\right)}}{2 \, b} + \frac{-3 i \, b^{4} d^{3} x^{4} - 12 i \, b^{4} c d^{2} x^{3} - 18 i \, b^{4} c^{2} d x^{2} + 12 i \, d^{3} {\rm Li}_{4}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(16 i \, b^{3} d^{3} x^{3} + 36 i \, b^{3} c d^{2} x^{2} + 36 i \, b^{3} c^{2} d x\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 6 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} - 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-24 i \, b^{2} d^{3} x^{2} - 36 i \, b^{2} c d^{2} x - 18 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 2 \, {\left(4 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 9 \, b^{3} c^{2} d x\right)} \log\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) + 6 \, {\left(4 \, b d^{3} x + 3 \, b c d^{2}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + 9 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \sin\left(2 \, b x + 2 \, a\right)}{12 \, b^{4}}"," ",0,"-1/2*c^3*(2*cos(2*b*x + 2*a) - log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2))/b + 1/12*(-3*I*b^4*d^3*x^4 - 12*I*b^4*c*d^2*x^3 - 18*I*b^4*c^2*d*x^2 + 12*I*d^3*polylog(4, -e^(2*I*b*x + 2*I*a)) + (16*I*b^3*d^3*x^3 + 36*I*b^3*c*d^2*x^2 + 36*I*b^3*c^2*d*x)*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 6*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 - 3*b*c*d^2 + 3*(2*b^3*c^2*d - b*d^3)*x)*cos(2*b*x + 2*a) + (-24*I*b^2*d^3*x^2 - 36*I*b^2*c*d^2*x - 18*I*b^2*c^2*d)*dilog(-e^(2*I*b*x + 2*I*a)) + 2*(4*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 9*b^3*c^2*d*x)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 6*(4*b*d^3*x + 3*b*c*d^2)*polylog(3, -e^(2*I*b*x + 2*I*a)) + 9*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*sin(2*b*x + 2*a))/b^4","B",0
384,1,301,0,0.447010," ","integrate((d*x+c)^2*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","-\frac{c^{2} {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right)\right)}}{2 \, b} + \frac{-2 i \, b^{3} d^{2} x^{3} - 6 i \, b^{3} c d x^{2} + 3 \, d^{2} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(6 i \, b^{2} d^{2} x^{2} + 12 i \, b^{2} c d x\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 3 \, {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x - d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) + 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x\right)} \log\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) + 6 \, {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)}{6 \, b^{3}}"," ",0,"-1/2*c^2*(2*cos(2*b*x + 2*a) - log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2))/b + 1/6*(-2*I*b^3*d^2*x^3 - 6*I*b^3*c*d*x^2 + 3*d^2*polylog(3, -e^(2*I*b*x + 2*I*a)) + (6*I*b^2*d^2*x^2 + 12*I*b^2*c*d*x)*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 3*(2*b^2*d^2*x^2 + 4*b^2*c*d*x - d^2)*cos(2*b*x + 2*a) + (-6*I*b*d^2*x - 6*I*b*c*d)*dilog(-e^(2*I*b*x + 2*I*a)) + 3*(b^2*d^2*x^2 + 2*b^2*c*d*x)*log(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + 6*(b*d^2*x + b*c*d)*sin(2*b*x + 2*a))/b^3","A",0
385,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""maxima"")","-\frac{c {\left(2 \, \cos\left(2 \, b x + 2 \, a\right) - \log\left(\cos\left(2 \, b x\right)^{2} + 2 \, \cos\left(2 \, b x\right) \cos\left(2 \, a\right) + \cos\left(2 \, a\right)^{2} + \sin\left(2 \, b x\right)^{2} - 2 \, \sin\left(2 \, b x\right) \sin\left(2 \, a\right) + \sin\left(2 \, a\right)^{2}\right)\right)}}{2 \, b} - \frac{{\left(i \, b^{2} x^{2} - 2 i \, b x \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, b x \cos\left(2 \, b x + 2 \, a\right) - b x \log\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) + i \, {\rm Li}_2\left(-e^{\left(2 i \, b x + 2 i \, a\right)}\right) - \sin\left(2 \, b x + 2 \, a\right)\right)} d}{2 \, b^{2}}"," ",0,"-1/2*c*(2*cos(2*b*x + 2*a) - log(cos(2*b*x)^2 + 2*cos(2*b*x)*cos(2*a) + cos(2*a)^2 + sin(2*b*x)^2 - 2*sin(2*b*x)*sin(2*a) + sin(2*a)^2))/b - 1/2*(2*b*x*cos(2*b*x + 2*a) + 4*b^2*integrate(x*sin(2*b*x + 2*a)/(cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1), x) - sin(2*b*x + 2*a))*d/b^2","F",0
386,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""maxima"")","-\frac{{\left(i \, E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, d \int \frac{\sin\left(2 \, b x + 2 \, a\right)}{{\left(d x + c\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)}}\,{d x} + {\left(E_{1}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{1}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{d}"," ",0,"-((I*exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 2*d*integrate(sin(2*b*x + 2*a)/((d*x + c)*cos(2*b*x + 2*a)^2 + (d*x + c)*sin(2*b*x + 2*a)^2 + d*x + 2*(d*x + c)*cos(2*b*x + 2*a) + c), x) + (exp_integral_e(1, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(1, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/d","F",0
387,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{{\left(i \, E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, {\left(d^{2} x + c d\right)} \int \frac{\sin\left(2 \, b x + 2 \, a\right)}{{\left(d x + c\right)}^{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)}}\,{d x} + {\left(E_{2}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{2}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{d^{2} x + c d}"," ",0,"-((I*exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 2*(d^2*x + c*d)*integrate(sin(2*b*x + 2*a)/(d^2*x^2 + 2*c*d*x + (d^2*x^2 + 2*c*d*x + c^2)*cos(2*b*x + 2*a)^2 + (d^2*x^2 + 2*c*d*x + c^2)*sin(2*b*x + 2*a)^2 + c^2 + 2*(d^2*x^2 + 2*c*d*x + c^2)*cos(2*b*x + 2*a)), x) + (exp_integral_e(2, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(2, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/(d^2*x + c*d)","F",0
388,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{{\left(i \, E_{3}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) - i \, E_{3}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, {\left(d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d\right)} \int \frac{\sin\left(2 \, b x + 2 \, a\right)}{{\left(d x + c\right)}^{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)}}\,{d x} + {\left(E_{3}\left(\frac{2 i \, b d x + 2 i \, b c}{d}\right) + E_{3}\left(-\frac{2 i \, b d x + 2 i \, b c}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{d^{3} x^{2} + 2 \, c d^{2} x + c^{2} d}"," ",0,"-((I*exp_integral_e(3, (2*I*b*d*x + 2*I*b*c)/d) - I*exp_integral_e(3, -(2*I*b*d*x + 2*I*b*c)/d))*cos(-2*(b*c - a*d)/d) + 2*(d^3*x^2 + 2*c*d^2*x + c^2*d)*integrate(sin(2*b*x + 2*a)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3 + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*cos(2*b*x + 2*a)^2 + (d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*sin(2*b*x + 2*a)^2 + 2*(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)*cos(2*b*x + 2*a)), x) + (exp_integral_e(3, (2*I*b*d*x + 2*I*b*c)/d) + exp_integral_e(3, -(2*I*b*d*x + 2*I*b*c)/d))*sin(-2*(b*c - a*d)/d))/(d^3*x^2 + 2*c*d^2*x + c^2*d)","F",0
