1,1,481,0,0.804489," ","integrate((d*x+c)^4*cos(b*x+a),x, algorithm=""maxima"")","\frac{c^{4} \sin\left(b x + a\right) - \frac{4 \, a c^{3} d \sin\left(b x + a\right)}{b} + \frac{6 \, a^{2} c^{2} d^{2} \sin\left(b x + a\right)}{b^{2}} - \frac{4 \, a^{3} c d^{3} \sin\left(b x + a\right)}{b^{3}} + \frac{a^{4} d^{4} \sin\left(b x + a\right)}{b^{4}} + \frac{4 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} c^{3} d}{b} - \frac{12 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{12 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{4 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{12 \, {\left(2 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a c d^{3}}{b^{3}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{4 \, {\left(3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) + {\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{4 \, {\left(3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) + {\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(4 \, {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \cos\left(b x + a\right) + {\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}}}{b}"," ",0,"(c^4*sin(b*x + a) - 4*a*c^3*d*sin(b*x + a)/b + 6*a^2*c^2*d^2*sin(b*x + a)/b^2 - 4*a^3*c*d^3*sin(b*x + a)/b^3 + a^4*d^4*sin(b*x + a)/b^4 + 4*((b*x + a)*sin(b*x + a) + cos(b*x + a))*c^3*d/b - 12*((b*x + a)*sin(b*x + a) + cos(b*x + a))*a*c^2*d^2/b^2 + 12*((b*x + a)*sin(b*x + a) + cos(b*x + a))*a^2*c*d^3/b^3 - 4*((b*x + a)*sin(b*x + a) + cos(b*x + a))*a^3*d^4/b^4 + 6*(2*(b*x + a)*cos(b*x + a) + ((b*x + a)^2 - 2)*sin(b*x + a))*c^2*d^2/b^2 - 12*(2*(b*x + a)*cos(b*x + a) + ((b*x + a)^2 - 2)*sin(b*x + a))*a*c*d^3/b^3 + 6*(2*(b*x + a)*cos(b*x + a) + ((b*x + a)^2 - 2)*sin(b*x + a))*a^2*d^4/b^4 + 4*(3*((b*x + a)^2 - 2)*cos(b*x + a) + ((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*c*d^3/b^3 - 4*(3*((b*x + a)^2 - 2)*cos(b*x + a) + ((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*a*d^4/b^4 + (4*((b*x + a)^3 - 6*b*x - 6*a)*cos(b*x + a) + ((b*x + a)^4 - 12*(b*x + a)^2 + 24)*sin(b*x + a))*d^4/b^4)/b","B",0
2,1,278,0,0.826319," ","integrate((d*x+c)^3*cos(b*x+a),x, algorithm=""maxima"")","\frac{c^{3} \sin\left(b x + a\right) - \frac{3 \, a c^{2} d \sin\left(b x + a\right)}{b} + \frac{3 \, a^{2} c d^{2} \sin\left(b x + a\right)}{b^{2}} - \frac{a^{3} d^{3} \sin\left(b x + a\right)}{b^{3}} + \frac{3 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} c^{2} d}{b} - \frac{6 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} a c d^{2}}{b^{2}} + \frac{3 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{3 \, {\left(2 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} c d^{2}}{b^{2}} - \frac{3 \, {\left(2 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(3 \, {\left({\left(b x + a\right)}^{2} - 2\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{3} - 6 \, b x - 6 \, a\right)} \sin\left(b x + a\right)\right)} d^{3}}{b^{3}}}{b}"," ",0,"(c^3*sin(b*x + a) - 3*a*c^2*d*sin(b*x + a)/b + 3*a^2*c*d^2*sin(b*x + a)/b^2 - a^3*d^3*sin(b*x + a)/b^3 + 3*((b*x + a)*sin(b*x + a) + cos(b*x + a))*c^2*d/b - 6*((b*x + a)*sin(b*x + a) + cos(b*x + a))*a*c*d^2/b^2 + 3*((b*x + a)*sin(b*x + a) + cos(b*x + a))*a^2*d^3/b^3 + 3*(2*(b*x + a)*cos(b*x + a) + ((b*x + a)^2 - 2)*sin(b*x + a))*c*d^2/b^2 - 3*(2*(b*x + a)*cos(b*x + a) + ((b*x + a)^2 - 2)*sin(b*x + a))*a*d^3/b^3 + (3*((b*x + a)^2 - 2)*cos(b*x + a) + ((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^3/b^3)/b","B",0
3,1,136,0,0.708473," ","integrate((d*x+c)^2*cos(b*x+a),x, algorithm=""maxima"")","\frac{c^{2} \sin\left(b x + a\right) - \frac{2 \, a c d \sin\left(b x + a\right)}{b} + \frac{a^{2} d^{2} \sin\left(b x + a\right)}{b^{2}} + \frac{2 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} c d}{b} - \frac{2 \, {\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left(2 \, {\left(b x + a\right)} \cos\left(b x + a\right) + {\left({\left(b x + a\right)}^{2} - 2\right)} \sin\left(b x + a\right)\right)} d^{2}}{b^{2}}}{b}"," ",0,"(c^2*sin(b*x + a) - 2*a*c*d*sin(b*x + a)/b + a^2*d^2*sin(b*x + a)/b^2 + 2*((b*x + a)*sin(b*x + a) + cos(b*x + a))*c*d/b - 2*((b*x + a)*sin(b*x + a) + cos(b*x + a))*a*d^2/b^2 + (2*(b*x + a)*cos(b*x + a) + ((b*x + a)^2 - 2)*sin(b*x + a))*d^2/b^2)/b","B",0
4,1,50,0,0.339933," ","integrate((d*x+c)*cos(b*x+a),x, algorithm=""maxima"")","\frac{c \sin\left(b x + a\right) - \frac{a d \sin\left(b x + a\right)}{b} + \frac{{\left({\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(b x + a\right)\right)} d}{b}}{b}"," ",0,"(c*sin(b*x + a) - a*d*sin(b*x + a)/b + ((b*x + a)*sin(b*x + a) + cos(b*x + a))*d/b)/b","A",0
5,1,142,0,0.822846," ","integrate(cos(b*x+a)/(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(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)}{2 \, b d}"," ",0,"-1/2*(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*(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*d)","C",0
6,1,166,0,0.920913," ","integrate(cos(b*x+a)/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{8 \, 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) - b^{2} {\left(8 i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - 8 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)}{16 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/16*(8*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) - b^2*(8*I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - 8*I*exp_integral_e(2, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d))/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
7,1,201,0,1.105638," ","integrate(cos(b*x+a)/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{8 \, 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) - b^{3} {\left(8 i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - 8 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)}{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*(8*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) - b^3*(8*I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - 8*I*exp_integral_e(3, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(b*c - a*d)/d))/((b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + a^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*b)","C",0
8,1,251,0,1.293442," ","integrate(cos(b*x+a)/(d*x+c)^4,x, algorithm=""maxima"")","-\frac{8 \, 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) - b^{4} {\left(8 i \, E_{4}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - 8 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)}{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*(8*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) - b^4*(8*I*exp_integral_e(4, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - 8*I*exp_integral_e(4, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*sin(-(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
9,1,717,0,0.765935," ","integrate((d*x+c)^4*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{10 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{4} - \frac{40 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{3} d}{b} + \frac{60 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{40 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} c d^{3}}{b^{3}} + \frac{10 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{4} d^{4}}{b^{4}} + \frac{20 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} c^{3} d}{b} - \frac{60 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d^{2}}{b^{2}} + \frac{60 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{3}}{b^{3}} - \frac{20 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{4}}{b^{4}} + \frac{10 \, {\left(4 \, {\left(b x + a\right)}^{3} + 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} d^{2}}{b^{2}} - \frac{20 \, {\left(4 \, {\left(b x + a\right)}^{3} + 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a c d^{3}}{b^{3}} + \frac{10 \, {\left(4 \, {\left(b x + a\right)}^{3} + 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{4}}{b^{4}} + \frac{10 \, {\left(2 \, {\left(b x + a\right)}^{4} + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{3}}{b^{3}} - \frac{10 \, {\left(2 \, {\left(b x + a\right)}^{4} + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{4}}{b^{4}} + \frac{{\left(4 \, {\left(b x + a\right)}^{5} + 10 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \cos\left(2 \, b x + 2 \, a\right) + 5 \, {\left(2 \, {\left(b x + a\right)}^{4} - 6 \, {\left(b x + a\right)}^{2} + 3\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{4}}{b^{4}}}{40 \, b}"," ",0,"1/40*(10*(2*b*x + 2*a + sin(2*b*x + 2*a))*c^4 - 40*(2*b*x + 2*a + sin(2*b*x + 2*a))*a*c^3*d/b + 60*(2*b*x + 2*a + sin(2*b*x + 2*a))*a^2*c^2*d^2/b^2 - 40*(2*b*x + 2*a + sin(2*b*x + 2*a))*a^3*c*d^3/b^3 + 10*(2*b*x + 2*a + sin(2*b*x + 2*a))*a^4*d^4/b^4 + 20*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*c^3*d/b - 60*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*a*c^2*d^2/b^2 + 60*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*a^2*c*d^3/b^3 - 20*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*a^3*d^4/b^4 + 10*(4*(b*x + a)^3 + 6*(b*x + a)*cos(2*b*x + 2*a) + 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c^2*d^2/b^2 - 20*(4*(b*x + a)^3 + 6*(b*x + a)*cos(2*b*x + 2*a) + 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*c*d^3/b^3 + 10*(4*(b*x + a)^3 + 6*(b*x + a)*cos(2*b*x + 2*a) + 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a^2*d^4/b^4 + 10*(2*(b*x + a)^4 + 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) + 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*c*d^3/b^3 - 10*(2*(b*x + a)^4 + 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) + 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*a*d^4/b^4 + (4*(b*x + a)^5 + 10*(2*(b*x + a)^3 - 3*b*x - 3*a)*cos(2*b*x + 2*a) + 5*(2*(b*x + a)^4 - 6*(b*x + a)^2 + 3)*sin(2*b*x + 2*a))*d^4/b^4)/b","B",0
10,1,428,0,0.724951," ","integrate((d*x+c)^3*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{4 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{3} - \frac{12 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a c^{2} d}{b} + \frac{12 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{4 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} d^{3}}{b^{3}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} c^{2} d}{b} - \frac{12 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} a c d^{2}}{b^{2}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{3}}{b^{3}} + \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{3} + 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} c d^{2}}{b^{2}} - \frac{2 \, {\left(4 \, {\left(b x + a\right)}^{3} + 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a d^{3}}{b^{3}} + \frac{{\left(2 \, {\left(b x + a\right)}^{4} + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(2 \, {\left(b x + a\right)}^{3} - 3 \, b x - 3 \, a\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{3}}{b^{3}}}{16 \, b}"," ",0,"1/16*(4*(2*b*x + 2*a + sin(2*b*x + 2*a))*c^3 - 12*(2*b*x + 2*a + sin(2*b*x + 2*a))*a*c^2*d/b + 12*(2*b*x + 2*a + sin(2*b*x + 2*a))*a^2*c*d^2/b^2 - 4*(2*b*x + 2*a + sin(2*b*x + 2*a))*a^3*d^3/b^3 + 6*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*c^2*d/b - 12*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*a*c*d^2/b^2 + 6*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*a^2*d^3/b^3 + 2*(4*(b*x + a)^3 + 6*(b*x + a)*cos(2*b*x + 2*a) + 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*c*d^2/b^2 - 2*(4*(b*x + a)^3 + 6*(b*x + a)*cos(2*b*x + 2*a) + 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a*d^3/b^3 + (2*(b*x + a)^4 + 3*(2*(b*x + a)^2 - 1)*cos(2*b*x + 2*a) + 2*(2*(b*x + a)^3 - 3*b*x - 3*a)*sin(2*b*x + 2*a))*d^3/b^3)/b","B",0
11,1,222,0,0.722276," ","integrate((d*x+c)^2*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{6 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} c^{2} - \frac{12 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a c d}{b} + \frac{6 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} d^{2}}{b^{2}} + \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} c d}{b} - \frac{6 \, {\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} a d^{2}}{b^{2}} + \frac{{\left(4 \, {\left(b x + a\right)}^{3} + 6 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + 3 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} d^{2}}{b^{2}}}{24 \, b}"," ",0,"1/24*(6*(2*b*x + 2*a + sin(2*b*x + 2*a))*c^2 - 12*(2*b*x + 2*a + sin(2*b*x + 2*a))*a*c*d/b + 6*(2*b*x + 2*a + sin(2*b*x + 2*a))*a^2*d^2/b^2 + 6*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*c*d/b - 6*(2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*a*d^2/b^2 + (4*(b*x + a)^3 + 6*(b*x + a)*cos(2*b*x + 2*a) + 3*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*d^2/b^2)/b","B",0
12,1,90,0,0.678056," ","integrate((d*x+c)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} c - \frac{2 \, {\left(2 \, b x + 2 \, a + \sin\left(2 \, b x + 2 \, a\right)\right)} a d}{b} + \frac{{\left(2 \, {\left(b x + a\right)}^{2} + 2 \, {\left(b x + a\right)} \sin\left(2 \, b x + 2 \, a\right) + \cos\left(2 \, b x + 2 \, a\right)\right)} d}{b}}{8 \, b}"," ",0,"1/8*(2*(2*b*x + 2*a + sin(2*b*x + 2*a))*c - 2*(2*b*x + 2*a + sin(2*b*x + 2*a))*a*d/b + (2*(b*x + a)^2 + 2*(b*x + a)*sin(2*b*x + 2*a) + cos(2*b*x + 2*a))*d/b)/b","A",0
13,1,161,0,0.994319," ","integrate(cos(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","-\frac{b {\left(E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{1}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - b {\left(i \, E_{1}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - i \, E_{1}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, b \log\left(b c + {\left(b x + a\right)} d - a d\right)}{4 \, b d}"," ",0,"-1/4*(b*(exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(1, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) - b*(I*exp_integral_e(1, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - I*exp_integral_e(1, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) - 2*b*log(b*c + (b*x + a)*d - a*d))/(b*d)","C",0
14,1,171,0,0.932987," ","integrate(cos(b*x+a)^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{16 \, b^{2} {\left(E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{2}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - b^{2} {\left(16 i \, E_{2}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 16 i \, E_{2}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 32 \, b^{2}}{64 \, {\left(b c d + {\left(b x + a\right)} d^{2} - a d^{2}\right)} b}"," ",0,"-1/64*(16*b^2*(exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(2, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) - b^2*(16*I*exp_integral_e(2, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 16*I*exp_integral_e(2, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) + 32*b^2)/((b*c*d + (b*x + a)*d^2 - a*d^2)*b)","C",0
15,1,206,0,0.998635," ","integrate(cos(b*x+a)^2/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{16 \, b^{3} {\left(E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) + E_{3}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - b^{3} {\left(16 i \, E_{3}\left(\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right) - 16 i \, E_{3}\left(-\frac{2 i \, b c + 2 i \, {\left(b x + a\right)} d - 2 i \, a d}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 16 \, b^{3}}{64 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + {\left(b x + a\right)}^{2} d^{3} + a^{2} d^{3} + 2 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}\right)} b}"," ",0,"-1/64*(16*b^3*(exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) + exp_integral_e(3, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*cos(-2*(b*c - a*d)/d) - b^3*(16*I*exp_integral_e(3, (2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d) - 16*I*exp_integral_e(3, -(2*I*b*c + 2*I*(b*x + a)*d - 2*I*a*d)/d))*sin(-2*(b*c - a*d)/d) + 16*b^3)/((b^2*c^2*d - 2*a*b*c*d^2 + (b*x + a)^2*d^3 + a^2*d^3 + 2*(b*c*d^2 - a*d^3)*(b*x + a))*b)","C",0
16,1,925,0,0.694927," ","integrate((d*x+c)^4*cos(b*x+a)^3,x, algorithm=""maxima"")","-\frac{108 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} c^{4} - \frac{432 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a c^{3} d}{b} + \frac{648 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a^{2} c^{2} d^{2}}{b^{2}} - \frac{432 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a^{3} c d^{3}}{b^{3}} + \frac{108 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a^{4} d^{4}}{b^{4}} - \frac{36 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 162 \, {\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) + 81 \, {\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) + 162 \, {\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) + 81 \, {\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) + 162 \, {\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) + 81 \, {\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) + 243 \, {\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) + 81 \, {\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) + 243 \, {\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) + 81 \, {\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) + 972 \, {\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) + 243 \, {\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*(sin(b*x + a)^3 - 3*sin(b*x + a))*c^4 - 432*(sin(b*x + a)^3 - 3*sin(b*x + a))*a*c^3*d/b + 648*(sin(b*x + a)^3 - 3*sin(b*x + a))*a^2*c^2*d^2/b^2 - 432*(sin(b*x + a)^3 - 3*sin(b*x + a))*a^3*c*d^3/b^3 + 108*(sin(b*x + a)^3 - 3*sin(b*x + a))*a^4*d^4/b^4 - 36*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*c^3*d/b + 108*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*a*c^2*d^2/b^2 - 108*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*a^2*c*d^3/b^3 + 36*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*a^3*d^4/b^4 - 18*(6*(b*x + a)*cos(3*b*x + 3*a) + 162*(b*x + 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^2*d^2/b^2 + 36*(6*(b*x + a)*cos(3*b*x + 3*a) + 162*(b*x + 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*c*d^3/b^3 - 18*(6*(b*x + a)*cos(3*b*x + 3*a) + 162*(b*x + 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^2*d^4/b^4 - 12*((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) + 243*((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) + 81*((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) + 243*((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) + 81*((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) + 972*((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) + 243*((b*x + a)^4 - 12*(b*x + a)^2 + 24)*sin(b*x + a))*d^4/b^4)/b","B",0
17,1,535,0,0.560421," ","integrate((d*x+c)^3*cos(b*x+a)^3,x, algorithm=""maxima"")","-\frac{36 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} c^{3} - \frac{108 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a c^{2} d}{b} + \frac{108 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a^{2} c d^{2}}{b^{2}} - \frac{36 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a^{3} d^{3}}{b^{3}} - \frac{9 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 162 \, {\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) + 81 \, {\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) + 162 \, {\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) + 81 \, {\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) + 243 \, {\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) + 81 \, {\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*(sin(b*x + a)^3 - 3*sin(b*x + a))*c^3 - 108*(sin(b*x + a)^3 - 3*sin(b*x + a))*a*c^2*d/b + 108*(sin(b*x + a)^3 - 3*sin(b*x + a))*a^2*c*d^2/b^2 - 36*(sin(b*x + a)^3 - 3*sin(b*x + a))*a^3*d^3/b^3 - 9*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*c^2*d/b + 18*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*a*c*d^2/b^2 - 9*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*a^2*d^3/b^3 - 3*(6*(b*x + a)*cos(3*b*x + 3*a) + 162*(b*x + 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^2/b^2 + 3*(6*(b*x + a)*cos(3*b*x + 3*a) + 162*(b*x + 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^3/b^3 - ((9*(b*x + a)^2 - 2)*cos(3*b*x + 3*a) + 243*((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) + 81*((b*x + a)^3 - 6*b*x - 6*a)*sin(b*x + a))*d^3/b^3)/b","B",0
18,1,267,0,0.384365," ","integrate((d*x+c)^2*cos(b*x+a)^3,x, algorithm=""maxima"")","-\frac{36 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} c^{2} - \frac{72 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a c d}{b} + \frac{36 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a^{2} d^{2}}{b^{2}} - \frac{6 \, {\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \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) + 162 \, {\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) + 81 \, {\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*(sin(b*x + a)^3 - 3*sin(b*x + a))*c^2 - 72*(sin(b*x + a)^3 - 3*sin(b*x + a))*a*c*d/b + 36*(sin(b*x + a)^3 - 3*sin(b*x + a))*a^2*d^2/b^2 - 6*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*c*d/b + 6*(3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*a*d^2/b^2 - (6*(b*x + a)*cos(3*b*x + 3*a) + 162*(b*x + 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^2/b^2)/b","B",0
19,1,103,0,0.348396," ","integrate((d*x+c)*cos(b*x+a)^3,x, algorithm=""maxima"")","-\frac{12 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} c - \frac{12 \, {\left(\sin\left(b x + a\right)^{3} - 3 \, \sin\left(b x + a\right)\right)} a d}{b} - \frac{{\left(3 \, {\left(b x + a\right)} \sin\left(3 \, b x + 3 \, a\right) + 27 \, {\left(b x + a\right)} \sin\left(b x + a\right) + \cos\left(3 \, b x + 3 \, a\right) + 27 \, \cos\left(b x + a\right)\right)} d}{b}}{36 \, b}"," ",0,"-1/36*(12*(sin(b*x + a)^3 - 3*sin(b*x + a))*c - 12*(sin(b*x + a)^3 - 3*sin(b*x + a))*a*d/b - (3*(b*x + a)*sin(3*b*x + 3*a) + 27*(b*x + a)*sin(b*x + a) + cos(3*b*x + 3*a) + 27*cos(b*x + a))*d/b)/b","A",0
20,1,276,0,0.591287," ","integrate(cos(b*x+a)^3/(d*x+c),x, algorithm=""maxima"")","-\frac{3 \, b {\left(E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) + E_{1}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \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(3 i \, E_{1}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - 3 i \, E_{1}\left(-\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right)\right)} \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*(3*b*(exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) + exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*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*(3*I*exp_integral_e(1, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - 3*I*exp_integral_e(1, -(I*b*c + I*(b*x + a)*d - I*a*d)/d))*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
21,1,304,0,0.639508," ","integrate(cos(b*x+a)^3/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{24576 \, 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(24576 i \, E_{2}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - 24576 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*(24576*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*(24576*I*exp_integral_e(2, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - 24576*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
22,1,339,0,1.007354," ","integrate(cos(b*x+a)^3/(d*x+c)^3,x, algorithm=""maxima"")","-\frac{24576 \, 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(24576 i \, E_{3}\left(\frac{i \, b c + i \, {\left(b x + a\right)} d - i \, a d}{d}\right) - 24576 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*(24576*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*(24576*I*exp_integral_e(3, (I*b*c + I*(b*x + a)*d - I*a*d)/d) - 24576*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
23,1,303,0,0.387860," ","integrate(x^3*cos(b*x+a)^4,x, algorithm=""maxima"")","\frac{96 \, {\left(b x + a\right)}^{4} - 32 \, {\left(12 \, b x + 12 \, a + \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{3} + 24 \, {\left(24 \, {\left(b x + a\right)}^{2} + 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) + \cos\left(4 \, b x + 4 \, a\right) + 16 \, \cos\left(2 \, b x + 2 \, a\right)\right)} a^{2} - 12 \, {\left(32 \, {\left(b x + a\right)}^{3} + 4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 64 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} a + 3 \, {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right) + 192 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\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)}{1024 \, b^{4}}"," ",0,"1/1024*(96*(b*x + a)^4 - 32*(12*b*x + 12*a + sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a^3 + 24*(24*(b*x + a)^2 + 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a) + cos(4*b*x + 4*a) + 16*cos(2*b*x + 2*a))*a^2 - 12*(32*(b*x + a)^3 + 4*(b*x + a)*cos(4*b*x + 4*a) + 64*(b*x + a)*cos(2*b*x + 2*a) + (8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) + 32*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))*a + 3*(8*(b*x + a)^2 - 1)*cos(4*b*x + 4*a) + 192*(2*(b*x + a)^2 - 1)*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))/b^4","A",0
24,1,188,0,0.348220," ","integrate(x^2*cos(b*x+a)^4,x, algorithm=""maxima"")","\frac{32 \, {\left(b x + a\right)}^{3} + 8 \, {\left(12 \, b x + 12 \, a + \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a^{2} - 4 \, {\left(24 \, {\left(b x + a\right)}^{2} + 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) + \cos\left(4 \, b x + 4 \, a\right) + 16 \, \cos\left(2 \, b x + 2 \, a\right)\right)} a + 4 \, {\left(b x + a\right)} \cos\left(4 \, b x + 4 \, a\right) + 64 \, {\left(b x + a\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(8 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right) + 32 \, {\left(2 \, {\left(b x + a\right)}^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)}{256 \, b^{3}}"," ",0,"1/256*(32*(b*x + a)^3 + 8*(12*b*x + 12*a + sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a^2 - 4*(24*(b*x + a)^2 + 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a) + cos(4*b*x + 4*a) + 16*cos(2*b*x + 2*a))*a + 4*(b*x + a)*cos(4*b*x + 4*a) + 64*(b*x + a)*cos(2*b*x + 2*a) + (8*(b*x + a)^2 - 1)*sin(4*b*x + 4*a) + 32*(2*(b*x + a)^2 - 1)*sin(2*b*x + 2*a))/b^3","A",0
25,1,98,0,0.532331," ","integrate(x*cos(b*x+a)^4,x, algorithm=""maxima"")","\frac{24 \, {\left(b x + a\right)}^{2} - 4 \, {\left(12 \, b x + 12 \, a + \sin\left(4 \, b x + 4 \, a\right) + 8 \, \sin\left(2 \, b x + 2 \, a\right)\right)} a + 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) + \cos\left(4 \, b x + 4 \, a\right) + 16 \, \cos\left(2 \, b x + 2 \, a\right)}{128 \, b^{2}}"," ",0,"1/128*(24*(b*x + a)^2 - 4*(12*b*x + 12*a + sin(4*b*x + 4*a) + 8*sin(2*b*x + 2*a))*a + 4*(b*x + a)*sin(4*b*x + 4*a) + 32*(b*x + a)*sin(2*b*x + 2*a) + cos(4*b*x + 4*a) + 16*cos(2*b*x + 2*a))/b^2","A",0
26,1,91,0,0.805695," ","integrate(cos(b*x+a)^4/x,x, algorithm=""maxima"")","-\frac{1}{16} \, {\left(E_{1}\left(4 i \, b x\right) + E_{1}\left(-4 i \, b x\right)\right)} \cos\left(4 \, a\right) - \frac{1}{4} \, {\left(E_{1}\left(2 i \, b x\right) + E_{1}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + \frac{1}{16} \, {\left(i \, E_{1}\left(4 i \, b x\right) - i \, E_{1}\left(-4 i \, b x\right)\right)} \sin\left(4 \, a\right) + \frac{1}{16} \, {\left(4 i \, E_{1}\left(2 i \, b x\right) - 4 i \, E_{1}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right) + \frac{3}{8} \, \log\left(b x\right)"," ",0,"-1/16*(exp_integral_e(1, 4*I*b*x) + exp_integral_e(1, -4*I*b*x))*cos(4*a) - 1/4*(exp_integral_e(1, 2*I*b*x) + exp_integral_e(1, -2*I*b*x))*cos(2*a) + 1/16*(I*exp_integral_e(1, 4*I*b*x) - I*exp_integral_e(1, -4*I*b*x))*sin(4*a) + 1/16*(4*I*exp_integral_e(1, 2*I*b*x) - 4*I*exp_integral_e(1, -2*I*b*x))*sin(2*a) + 3/8*log(b*x)","C",0