389,0,0,0,0.000000," ","integrate((d*x+c)^3*sec(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\cos\left(3 \, b x + 3 \, a\right) + \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + {\left(\sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} c^{3}}{b \cos\left(3 \, b x + 3 \, a\right)^{2} + 2 \, b \cos\left(3 \, b x + 3 \, a\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(3 \, b x + 3 \, a\right)^{2} + 2 \, b \sin\left(3 \, b x + 3 \, a\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2}} - \frac{3 \, {\left(4 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b x \cos\left(b x + a\right) + 12 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + 2 \, a\right) + b x \cos\left(b x + 2 \, a\right) \cos\left(a\right) + b x \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + 2 \, a\right) + b x \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 4 \, {\left(b x \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + 12 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + 2 \, a\right) + b x \cos\left(b x + 2 \, a\right) \cos\left(a\right) + b x \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + 2 \, a\right) + b x \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + 4 \, {\left(b x \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 4 \, {\left({\left(b x \cos\left(2 \, b x + 3 \, a\right) + b x \cos\left(a\right) + \sin\left(2 \, b x + 3 \, a\right) + \sin\left(a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \cos\left(b x + a\right)^{2} + {\left(b x \cos\left(2 \, b x + 3 \, a\right) + b x \cos\left(a\right) + \sin\left(2 \, b x + 3 \, a\right) + \sin\left(a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \sin\left(b x + a\right) + \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 4 \, a\right) + 4 \, {\left(6 \, b x \cos\left(b x + 2 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + 6 \, b x \cos\left(b x + a\right) \sin\left(b x + 2 \, a\right) \sin\left(a\right) + b x \cos\left(2 \, b x + 3 \, a\right)^{2} + b x \sin\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b x + 2 \, {\left(3 \, b x \cos\left(b x + 2 \, a\right) \cos\left(b x + a\right) + b x \cos\left(a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(3 \, b x \cos\left(b x + a\right) \sin\left(b x + 2 \, a\right) + b x \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 4 \, {\left(2 \, b x \cos\left(b x + a\right) \cos\left(a\right) + 3 \, {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \cos\left(b x + 2 \, a\right) - 2 \, \cos\left(a\right) \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 12 \, {\left(b x \cos\left(b x + a\right)^{2} \cos\left(a\right) + b x \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(b x + 2 \, a\right) - {\left({\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \cos\left(a\right) + \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \sin\left(a\right) + \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \cos\left(a\right) + \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \sin\left(a\right) + \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b x \sin\left(2 \, b x + 3 \, a\right) + b x \sin\left(a\right) - \cos\left(2 \, b x + 3 \, a\right) - \cos\left(a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \cos\left(b x + a\right)^{2} + {\left(b x \sin\left(2 \, b x + 3 \, a\right) + b x \sin\left(a\right) - \cos\left(2 \, b x + 3 \, a\right) - \cos\left(a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(b x \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \cos\left(b x + a\right) - \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b x \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \sin\left(b x + a\right) - \cos\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 4 \, a\right) + 4 \, {\left(6 \, b x \cos\left(b x + 2 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + 6 \, b x \sin\left(b x + 2 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + 2 \, {\left(3 \, b x \cos\left(b x + 2 \, a\right) \sin\left(b x + a\right) - \cos\left(a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) - \cos\left(2 \, b x + 3 \, a\right)^{2} - \cos\left(a\right)^{2} + 2 \, {\left(3 \, b x \sin\left(b x + 2 \, a\right) \sin\left(b x + a\right) - \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) - \sin\left(2 \, b x + 3 \, a\right)^{2} - \sin\left(a\right)^{2}\right)} \sin\left(3 \, b x + 3 \, a\right) + 4 \, {\left(2 \, b x \cos\left(b x + a\right) \sin\left(a\right) + 3 \, {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \sin\left(b x + 2 \, a\right) - 2 \, \sin\left(b x + a\right) \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) + 12 \, {\left(b x \cos\left(b x + a\right)^{2} \sin\left(a\right) + b x \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(b x + 2 \, a\right) - 4 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)\right)} c^{2} d}{2 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \cos\left(b x + a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \sin\left(b x + a\right)^{2} + {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{2} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{2} \cos\left(b x + a\right)^{2} + b^{2} \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{2} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{2} \cos\left(b x + a\right)^{2} + b^{2} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + b^{2} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} \cos\left(b x + a\right)^{2} \cos\left(a\right) + b^{2} \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + b^{2} \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{2} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} \cos\left(b x + a\right)^{2} \sin\left(a\right) + b^{2} \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)}} - \frac{6 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + 2 \, a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + 2 \, a\right) + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 4 \, b d^{3} x \cos\left(a\right) - 4 \, b c d^{2} \cos\left(a\right)\right)} \cos\left(b x + 2 \, a\right) + {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 4 \, b d^{3} x \sin\left(a\right) - 4 \, b c d^{2} \sin\left(a\right)\right)} \sin\left(b x + 2 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + 6 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + 2 \, a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + 2 \, a\right) + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 4 \, b d^{3} x \cos\left(a\right) - 4 \, b c d^{2} \cos\left(a\right)\right)} \cos\left(b x + 2 \, a\right) + {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 4 \, b d^{3} x \sin\left(a\right) - 4 \, b c d^{2} \sin\left(a\right)\right)} \sin\left(b x + 2 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, {\left({\left(b^{3} d^{3} x^{3} \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) - 6 \, d^{3} \sin\left(a\right) + 3 \, {\left(b^{3} c d^{2} \cos\left(a\right) + b^{2} d^{3} \sin\left(a\right)\right)} x^{2} + 6 \, {\left(b^{2} c d^{2} \sin\left(a\right) - b d^{3} \cos\left(a\right)\right)} x + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) - 6 \, d^{3} \sin\left(a\right) + 3 \, {\left(b^{3} c d^{2} \cos\left(a\right) + b^{2} d^{3} \sin\left(a\right)\right)} x^{2} + 6 \, {\left(b^{2} c d^{2} \sin\left(a\right) - b d^{3} \cos\left(a\right)\right)} x\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) - 6 \, d^{3} \sin\left(a\right) + 3 \, {\left(b^{3} c d^{2} \cos\left(a\right) + b^{2} d^{3} \sin\left(a\right)\right)} x^{2} + 6 \, {\left(b^{2} c d^{2} \sin\left(a\right) - b d^{3} \cos\left(a\right)\right)} x + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) - 