27,1,726,0,0.920621," ","integrate(cos(b*x+a)^4/x^2,x, algorithm=""maxima"")","\frac{{\left(32768 \, {\left({\left(E_{2}\left(4 i \, b x\right) + E_{2}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(E_{2}\left(4 i \, b x\right) + E_{2}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{3} - {\left({\left(32768 i \, E_{2}\left(4 i \, b x\right) - 32768 i \, E_{2}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(32768 i \, E_{2}\left(4 i \, b x\right) - 32768 i \, E_{2}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{3} + {\left(131072 \, {\left(E_{2}\left(2 i \, b x\right) + E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{3} - {\left(131072 i \, E_{2}\left(2 i \, b x\right) - 131072 i \, E_{2}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)^{3} + 131072 \, {\left({\left(E_{2}\left(2 i \, b x\right) + E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 3\right)} \sin\left(2 \, a\right)^{2} + 131072 \, {\left(E_{2}\left(2 i \, b x\right) + E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 393216 \, \cos\left(2 \, a\right)^{2} - {\left({\left(131072 i \, E_{2}\left(2 i \, b x\right) - 131072 i \, E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + 131072 i \, E_{2}\left(2 i \, b x\right) - 131072 i \, E_{2}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)\right)} \cos\left(4 \, a\right)^{2} + {\left(131072 \, {\left(E_{2}\left(2 i \, b x\right) + E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{3} - {\left(131072 i \, E_{2}\left(2 i \, b x\right) - 131072 i \, E_{2}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)^{3} + 131072 \, {\left({\left(E_{2}\left(2 i \, b x\right) + E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 3\right)} \sin\left(2 \, a\right)^{2} + 32768 \, {\left({\left(E_{2}\left(4 i \, b x\right) + E_{2}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(E_{2}\left(4 i \, b x\right) + E_{2}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right) + 131072 \, {\left(E_{2}\left(2 i \, b x\right) + E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 393216 \, \cos\left(2 \, a\right)^{2} - {\left({\left(131072 i \, E_{2}\left(2 i \, b x\right) - 131072 i \, E_{2}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + 131072 i \, E_{2}\left(2 i \, b x\right) - 131072 i \, E_{2}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)\right)} \sin\left(4 \, a\right)^{2} + 32768 \, {\left({\left(E_{2}\left(4 i \, b x\right) + E_{2}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(E_{2}\left(4 i \, b x\right) + E_{2}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right) - {\left({\left({\left(32768 i \, E_{2}\left(4 i \, b x\right) - 32768 i \, E_{2}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(32768 i \, E_{2}\left(4 i \, b x\right) - 32768 i \, E_{2}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(32768 i \, E_{2}\left(4 i \, b x\right) - 32768 i \, E_{2}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(32768 i \, E_{2}\left(4 i \, b x\right) - 32768 i \, E_{2}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)\right)} b}{1048576 \, {\left({\left(a \cos\left(2 \, a\right)^{2} + a \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(a \cos\left(2 \, a\right)^{2} + a \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{2} - {\left({\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{2}\right)} {\left(b x + a\right)}\right)}}"," ",0,"1/1048576*(32768*((exp_integral_e(2, 4*I*b*x) + exp_integral_e(2, -4*I*b*x))*cos(2*a)^2 + (exp_integral_e(2, 4*I*b*x) + exp_integral_e(2, -4*I*b*x))*sin(2*a)^2)*cos(4*a)^3 - ((32768*I*exp_integral_e(2, 4*I*b*x) - 32768*I*exp_integral_e(2, -4*I*b*x))*cos(2*a)^2 + (32768*I*exp_integral_e(2, 4*I*b*x) - 32768*I*exp_integral_e(2, -4*I*b*x))*sin(2*a)^2)*sin(4*a)^3 + (131072*(exp_integral_e(2, 2*I*b*x) + exp_integral_e(2, -2*I*b*x))*cos(2*a)^3 - (131072*I*exp_integral_e(2, 2*I*b*x) - 131072*I*exp_integral_e(2, -2*I*b*x))*sin(2*a)^3 + 131072*((exp_integral_e(2, 2*I*b*x) + exp_integral_e(2, -2*I*b*x))*cos(2*a) + 3)*sin(2*a)^2 + 131072*(exp_integral_e(2, 2*I*b*x) + exp_integral_e(2, -2*I*b*x))*cos(2*a) + 393216*cos(2*a)^2 - ((131072*I*exp_integral_e(2, 2*I*b*x) - 131072*I*exp_integral_e(2, -2*I*b*x))*cos(2*a)^2 + 131072*I*exp_integral_e(2, 2*I*b*x) - 131072*I*exp_integral_e(2, -2*I*b*x))*sin(2*a))*cos(4*a)^2 + (131072*(exp_integral_e(2, 2*I*b*x) + exp_integral_e(2, -2*I*b*x))*cos(2*a)^3 - (131072*I*exp_integral_e(2, 2*I*b*x) - 131072*I*exp_integral_e(2, -2*I*b*x))*sin(2*a)^3 + 131072*((exp_integral_e(2, 2*I*b*x) + exp_integral_e(2, -2*I*b*x))*cos(2*a) + 3)*sin(2*a)^2 + 32768*((exp_integral_e(2, 4*I*b*x) + exp_integral_e(2, -4*I*b*x))*cos(2*a)^2 + (exp_integral_e(2, 4*I*b*x) + exp_integral_e(2, -4*I*b*x))*sin(2*a)^2)*cos(4*a) + 131072*(exp_integral_e(2, 2*I*b*x) + exp_integral_e(2, -2*I*b*x))*cos(2*a) + 393216*cos(2*a)^2 - ((131072*I*exp_integral_e(2, 2*I*b*x) - 131072*I*exp_integral_e(2, -2*I*b*x))*cos(2*a)^2 + 131072*I*exp_integral_e(2, 2*I*b*x) - 131072*I*exp_integral_e(2, -2*I*b*x))*sin(2*a))*sin(4*a)^2 + 32768*((exp_integral_e(2, 4*I*b*x) + exp_integral_e(2, -4*I*b*x))*cos(2*a)^2 + (exp_integral_e(2, 4*I*b*x) + exp_integral_e(2, -4*I*b*x))*sin(2*a)^2)*cos(4*a) - (((32768*I*exp_integral_e(2, 4*I*b*x) - 32768*I*exp_integral_e(2, -4*I*b*x))*cos(2*a)^2 + (32768*I*exp_integral_e(2, 4*I*b*x) - 32768*I*exp_integral_e(2, -4*I*b*x))*sin(2*a)^2)*cos(4*a)^2 + (32768*I*exp_integral_e(2, 4*I*b*x) - 32768*I*exp_integral_e(2, -4*I*b*x))*cos(2*a)^2 + (32768*I*exp_integral_e(2, 4*I*b*x) - 32768*I*exp_integral_e(2, -4*I*b*x))*sin(2*a)^2)*sin(4*a))*b/((a*cos(2*a)^2 + a*sin(2*a)^2)*cos(4*a)^2 + (a*cos(2*a)^2 + a*sin(2*a)^2)*sin(4*a)^2 - ((cos(2*a)^2 + sin(2*a)^2)*cos(4*a)^2 + (cos(2*a)^2 + sin(2*a)^2)*sin(4*a)^2)*(b*x + a))","C",0
28,1,795,0,0.766121," ","integrate(cos(b*x+a)^4/x^3,x, algorithm=""maxima"")","-\frac{{\left(65536 \, {\left({\left(E_{3}\left(4 i \, b x\right) + E_{3}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(E_{3}\left(4 i \, b x\right) + E_{3}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{3} - {\left({\left(65536 i \, E_{3}\left(4 i \, b x\right) - 65536 i \, E_{3}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(65536 i \, E_{3}\left(4 i \, b x\right) - 65536 i \, E_{3}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{3} + {\left(262144 \, {\left(E_{3}\left(2 i \, b x\right) + E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{3} - {\left(262144 i \, E_{3}\left(2 i \, b x\right) - 262144 i \, E_{3}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)^{3} + 131072 \, {\left(2 \, {\left(E_{3}\left(2 i \, b x\right) + E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 3\right)} \sin\left(2 \, a\right)^{2} + 262144 \, {\left(E_{3}\left(2 i \, b x\right) + E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 393216 \, \cos\left(2 \, a\right)^{2} - {\left({\left(262144 i \, E_{3}\left(2 i \, b x\right) - 262144 i \, E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + 262144 i \, E_{3}\left(2 i \, b x\right) - 262144 i \, E_{3}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)\right)} \cos\left(4 \, a\right)^{2} + {\left(262144 \, {\left(E_{3}\left(2 i \, b x\right) + E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{3} - {\left(262144 i \, E_{3}\left(2 i \, b x\right) - 262144 i \, E_{3}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)^{3} + 131072 \, {\left(2 \, {\left(E_{3}\left(2 i \, b x\right) + E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 3\right)} \sin\left(2 \, a\right)^{2} + 65536 \, {\left({\left(E_{3}\left(4 i \, b x\right) + E_{3}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(E_{3}\left(4 i \, b x\right) + E_{3}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right) + 262144 \, {\left(E_{3}\left(2 i \, b x\right) + E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right) + 393216 \, \cos\left(2 \, a\right)^{2} - {\left({\left(262144 i \, E_{3}\left(2 i \, b x\right) - 262144 i \, E_{3}\left(-2 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + 262144 i \, E_{3}\left(2 i \, b x\right) - 262144 i \, E_{3}\left(-2 i \, b x\right)\right)} \sin\left(2 \, a\right)\right)} \sin\left(4 \, a\right)^{2} + 65536 \, {\left({\left(E_{3}\left(4 i \, b x\right) + E_{3}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(E_{3}\left(4 i \, b x\right) + E_{3}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right) - {\left({\left({\left(65536 i \, E_{3}\left(4 i \, b x\right) - 65536 i \, E_{3}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(65536 i \, E_{3}\left(4 i \, b x\right) - 65536 i \, E_{3}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(65536 i \, E_{3}\left(4 i \, b x\right) - 65536 i \, E_{3}\left(-4 i \, b x\right)\right)} \cos\left(2 \, a\right)^{2} + {\left(65536 i \, E_{3}\left(4 i \, b x\right) - 65536 i \, E_{3}\left(-4 i \, b x\right)\right)} \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)\right)} b^{2}}{2097152 \, {\left({\left({\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(\cos\left(2 \, a\right)^{2} + \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{2}\right)} {\left(b x + a\right)}^{2} + {\left(a^{2} \cos\left(2 \, a\right)^{2} + a^{2} \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(a^{2} \cos\left(2 \, a\right)^{2} + a^{2} \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{2} - 2 \, {\left({\left(a \cos\left(2 \, a\right)^{2} + a \sin\left(2 \, a\right)^{2}\right)} \cos\left(4 \, a\right)^{2} + {\left(a \cos\left(2 \, a\right)^{2} + a \sin\left(2 \, a\right)^{2}\right)} \sin\left(4 \, a\right)^{2}\right)} {\left(b x + a\right)}\right)}}"," ",0,"-1/2097152*(65536*((exp_integral_e(3, 4*I*b*x) + exp_integral_e(3, -4*I*b*x))*cos(2*a)^2 + (exp_integral_e(3, 4*I*b*x) + exp_integral_e(3, -4*I*b*x))*sin(2*a)^2)*cos(4*a)^3 - ((65536*I*exp_integral_e(3, 4*I*b*x) - 65536*I*exp_integral_e(3, -4*I*b*x))*cos(2*a)^2 + (65536*I*exp_integral_e(3, 4*I*b*x) - 65536*I*exp_integral_e(3, -4*I*b*x))*sin(2*a)^2)*sin(4*a)^3 + (262144*(exp_integral_e(3, 2*I*b*x) + exp_integral_e(3, -2*I*b*x))*cos(2*a)^3 - (262144*I*exp_integral_e(3, 2*I*b*x) - 262144*I*exp_integral_e(3, -2*I*b*x))*sin(2*a)^3 + 131072*(2*(exp_integral_e(3, 2*I*b*x) + exp_integral_e(3, -2*I*b*x))*cos(2*a) + 3)*sin(2*a)^2 + 262144*(exp_integral_e(3, 2*I*b*x) + exp_integral_e(3, -2*I*b*x))*cos(2*a) + 393216*cos(2*a)^2 - ((262144*I*exp_integral_e(3, 2*I*b*x) - 262144*I*exp_integral_e(3, -2*I*b*x))*cos(2*a)^2 + 262144*I*exp_integral_e(3, 2*I*b*x) - 262144*I*exp_integral_e(3, -2*I*b*x))*sin(2*a))*cos(4*a)^2 + (262144*(exp_integral_e(3, 2*I*b*x) + exp_integral_e(3, -2*I*b*x))*cos(2*a)^3 - (262144*I*exp_integral_e(3, 2*I*b*x) - 262144*I*exp_integral_e(3, -2*I*b*x))*sin(2*a)^3 + 131072*(2*(exp_integral_e(3, 2*I*b*x) + exp_integral_e(3, -2*I*b*x))*cos(2*a) + 3)*sin(2*a)^2 + 65536*((exp_integral_e(3, 4*I*b*x) + exp_integral_e(3, -4*I*b*x))*cos(2*a)^2 + (exp_integral_e(3, 4*I*b*x) + exp_integral_e(3, -4*I*b*x))*sin(2*a)^2)*cos(4*a) + 262144*(exp_integral_e(3, 2*I*b*x) + exp_integral_e(3, -2*I*b*x))*cos(2*a) + 393216*cos(2*a)^2 - ((262144*I*exp_integral_e(3, 2*I*b*x) - 262144*I*exp_integral_e(3, -2*I*b*x))*cos(2*a)^2 + 262144*I*exp_integral_e(3, 2*I*b*x) - 262144*I*exp_integral_e(3, -2*I*b*x))*sin(2*a))*sin(4*a)^2 + 65536*((exp_integral_e(3, 4*I*b*x) + exp_integral_e(3, -4*I*b*x))*cos(2*a)^2 + (exp_integral_e(3, 4*I*b*x) + exp_integral_e(3, -4*I*b*x))*sin(2*a)^2)*cos(4*a) - (((65536*I*exp_integral_e(3, 4*I*b*x) - 65536*I*exp_integral_e(3, -4*I*b*x))*cos(2*a)^2 + (65536*I*exp_integral_e(3, 4*I*b*x) - 65536*I*exp_integral_e(3, -4*I*b*x))*sin(2*a)^2)*cos(4*a)^2 + (65536*I*exp_integral_e(3, 4*I*b*x) - 65536*I*exp_integral_e(3, -4*I*b*x))*cos(2*a)^2 + (65536*I*exp_integral_e(3, 4*I*b*x) - 65536*I*exp_integral_e(3, -4*I*b*x))*sin(2*a)^2)*sin(4*a))*b^2/(((cos(2*a)^2 + sin(2*a)^2)*cos(4*a)^2 + (cos(2*a)^2 + sin(2*a)^2)*sin(4*a)^2)*(b*x + a)^2 + (a^2*cos(2*a)^2 + a^2*sin(2*a)^2)*cos(4*a)^2 + (a^2*cos(2*a)^2 + a^2*sin(2*a)^2)*sin(4*a)^2 - 2*((a*cos(2*a)^2 + a*sin(2*a)^2)*cos(4*a)^2 + (a*cos(2*a)^2 + a*sin(2*a)^2)*sin(4*a)^2)*(b*x + a))","C",0
29,1,712,0,1.142365," ","integrate((d*x+c)^3*sec(b*x+a),x, algorithm=""maxima"")","\frac{2 \, c^{3} \log\left(\sec\left(b x + a\right) + \tan\left(b x + a\right)\right) - \frac{6 \, a c^{2} d \log\left(\sec\left(b x + a\right) + \tan\left(b x + a\right)\right)}{b} + \frac{6 \, a^{2} c d^{2} \log\left(\sec\left(b x + a\right) + \tan\left(b x + a\right)\right)}{b^{2}} - \frac{2 \, a^{3} d^{3} \log\left(\sec\left(b x + a\right) + \tan\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) + {\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)})}{b^{3}}}{2 \, b}"," ",0,"1/2*(2*c^3*log(sec(b*x + a) + tan(b*x + a)) - 6*a*c^2*d*log(sec(b*x + a) + tan(b*x + a))/b + 6*a^2*c*d^2*log(sec(b*x + a) + tan(b*x + a))/b^2 - 2*a^3*d^3*log(sec(b*x + a) + tan(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*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)))/b^3)/b","B",0
30,1,396,0,0.725764," ","integrate((d*x+c)^2*sec(b*x+a),x, algorithm=""maxima"")","\frac{2 \, c^{2} \log\left(\sec\left(b x + a\right) + \tan\left(b x + a\right)\right) - \frac{4 \, a c d \log\left(\sec\left(b x + a\right) + \tan\left(b x + a\right)\right)}{b} + \frac{2 \, a^{2} d^{2} \log\left(\sec\left(b x + a\right) + \tan\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) + {\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)}{b^{2}}}{2 \, b}"," ",0,"1/2*(2*c^2*log(sec(b*x + a) + tan(b*x + a)) - 4*a*c*d*log(sec(b*x + a) + tan(b*x + a))/b + 2*a^2*d^2*log(sec(b*x + a) + tan(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*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))/b^2)/b","B",0
31,-1,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,0,0,0,0.000000," ","integrate(sec(b*x+a)/(d*x+c),x, algorithm=""maxima"")","\int \frac{\sec\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(sec(b*x + a)/(d*x + c), x)","F",0
33,1,1056,0,1.424864," ","integrate((d*x+c)^3*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, c^{3} \tan\left(b x + a\right) - \frac{6 \, a c^{2} d \tan\left(b x + a\right)}{b} + \frac{6 \, a^{2} c d^{2} \tan\left(b x + a\right)}{b^{2}} - \frac{2 \, a^{3} d^{3} \tan\left(b x + a\right)}{b^{3}} + \frac{3 \, {\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(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(\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(\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({\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(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^{3} + 3 \, {\left(b c d^{2} - a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(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(2 \, b x + 2 \, 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(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^{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(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^{3} \cos\left(2 \, b x + 2 \, a\right) + 3 \, d^{3} \sin\left(2 \, b x + 2 \, a\right) - 3 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(2 i \, b x + 2 i \, a\right)}) + {\left(-4 i \, {\left(b x + a\right)}^{3} d^{3} + {\left(-12 i \, b c d^{2} + 12 i \, a d^{3}\right)} {\left(b x + a\right)}^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)\right)}}{-2 i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + 2 \, b^{3} \sin\left(2 \, b x + 2 \, a\right) - 2 i \, b^{3}}}{2 \, b}"," ",0,"1/2*(2*c^3*tan(b*x + a) - 6*a*c^2*d*tan(b*x + a)/b + 6*a^2*c*d^2*tan(b*x + a)/b^2 - 2*a^3*d^3*tan(b*x + a)/b^3 + 3*((cos(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1)*log(cos(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*((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*((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*((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(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 4*((b*x + a)^3*d^3 + 3*(b*c*d^2 - a*d^3)*(b*x + a)^2)*cos(2*b*x + 2*a) - (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(2*b*x + 2*a) - (-6*I*b*c*d^2 - 6*I*(b*x + a)*d^3 + 6*I*a*d^3)*sin(2*b*x + 2*a))*dilog(-e^(2*I*b*x + 2*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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (-3*I*d^3*cos(2*b*x + 2*a) + 3*d^3*sin(2*b*x + 2*a) - 3*I*d^3)*polylog(3, -e^(2*I*b*x + 2*I*a)) + (-4*I*(b*x + a)^3*d^3 + (-12*I*b*c*d^2 + 12*I*a*d^3)*(b*x + a)^2)*sin(2*b*x + 2*a))/(-2*I*b^3*cos(2*b*x + 2*a) + 2*b^3*sin(2*b*x + 2*a) - 2*I*b^3))/b","B",0
34,1,324,0,1.483660," ","integrate((d*x+c)^2*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, b^{2} c^{2} + {\left(2 \, b d^{2} x + 2 \, b c d + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sin\left(2 \, b x + 2 \, a\right)\right)} \arctan\left(\sin\left(2 \, b x + 2 \, a\right), \cos\left(2 \, b x + 2 \, a\right) + 1\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x\right)} \cos\left(2 \, b x + 2 \, a\right) - {\left(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(-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(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 \, b^{2} d^{2} x^{2} - 4 i \, b^{2} c d x\right)} \sin\left(2 \, b x + 2 \, a\right)}{-i \, b^{3} \cos\left(2 \, b x + 2 \, a\right) + b^{3} \sin\left(2 \, b x + 2 \, a\right) - i \, b^{3}}"," ",0,"(2*b^2*c^2 + (2*b*d^2*x + 2*b*c*d + 2*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a) + (2*I*b*d^2*x + 2*I*b*c*d)*sin(2*b*x + 2*a))*arctan2(sin(2*b*x + 2*a), cos(2*b*x + 2*a) + 1) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x)*cos(2*b*x + 2*a) - (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)) + (-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(2*b*x + 2*a)^2 + sin(2*b*x + 2*a)^2 + 2*cos(2*b*x + 2*a) + 1) + (-2*I*b^2*d^2*x^2 - 4*I*b^2*c*d*x)*sin(2*b*x + 2*a))/(-I*b^3*cos(2*b*x + 2*a) + b^3*sin(2*b*x + 2*a) - I*b^3)","B",0
35,1,159,0,1.012692," ","integrate((d*x+c)*sec(b*x+a)^2,x, algorithm=""maxima"")","\frac{2 \, c \tan\left(b x + a\right) - \frac{2 \, a d \tan\left(b x + a\right)}{b} + \frac{{\left({\left(\cos\left(2 \, b x + 2 \, a\right)^{2} + \sin\left(2 \, b x + 2 \, a\right)^{2} + 2 \, \cos\left(2 \, b x + 2 \, a\right) + 1\right)} \log\left(\cos\left(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*c*tan(b*x + a) - 2*a*d*tan(b*x + a)/b + ((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
36,0,0,0,0.000000," ","integrate(sec(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\frac{2 \, {\left(\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(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} + \sin\left(2 \, b x + 2 \, a\right)\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,"2*((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(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) + sin(2*b*x + 2*a))/(b*d*x + (b*d*x + b*c)*cos(2*b*x + 2*a)^2 + (b*d*x + b*c)*sin(2*b*x + 2*a)^2 + b*c + 2*(b*d*x + b*c)*cos(2*b*x + 2*a))","F",0
37,1,3828,0,5.469417," ","integrate((d*x+c)^3*sec(b*x+a)^3,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} + {\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(3 \, b x + 3 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{3} d^{3} - 12 \, b^{2} c^{2} d + 24 \, a b c d^{2} - 12 \, a^{2} d^{3} - 12 \, {\left(-i \, b c d^{2} + {\left(i \, a + 1\right)} d^{3}\right)} {\left(b x + a\right)}^{2} + {\left(12 i \, b^{2} c^{2} d - 24 \, {\left(i \, a + 1\right)} b c d^{2} + {\left(12 i \, a^{2} + 24 \, a\right)} d^{3}\right)} {\left(b x + a\right)}\right)} \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 - 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(3*b*x + 3*a) - (4*I*(b*x + a)^3*d^3 - 12*b^2*c^2*d + 24*a*b*c*d^2 - 12*a^2*d^3 - 12*(-I*b*c*d^2 + (I*a + 1)*d^3)*(b*x + a)^2 + (12*I*b^2*c^2*d - 24*(I*a + 1)*b*c*d^2 + (12*I*a^2 + 24*a)*d^3)*(b*x + a))*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
38,1,1893,0,2.704177," ","integrate((d*x+c)^2*sec(b*x+a)^3,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)}) - {\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(3 \, b x + 3 \, a\right) - {\left(4 i \, {\left(b x + a\right)}^{2} d^{2} - 8 \, b c d + 8 \, a d^{2} - 8 \, {\left(-i \, b c d + {\left(i \, a + 1\right)} d^{2}\right)} {\left(b x + a\right)}\right)} \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 - 8*b*c*d + 8*a*d^2 + (-8*I*b*c*d - 8*(-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 + (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
39,-1,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate(sec(b*x+a)^2/(d*x+c),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,1,261,0,0.943110," ","integrate((d*x+c)^(5/2)*cos(b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(40 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(15 i + 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(15 i - 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(15 i - 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(15 i + 15\right) \, \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + 4 \, {\left(4 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3} - 15 \, \sqrt{2} \sqrt{d x + c} b d^{2}\right)} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right)\right)}}{32 \, b^{4}}"," ",0,"1/32*sqrt(2)*(40*sqrt(2)*(d*x + c)^(3/2)*b^2*d*cos(((d*x + c)*b - b*c + a*d)/d) + ((15*I + 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (15*I - 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(15*I - 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (15*I + 15)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + 4*(4*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*sin(((d*x + c)*b - b*c + a*d)/d))/b^4","C",0
42,1,240,0,1.082714," ","integrate((d*x+c)^(3/2)*cos(b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(8 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + 12 \, \sqrt{2} \sqrt{d x + c} b d \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(\left(3 i - 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(3 i + 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(3 i + 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(3 i - 3\right) \, \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{16 \, b^{3}}"," ",0,"1/16*sqrt(2)*(8*sqrt(2)*(d*x + c)^(3/2)*b^2*sin(((d*x + c)*b - b*c + a*d)/d) + 12*sqrt(2)*sqrt(d*x + c)*b*d*cos(((d*x + c)*b - b*c + a*d)/d) + ((3*I - 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (3*I + 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(3*I + 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (3*I - 3)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b^3","C",0
43,1,196,0,1.070727," ","integrate((d*x+c)^(1/2)*cos(b*x+a),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(4 \, \sqrt{2} \sqrt{d x + c} b \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left(-\left(i + 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(i - 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(\left(i - 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(i + 1\right) \, \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{8 \, b^{2}}"," ",0,"1/8*sqrt(2)*(4*sqrt(2)*sqrt(d*x + c)*b*sin(((d*x + c)*b - b*c + a*d)/d) + (-(I + 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (I - 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((I - 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (I + 1)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b^2","C",0
44,1,159,0,0.987883," ","integrate(cos(b*x+a)/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(\left(i - 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(i + 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(i + 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(i - 1\right) \, \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right)\right)}}{4 \, b}"," ",0,"-1/4*sqrt(2)*(((I - 1)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (I + 1)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(I + 1)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (I - 1)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)))/b","C",0
45,1,129,0,1.741424," ","integrate(cos(b*x+a)/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{{\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}}}{4 \, \sqrt{d x + c} d}"," ",0,"1/4*((-(I + 1)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*sqrt((d*x + c)*b/d)/(sqrt(d*x + c)*d)","C",0
46,1,129,0,1.719847," ","integrate(cos(b*x+a)/(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{{\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}}}{4 \, {\left(d x + c\right)}^{\frac{3}{2}} d}"," ",0,"-1/4*(((I - 1)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((I + 1)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) - (I - 1)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2)/((d*x + c)^(3/2)*d)","C",0
47,1,129,0,1.796204," ","integrate(cos(b*x+a)/(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{{\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}}}{4 \, {\left(d x + c\right)}^{\frac{5}{2}} d}"," ",0,"-1/4*((-(I + 1)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2)/((d*x + c)^(5/2)*d)","C",0
48,1,293,0,2.163573," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{512 \, \sqrt{2} {\left(d x + c\right)}^{\frac{7}{2}} b^{4}}{d} + 1120 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} d \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(105 i + 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(105 i - 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) + {\left(-\left(105 i - 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(105 i + 105\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{3} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right) + 56 \, {\left(16 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3} - 15 \, \sqrt{2} \sqrt{d x + c} b d^{2}\right)} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right)\right)}}{7168 \, b^{4}}"," ",0,"1/7168*sqrt(2)*(512*sqrt(2)*(d*x + c)^(7/2)*b^4/d + 1120*sqrt(2)*(d*x + c)^(3/2)*b^2*d*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((105*I + 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (105*I - 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + (-(105*I - 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (105*I + 105)*4^(1/4)*sqrt(pi)*d^3*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) + 56*(16*sqrt(2)*(d*x + c)^(5/2)*b^3 - 15*sqrt(2)*sqrt(d*x + c)*b*d^2)*sin(2*((d*x + c)*b - b*c + a*d)/d))/b^4","C",0
49,1,272,0,1.605578," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{128 \, \sqrt{2} {\left(d x + c\right)}^{\frac{5}{2}} b^{3}}{d} + 160 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2} \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + 120 \, \sqrt{2} \sqrt{d x + c} b d \cos\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(\left(15 i - 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(15 i + 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) + {\left(-\left(15 i + 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(15 i - 15\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right)\right)}}{1280 \, b^{3}}"," ",0,"1/1280*sqrt(2)*(128*sqrt(2)*(d*x + c)^(5/2)*b^3/d + 160*sqrt(2)*(d*x + c)^(3/2)*b^2*sin(2*((d*x + c)*b - b*c + a*d)/d) + 120*sqrt(2)*sqrt(d*x + c)*b*d*cos(2*((d*x + c)*b - b*c + a*d)/d) + ((15*I - 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (15*I + 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + (-(15*I + 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (15*I - 15)*4^(1/4)*sqrt(pi)*d^2*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))/b^3","C",0
50,1,227,0,1.385195," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{\sqrt{2} {\left(\frac{32 \, \sqrt{2} {\left(d x + c\right)}^{\frac{3}{2}} b^{2}}{d} + 24 \, \sqrt{2} \sqrt{d x + c} b \sin\left(\frac{2 \, {\left({\left(d x + c\right)} b - b c + a d\right)}}{d}\right) + {\left(-\left(3 i + 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(3 i - 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) + {\left(\left(3 i - 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(3 i + 3\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right)\right)}}{192 \, b^{2}}"," ",0,"1/192*sqrt(2)*(32*sqrt(2)*(d*x + c)^(3/2)*b^2/d + 24*sqrt(2)*sqrt(d*x + c)*b*sin(2*((d*x + c)*b - b*c + a*d)/d) + (-(3*I + 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (3*I - 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + ((3*I - 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (3*I + 3)*4^(1/4)*sqrt(pi)*d*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)))/b^2","C",0
51,1,187,0,1.443657," ","integrate(cos(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(\left(i - 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + \left(i + 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{2 i \, b}{d}}\right) + {\left(-\left(i + 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - \left(i - 1\right) \cdot 4^{\frac{1}{4}} \sqrt{\pi} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{2 i \, b}{d}}\right) - \frac{8 \, \sqrt{2} \sqrt{d x + c} b}{d}\right)}}{16 \, b}"," ",0,"-1/16*sqrt(2)*(((I - 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) + (I + 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(2*I*b/d)) + (-(I + 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*cos(-2*(b*c - a*d)/d) - (I - 1)*4^(1/4)*sqrt(pi)*(b^2/d^2)^(1/4)*sin(-2*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-2*I*b/d)) - 8*sqrt(2)*sqrt(d*x + c)*b/d)/b","C",0
52,1,135,0,1.817943," ","integrate(cos(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}} - 8}{8 \, \sqrt{d x + c} d}"," ",0,"1/8*(sqrt(2)*((-(I + 1)*sqrt(2)*gamma(-1/2, 2*I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-1/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-1/2, 2*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-1/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*sqrt((d*x + c)*b/d) - 8)/(sqrt(d*x + c)*d)","C",0
53,1,135,0,2.205336," ","integrate(cos(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}} + 4}{12 \, {\left(d x + c\right)}^{\frac{3}{2}} d}"," ",0,"-1/12*(sqrt(2)*(((3*I - 3)*sqrt(2)*gamma(-3/2, 2*I*(d*x + c)*b/d) - (3*I + 3)*sqrt(2)*gamma(-3/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((3*I + 3)*sqrt(2)*gamma(-3/2, 2*I*(d*x + c)*b/d) - (3*I - 3)*sqrt(2)*gamma(-3/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2) + 4)/((d*x + c)^(3/2)*d)","C",0
54,1,135,0,1.751610," ","integrate(cos(b*x+a)^2/(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} {\left({\left(-\left(5 i + 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) + \left(5 i - 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(5 i - 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(5 i + 5\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}} + 2}{10 \, {\left(d x + c\right)}^{\frac{5}{2}} d}"," ",0,"-1/10*(sqrt(2)*((-(5*I + 5)*sqrt(2)*gamma(-5/2, 2*I*(d*x + c)*b/d) + (5*I - 5)*sqrt(2)*gamma(-5/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((5*I - 5)*sqrt(2)*gamma(-5/2, 2*I*(d*x + c)*b/d) - (5*I + 5)*sqrt(2)*gamma(-5/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2) + 2)/((d*x + c)^(5/2)*d)","C",0