6 \, d^{3} \sin\left(a\right) + 3 \, {\left(b^{3} c d^{2} \cos\left(a\right) + b^{2} d^{3} \sin\left(a\right)\right)} x^{2} + 6 \, {\left(b^{2} c d^{2} \sin\left(a\right) - b d^{3} \cos\left(a\right)\right)} x\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) - 6 \, d^{3} \sin\left(a\right) + 3 \, {\left(b^{3} c d^{2} \cos\left(a\right) + b^{2} d^{3} \sin\left(a\right)\right)} x^{2} + 6 \, {\left(b^{2} c d^{2} \sin\left(a\right) - b d^{3} \cos\left(a\right)\right)} x\right)} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) - 6 \, d^{3} \sin\left(a\right) + 3 \, {\left(b^{3} c d^{2} \cos\left(a\right) + b^{2} d^{3} \sin\left(a\right)\right)} x^{2} + 6 \, {\left(b^{2} c d^{2} \sin\left(a\right) - b d^{3} \cos\left(a\right)\right)} x\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 3 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 4 \, a\right) + 2 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{3} d^{3} x^{3} + 3 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{3} c d^{2} x^{2} - 6 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b d^{3} x - 6 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b c d^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 4 \, b d^{3} x \cos\left(a\right) - 4 \, b c d^{2} \cos\left(a\right)\right)} \cos\left(b x + 2 \, a\right) \cos\left(b x + a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 6 \, {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 4 \, b d^{3} x \sin\left(a\right) - 4 \, b c d^{2} \sin\left(a\right)\right)} \cos\left(b x + a\right) \sin\left(b x + 2 \, a\right) + 2 \, {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 6 \, b d^{3} x \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(b x + 2 \, a\right) \cos\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 6 \, b d^{3} x \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(b x + a\right) \sin\left(b x + 2 \, a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \sin\left(b x + a\right)^{2}\right)} \cos\left(b x + 2 \, a\right) + 2 \, {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 6 \, b d^{3} x \cos\left(a\right) - 6 \, b c d^{2} \cos\left(a\right)\right)} \cos\left(b x + a\right) - 6 \, {\left(b^{2} d^{3} x^{2} \cos\left(a\right) + 2 \, b^{2} c d^{2} x \cos\left(a\right) - 2 \, d^{3} \cos\left(a\right)\right)} \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 6 \, {\left({\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 4 \, b d^{3} x \cos\left(a\right) - 4 \, b c d^{2} \cos\left(a\right)\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 4 \, b d^{3} x \cos\left(a\right) - 4 \, b c d^{2} \cos\left(a\right)\right)} \sin\left(b x + a\right)^{2}\right)} \cos\left(b x + 2 \, a\right) + 2 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{3} d^{3} x^{3} + 3 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{3} c d^{2} x^{2} - 6 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b d^{3} x - 6 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b c d^{2}\right)} \cos\left(b x + a\right) - 6 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \cos\left(b x + a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \sin\left(b x + a\right)^{2} + {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{4} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{4} \cos\left(b x + a\right)^{2} + b^{4} \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{4} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{4} \cos\left(b x + a\right)^{2} + b^{4} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + b^{4} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{4} \cos\left(b x + a\right)^{2} \cos\left(a\right) + b^{4} \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + b^{4} \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{4} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{4} \cos\left(b x + a\right)^{2} \sin\left(a\right) + b^{4} \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \int \frac{{\left(d^{3} x^{2} + 2 \, c d^{2} x\right)} \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + {\left(d^{3} x^{2} + 2 \, c d^{2} x\right)} \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + {\left(d^{3} x^{2} + 2 \, c d^{2} x\right)} \cos\left(b x + a\right)}{b \cos\left(2 \, b x + 2 \, a\right)^{2} + b \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, b \cos\left(2 \, b x + 2 \, a\right) + b}\,{d x} + 2 \, {\left({\left(b^{3} d^{3} x^{3} \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 6 \, d^{3} \cos\left(a\right) + 3 \, {\left(b^{3} c d^{2} \sin\left(a\right) - b^{2} d^{3} \cos\left(a\right)\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} \cos\left(a\right) + b d^{3} \sin\left(a\right)\right)} x - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{3} d^{3} x^{3} \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 6 \, d^{3} \cos\left(a\right) + 3 \, {\left(b^{3} c d^{2} \sin\left(a\right) - b^{2} d^{3} \cos\left(a\right)\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} \cos\left(a\right) + b d^{3} \sin\left(a\right)\right)} x\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 6 \, d^{3} \cos\left(a\right) + 3 \, {\left(b^{3} c d^{2} \sin\left(a\right) - b^{2} d^{3} \cos\left(a\right)\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} \cos\left(a\right) + b d^{3} \sin\left(a\right)\right)} x - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(2 \, b x + 3 \, a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{3} d^{3} x^{3} \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 6 \, d^{3} \cos\left(a\right) + 3 \, {\left(b^{3} c d^{2} \sin\left(a\right) - b^{2} d^{3} \cos\left(a\right)\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} \cos\left(a\right) + b d^{3} \sin\left(a\right)\right)} x\right)} \sin\left(b x + a\right)^{2} - 2 \, {\left(3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) - {\left(b^{3} d^{3} x^{3} \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 6 \, d^{3} \cos\left(a\right) + 3 \, {\left(b^{3} c d^{2} \sin\left(a\right) - b^{2} d^{3} \cos\left(a\right)\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} \cos\left(a\right) + b d^{3} \sin\left(a\right)\right)} x\right)} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - 3 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) - 2 \, {\left(3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) - {\left(b^{3} d^{3} x^{3} \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right) + 6 \, d^{3} \cos\left(a\right) + 3 \, {\left(b^{3} c d^{2} \sin\left(a\right) - b^{2} d^{3} \cos\left(a\right)\right)} x^{2} - 6 \, {\left(b^{2} c d^{2} \cos\left(a\right) + b d^{3} \sin\left(a\right)\right)} x\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 4 \, a\right) - 6 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} d^{3} x^{2} + 2 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} c d^{2} x - 2 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} d^{3} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x - 2 \, d^{3}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} - 2 \, {\left(b^{3} d^{3} x^{3} \cos\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \cos\left(a\right) - 4 \, b d^{3} x \cos\left(a\right) - 4 \, b c d^{2} \cos\left(a\right)\right)} \cos\left(b x + 2 \, a\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 4 \, b d^{3} x \sin\left(a\right) - 4 \, b c d^{2} \sin\left(a\right)\right)} \sin\left(b x + 2 \, a\right) \sin\left(b x + a\right) + 2 \, {\left(b^{2} d^{3} x^{2} \cos\left(a\right) + 2 \, b^{2} c d^{2} x \cos\left(a\right) - 2 \, d^{3} \cos\left(a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(b x + 2 \, a\right) \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} d^{3} x^{2} \sin\left(a\right) + 2 \, b^{2} c d^{2} x \sin\left(a\right) - 2 \, d^{3} \sin\left(a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \sin\left(b x + 2 \, a\right) \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(2 \, {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 6 \, b d^{3} x \sin\left(a\right) - 6 \, b c d^{2} \sin\left(a\right)\right)} \cos\left(b x + a\right) + 3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} - 4 \, b d^{3} x - 4 \, b c d^{2}\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(b x + 2 \, a\right) - 6 \, {\left(b^{2} d^{3} x^{2} \sin\left(a\right) + 2 \, b^{2} c d^{2} x \sin\left(a\right) - 2 \, d^{3} \sin\left(a\right)\right)} \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) + 6 \, {\left({\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 4 \, b d^{3} x \sin\left(a\right) - 4 \, b c d^{2} \sin\left(a\right)\right)} \cos\left(b x + a\right)^{2} + {\left(b^{3} d^{3} x^{3} \sin\left(a\right) + 3 \, b^{3} c d^{2} x^{2} \sin\left(a\right) - 4 \, b d^{3} x \sin\left(a\right) - 4 \, b c d^{2} \sin\left(a\right)\right)} \sin\left(b x + a\right)^{2}\right)} \sin\left(b x + 2 \, a\right) - 6 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} d^{3} x^{2} + 2 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} c d^{2} x - 2 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} d^{3}\right)} \sin\left(b x + a\right)}{{\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \cos\left(b x + a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \sin\left(b x + a\right)^{2} + {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{4} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{4} \cos\left(b x + a\right)^{2} + b^{4} \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{4} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{4} \cos\left(b x + a\right)^{2} + b^{4} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + b^{4} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{4} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{4} \cos\left(b x + a\right)^{2} \cos\left(a\right) + b^{4} \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b^{4} \cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{4} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + b^{4} \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{4} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{4} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{4} \cos\left(b x + a\right)^{2} \sin\left(a\right) + b^{4} \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)}"," ",0,"-2*((cos(3*b*x + 3*a) + cos(b*x + a))*cos(4*b*x + 4*a) + (3*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) + 3*cos(2*b*x + 2*a)*cos(b*x + a) + (sin(3*b*x + 3*a) + sin(b*x + a))*sin(4*b*x + 4*a) + 3*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) + 3*sin(2*b*x + 2*a)*sin(b*x + a) + cos(b*x + a))*c^3/(b*cos(3*b*x + 3*a)^2 + 2*b*cos(3*b*x + 3*a)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(3*b*x + 3*a)^2 + 2*b*sin(3*b*x + 3*a)*sin(b*x + a) + b*sin(b*x + a)^2) - 3/2*(4*(cos(a)^2 + sin(a)^2)*b*x*cos(b*x + a) + 12*(b*x*cos(2*b*x + 3*a)*cos(b*x + 2*a) + b*x*cos(b*x + 2*a)*cos(a) + b*x*sin(2*b*x + 3*a)*sin(b*x + 2*a) + b*x*sin(b*x + 2*a)*sin(a))*cos(3*b*x + 3*a)^2 + 4*(b*x*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 3*a)^2 + 12*(b*x*cos(2*b*x + 3*a)*cos(b*x + 2*a) + b*x*cos(b*x + 2*a)*cos(a) + b*x*sin(2*b*x + 3*a)*sin(b*x + 2*a) + b*x*sin(b*x + 2*a)*sin(a))*sin(3*b*x + 3*a)^2 + 4*(b*x*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 3*a)^2 + 4*((b*x*cos(2*b*x + 3*a) + b*x*cos(a) + sin(2*b*x + 3*a) + sin(a))*cos(3*b*x + 3*a)^2 + (b*x*cos(a) + sin(a))*cos(b*x + a)^2 + (b*x*cos(2*b*x + 3*a) + b*x*cos(a) + sin(2*b*x + 3*a) + sin(a))*sin(3*b*x + 3*a)^2 + (b*x*cos(a) + sin(a))*sin(b*x + a)^2 + 2*(b*x*cos(2*b*x + 3*a)*cos(b*x + a) + (b*x*cos(a) + sin(a))*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + (b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b*x*cos(2*b*x + 3*a)*sin(b*x + a) + (b*x*cos(a) + sin(a))*sin(b*x + a) + sin(2*b*x + 3*a)*sin(b*x + a))*sin(3*b*x + 3*a) + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 3*a))*cos(3*b*x + 4*a) + 4*(6*b*x*cos(b*x + 2*a)*cos(b*x + a)*cos(a) + 6*b*x*cos(b*x + a)*sin(b*x + 2*a)*sin(a) + b*x*cos(2*b*x + 3*a)^2 + b*x*sin(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*b*x + 2*(3*b*x*cos(b*x + 2*a)*cos(b*x + a) + b*x*cos(a))*cos(2*b*x + 3*a) + 2*(3*b*x*cos(b*x + a)*sin(b*x + 2*a) + b*x*sin(a))*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + 4*(2*b*x*cos(b*x + a)*cos(a) + 3*(b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*cos(b*x + 2*a) - 2*cos(a)*sin(b*x + a))*cos(2*b*x + 3*a) + 12*(b*x*cos(b*x + a)^2*cos(a) + b*x*cos(a)*sin(b*x + a)^2)*cos(b*x + 2*a) - ((cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*cos(b*x + a)^2 + (cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*sin(b*x + a)^2 + 2*(cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2*cos(a) + cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(cos(b*x + a)^2*sin(a) + sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) + ((cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*cos(b*x + a)^2 + (cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*sin(b*x + a)^2 + 2*(cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2*cos(a) + cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(cos(b*x + a)^2*sin(a) + sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + 4*((b*x*sin(2*b*x + 3*a) + b*x*sin(a) - cos(2*b*x + 3*a) - cos(a))*cos(3*b*x + 3*a)^2 + (b*x*sin(a) - cos(a))*cos(b*x + a)^2 + (b*x*sin(2*b*x + 3*a) + b*x*sin(a) - cos(2*b*x + 3*a) - cos(a))*sin(3*b*x + 3*a)^2 + (b*x*sin(a) - cos(a))*sin(b*x + a)^2 + 2*(b*x*cos(b*x + a)*sin(2*b*x + 3*a) + (b*x*sin(a) - cos(a))*cos(b*x + a) - cos(2*b*x + 3*a)*cos(b*x + a))*cos(3*b*x + 3*a) - (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b*x*sin(2*b*x + 3*a)*sin(b*x + a) + (b*x*sin(a) - cos(a))*sin(b*x + a) - cos(2*b*x + 3*a)*sin(b*x + a))*sin(3*b*x + 3*a) + (b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*sin(2*b*x + 3*a))*sin(3*b*x + 4*a) + 4*(6*b*x*cos(b*x + 2*a)*cos(a)*sin(b*x + a) + 6*b*x*sin(b*x + 2*a)*sin(b*x + a)*sin(a) + 2*(3*b*x*cos(b*x + 2*a)*sin(b*x + a) - cos(a))*cos(2*b*x + 3*a) - cos(2*b*x + 3*a)^2 - cos(a)^2 + 2*(3*b*x*sin(b*x + 2*a)*sin(b*x + a) - sin(a))*sin(2*b*x + 3*a) - sin(2*b*x + 3*a)^2 - sin(a)^2)*sin(3*b*x + 3*a) + 4*(2*b*x*cos(b*x + a)*sin(a) + 3*(b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*sin(b*x + 2*a) - 2*sin(b*x + a)*sin(a))*sin(2*b*x + 3*a) + 12*(b*x*cos(b*x + a)^2*sin(a) + b*x*sin(b*x + a)^2*sin(a))*sin(b*x + 2*a) - 4*(cos(a)^2 + sin(a)^2)*sin(b*x + a))*c^2*d/((cos(a)^2 + sin(a)^2)*b^2*cos(b*x + a)^2 + (cos(a)^2 + sin(a)^2)*b^2*sin(b*x + a)^2 + (b^2*cos(2*b*x + 3*a)^2 + 2*b^2*cos(2*b*x + 3*a)*cos(a) + b^2*sin(2*b*x + 3*a)^2 + 2*b^2*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2)*cos(3*b*x + 3*a)^2 + (b^2*cos(b*x + a)^2 + b^2*sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (b^2*cos(2*b*x + 3*a)^2 + 2*b^2*cos(2*b*x + 3*a)*cos(a) + b^2*sin(2*b*x + 3*a)^2 + 2*b^2*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2)*sin(3*b*x + 3*a)^2 + (b^2*cos(b*x + a)^2 + b^2*sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + 2*(b^2*cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*b^2*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + b^2*cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*b^2*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(b^2*cos(b*x + a)^2*cos(a) + b^2*cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b^2*cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^2*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + b^2*sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^2*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(b^2*cos(b*x + a)^2*sin(a) + b^2*sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a)) - (6*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(2*b*x + 3*a)*cos(b*x + 2*a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*sin(2*b*x + 3*a)*sin(b*x + 2*a) + (b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 4*b*d^3*x*cos(a) - 4*b*c*d^2*cos(a))*cos(b*x + 2*a) + (b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 4*b*d^3*x*sin(a) - 4*b*c*d^2*sin(a))*sin(b*x + 2*a))*cos(3*b*x + 3*a)^2 + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(b*x + a))*cos(2*b*x + 3*a)^2 + 6*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(2*b*x + 3*a)*cos(b*x + 2*a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*sin(2*b*x + 3*a)*sin(b*x + 2*a) + (b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 4*b*d^3*x*cos(a) - 4*b*c*d^2*cos(a))*cos(b*x + 2*a) + (b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 4*b*d^3*x*sin(a) - 4*b*c*d^2*sin(a))*sin(b*x + 2*a))*sin(3*b*x + 3*a)^2 + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(b*x + a))*sin(2*b*x + 3*a)^2 + 2*((b^3*d^3*x^3*cos(a) - 6*b*c*d^2*cos(a) - 6*d^3*sin(a) + 3*(b^3*c*d^2*cos(a) + b^2*d^3*sin(a))*x^2 + 6*(b^2*c*d^2*sin(a) - b*d^3*cos(a))*x + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(2*b*x + 3*a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a)^2 + (b^3*d^3*x^3*cos(a) - 6*b*c*d^2*cos(a) - 6*d^3*sin(a) + 3*(b^3*c*d^2*cos(a) + b^2*d^3*sin(a))*x^2 + 6*(b^2*c*d^2*sin(a) - b*d^3*cos(a))*x)*cos(b*x + a)^2 + (b^3*d^3*x^3*cos(a) - 6*b*c*d^2*cos(a) - 6*d^3*sin(a) + 3*(b^3*c*d^2*cos(a) + b^2*d^3*sin(a))*x^2 + 6*(b^2*c*d^2*sin(a) - b*d^3*cos(a))*x + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(2*b*x + 3*a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(2*b*x + 3*a))*sin(3*b*x + 3*a)^2 + (b^3*d^3*x^3*cos(a) - 6*b*c*d^2*cos(a) - 6*d^3*sin(a) + 3*(b^3*c*d^2*cos(a) + b^2*d^3*sin(a))*x^2 + 6*(b^2*c*d^2*sin(a) - b*d^3*cos(a))*x)*sin(b*x + a)^2 + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(2*b*x + 3*a)*cos(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(b*x + a)*sin(2*b*x + 3*a) + (b^3*d^3*x^3*cos(a) - 6*b*c*d^2*cos(a) - 6*d^3*sin(a) + 3*(b^3*c*d^2*cos(a) + b^2*d^3*sin(a))*x^2 + 6*(b^2*c*d^2*sin(a) - b*d^3*cos(a))*x)*cos(b*x + a))*cos(3*b*x + 3*a) + ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(b*x + a)^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(2*b*x + 3*a)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(2*b*x + 3*a)*sin(b*x + a) + (b^3*d^3*x^3*cos(a) - 6*b*c*d^2*cos(a) - 6*d^3*sin(a) + 3*(b^3*c*d^2*cos(a) + b^2*d^3*sin(a))*x^2 + 6*(b^2*c*d^2*sin(a) - b*d^3*cos(a))*x)*sin(b*x + a))*sin(3*b*x + 3*a) + 3*((b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(b*x + a)^2 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(b*x + a)^2)*sin(2*b*x + 3*a))*cos(3*b*x + 4*a) + 2*((cos(a)^2 + sin(a)^2)*b^3*d^3*x^3 + 3*(cos(a)^2 + sin(a)^2)*b^3*c*d^2*x^2 - 6*(cos(a)^2 + sin(a)^2)*b*d^3*x - 6*(cos(a)^2 + sin(a)^2)*b*c*d^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(2*b*x + 3*a)^2 + 6*(b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 4*b*d^3*x*cos(a) - 4*b*c*d^2*cos(a))*cos(b*x + 2*a)*cos(b*x + a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*sin(2*b*x + 3*a)^2 + 6*(b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 4*b*d^3*x*sin(a) - 4*b*c*d^2*sin(a))*cos(b*x + a)*sin(b*x + 2*a) + 2*(b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 6*b*d^3*x*cos(a) - 6*b*c*d^2*cos(a) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(b*x + 2*a)*cos(b*x + a))*cos(2*b*x + 3*a) + 2*(b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 6*b*d^3*x*sin(a) - 6*b*c*d^2*sin(a) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(b*x + a)*sin(b*x + 2*a))*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + 2*(3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(b*x + a)^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*sin(b*x + a)^2)*cos(b*x + 2*a) + 2*(b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 6*b*d^3*x*cos(a) - 6*b*c*d^2*cos(a))*cos(b*x + a) - 6*(b^2*d^3*x^2*cos(a) + 2*b^2*c*d^2*x*cos(a) - 2*d^3*cos(a))*sin(b*x + a))*cos(2*b*x + 3*a) + 6*((b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 4*b*d^3*x*cos(a) - 4*b*c*d^2*cos(a))*cos(b*x + a)^2 + (b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 4*b*d^3*x*cos(a) - 4*b*c*d^2*cos(a))*sin(b*x + a)^2)*cos(b*x + 2*a) + 2*((cos(a)^2 + sin(a)^2)*b^3*d^3*x^3 + 3*(cos(a)^2 + sin(a)^2)*b^3*c*d^2*x^2 - 6*(cos(a)^2 + sin(a)^2)*b*d^3*x - 6*(cos(a)^2 + sin(a)^2)*b*c*d^2)*cos(b*x + a) - ((cos(a)^2 + sin(a)^2)*b^4*cos(b*x + a)^2 + (cos(a)^2 + sin(a)^2)*b^4*sin(b*x + a)^2 + (b^4*cos(2*b*x + 3*a)^2 + 2*b^4*cos(2*b*x + 3*a)*cos(a) + b^4*sin(2*b*x + 3*a)^2 + 2*b^4*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4)*cos(3*b*x + 3*a)^2 + (b^4*cos(b*x + a)^2 + b^4*sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (b^4*cos(2*b*x + 3*a)^2 + 2*b^4*cos(2*b*x + 3*a)*cos(a) + b^4*sin(2*b*x + 3*a)^2 + 2*b^4*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4)*sin(3*b*x + 3*a)^2 + (b^4*cos(b*x + a)^2 + b^4*sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + 2*(b^4*cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*b^4*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + b^4*cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*b^4*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(b^4*cos(b*x + a)^2*cos(a) + b^4*cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b^4*cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^4*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + b^4*sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^4*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(b^4*cos(b*x + a)^2*sin(a) + b^4*sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))*integrate(6*((d^3*x^2 + 2*c*d^2*x)*cos(2*b*x + 2*a)*cos(b*x + a) + (d^3*x^2 + 2*c*d^2*x)*sin(2*b*x + 2*a)*sin(b*x + a) + (d^3*x^2 + 2*c*d^2*x)*cos(b*x + a))/(b*cos(2*b*x + 2*a)^2 + b*sin(2*b*x + 2*a)^2 + 2*b*cos(2*b*x + 2*a) + b), x) + 2*((b^3*d^3*x^3*sin(a) - 6*b*c*d^2*sin(a) + 6*d^3*cos(a) + 3*(b^3*c*d^2*sin(a) - b^2*d^3*cos(a))*x^2 - 6*(b^2*c*d^2*cos(a) + b*d^3*sin(a))*x - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(2*b*x + 3*a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a)^2 + (b^3*d^3*x^3*sin(a) - 