55,1,135,0,1.790026," ","integrate(cos(b*x+a)^2/(d*x+c)^(9/2),x, algorithm=""maxima"")","\frac{\sqrt{2} {\left({\left(\left(7 i - 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(7 i + 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(7 i + 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, \frac{2 i \, {\left(d x + c\right)} b}{d}\right) - \left(7 i - 7\right) \, \sqrt{2} \Gamma\left(-\frac{7}{2}, -\frac{2 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{7}{2}} - 1}{7 \, {\left(d x + c\right)}^{\frac{7}{2}} d}"," ",0,"1/7*(sqrt(2)*(((7*I - 7)*sqrt(2)*gamma(-7/2, 2*I*(d*x + c)*b/d) - (7*I + 7)*sqrt(2)*gamma(-7/2, -2*I*(d*x + c)*b/d))*cos(-2*(b*c - a*d)/d) + ((7*I + 7)*sqrt(2)*gamma(-7/2, 2*I*(d*x + c)*b/d) - (7*I - 7)*sqrt(2)*gamma(-7/2, -2*I*(d*x + c)*b/d))*sin(-2*(b*c - a*d)/d))*((d*x + c)*b/d)^(7/2) - 1)/((d*x + c)^(7/2)*d)","C",0
56,1,543,0,1.410177," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3,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) + 6480 \, {\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(1215 i + 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(1215 i - 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(1215 i - 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(1215 i + 1215\right) \, \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(5 i - 5\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \left(5 i + 5\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d^{2} \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right) + 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) + 648 \, {\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) + 6480*(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)) + ((1215*I + 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (1215*I - 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(1215*I - 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (1215*I + 1215)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(5*I - 5)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) + (5*I + 5)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d^2*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)) + 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) + 648*(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
57,1,495,0,1.889984," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3,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{432 \, {\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) + 648 \, \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(81 i - 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(81 i + 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\left(81 i + 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(81 i - 81\right) \, \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b d \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{576 \, b^{4}}"," ",0,"1/576*(48*(d*x + c)^(3/2)*b^3*sin(3*((d*x + c)*b - b*c + a*d)/d)/d + 432*(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) + 648*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)) + ((81*I - 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (81*I + 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(81*I + 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (81*I - 81)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*d*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^4","C",0
58,1,422,0,1.627950," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3,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{216 \, \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(27 i + 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) + \left(27 i - 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(\left(27 i - 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right) - \left(27 i + 27\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{288 \, b^{3}}"," ",0,"1/288*(24*sqrt(d*x + c)*b^2*sin(3*((d*x + c)*b - b*c + a*d)/d)/d + 216*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)) + (-(27*I + 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) + (27*I - 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(I*b/d)) + ((27*I - 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d) - (27*I + 27)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + ((I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d) - (I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^3","C",0
59,1,375,0,1.384848," ","integrate(cos(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""maxima"")","-\frac{{\left({\left(\frac{\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d} + \frac{\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{3 i \, b}{d}}\right) + {\left(\frac{\left(9 i - 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} + \frac{\left(9 i + 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{i \, b}{d}}\right) + {\left(-\frac{\left(9 i + 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{b c - a d}{d}\right)}{d} - \frac{\left(9 i - 9\right) \, \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{b c - a d}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{i \, b}{d}}\right) + {\left(-\frac{\left(i + 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d} - \frac{\left(i - 1\right) \cdot 9^{\frac{1}{4}} \sqrt{2} \sqrt{\pi} b \left(\frac{b^{2}}{d^{2}}\right)^{\frac{1}{4}} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{d}\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{3 i \, b}{d}}\right)\right)} d}{48 \, b^{2}}"," ",0,"-1/48*(((I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d + (I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(3*I*b/d)) + ((9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d + (9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(I*b/d)) + (-(9*I + 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-(b*c - a*d)/d)/d - (9*I - 9)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-I*b/d)) + (-(I + 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*cos(-3*(b*c - a*d)/d)/d - (I - 1)*9^(1/4)*sqrt(2)*sqrt(pi)*b*(b^2/d^2)^(1/4)*sin(-3*(b*c - a*d)/d)/d)*erf(sqrt(d*x + c)*sqrt(-3*I*b/d)))*d/b^2","C",0
60,1,252,0,1.980705," ","integrate(cos(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""maxima"")","\frac{\sqrt{3} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}} + {\left({\left(-\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \sqrt{\frac{{\left(d x + c\right)} b}{d}}}{16 \, \sqrt{d x + c} d}"," ",0,"1/16*(sqrt(3)*((-(I + 1)*sqrt(2)*gamma(-1/2, 3*I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-1/2, -3*I*(d*x + c)*b/d))*cos(-3*(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-1/2, 3*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-1/2, -3*I*(d*x + c)*b/d))*sin(-3*(b*c - a*d)/d))*sqrt((d*x + c)*b/d) + ((-(3*I + 3)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) + (3*I - 3)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((3*I - 3)*sqrt(2)*gamma(-1/2, I*(d*x + c)*b/d) - (3*I + 3)*sqrt(2)*gamma(-1/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*sqrt((d*x + c)*b/d))/(sqrt(d*x + c)*d)","C",0
61,1,253,0,2.024072," ","integrate(cos(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""maxima"")","-\frac{3 \, \sqrt{3} {\left({\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}} + {\left({\left(\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{3}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{3}{2}}}{16 \, {\left(d x + c\right)}^{\frac{3}{2}} d}"," ",0,"-1/16*(3*sqrt(3)*(((I - 1)*sqrt(2)*gamma(-3/2, 3*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-3/2, -3*I*(d*x + c)*b/d))*cos(-3*(b*c - a*d)/d) + ((I + 1)*sqrt(2)*gamma(-3/2, 3*I*(d*x + c)*b/d) - (I - 1)*sqrt(2)*gamma(-3/2, -3*I*(d*x + c)*b/d))*sin(-3*(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2) + (((3*I - 3)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) - (3*I + 3)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((3*I + 3)*sqrt(2)*gamma(-3/2, I*(d*x + c)*b/d) - (3*I - 3)*sqrt(2)*gamma(-3/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(3/2))/((d*x + c)^(3/2)*d)","C",0
62,1,253,0,2.089508," ","integrate(cos(b*x+a)^3/(d*x+c)^(7/2),x, algorithm=""maxima"")","-\frac{9 \, \sqrt{3} {\left({\left(-\left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) + \left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(\left(i - 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{3 i \, {\left(d x + c\right)} b}{d}\right) - \left(i + 1\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{3 i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}} + {\left({\left(-\left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + \left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\left(3 i - 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, \frac{i \, {\left(d x + c\right)} b}{d}\right) - \left(3 i + 3\right) \, \sqrt{2} \Gamma\left(-\frac{5}{2}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{5}{2}}}{16 \, {\left(d x + c\right)}^{\frac{5}{2}} d}"," ",0,"-1/16*(9*sqrt(3)*((-(I + 1)*sqrt(2)*gamma(-5/2, 3*I*(d*x + c)*b/d) + (I - 1)*sqrt(2)*gamma(-5/2, -3*I*(d*x + c)*b/d))*cos(-3*(b*c - a*d)/d) + ((I - 1)*sqrt(2)*gamma(-5/2, 3*I*(d*x + c)*b/d) - (I + 1)*sqrt(2)*gamma(-5/2, -3*I*(d*x + c)*b/d))*sin(-3*(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2) + ((-(3*I + 3)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) + (3*I - 3)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((3*I - 3)*sqrt(2)*gamma(-5/2, I*(d*x + c)*b/d) - (3*I + 3)*sqrt(2)*gamma(-5/2, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(5/2))/((d*x + c)^(5/2)*d)","C",0
63,1,74,0,1.330108," ","integrate(x^(3/2)*cos(x),x, algorithm=""maxima"")","x^{\frac{3}{2}} \sin\left(x\right) + \frac{1}{32} \, \sqrt{\pi} {\left(\left(3 i - 3\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) + \left(3 i + 3\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) - \left(3 i + 3\right) \, \sqrt{2} \operatorname{erf}\left(\sqrt{-i} \sqrt{x}\right) + \left(3 i - 3\right) \, \sqrt{2} \operatorname{erf}\left(\left(-1\right)^{\frac{1}{4}} \sqrt{x}\right)\right)} + \frac{3}{2} \, \sqrt{x} \cos\left(x\right)"," ",0,"x^(3/2)*sin(x) + 1/32*sqrt(pi)*((3*I - 3)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*sqrt(x)) + (3*I + 3)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x)) - (3*I + 3)*sqrt(2)*erf(sqrt(-I)*sqrt(x)) + (3*I - 3)*sqrt(2)*erf((-1)^(1/4)*sqrt(x))) + 3/2*sqrt(x)*cos(x)","C",0
64,1,67,0,1.050738," ","integrate(x^(1/2)*cos(x),x, algorithm=""maxima"")","-\frac{1}{16} \, \sqrt{\pi} {\left(\left(i + 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) + \left(i - 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) - \left(i - 1\right) \, \sqrt{2} \operatorname{erf}\left(\sqrt{-i} \sqrt{x}\right) + \left(i + 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(-1\right)^{\frac{1}{4}} \sqrt{x}\right)\right)} + \sqrt{x} \sin\left(x\right)"," ",0,"-1/16*sqrt(pi)*((I + 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*sqrt(x)) + (I - 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x)) - (I - 1)*sqrt(2)*erf(sqrt(-I)*sqrt(x)) + (I + 1)*sqrt(2)*erf((-1)^(1/4)*sqrt(x))) + sqrt(x)*sin(x)","C",0
65,1,60,0,0.749896," ","integrate(cos(x)/x^(1/2),x, algorithm=""maxima"")","-\frac{1}{8} \, \sqrt{\pi} {\left(\left(i - 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) + \left(i + 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) - \left(i + 1\right) \, \sqrt{2} \operatorname{erf}\left(\sqrt{-i} \sqrt{x}\right) + \left(i - 1\right) \, \sqrt{2} \operatorname{erf}\left(\left(-1\right)^{\frac{1}{4}} \sqrt{x}\right)\right)}"," ",0,"-1/8*sqrt(pi)*((I - 1)*sqrt(2)*erf((1/2*I + 1/2)*sqrt(2)*sqrt(x)) + (I + 1)*sqrt(2)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x)) - (I + 1)*sqrt(2)*erf(sqrt(-I)*sqrt(x)) + (I - 1)*sqrt(2)*erf((-1)^(1/4)*sqrt(x)))","C",0
66,1,21,0,1.395489," ","integrate(cos(x)/x^(3/2),x, algorithm=""maxima"")","-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, i \, x\right) + \left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} \Gamma\left(-\frac{1}{2}, -i \, x\right)"," ",0,"-(1/4*I + 1/4)*sqrt(2)*gamma(-1/2, I*x) + (1/4*I - 1/4)*sqrt(2)*gamma(-1/2, -I*x)","C",0
67,1,235,0,1.334620," ","integrate((d*x+c)^(4/3)*cos(b*x+a),x, algorithm=""maxima"")","\frac{9 \, {\left(d x + c\right)}^{\frac{4}{3}} b \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}} d \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + 12 \, {\left(d x + c\right)}^{\frac{1}{3}} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}} d^{2} \cos\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} d^{2} \cos\left(-\frac{b c - a d}{d}\right) + {\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} d^{2} \sin\left(-\frac{b c - a d}{d}\right)\right)} {\left(d x + c\right)}^{\frac{1}{3}}}{9 \, b^{2} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}} d}"," ",0,"1/9*(9*(d*x + c)^(4/3)*b*((d*x + c)*b/d)^(1/3)*d*sin(((d*x + c)*b - b*c + a*d)/d) + 12*(d*x + c)^(1/3)*((d*x + c)*b/d)^(1/3)*d^2*cos(((d*x + c)*b - b*c + a*d)/d) + (((sqrt(3) - I)*gamma(1/3, I*(d*x + c)*b/d) + (sqrt(3) + I)*gamma(1/3, -I*(d*x + c)*b/d))*d^2*cos(-(b*c - a*d)/d) + ((-I*sqrt(3) - 1)*gamma(1/3, I*(d*x + c)*b/d) + (I*sqrt(3) - 1)*gamma(1/3, -I*(d*x + c)*b/d))*d^2*sin(-(b*c - a*d)/d))*(d*x + c)^(1/3))/(b^2*((d*x + c)*b/d)^(1/3)*d)","A",0
68,1,186,0,1.872156," ","integrate((d*x+c)^(2/3)*cos(b*x+a),x, algorithm=""maxima"")","\frac{6 \, {\left(d x + c\right)}^{\frac{2}{3}} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{2}{3}} d \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} d \cos\left(-\frac{b c - a d}{d}\right) + {\left({\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} d \sin\left(-\frac{b c - a d}{d}\right)\right)} {\left(d x + c\right)}^{\frac{2}{3}}}{6 \, b \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{2}{3}} d}"," ",0,"1/6*(6*(d*x + c)^(2/3)*((d*x + c)*b/d)^(2/3)*d*sin(((d*x + c)*b - b*c + a*d)/d) + (((sqrt(3) + I)*gamma(2/3, I*(d*x + c)*b/d) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)*b/d))*d*cos(-(b*c - a*d)/d) + ((-I*sqrt(3) + 1)*gamma(2/3, I*(d*x + c)*b/d) + (I*sqrt(3) + 1)*gamma(2/3, -I*(d*x + c)*b/d))*d*sin(-(b*c - a*d)/d))*(d*x + c)^(2/3))/(b*((d*x + c)*b/d)^(2/3)*d)","A",0
69,1,186,0,1.734351," ","integrate((d*x+c)^(1/3)*cos(b*x+a),x, algorithm=""maxima"")","\frac{12 \, {\left(d x + c\right)}^{\frac{1}{3}} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}} d \sin\left(\frac{{\left(d x + c\right)} b - b c + a d}{d}\right) + {\left({\left({\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} d \cos\left(-\frac{b c - a d}{d}\right) + {\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} d \sin\left(-\frac{b c - a d}{d}\right)\right)} {\left(d x + c\right)}^{\frac{1}{3}}}{12 \, b \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}} d}"," ",0,"1/12*(12*(d*x + c)^(1/3)*((d*x + c)*b/d)^(1/3)*d*sin(((d*x + c)*b - b*c + a*d)/d) + (((I*sqrt(3) + 1)*gamma(1/3, I*(d*x + c)*b/d) + (-I*sqrt(3) + 1)*gamma(1/3, -I*(d*x + c)*b/d))*d*cos(-(b*c - a*d)/d) + ((sqrt(3) - I)*gamma(1/3, I*(d*x + c)*b/d) + (sqrt(3) + I)*gamma(1/3, -I*(d*x + c)*b/d))*d*sin(-(b*c - a*d)/d))*(d*x + c)^(1/3))/(b*((d*x + c)*b/d)^(1/3)*d)","A",0
70,1,137,0,2.072958," ","integrate(cos(b*x+a)/(d*x+c)^(1/3),x, algorithm=""maxima"")","\frac{{\left(d x + c\right)}^{\frac{2}{3}} {\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(\frac{2}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)}}{4 \, \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{2}{3}} d}"," ",0,"1/4*(d*x + c)^(2/3)*(((I*sqrt(3) - 1)*gamma(2/3, I*(d*x + c)*b/d) + (-I*sqrt(3) - 1)*gamma(2/3, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((sqrt(3) + I)*gamma(2/3, I*(d*x + c)*b/d) + (sqrt(3) - I)*gamma(2/3, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))/(((d*x + c)*b/d)^(2/3)*d)","A",0
71,1,138,0,1.741415," ","integrate(cos(b*x+a)/(d*x+c)^(2/3),x, algorithm=""maxima"")","-\frac{{\left(d x + c\right)}^{\frac{1}{3}} {\left({\left({\left(\sqrt{3} - i\right)} \Gamma\left(\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - {\left({\left(i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(-i \, \sqrt{3} + 1\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)}}{4 \, \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}} d}"," ",0,"-1/4*(d*x + c)^(1/3)*(((sqrt(3) - I)*gamma(1/3, I*(d*x + c)*b/d) + (sqrt(3) + I)*gamma(1/3, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) - ((I*sqrt(3) + 1)*gamma(1/3, I*(d*x + c)*b/d) + (-I*sqrt(3) + 1)*gamma(1/3, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))/(((d*x + c)*b/d)^(1/3)*d)","A",0
72,1,138,0,1.558146," ","integrate(cos(b*x+a)/(d*x+c)^(4/3),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - {\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{1}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{1}{3}}}{4 \, {\left(d x + c\right)}^{\frac{1}{3}} d}"," ",0,"-1/4*(((sqrt(3) + I)*gamma(-1/3, I*(d*x + c)*b/d) + (sqrt(3) - I)*gamma(-1/3, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) - ((I*sqrt(3) - 1)*gamma(-1/3, I*(d*x + c)*b/d) + (-I*sqrt(3) - 1)*gamma(-1/3, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(1/3)/((d*x + c)^(1/3)*d)","A",0
73,1,138,0,1.960032," ","integrate(cos(b*x+a)/(d*x+c)^(5/3),x, algorithm=""maxima"")","\frac{{\left({\left({\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{2}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{2}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - {\left({\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{2}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{2}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{2}{3}}}{4 \, {\left(d x + c\right)}^{\frac{2}{3}} d}"," ",0,"1/4*(((-I*sqrt(3) - 1)*gamma(-2/3, I*(d*x + c)*b/d) + (I*sqrt(3) - 1)*gamma(-2/3, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) - ((sqrt(3) - I)*gamma(-2/3, I*(d*x + c)*b/d) + (sqrt(3) + I)*gamma(-2/3, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(2/3)/((d*x + c)^(2/3)*d)","A",0
74,1,137,0,1.818292," ","integrate(cos(b*x+a)/(d*x+c)^(7/3),x, algorithm=""maxima"")","-\frac{{\left({\left({\left(i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{4}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(-i \, \sqrt{3} - 1\right)} \Gamma\left(-\frac{4}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + {\left({\left(\sqrt{3} + i\right)} \Gamma\left(-\frac{4}{3}, \frac{i \, {\left(d x + c\right)} b}{d}\right) + {\left(\sqrt{3} - i\right)} \Gamma\left(-\frac{4}{3}, -\frac{i \, {\left(d x + c\right)} b}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)\right)} \left(\frac{{\left(d x + c\right)} b}{d}\right)^{\frac{4}{3}}}{4 \, {\left(d x + c\right)}^{\frac{4}{3}} d}"," ",0,"-1/4*(((I*sqrt(3) - 1)*gamma(-4/3, I*(d*x + c)*b/d) + (-I*sqrt(3) - 1)*gamma(-4/3, -I*(d*x + c)*b/d))*cos(-(b*c - a*d)/d) + ((sqrt(3) + I)*gamma(-4/3, I*(d*x + c)*b/d) + (sqrt(3) - I)*gamma(-4/3, -I*(d*x + c)*b/d))*sin(-(b*c - a*d)/d))*((d*x + c)*b/d)^(4/3)/((d*x + c)^(4/3)*d)","A",0
75,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\cos\left(b x + a\right)}\,{d x}"," ",0,"integrate(x*sqrt(cos(b*x + a)), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \sqrt{\cos\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(cos(b*x + a)), x)","F",0
77,0,0,0,0.000000," ","integrate(cos(b*x+a)^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{\cos\left(b x + a\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(cos(b*x + a))/x, x)","F",0
78,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)^(3/2), x)","F",0
79,0,0,0,0.000000," ","integrate(cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \cos\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(3/2), x)","F",0
80,0,0,0,0.000000," ","integrate(cos(b*x+a)^(3/2)/x,x, algorithm=""maxima"")","\int \frac{\cos\left(b x + a\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(cos(b*x + a)^(3/2)/x, x)","F",0
81,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2)-1/3*x/cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \cos\left(b x + a\right)^{\frac{3}{2}} - \frac{x}{3 \, \sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)^(3/2) - 1/3*x/sqrt(cos(b*x + a)), x)","F",0
82,0,0,0,0.000000," ","integrate(cos(x)^(3/2)/x^3,x, algorithm=""maxima"")","\int \frac{\cos\left(x\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(cos(x)^(3/2)/x^3, x)","F",0
83,0,0,0,0.000000," ","integrate(x/cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x/sqrt(cos(b*x + a)), x)","F",0
84,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(cos(b*x + a)), x)","F",0
85,0,0,0,0.000000," ","integrate(1/x/cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int \frac{1}{x \sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/(x*sqrt(cos(b*x + a))), x)","F",0
86,0,0,0,0.000000," ","integrate(x/cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{x}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/cos(b*x + a)^(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-3/2), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x/cos(b*x+a)^(3/2),x, algorithm=""maxima"")","\int \frac{1}{x \cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*cos(b*x + a)^(3/2)), x)","F",0
89,0,0,0,0.000000," ","integrate(x/cos(b*x+a)^(3/2)+x*cos(b*x+a)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\cos\left(b x + a\right)} + \frac{x}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sqrt(cos(b*x + a)) + x/cos(b*x + a)^(3/2), x)","F",0
90,0,0,0,0.000000," ","integrate(x/cos(x)^(3/2)+x*cos(x)^(1/2),x, algorithm=""maxima"")","\int x \sqrt{\cos\left(x\right)} + \frac{x}{\cos\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sqrt(cos(x)) + x/cos(x)^(3/2), x)","F",0
91,0,0,0,0.000000," ","integrate(x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2),x, algorithm=""maxima"")","\int -\frac{x}{3 \, \sqrt{\cos\left(x\right)}} + \frac{x}{\cos\left(x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-1/3*x/sqrt(cos(x)) + x/cos(x)^(5/2), x)","F",0
92,0,0,0,0.000000," ","integrate(x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2),x, algorithm=""maxima"")","\int \frac{3}{5} \, x \sqrt{\cos\left(x\right)} + \frac{x}{\cos\left(x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(3/5*x*sqrt(cos(x)) + x/cos(x)^(7/2), x)","F",0
93,0,0,0,0.000000," ","integrate(x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2),x, algorithm=""maxima"")","\int x^{2} \sqrt{\cos\left(x\right)} + \frac{x^{2}}{\cos\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*sqrt(cos(x)) + x^2/cos(x)^(3/2), x)","F",0
94,0,0,0,0.000000," ","integrate(x/sec(x)^(3/2)-1/3*x*sec(x)^(1/2),x, algorithm=""maxima"")","\int -\frac{1}{3} \, x \sqrt{\sec\left(x\right)} + \frac{x}{\sec\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/3*x*sqrt(sec(x)) + x/sec(x)^(3/2), x)","F",0
95,0,0,0,0.000000," ","integrate(x/sec(x)^(5/2)-3/5*x/sec(x)^(1/2),x, algorithm=""maxima"")","\int -\frac{3 \, x}{5 \, \sqrt{\sec\left(x\right)}} + \frac{x}{\sec\left(x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-3/5*x/sqrt(sec(x)) + x/sec(x)^(5/2), x)","F",0
96,0,0,0,0.000000," ","integrate(x/sec(x)^(7/2)-5/21*x*sec(x)^(1/2),x, algorithm=""maxima"")","\int -\frac{5}{21} \, x \sqrt{\sec\left(x\right)} + \frac{x}{\sec\left(x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-5/21*x*sqrt(sec(x)) + x/sec(x)^(7/2), x)","F",0
97,0,0,0,0.000000," ","integrate(x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(1/2),x, algorithm=""maxima"")","\int -\frac{1}{3} \, x^{2} \sqrt{\sec\left(x\right)} + \frac{x^{2}}{\sec\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/3*x^2*sqrt(sec(x)) + x^2/sec(x)^(3/2), x)","F",0
98,0,0,0,0.000000," ","integrate((d*x+c)^m*(b*cos(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \left(b \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(b*cos(f*x + e))^n, x)","F",0
99,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^3,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^3, x)","F",0
100,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(d m + d\right)} \int {\left(d x + c\right)}^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} + e^{\left(m \log\left(d x + c\right) + \log\left(d x + c\right)\right)}}{2 \, {\left(d m + d\right)}}"," ",0,"1/2*((d*m + d)*integrate((d*x + c)^m*cos(2*b*x + 2*a), x) + e^(m*log(d*x + c) + log(d*x + c)))/(d*m + d)","F",0
101,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a), x)","F",0
102,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a),x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a), x)","F",0
103,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)^2,x, algorithm=""maxima"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)^2, x)","F",0
104,0,0,0,0.000000," ","integrate(x^(3+m)*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m + 3} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 3)*cos(b*x + a), x)","F",0
105,0,0,0,0.000000," ","integrate(x^(2+m)*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m + 2} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 2)*cos(b*x + a), x)","F",0
106,0,0,0,0.000000," ","integrate(x^(1+m)*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m + 1} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 1)*cos(b*x + a), x)","F",0
107,0,0,0,0.000000," ","integrate(x^m*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^m*cos(b*x + a), x)","F",0
108,0,0,0,0.000000," ","integrate(x^(-1+m)*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m - 1} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 1)*cos(b*x + a), x)","F",0
109,0,0,0,0.000000," ","integrate(x^(-2+m)*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m - 2} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 2)*cos(b*x + a), x)","F",0
110,0,0,0,0.000000," ","integrate(x^(-3+m)*cos(b*x+a),x, algorithm=""maxima"")","\int x^{m - 3} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 3)*cos(b*x + a), x)","F",0
111,0,0,0,0.000000," ","integrate(x^(3+m)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(m + 4\right)} \int x^{3} x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} + e^{\left(m \log\left(x\right) + 4 \, \log\left(x\right)\right)}}{2 \, {\left(m + 4\right)}}"," ",0,"1/2*((m + 4)*integrate(x^3*x^m*cos(2*b*x + 2*a), x) + e^(m*log(x) + 4*log(x)))/(m + 4)","F",0
112,0,0,0,0.000000," ","integrate(x^(2+m)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(m + 3\right)} \int x^{2} x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} + e^{\left(m \log\left(x\right) + 3 \, \log\left(x\right)\right)}}{2 \, {\left(m + 3\right)}}"," ",0,"1/2*((m + 3)*integrate(x^2*x^m*cos(2*b*x + 2*a), x) + e^(m*log(x) + 3*log(x)))/(m + 3)","F",0
113,0,0,0,0.000000," ","integrate(x^(1+m)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(m + 2\right)} \int x x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} + e^{\left(m \log\left(x\right) + 2 \, \log\left(x\right)\right)}}{2 \, {\left(m + 2\right)}}"," ",0,"1/2*((m + 2)*integrate(x*x^m*cos(2*b*x + 2*a), x) + e^(m*log(x) + 2*log(x)))/(m + 2)","F",0
114,0,0,0,0.000000," ","integrate(x^m*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(m + 1\right)} \int x^{m} \cos\left(2 \, b x + 2 \, a\right)\,{d x} + e^{\left(m \log\left(x\right) + \log\left(x\right)\right)}}{2 \, {\left(m + 1\right)}}"," ",0,"1/2*((m + 1)*integrate(x^m*cos(2*b*x + 2*a), x) + e^(m*log(x) + log(x)))/(m + 1)","F",0
115,0,0,0,0.000000," ","integrate(x^(-1+m)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{m \int \frac{x^{m} \cos\left(2 \, b x + 2 \, a\right)}{x}\,{d x} + x^{m}}{2 \, m}"," ",0,"1/2*(m*integrate(x^m*cos(2*b*x + 2*a)/x, x) + x^m)/m","F",0
116,0,0,0,0.000000," ","integrate(x^(-2+m)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(m - 1\right)} x \int \frac{x^{m} \cos\left(2 \, b x + 2 \, a\right)}{x^{2}}\,{d x} + x^{m}}{2 \, {\left(m - 1\right)} x}"," ",0,"1/2*((m - 1)*x*integrate(x^m*cos(2*b*x + 2*a)/x^2, x) + x^m)/((m - 1)*x)","F",0
117,0,0,0,0.000000," ","integrate(x^(-3+m)*cos(b*x+a)^2,x, algorithm=""maxima"")","\frac{{\left(m - 2\right)} x^{2} \int \frac{x^{m} \cos\left(2 \, b x + 2 \, a\right)}{x^{3}}\,{d x} + x^{m}}{2 \, {\left(m - 2\right)} x^{2}}"," ",0,"1/2*((m - 2)*x^2*integrate(x^m*cos(2*b*x + 2*a)/x^3, x) + x^m)/((m - 2)*x^2)","F",0
118,1,456,0,0.624436," ","integrate((d*x+c)^3*(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{4 \, {\left(f x + e\right)} a c^{3} + \frac{{\left(f x + e\right)}^{4} a d^{3}}{f^{3}} - \frac{4 \, {\left(f x + e\right)}^{3} a d^{3} e}{f^{3}} + \frac{6 \, {\left(f x + e\right)}^{2} a d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(f x + e\right)} a d^{3} e^{3}}{f^{3}} + \frac{4 \, {\left(f x + e\right)}^{3} a c d^{2}}{f^{2}} - \frac{12 \, {\left(f x + e\right)}^{2} a c d^{2} e}{f^{2}} + \frac{12 \, {\left(f x + e\right)} a c d^{2} e^{2}}{f^{2}} + \frac{6 \, {\left(f x + e\right)}^{2} a c^{2} d}{f} - \frac{12 \, {\left(f x + e\right)} a c^{2} d e}{f} + 4 \, a c^{3} \sin\left(f x + e\right) - \frac{4 \, a d^{3} e^{3} \sin\left(f x + e\right)}{f^{3}} + \frac{12 \, a c d^{2} e^{2} \sin\left(f x + e\right)}{f^{2}} - \frac{12 \, a c^{2} d e \sin\left(f x + e\right)}{f} + \frac{12 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a d^{3} e^{2}}{f^{3}} - \frac{24 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a c d^{2} e}{f^{2}} + \frac{12 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a c^{2} d}{f} - \frac{12 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a d^{3} e}{f^{3}} + \frac{12 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a c d^{2}}{f^{2}} + \frac{4 \, {\left(3 \, {\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{3} - 6 \, f x - 6 \, e\right)} \sin\left(f x + e\right)\right)} a d^{3}}{f^{3}}}{4 \, f}"," ",0,"1/4*(4*(f*x + e)*a*c^3 + (f*x + e)^4*a*d^3/f^3 - 4*(f*x + e)^3*a*d^3*e/f^3 + 6*(f*x + e)^2*a*d^3*e^2/f^3 - 4*(f*x + e)*a*d^3*e^3/f^3 + 4*(f*x + e)^3*a*c*d^2/f^2 - 12*(f*x + e)^2*a*c*d^2*e/f^2 + 12*(f*x + e)*a*c*d^2*e^2/f^2 + 6*(f*x + e)^2*a*c^2*d/f - 12*(f*x + e)*a*c^2*d*e/f + 4*a*c^3*sin(f*x + e) - 4*a*d^3*e^3*sin(f*x + e)/f^3 + 12*a*c*d^2*e^2*sin(f*x + e)/f^2 - 12*a*c^2*d*e*sin(f*x + e)/f + 12*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a*d^3*e^2/f^3 - 24*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a*c*d^2*e/f^2 + 12*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a*c^2*d/f - 12*(2*(f*x + e)*cos(f*x + e) + ((f*x + e)^2 - 2)*sin(f*x + e))*a*d^3*e/f^3 + 12*(2*(f*x + e)*cos(f*x + e) + ((f*x + e)^2 - 2)*sin(f*x + e))*a*c*d^2/f^2 + 4*(3*((f*x + e)^2 - 2)*cos(f*x + e) + ((f*x + e)^3 - 6*f*x - 6*e)*sin(f*x + e))*a*d^3/f^3)/f","B",0