6*b*c*d^2*sin(a) + 6*d^3*cos(a) + 3*(b^3*c*d^2*sin(a) - b^2*d^3*cos(a))*x^2 - 6*(b^2*c*d^2*cos(a) + b*d^3*sin(a))*x)*cos(b*x + a)^2 + (b^3*d^3*x^3*sin(a) - 6*b*c*d^2*sin(a) + 6*d^3*cos(a) + 3*(b^3*c*d^2*sin(a) - b^2*d^3*cos(a))*x^2 - 6*(b^2*c*d^2*cos(a) + b*d^3*sin(a))*x - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(2*b*x + 3*a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*sin(2*b*x + 3*a))*sin(3*b*x + 3*a)^2 + (b^3*d^3*x^3*sin(a) - 6*b*c*d^2*sin(a) + 6*d^3*cos(a) + 3*(b^3*c*d^2*sin(a) - b^2*d^3*cos(a))*x^2 - 6*(b^2*c*d^2*cos(a) + b*d^3*sin(a))*x)*sin(b*x + a)^2 - 2*(3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(2*b*x + 3*a)*cos(b*x + a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(b*x + a)*sin(2*b*x + 3*a) - (b^3*d^3*x^3*sin(a) - 6*b*c*d^2*sin(a) + 6*d^3*cos(a) + 3*(b^3*c*d^2*sin(a) - b^2*d^3*cos(a))*x^2 - 6*(b^2*c*d^2*cos(a) + b*d^3*sin(a))*x)*cos(b*x + a))*cos(3*b*x + 3*a) - 3*((b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(b*x + a)^2 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(b*x + a)^2)*cos(2*b*x + 3*a) - 2*(3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(2*b*x + 3*a)*sin(b*x + a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*sin(2*b*x + 3*a)*sin(b*x + a) - (b^3*d^3*x^3*sin(a) - 6*b*c*d^2*sin(a) + 6*d^3*cos(a) + 3*(b^3*c*d^2*sin(a) - b^2*d^3*cos(a))*x^2 - 6*(b^2*c*d^2*cos(a) + b*d^3*sin(a))*x)*sin(b*x + a))*sin(3*b*x + 3*a) + ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*cos(b*x + a)^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 6*b*d^3*x - 6*b*c*d^2)*sin(b*x + a)^2)*sin(2*b*x + 3*a))*sin(3*b*x + 4*a) - 6*((cos(a)^2 + sin(a)^2)*b^2*d^3*x^2 + 2*(cos(a)^2 + sin(a)^2)*b^2*c*d^2*x - 2*(cos(a)^2 + sin(a)^2)*d^3 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*cos(2*b*x + 3*a)^2 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x - 2*d^3)*sin(2*b*x + 3*a)^2 - 2*(b^3*d^3*x^3*cos(a) + 3*b^3*c*d^2*x^2*cos(a) - 4*b*d^3*x*cos(a) - 4*b*c*d^2*cos(a))*cos(b*x + 2*a)*sin(b*x + a) - 2*(b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 4*b*d^3*x*sin(a) - 4*b*c*d^2*sin(a))*sin(b*x + 2*a)*sin(b*x + a) + 2*(b^2*d^3*x^2*cos(a) + 2*b^2*c*d^2*x*cos(a) - 2*d^3*cos(a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(b*x + 2*a)*sin(b*x + a))*cos(2*b*x + 3*a) + 2*(b^2*d^3*x^2*sin(a) + 2*b^2*c*d^2*x*sin(a) - 2*d^3*sin(a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*sin(b*x + 2*a)*sin(b*x + a))*sin(2*b*x + 3*a))*sin(3*b*x + 3*a) + 2*(2*(b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 6*b*d^3*x*sin(a) - 6*b*c*d^2*sin(a))*cos(b*x + a) + 3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*cos(b*x + a)^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 - 4*b*d^3*x - 4*b*c*d^2)*sin(b*x + a)^2)*sin(b*x + 2*a) - 6*(b^2*d^3*x^2*sin(a) + 2*b^2*c*d^2*x*sin(a) - 2*d^3*sin(a))*sin(b*x + a))*sin(2*b*x + 3*a) + 6*((b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 4*b*d^3*x*sin(a) - 4*b*c*d^2*sin(a))*cos(b*x + a)^2 + (b^3*d^3*x^3*sin(a) + 3*b^3*c*d^2*x^2*sin(a) - 4*b*d^3*x*sin(a) - 4*b*c*d^2*sin(a))*sin(b*x + a)^2)*sin(b*x + 2*a) - 6*((cos(a)^2 + sin(a)^2)*b^2*d^3*x^2 + 2*(cos(a)^2 + sin(a)^2)*b^2*c*d^2*x - 2*(cos(a)^2 + sin(a)^2)*d^3)*sin(b*x + a))/((cos(a)^2 + sin(a)^2)*b^4*cos(b*x + a)^2 + (cos(a)^2 + sin(a)^2)*b^4*sin(b*x + a)^2 + (b^4*cos(2*b*x + 3*a)^2 + 2*b^4*cos(2*b*x + 3*a)*cos(a) + b^4*sin(2*b*x + 3*a)^2 + 2*b^4*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4)*cos(3*b*x + 3*a)^2 + (b^4*cos(b*x + a)^2 + b^4*sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (b^4*cos(2*b*x + 3*a)^2 + 2*b^4*cos(2*b*x + 3*a)*cos(a) + b^4*sin(2*b*x + 3*a)^2 + 2*b^4*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4)*sin(3*b*x + 3*a)^2 + (b^4*cos(b*x + a)^2 + b^4*sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + 2*(b^4*cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*b^4*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + b^4*cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*b^4*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(b^4*cos(b*x + a)^2*cos(a) + b^4*cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b^4*cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^4*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + b^4*sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^4*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^4*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(b^4*cos(b*x + a)^2*sin(a) + b^4*sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))","F",0
390,-1,0,0,0.000000," ","integrate((d*x+c)^2*sec(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,1,3330,0,1.120646," ","integrate((d*x+c)*sec(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(\cos\left(3 \, b x + 3 \, a\right) + \cos\left(b x + a\right)\right)} \cos\left(4 \, b x + 4 \, a\right) + {\left(3 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \cos\left(3 \, b x + 3 \, a\right) + 3 \, \cos\left(2 \, b x + 2 \, a\right) \cos\left(b x + a\right) + {\left(\sin\left(3 \, b x + 3 \, a\right) + \sin\left(b x + a\right)\right)} \sin\left(4 \, b x + 4 \, a\right) + 3 \, \sin\left(3 \, b x + 3 \, a\right) \sin\left(2 \, b x + 2 \, a\right) + 3 \, \sin\left(2 \, b x + 2 \, a\right) \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} c}{b \cos\left(3 \, b x + 3 \, a\right)^{2} + 2 \, b \cos\left(3 \, b x + 3 \, a\right) \cos\left(b x + a\right) + b \cos\left(b x + a\right)^{2} + b \sin\left(3 \, b x + 3 \, a\right)^{2} + 2 \, b \sin\left(3 \, b x + 3 \, a\right) \sin\left(b x + a\right) + b \sin\left(b x + a\right)^{2}} - \frac{{\left(4 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b x \cos\left(b x + a\right) + 12 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + 2 \, a\right) + b x \cos\left(b x + 2 \, a\right) \cos\left(a\right) + b x \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + 2 \, a\right) + b x \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + 4 \, {\left(b x \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + 12 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + 2 \, a\right) + b x \cos\left(b x + 2 \, a\right) \cos\left(a\right) + b x \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + 2 \, a\right) + b x \sin\left(b x + 2 \, a\right) \sin\left(a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + 4 \, {\left(b x \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 4 \, {\left({\left(b x \cos\left(2 \, b x + 3 \, a\right) + b x \cos\left(a\right) + \sin\left(2 \, b x + 3 \, a\right) + \sin\left(a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \cos\left(b x + a\right)^{2} + {\left(b x \cos\left(2 \, b x + 3 \, a\right) + b x \cos\left(a\right) + \sin\left(2 \, b x + 3 \, a\right) + \sin\left(a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \cos\left(b x + a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b x \cos\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) + {\left(b x \cos\left(a\right) + \sin\left(a\right)\right)} \sin\left(b x + a\right) + \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 4 \, a\right) + 4 \, {\left(6 \, b x \cos\left(b x + 2 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + 6 \, b x \cos\left(b x + a\right) \sin\left(b x + 2 \, a\right) \sin\left(a\right) + b x \cos\left(2 \, b x + 3 \, a\right)^{2} + b x \sin\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b x + 2 \, {\left(3 \, b x \cos\left(b x + 2 \, a\right) \cos\left(b x + a\right) + b x \cos\left(a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(3 \, b x \cos\left(b x + a\right) \sin\left(b x + 2 \, a\right) + b x \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 4 \, {\left(2 \, b x \cos\left(b x + a\right) \cos\left(a\right) + 3 \, {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \cos\left(b x + 2 \, a\right) - 2 \, \cos\left(a\right) \sin\left(b x + a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) + 12 \, {\left(b x \cos\left(b x + a\right)^{2} \cos\left(a\right) + b x \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(b x + 2 \, a\right) - {\left({\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \cos\left(a\right) + \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \sin\left(a\right) + \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} + 2 \, \sin\left(b x + a\right) + 1\right) + {\left({\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)^{2} + {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + \cos\left(a\right)^{2} + \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + \sin\left(a\right)^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \cos\left(a\right) + \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(\cos\left(b x + a\right)^{2} \sin\left(a\right) + \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \log\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2} - 2 \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b x \sin\left(2 \, b x + 3 \, a\right) + b x \sin\left(a\right) - \cos\left(2 \, b x + 3 \, a\right) - \cos\left(a\right)\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \cos\left(b x + a\right)^{2} + {\left(b x \sin\left(2 \, b x + 3 \, a\right) + b x \sin\left(a\right) - \cos\left(2 \, b x + 3 \, a\right) - \cos\left(a\right)\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \sin\left(b x + a\right)^{2} + 2 \, {\left(b x \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \cos\left(b x + a\right) - \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) - {\left(\cos\left(b x + a\right)^{2} + \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b x \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) + {\left(b x \sin\left(a\right) - \cos\left(a\right)\right)} \sin\left(b x + a\right) - \cos\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)\right)} \sin\left(3 \, b x + 4 \, a\right) + 4 \, {\left(6 \, b x \cos\left(b x + 2 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + 6 \, b x \sin\left(b x + 2 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + 2 \, {\left(3 \, b x \cos\left(b x + 2 \, a\right) \sin\left(b x + a\right) - \cos\left(a\right)\right)} \cos\left(2 \, b x + 3 \, a\right) - \cos\left(2 \, b x + 3 \, a\right)^{2} - \cos\left(a\right)^{2} + 2 \, {\left(3 \, b x \sin\left(b x + 2 \, a\right) \sin\left(b x + a\right) - \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) - \sin\left(2 \, b x + 3 \, a\right)^{2} - \sin\left(a\right)^{2}\right)} \sin\left(3 \, b x + 3 \, a\right) + 4 \, {\left(2 \, b x \cos\left(b x + a\right) \sin\left(a\right) + 3 \, {\left(b x \cos\left(b x + a\right)^{2} + b x \sin\left(b x + a\right)^{2}\right)} \sin\left(b x + 2 \, a\right) - 2 \, \sin\left(b x + a\right) \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right) + 12 \, {\left(b x \cos\left(b x + a\right)^{2} \sin\left(a\right) + b x \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(b x + 2 \, a\right) - 4 \, {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} \sin\left(b x + a\right)\right)} d}{2 \, {\left({\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \cos\left(b x + a\right)^{2} + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \sin\left(b x + a\right)^{2} + {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{2} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2}\right)} \cos\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{2} \cos\left(b x + a\right)^{2} + b^{2} \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right)^{2} + {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) + b^{2} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)^{2} + {\left(b^{2} \cos\left(b x + a\right)^{2} + b^{2} \sin\left(b x + a\right)^{2}\right)} \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} \cos\left(b x + a\right) + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(b x + a\right) \cos\left(a\right) + b^{2} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right)^{2} + 2 \, b^{2} \cos\left(b x + a\right) \sin\left(2 \, b x + 3 \, a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \cos\left(b x + a\right)\right)} \cos\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} \cos\left(b x + a\right)^{2} \cos\left(a\right) + b^{2} \cos\left(a\right) \sin\left(b x + a\right)^{2}\right)} \cos\left(2 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} \cos\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{2} \cos\left(2 \, b x + 3 \, a\right) \cos\left(a\right) \sin\left(b x + a\right) + b^{2} \sin\left(2 \, b x + 3 \, a\right)^{2} \sin\left(b x + a\right) + 2 \, b^{2} \sin\left(2 \, b x + 3 \, a\right) \sin\left(b x + a\right) \sin\left(a\right) + {\left(\cos\left(a\right)^{2} + \sin\left(a\right)^{2}\right)} b^{2} \sin\left(b x + a\right)\right)} \sin\left(3 \, b x + 3 \, a\right) + 2 \, {\left(b^{2} \cos\left(b x + a\right)^{2} \sin\left(a\right) + b^{2} \sin\left(b x + a\right)^{2} \sin\left(a\right)\right)} \sin\left(2 \, b x + 3 \, a\right)\right)}}"," ",0,"-2*((cos(3*b*x + 3*a) + cos(b*x + a))*cos(4*b*x + 4*a) + (3*cos(2*b*x + 2*a) + 1)*cos(3*b*x + 3*a) + 3*cos(2*b*x + 2*a)*cos(b*x + a) + (sin(3*b*x + 3*a) + sin(b*x + a))*sin(4*b*x + 4*a) + 3*sin(3*b*x + 3*a)*sin(2*b*x + 2*a) + 3*sin(2*b*x + 2*a)*sin(b*x + a) + cos(b*x + a))*c/(b*cos(3*b*x + 3*a)^2 + 2*b*cos(3*b*x + 3*a)*cos(b*x + a) + b*cos(b*x + a)^2 + b*sin(3*b*x + 3*a)^2 + 2*b*sin(3*b*x + 3*a)*sin(b*x + a) + b*sin(b*x + a)^2) - 1/2*(4*(cos(a)^2 + sin(a)^2)*b*x*cos(b*x + a) + 12*(b*x*cos(2*b*x + 3*a)*cos(b*x + 2*a) + b*x*cos(b*x + 2*a)*cos(a) + b*x*sin(2*b*x + 3*a)*sin(b*x + 2*a) + b*x*sin(b*x + 2*a)*sin(a))*cos(3*b*x + 3*a)^2 + 4*(b*x*cos(b*x + a) - sin(b*x + a))*cos(2*b*x + 3*a)^2 + 12*(b*x*cos(2*b*x + 3*a)*cos(b*x + 2*a) + b*x*cos(b*x + 2*a)*cos(a) + b*x*sin(2*b*x + 3*a)*sin(b*x + 2*a) + b*x*sin(b*x + 2*a)*sin(a))*sin(3*b*x + 3*a)^2 + 4*(b*x*cos(b*x + a) - sin(b*x + a))*sin(2*b*x + 3*a)^2 + 4*((b*x*cos(2*b*x + 3*a) + b*x*cos(a) + sin(2*b*x + 3*a) + sin(a))*cos(3*b*x + 3*a)^2 + (b*x*cos(a) + sin(a))*cos(b*x + a)^2 + (b*x*cos(2*b*x + 3*a) + b*x*cos(a) + sin(2*b*x + 3*a) + sin(a))*sin(3*b*x + 3*a)^2 + (b*x*cos(a) + sin(a))*sin(b*x + a)^2 + 2*(b*x*cos(2*b*x + 3*a)*cos(b*x + a) + (b*x*cos(a) + sin(a))*cos(b*x + a) + cos(b*x + a)*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + (b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b*x*cos(2*b*x + 3*a)*sin(b*x + a) + (b*x*cos(a) + sin(a))*sin(b*x + a) + sin(2*b*x + 3*a)*sin(b*x + a))*sin(3*b*x + 3*a) + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 3*a))*cos(3*b*x + 4*a) + 4*(6*b*x*cos(b*x + 2*a)*cos(b*x + a)*cos(a) + 6*b*x*cos(b*x + a)*sin(b*x + 2*a)*sin(a) + b*x*cos(2*b*x + 3*a)^2 + b*x*sin(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*b*x + 2*(3*b*x*cos(b*x + 2*a)*cos(b*x + a) + b*x*cos(a))*cos(2*b*x + 3*a) + 2*(3*b*x*cos(b*x + a)*sin(b*x + 2*a) + b*x*sin(a))*sin(2*b*x + 3*a))*cos(3*b*x + 3*a) + 4*(2*b*x*cos(b*x + a)*cos(a) + 3*(b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*cos(b*x + 2*a) - 2*cos(a)*sin(b*x + a))*cos(2*b*x + 3*a) + 12*(b*x*cos(b*x + a)^2*cos(a) + b*x*cos(a)*sin(b*x + a)^2)*cos(b*x + 2*a) - ((cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*cos(b*x + a)^2 + (cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*sin(b*x + a)^2 + 2*(cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2*cos(a) + cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(cos(b*x + a)^2*sin(a) + sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 + 2*sin(b*x + a) + 1) + ((cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*cos(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*cos(b*x + a)^2 + (cos(2*b*x + 3*a)^2 + 2*cos(2*b*x + 3*a)*cos(a) + cos(a)^2 + sin(2*b*x + 3*a)^2 + 2*sin(2*b*x + 3*a)*sin(a) + sin(a)^2)*sin(3*b*x + 3*a)^2 + (cos(b*x + a)^2 + sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + (cos(a)^2 + sin(a)^2)*sin(b*x + a)^2 + 2*(cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(cos(b*x + a)^2*cos(a) + cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(cos(b*x + a)^2*sin(a) + sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))*log(cos(b*x + a)^2 + sin(b*x + a)^2 - 2*sin(b*x + a) + 1) + 4*((b*x*sin(2*b*x + 3*a) + b*x*sin(a) - cos(2*b*x + 3*a) - cos(a))*cos(3*b*x + 3*a)^2 + (b*x*sin(a) - cos(a))*cos(b*x + a)^2 + (b*x*sin(2*b*x + 3*a) + b*x*sin(a) - cos(2*b*x + 3*a) - cos(a))*sin(3*b*x + 3*a)^2 + (b*x*sin(a) - cos(a))*sin(b*x + a)^2 + 2*(b*x*cos(b*x + a)*sin(2*b*x + 3*a) + (b*x*sin(a) - cos(a))*cos(b*x + a) - cos(2*b*x + 3*a)*cos(b*x + a))*cos(3*b*x + 3*a) - (cos(b*x + a)^2 + sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b*x*sin(2*b*x + 3*a)*sin(b*x + a) + (b*x*sin(a) - cos(a))*sin(b*x + a) - cos(2*b*x + 3*a)*sin(b*x + a))*sin(3*b*x + 3*a) + (b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*sin(2*b*x + 3*a))*sin(3*b*x + 4*a) + 4*(6*b*x*cos(b*x + 2*a)*cos(a)*sin(b*x + a) + 6*b*x*sin(b*x + 2*a)*sin(b*x + a)*sin(a) + 2*(3*b*x*cos(b*x + 2*a)*sin(b*x + a) - cos(a))*cos(2*b*x + 3*a) - cos(2*b*x + 3*a)^2 - cos(a)^2 + 2*(3*b*x*sin(b*x + 2*a)*sin(b*x + a) - sin(a))*sin(2*b*x + 3*a) - sin(2*b*x + 3*a)^2 - sin(a)^2)*sin(3*b*x + 3*a) + 4*(2*b*x*cos(b*x + a)*sin(a) + 3*(b*x*cos(b*x + a)^2 + b*x*sin(b*x + a)^2)*sin(b*x + 2*a) - 2*sin(b*x + a)*sin(a))*sin(2*b*x + 3*a) + 12*(b*x*cos(b*x + a)^2*sin(a) + b*x*sin(b*x + a)^2*sin(a))*sin(b*x + 2*a) - 4*(cos(a)^2 + sin(a)^2)*sin(b*x + a))*d/((cos(a)^2 + sin(a)^2)*b^2*cos(b*x + a)^2 + (cos(a)^2 + sin(a)^2)*b^2*sin(b*x + a)^2 + (b^2*cos(2*b*x + 3*a)^2 + 2*b^2*cos(2*b*x + 3*a)*cos(a) + b^2*sin(2*b*x + 3*a)^2 + 2*b^2*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2)*cos(3*b*x + 3*a)^2 + (b^2*cos(b*x + a)^2 + b^2*sin(b*x + a)^2)*cos(2*b*x + 3*a)^2 + (b^2*cos(2*b*x + 3*a)^2 + 2*b^2*cos(2*b*x + 3*a)*cos(a) + b^2*sin(2*b*x + 3*a)^2 + 2*b^2*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2)*sin(3*b*x + 3*a)^2 + (b^2*cos(b*x + a)^2 + b^2*sin(b*x + a)^2)*sin(2*b*x + 3*a)^2 + 2*(b^2*cos(2*b*x + 3*a)^2*cos(b*x + a) + 2*b^2*cos(2*b*x + 3*a)*cos(b*x + a)*cos(a) + b^2*cos(b*x + a)*sin(2*b*x + 3*a)^2 + 2*b^2*cos(b*x + a)*sin(2*b*x + 3*a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2*cos(b*x + a))*cos(3*b*x + 3*a) + 2*(b^2*cos(b*x + a)^2*cos(a) + b^2*cos(a)*sin(b*x + a)^2)*cos(2*b*x + 3*a) + 2*(b^2*cos(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^2*cos(2*b*x + 3*a)*cos(a)*sin(b*x + a) + b^2*sin(2*b*x + 3*a)^2*sin(b*x + a) + 2*b^2*sin(2*b*x + 3*a)*sin(b*x + a)*sin(a) + (cos(a)^2 + sin(a)^2)*b^2*sin(b*x + a))*sin(3*b*x + 3*a) + 2*(b^2*cos(b*x + a)^2*sin(a) + b^2*sin(b*x + a)^2*sin(a))*sin(2*b*x + 3*a))","B",0
392,-1,0,0,0.000000," ","integrate(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,-1,0,0,0.000000," ","integrate(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
395,0,0,0,0.000000," ","integrate(x*cos(2*x)*sec(x),x, algorithm=""maxima"")","2 \, x \sin\left(x\right) + 2 \, \cos\left(x\right) - 2 \, \int \frac{x \cos\left(2 \, x\right) \cos\left(x\right) + x \sin\left(2 \, x\right) \sin\left(x\right) + x \cos\left(x\right)}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x}"," ",0,"2*x*sin(x) + 2*cos(x) - 2*integrate((x*cos(2*x)*cos(x) + x*sin(2*x)*sin(x) + x*cos(x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1), x)","F",0
396,1,111,0,0.418310," ","integrate(x*cos(2*x)*sec(x)^2,x, algorithm=""maxima"")","\frac{2 \, x^{2} \cos\left(2 \, x\right)^{2} + 2 \, x^{2} \sin\left(2 \, x\right)^{2} + 4 \, x^{2} \cos\left(2 \, x\right) + 2 \, x^{2} - {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)} \log\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right) - 4 \, x \sin\left(2 \, x\right)}{2 \, {\left(\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1\right)}}"," ",0,"1/2*(2*x^2*cos(2*x)^2 + 2*x^2*sin(2*x)^2 + 4*x^2*cos(2*x) + 2*x^2 - (cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)*log(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1) - 4*x*sin(2*x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1)","B",0
397,0,0,0,0.000000," ","integrate(x*cos(2*x)*sec(x)^3,x, algorithm=""maxima"")","-\frac{{\left(x \sin\left(3 \, x\right) - x \sin\left(x\right) - \cos\left(3 \, x\right) - \cos\left(x\right)\right)} \cos\left(4 \, x\right) - {\left(2 \, x \sin\left(2 \, x\right) + 2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(3 \, x\right) - 2 \, {\left(x \sin\left(x\right) + \cos\left(x\right)\right)} \cos\left(2 \, x\right) - 3 \, {\left(2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1\right)} \int \frac{{\left(\cos\left(2 \, x\right) \cos\left(x\right) + \sin\left(2 \, x\right) \sin\left(x\right) + \cos\left(x\right)\right)} x}{\cos\left(2 \, x\right)^{2} + \sin\left(2 \, x\right)^{2} + 2 \, \cos\left(2 \, x\right) + 1}\,{d x} - {\left(x \cos\left(3 \, x\right) - x \cos\left(x\right) + \sin\left(3 \, x\right) + \sin\left(x\right)\right)} \sin\left(4 \, x\right) + {\left(2 \, x \cos\left(2 \, x\right) + x - 2 \, \sin\left(2 \, x\right)\right)} \sin\left(3 \, x\right) + 2 \, {\left(x \cos\left(x\right) - \sin\left(x\right)\right)} \sin\left(2 \, x\right) - x \sin\left(x\right) - \cos\left(x\right)}{2 \, {\left(2 \, \cos\left(2 \, x\right) + 1\right)} \cos\left(4 \, x\right) + \cos\left(4 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right)^{2} + \sin\left(4 \, x\right)^{2} + 4 \, \sin\left(4 \, x\right) \sin\left(2 \, x\right) + 4 \, \sin\left(2 \, x\right)^{2} + 4 \, \cos\left(2 \, x\right) + 1}"," ",0,"-((x*sin(3*x) - x*sin(x) - cos(3*x) - cos(x))*cos(4*x) - (2*x*sin(2*x) + 2*cos(2*x) + 1)*cos(3*x) - 2*(x*sin(x) + cos(x))*cos(2*x) - 3*(2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)*integrate((x*cos(2*x)*cos(x) + x*sin(2*x)*sin(x) + x*cos(x))/(cos(2*x)^2 + sin(2*x)^2 + 2*cos(2*x) + 1), x) - (x*cos(3*x) - x*cos(x) + sin(3*x) + sin(x))*sin(4*x) + (2*x*cos(2*x) + x - 2*sin(2*x))*sin(3*x) + 2*(x*cos(x) - sin(x))*sin(2*x) - x*sin(x) - cos(x))/(2*(2*cos(2*x) + 1)*cos(4*x) + cos(4*x)^2 + 4*cos(2*x)^2 + sin(4*x)^2 + 4*sin(4*x)*sin(2*x) + 4*sin(2*x)^2 + 4*cos(2*x) + 1)","F",0