119,1,235,0,0.750080," ","integrate((d*x+c)^2*(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, {\left(f x + e\right)} a c^{2} + \frac{{\left(f x + e\right)}^{3} a d^{2}}{f^{2}} - \frac{3 \, {\left(f x + e\right)}^{2} a d^{2} e}{f^{2}} + \frac{3 \, {\left(f x + e\right)} a d^{2} e^{2}}{f^{2}} + \frac{3 \, {\left(f x + e\right)}^{2} a c d}{f} - \frac{6 \, {\left(f x + e\right)} a c d e}{f} + 3 \, a c^{2} \sin\left(f x + e\right) + \frac{3 \, a d^{2} e^{2} \sin\left(f x + e\right)}{f^{2}} - \frac{6 \, a c d e \sin\left(f x + e\right)}{f} - \frac{6 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a d^{2} e}{f^{2}} + \frac{6 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a c d}{f} + \frac{3 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a d^{2}}{f^{2}}}{3 \, f}"," ",0,"1/3*(3*(f*x + e)*a*c^2 + (f*x + e)^3*a*d^2/f^2 - 3*(f*x + e)^2*a*d^2*e/f^2 + 3*(f*x + e)*a*d^2*e^2/f^2 + 3*(f*x + e)^2*a*c*d/f - 6*(f*x + e)*a*c*d*e/f + 3*a*c^2*sin(f*x + e) + 3*a*d^2*e^2*sin(f*x + e)/f^2 - 6*a*c*d*e*sin(f*x + e)/f - 6*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a*d^2*e/f^2 + 6*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a*c*d/f + 3*(2*(f*x + e)*cos(f*x + e) + ((f*x + e)^2 - 2)*sin(f*x + e))*a*d^2/f^2)/f","B",0
120,1,91,0,0.344192," ","integrate((d*x+c)*(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(f x + e\right)} a c + \frac{{\left(f x + e\right)}^{2} a d}{f} - \frac{2 \, {\left(f x + e\right)} a d e}{f} + 2 \, a c \sin\left(f x + e\right) - \frac{2 \, a d e \sin\left(f x + e\right)}{f} + \frac{2 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a d}{f}}{2 \, f}"," ",0,"1/2*(2*(f*x + e)*a*c + (f*x + e)^2*a*d/f - 2*(f*x + e)*a*d*e/f + 2*a*c*sin(f*x + e) - 2*a*d*e*sin(f*x + e)/f + 2*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a*d/f)/f","B",0
121,1,172,0,0.928281," ","integrate((a+a*cos(f*x+e))/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{2 \, a f \log\left(c + \frac{{\left(f x + e\right)} d}{f} - \frac{d e}{f}\right)}{d} - \frac{{\left(f {\left(E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f {\left(i \, E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) - i \, E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a}{d}}{2 \, f}"," ",0,"1/2*(2*a*f*log(c + (f*x + e)*d/f - d*e/f)/d - (f*(exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f*(I*exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) - I*exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a/d)/f","C",0
122,1,196,0,1.000474," ","integrate((a+a*cos(f*x+e))/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{\frac{16 \, a f^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} + \frac{{\left(8 \, f^{2} {\left(E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{2} {\left(8 i \, E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) - 8 i \, E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f}}{16 \, f}"," ",0,"-1/16*(16*a*f^2/((f*x + e)*d^2 - d^2*e + c*d*f) + (8*f^2*(exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^2*(8*I*exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) - 8*I*exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a/((f*x + e)*d^2 - d^2*e + c*d*f))/f","C",0
123,1,949,0,0.973625," ","integrate((d*x+c)^3*(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{3} + 16 \, {\left(f x + e\right)} a^{2} c^{3} + \frac{4 \, {\left(f x + e\right)}^{4} a^{2} d^{3}}{f^{3}} - \frac{16 \, {\left(f x + e\right)}^{3} a^{2} d^{3} e}{f^{3}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} d^{3} e^{2}}{f^{3}} - \frac{4 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} e^{3}}{f^{3}} - \frac{16 \, {\left(f x + e\right)} a^{2} d^{3} e^{3}}{f^{3}} + \frac{16 \, {\left(f x + e\right)}^{3} a^{2} c d^{2}}{f^{2}} - \frac{48 \, {\left(f x + e\right)}^{2} a^{2} c d^{2} e}{f^{2}} + \frac{12 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{48 \, {\left(f x + e\right)} a^{2} c d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} c^{2} d}{f} - \frac{12 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d e}{f} - \frac{48 \, {\left(f x + e\right)} a^{2} c^{2} d e}{f} + 32 \, a^{2} c^{3} \sin\left(f x + e\right) - \frac{32 \, a^{2} d^{3} e^{3} \sin\left(f x + e\right)}{f^{3}} + \frac{96 \, a^{2} c d^{2} e^{2} \sin\left(f x + e\right)}{f^{2}} - \frac{96 \, a^{2} c^{2} d e \sin\left(f x + e\right)}{f} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} e^{2}}{f^{3}} + \frac{96 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a^{2} d^{3} e^{2}}{f^{3}} - \frac{12 \, {\left(2 \, {\left(f x + e\right)}^{2} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2} e}{f^{2}} - \frac{192 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a^{2} c d^{2} e}{f^{2}} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} d}{f} + \frac{96 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a^{2} c^{2} d}{f} - \frac{2 \, {\left(4 \, {\left(f x + e\right)}^{3} + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3} e}{f^{3}} - \frac{96 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a^{2} d^{3} e}{f^{3}} + \frac{2 \, {\left(4 \, {\left(f x + e\right)}^{3} + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d^{2}}{f^{2}} + \frac{96 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a^{2} c d^{2}}{f^{2}} + \frac{{\left(2 \, {\left(f x + e\right)}^{4} + 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(2 \, {\left(f x + e\right)}^{3} - 3 \, f x - 3 \, e\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{3}}{f^{3}} + \frac{32 \, {\left(3 \, {\left({\left(f x + e\right)}^{2} - 2\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{3} - 6 \, f x - 6 \, e\right)} \sin\left(f x + e\right)\right)} a^{2} d^{3}}{f^{3}}}{16 \, f}"," ",0,"1/16*(4*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*c^3 + 16*(f*x + e)*a^2*c^3 + 4*(f*x + e)^4*a^2*d^3/f^3 - 16*(f*x + e)^3*a^2*d^3*e/f^3 + 24*(f*x + e)^2*a^2*d^3*e^2/f^3 - 4*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*d^3*e^3/f^3 - 16*(f*x + e)*a^2*d^3*e^3/f^3 + 16*(f*x + e)^3*a^2*c*d^2/f^2 - 48*(f*x + e)^2*a^2*c*d^2*e/f^2 + 12*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*c*d^2*e^2/f^2 + 48*(f*x + e)*a^2*c*d^2*e^2/f^2 + 24*(f*x + e)^2*a^2*c^2*d/f - 12*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*c^2*d*e/f - 48*(f*x + e)*a^2*c^2*d*e/f + 32*a^2*c^3*sin(f*x + e) - 32*a^2*d^3*e^3*sin(f*x + e)/f^3 + 96*a^2*c*d^2*e^2*sin(f*x + e)/f^2 - 96*a^2*c^2*d*e*sin(f*x + e)/f + 6*(2*(f*x + e)^2 + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*a^2*d^3*e^2/f^3 + 96*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a^2*d^3*e^2/f^3 - 12*(2*(f*x + e)^2 + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*a^2*c*d^2*e/f^2 - 192*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a^2*c*d^2*e/f^2 + 6*(2*(f*x + e)^2 + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*a^2*c^2*d/f + 96*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a^2*c^2*d/f - 2*(4*(f*x + e)^3 + 6*(f*x + e)*cos(2*f*x + 2*e) + 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*a^2*d^3*e/f^3 - 96*(2*(f*x + e)*cos(f*x + e) + ((f*x + e)^2 - 2)*sin(f*x + e))*a^2*d^3*e/f^3 + 2*(4*(f*x + e)^3 + 6*(f*x + e)*cos(2*f*x + 2*e) + 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*a^2*c*d^2/f^2 + 96*(2*(f*x + e)*cos(f*x + e) + ((f*x + e)^2 - 2)*sin(f*x + e))*a^2*c*d^2/f^2 + (2*(f*x + e)^4 + 3*(2*(f*x + e)^2 - 1)*cos(2*f*x + 2*e) + 2*(2*(f*x + e)^3 - 3*f*x - 3*e)*sin(2*f*x + 2*e))*a^2*d^3/f^3 + 32*(3*((f*x + e)^2 - 2)*cos(f*x + e) + ((f*x + e)^3 - 6*f*x - 6*e)*sin(f*x + e))*a^2*d^3/f^3)/f","B",0
124,1,494,0,1.000097," ","integrate((d*x+c)^2*(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{6 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c^{2} + 24 \, {\left(f x + e\right)} a^{2} c^{2} + \frac{8 \, {\left(f x + e\right)}^{3} a^{2} d^{2}}{f^{2}} - \frac{24 \, {\left(f x + e\right)}^{2} a^{2} d^{2} e}{f^{2}} + \frac{6 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)} a^{2} d^{2} e^{2}}{f^{2}} + \frac{24 \, {\left(f x + e\right)}^{2} a^{2} c d}{f} - \frac{12 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d e}{f} - \frac{48 \, {\left(f x + e\right)} a^{2} c d e}{f} + 48 \, a^{2} c^{2} \sin\left(f x + e\right) + \frac{48 \, a^{2} d^{2} e^{2} \sin\left(f x + e\right)}{f^{2}} - \frac{96 \, a^{2} c d e \sin\left(f x + e\right)}{f} - \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2} e}{f^{2}} - \frac{96 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a^{2} d^{2} e}{f^{2}} + \frac{6 \, {\left(2 \, {\left(f x + e\right)}^{2} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} c d}{f} + \frac{96 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a^{2} c d}{f} + \frac{{\left(4 \, {\left(f x + e\right)}^{3} + 6 \, {\left(f x + e\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(2 \, {\left(f x + e\right)}^{2} - 1\right)} \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d^{2}}{f^{2}} + \frac{48 \, {\left(2 \, {\left(f x + e\right)} \cos\left(f x + e\right) + {\left({\left(f x + e\right)}^{2} - 2\right)} \sin\left(f x + e\right)\right)} a^{2} d^{2}}{f^{2}}}{24 \, f}"," ",0,"1/24*(6*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*c^2 + 24*(f*x + e)*a^2*c^2 + 8*(f*x + e)^3*a^2*d^2/f^2 - 24*(f*x + e)^2*a^2*d^2*e/f^2 + 6*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*d^2*e^2/f^2 + 24*(f*x + e)*a^2*d^2*e^2/f^2 + 24*(f*x + e)^2*a^2*c*d/f - 12*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*c*d*e/f - 48*(f*x + e)*a^2*c*d*e/f + 48*a^2*c^2*sin(f*x + e) + 48*a^2*d^2*e^2*sin(f*x + e)/f^2 - 96*a^2*c*d*e*sin(f*x + e)/f - 6*(2*(f*x + e)^2 + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*a^2*d^2*e/f^2 - 96*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a^2*d^2*e/f^2 + 6*(2*(f*x + e)^2 + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*a^2*c*d/f + 96*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a^2*c*d/f + (4*(f*x + e)^3 + 6*(f*x + e)*cos(2*f*x + 2*e) + 3*(2*(f*x + e)^2 - 1)*sin(2*f*x + 2*e))*a^2*d^2/f^2 + 48*(2*(f*x + e)*cos(f*x + e) + ((f*x + e)^2 - 2)*sin(f*x + e))*a^2*d^2/f^2)/f","B",0
125,1,197,0,0.994385," ","integrate((d*x+c)*(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c + 8 \, {\left(f x + e\right)} a^{2} c + \frac{4 \, {\left(f x + e\right)}^{2} a^{2} d}{f} - \frac{2 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} d e}{f} - \frac{8 \, {\left(f x + e\right)} a^{2} d e}{f} + 16 \, a^{2} c \sin\left(f x + e\right) - \frac{16 \, a^{2} d e \sin\left(f x + e\right)}{f} + \frac{{\left(2 \, {\left(f x + e\right)}^{2} + 2 \, {\left(f x + e\right)} \sin\left(2 \, f x + 2 \, e\right) + \cos\left(2 \, f x + 2 \, e\right)\right)} a^{2} d}{f} + \frac{16 \, {\left({\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} a^{2} d}{f}}{8 \, f}"," ",0,"1/8*(2*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*c + 8*(f*x + e)*a^2*c + 4*(f*x + e)^2*a^2*d/f - 2*(2*f*x + 2*e + sin(2*f*x + 2*e))*a^2*d*e/f - 8*(f*x + e)*a^2*d*e/f + 16*a^2*c*sin(f*x + e) - 16*a^2*d*e*sin(f*x + e)/f + (2*(f*x + e)^2 + 2*(f*x + e)*sin(2*f*x + 2*e) + cos(2*f*x + 2*e))*a^2*d/f + 16*((f*x + e)*sin(f*x + e) + cos(f*x + e))*a^2*d/f)/f","A",0
126,1,337,0,1.138721," ","integrate((a+a*cos(f*x+e))^2/(d*x+c),x, algorithm=""maxima"")","\frac{\frac{4 \, a^{2} f \log\left(c + \frac{{\left(f x + e\right)} d}{f} - \frac{d e}{f}\right)}{d} - \frac{4 \, {\left(f {\left(E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f {\left(i \, E_{1}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) - i \, E_{1}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a^{2}}{d} - \frac{{\left(f {\left(E_{1}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - f {\left(-i \, E_{1}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + i \, E_{1}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, f \log\left({\left(f x + e\right)} d - d e + c f\right)\right)} a^{2}}{d}}{4 \, f}"," ",0,"1/4*(4*a^2*f*log(c + (f*x + e)*d/f - d*e/f)/d - 4*(f*(exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f*(I*exp_integral_e(1, (I*(f*x + e)*d - I*d*e + I*c*f)/d) - I*exp_integral_e(1, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a^2/d - (f*(exp_integral_e(1, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) - f*(-I*exp_integral_e(1, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + I*exp_integral_e(1, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) - 2*f*log((f*x + e)*d - d*e + c*f))*a^2/d)/f","C",0
127,1,370,0,1.345092," ","integrate((a+a*cos(f*x+e))^2/(d*x+c)^2,x, algorithm=""maxima"")","-\frac{\frac{64 \, a^{2} f^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} + \frac{8 \, {\left(8 \, f^{2} {\left(E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) + E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) + f^{2} {\left(8 i \, E_{2}\left(\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right) - 8 i \, E_{2}\left(-\frac{i \, {\left(f x + e\right)} d - i \, d e + i \, c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)\right)} a^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f} + \frac{{\left(16 \, f^{2} {\left(E_{2}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) + E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + f^{2} {\left(16 i \, E_{2}\left(\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right) - 16 i \, E_{2}\left(-\frac{2 i \, {\left(f x + e\right)} d - 2 i \, d e + 2 i \, c f}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 32 \, f^{2}\right)} a^{2}}{{\left(f x + e\right)} d^{2} - d^{2} e + c d f}}{64 \, f}"," ",0,"-1/64*(64*a^2*f^2/((f*x + e)*d^2 - d^2*e + c*d*f) + 8*(8*f^2*(exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) + exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*cos(-(d*e - c*f)/d) + f^2*(8*I*exp_integral_e(2, (I*(f*x + e)*d - I*d*e + I*c*f)/d) - 8*I*exp_integral_e(2, -(I*(f*x + e)*d - I*d*e + I*c*f)/d))*sin(-(d*e - c*f)/d))*a^2/((f*x + e)*d^2 - d^2*e + c*d*f) + (16*f^2*(exp_integral_e(2, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) + exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*cos(-2*(d*e - c*f)/d) + f^2*(16*I*exp_integral_e(2, (2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d) - 16*I*exp_integral_e(2, -(2*I*(f*x + e)*d - 2*I*d*e + 2*I*c*f)/d))*sin(-2*(d*e - c*f)/d) + 32*f^2)*a^2/((f*x + e)*d^2 - d^2*e + c*d*f))/f","C",0
128,1,936,0,1.163614," ","integrate((d*x+c)^3/(a+a*cos(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left({\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c d^{2} e}{a f^{2} \cos\left(f x + e\right)^{2} + a f^{2} \sin\left(f x + e\right)^{2} + 2 \, a f^{2} \cos\left(f x + e\right) + a f^{2}} - \frac{3 \, {\left({\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c^{2} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} + 2 \, a f \cos\left(f x + e\right) + a f} - \frac{c^{3} \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{3 \, c d^{2} e^{2} \sin\left(f x + e\right)}{a f^{2} {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{3 \, c^{2} d e \sin\left(f x + e\right)}{a f {\left(\cos\left(f x + e\right) + 1\right)}} + \frac{2 \, d^{3} e^{3} - {\left(6 \, {\left(f x + e\right)}^{2} d^{3} + 6 \, d^{3} e^{2} - 12 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} + 6 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(6 i \, {\left(f x + e\right)}^{2} d^{3} + 6 i \, d^{3} e^{2} + {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + 2 \, {\left({\left(f x + e\right)}^{3} d^{3} + 3 \, {\left(f x + e\right)} d^{3} e^{2} - 3 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \cos\left(f x + e\right) + {\left(12 \, {\left(f x + e\right)} d^{3} - 12 \, d^{3} e + 12 \, c d^{2} f + 12 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) - {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) - {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + 3 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - {\left(-12 i \, d^{3} \cos\left(f x + e\right) + 12 \, d^{3} \sin\left(f x + e\right) - 12 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) - {\left(-2 i \, {\left(f x + e\right)}^{3} d^{3} - 6 i \, {\left(f x + e\right)} d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) - i \, a f^{3}}}{f}"," ",0,"-(6*((cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + 2*(f*x + e)*sin(f*x + e))*c*d^2*e/(a*f^2*cos(f*x + e)^2 + a*f^2*sin(f*x + e)^2 + 2*a*f^2*cos(f*x + e) + a*f^2) - 3*((cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + 2*(f*x + e)*sin(f*x + e))*c^2*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 + 2*a*f*cos(f*x + e) + a*f) - c^3*sin(f*x + e)/(a*(cos(f*x + e) + 1)) - 3*c*d^2*e^2*sin(f*x + e)/(a*f^2*(cos(f*x + e) + 1)) + 3*c^2*d*e*sin(f*x + e)/(a*f*(cos(f*x + e) + 1)) + (2*d^3*e^3 - (6*(f*x + e)^2*d^3 + 6*d^3*e^2 - 12*(d^3*e - c*d^2*f)*(f*x + e) + 6*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (6*I*(f*x + e)^2*d^3 + 6*I*d^3*e^2 + (-12*I*d^3*e + 12*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + 2*((f*x + e)^3*d^3 + 3*(f*x + e)*d^3*e^2 - 3*(d^3*e - c*d^2*f)*(f*x + e)^2)*cos(f*x + e) + (12*(f*x + e)*d^3 - 12*d^3*e + 12*c*d^2*f + 12*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) - (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f)*sin(f*x + e))*dilog(-e^(I*f*x + I*e)) - (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e) + (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e))*cos(f*x + e) + 3*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - (-12*I*d^3*cos(f*x + e) + 12*d^3*sin(f*x + e) - 12*I*d^3)*polylog(3, -e^(I*f*x + I*e)) - (-2*I*(f*x + e)^3*d^3 - 6*I*(f*x + e)*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e)^2)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) - I*a*f^3))/f","B",0
129,1,286,0,1.062271," ","integrate((d*x+c)^2/(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, c^{2} f^{2} + {\left(4 \, d^{2} f x + 4 \, c d f + 4 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + {\left(4 i \, d^{2} f x + 4 i \, c d f\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x\right)} \cos\left(f x + e\right) - {\left(4 \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} \sin\left(f x + e\right) + 4 \, d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-2 i \, d^{2} f x - 2 i \, c d f + {\left(-2 i \, d^{2} f x - 2 i \, c d f\right)} \cos\left(f x + e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) - i \, a f^{3}}"," ",0,"(2*c^2*f^2 + (4*d^2*f*x + 4*c*d*f + 4*(d^2*f*x + c*d*f)*cos(f*x + e) + (4*I*d^2*f*x + 4*I*c*d*f)*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x)*cos(f*x + e) - (4*d^2*cos(f*x + e) + 4*I*d^2*sin(f*x + e) + 4*d^2)*dilog(-e^(I*f*x + I*e)) + (-2*I*d^2*f*x - 2*I*c*d*f + (-2*I*d^2*f*x - 2*I*c*d*f)*cos(f*x + e) + 2*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) - I*a*f^3)","B",0
130,1,160,0,0.428240," ","integrate((d*x+c)/(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} + 2 \, a f \cos\left(f x + e\right) + a f} + \frac{c \sin\left(f x + e\right)}{a {\left(\cos\left(f x + e\right) + 1\right)}} - \frac{d e \sin\left(f x + e\right)}{a f {\left(\cos\left(f x + e\right) + 1\right)}}}{f}"," ",0,"(((cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + 2*(f*x + e)*sin(f*x + e))*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 + 2*a*f*cos(f*x + e) + a*f) + c*sin(f*x + e)/(a*(cos(f*x + e) + 1)) - d*e*sin(f*x + e)/(a*f*(cos(f*x + e) + 1)))/f","B",0
131,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{{\left(a d^{2} f x + a c d f + {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)^{2} + {\left(a d^{2} f x + a c d f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)\right)} \int \frac{\sin\left(f x + e\right)}{{\left(d x + c\right)}^{2} {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right)}}\,{d x}}{a f} + \sin\left(f x + e\right)\right)}}{a d f x + a c f + {\left(a d f x + a c f\right)} \cos\left(f x + e\right)^{2} + {\left(a d f x + a c f\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a d f x + a c f\right)} \cos\left(f x + e\right)}"," ",0,"2*((a*d^2*f*x + a*c*d*f + (a*d^2*f*x + a*c*d*f)*cos(f*x + e)^2 + (a*d^2*f*x + a*c*d*f)*sin(f*x + e)^2 + 2*(a*d^2*f*x + a*c*d*f)*cos(f*x + e))*integrate(sin(f*x + e)/(a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*cos(f*x + e)^2 + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*sin(f*x + e)^2 + 2*(a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*cos(f*x + e)), x) + sin(f*x + e))/(a*d*f*x + a*c*f + (a*d*f*x + a*c*f)*cos(f*x + e)^2 + (a*d*f*x + a*c*f)*sin(f*x + e)^2 + 2*(a*d*f*x + a*c*f)*cos(f*x + e))","F",0
132,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*cos(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,1,3274,0,3.961394," ","integrate((d*x+c)^3/(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{12 \, {\left(2 \, {\left(3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(2 \, f x + 2 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 6 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, \cos\left(f x + e\right)^{2} + 6 \, {\left(\sin\left(2 \, f x + 2 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, \sin\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(f x + 3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - \sin\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + 3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - 2 \, \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right)\right)} c d^{2} e}{a^{2} f^{2} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f^{2} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f^{2} \cos\left(f x + e\right)^{2} + a^{2} f^{2} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, a^{2} f^{2} \sin\left(f x + e\right)^{2} + 6 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2} + 2 \, {\left(3 \, a^{2} f^{2} \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2}\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2}\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} f^{2} \sin\left(2 \, f x + 2 \, e\right) + a^{2} f^{2} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)} - \frac{6 \, {\left(2 \, {\left(3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(2 \, f x + 2 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 6 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, \cos\left(f x + e\right)^{2} + 6 \, {\left(\sin\left(2 \, f x + 2 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, \sin\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(f x + 3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - \sin\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + 3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - 2 \, \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right)\right)} c^{2} d}{a^{2} f \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, a^{2} f \sin\left(f x + e\right)^{2} + 6 \, a^{2} f \cos\left(f x + e\right) + a^{2} f + 2 \, {\left(3 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} f \sin\left(2 \, f x + 2 \, e\right) + a^{2} f \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)} + \frac{c^{3} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{3 \, c d^{2} e^{2} {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} f^{2}} - \frac{3 \, c^{2} d e {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} f} - \frac{6 \, {\left(2 \, d^{3} e^{3} + 12 \, d^{3} e - 12 \, c d^{2} f - {\left(6 \, {\left(f x + e\right)}^{2} d^{3} + 6 \, d^{3} e^{2} + 12 \, d^{3} - 12 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} + 6 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + 18 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + 18 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(6 i \, {\left(f x + e\right)}^{2} d^{3} + 6 i \, d^{3} e^{2} + 12 i \, d^{3} + {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(18 i \, {\left(f x + e\right)}^{2} d^{3} + 18 i \, d^{3} e^{2} + 36 i \, d^{3} + {\left(-36 i \, d^{3} e + 36 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(18 i \, {\left(f x + e\right)}^{2} d^{3} + 18 i \, d^{3} e^{2} + 36 i \, d^{3} + {\left(-36 i \, d^{3} e + 36 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) + 2 \, {\left({\left(f x + e\right)}^{3} d^{3} - 3 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}^{2} + 3 \, {\left(d^{3} e^{2} + 2 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(6 \, {\left(f x + e\right)}^{3} d^{3} - 6 i \, d^{3} e^{2} + 12 \, d^{3} e - 12 \, c d^{2} f - 6 \, {\left(3 \, d^{3} e - 3 \, c d^{2} f + i \, d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(18 \, d^{3} e^{2} + 12 i \, d^{3} e - 12 i \, c d^{2} f + 24 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, d^{3} e^{3} - 6 i \, {\left(f x + e\right)}^{2} d^{3} - 6 i \, d^{3} e^{2} + 24 \, d^{3} e - 24 \, c d^{2} f - {\left(-12 i \, d^{3} e + 12 i \, c d^{2} f - 12 \, d^{3}\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(12 \, {\left(f x + e\right)} d^{3} - 12 \, d^{3} e + 12 \, c d^{2} f + 12 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + 36 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 36 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) - {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(-36 i \, {\left(f x + e\right)} d^{3} + 36 i \, d^{3} e - 36 i \, c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(-36 i \, {\left(f x + e\right)} d^{3} + 36 i \, d^{3} e - 36 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) - {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} - 6 i \, d^{3} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} - 6 i \, d^{3} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-9 i \, {\left(f x + e\right)}^{2} d^{3} - 9 i \, d^{3} e^{2} - 18 i \, d^{3} + {\left(18 i \, d^{3} e - 18 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-9 i \, {\left(f x + e\right)}^{2} d^{3} - 9 i \, d^{3} e^{2} - 18 i \, d^{3} + {\left(18 i \, d^{3} e - 18 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + 3 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) + 9 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) + 9 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} + 2 \, d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - {\left(-12 i \, d^{3} \cos\left(3 \, f x + 3 \, e\right) - 36 i \, d^{3} \cos\left(2 \, f x + 2 \, e\right) - 36 i \, d^{3} \cos\left(f x + e\right) + 12 \, d^{3} \sin\left(3 \, f x + 3 \, e\right) + 36 \, d^{3} \sin\left(2 \, f x + 2 \, e\right) + 36 \, d^{3} \sin\left(f x + e\right) - 12 i \, d^{3}\right)} {\rm Li}_{3}(-e^{\left(i \, f x + i \, e\right)}) - {\left(-2 i \, {\left(f x + e\right)}^{3} d^{3} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2} + {\left(-6 i \, d^{3} e^{2} - 12 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(3 \, f x + 3 \, e\right) - {\left(-6 i \, {\left(f x + e\right)}^{3} d^{3} - 6 \, d^{3} e^{2} - 12 i \, d^{3} e + 12 i \, c d^{2} f + {\left(18 i \, d^{3} e - 18 i \, c d^{2} f - 6 \, d^{3}\right)} {\left(f x + e\right)}^{2} + {\left(-18 i \, d^{3} e^{2} + 12 \, d^{3} e - 12 \, c d^{2} f - 24 i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(2 \, f x + 2 \, e\right) - {\left(-6 i \, d^{3} e^{3} - 6 \, {\left(f x + e\right)}^{2} d^{3} - 6 \, d^{3} e^{2} - 24 i \, d^{3} e + 24 i \, c d^{2} f + 12 \, {\left(d^{3} e - c d^{2} f - i \, d^{3}\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)}}{-3 i \, a^{2} f^{3} \cos\left(3 \, f x + 3 \, e\right) - 9 i \, a^{2} f^{3} \cos\left(2 \, f x + 2 \, e\right) - 9 i \, a^{2} f^{3} \cos\left(f x + e\right) + 3 \, a^{2} f^{3} \sin\left(3 \, f x + 3 \, e\right) + 9 \, a^{2} f^{3} \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} f^{3} \sin\left(f x + e\right) - 3 i \, a^{2} f^{3}}}{6 \, f}"," ",0,"1/6*(12*(2*(3*(f*x + e)*sin(f*x + e) + cos(2*f*x + 2*e) + cos(f*x + e))*cos(3*f*x + 3*e) + 2*(9*(f*x + e)*sin(f*x + e) + 6*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 6*cos(2*f*x + 2*e)^2 + 6*cos(f*x + e)^2 - (2*(3*cos(2*f*x + 2*e) + 3*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + cos(3*f*x + 3*e)^2 + 6*(3*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)^2 + 9*cos(f*x + e)^2 + 6*(sin(2*f*x + 2*e) + sin(f*x + e))*sin(3*f*x + 3*e) + sin(3*f*x + 3*e)^2 + 9*sin(2*f*x + 2*e)^2 + 18*sin(2*f*x + 2*e)*sin(f*x + e) + 9*sin(f*x + e)^2 + 6*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 2*(f*x + 3*(f*x + e)*cos(f*x + e) + e - sin(2*f*x + 2*e) - sin(f*x + e))*sin(3*f*x + 3*e) - 6*(f*x + 3*(f*x + e)*cos(f*x + e) + e - 2*sin(f*x + e))*sin(2*f*x + 2*e) + 6*sin(2*f*x + 2*e)^2 + 6*sin(f*x + e)^2 + 2*cos(f*x + e))*c*d^2*e/(a^2*f^2*cos(3*f*x + 3*e)^2 + 9*a^2*f^2*cos(2*f*x + 2*e)^2 + 9*a^2*f^2*cos(f*x + e)^2 + a^2*f^2*sin(3*f*x + 3*e)^2 + 9*a^2*f^2*sin(2*f*x + 2*e)^2 + 18*a^2*f^2*sin(2*f*x + 2*e)*sin(f*x + e) + 9*a^2*f^2*sin(f*x + e)^2 + 6*a^2*f^2*cos(f*x + e) + a^2*f^2 + 2*(3*a^2*f^2*cos(2*f*x + 2*e) + 3*a^2*f^2*cos(f*x + e) + a^2*f^2)*cos(3*f*x + 3*e) + 6*(3*a^2*f^2*cos(f*x + e) + a^2*f^2)*cos(2*f*x + 2*e) + 6*(a^2*f^2*sin(2*f*x + 2*e) + a^2*f^2*sin(f*x + e))*sin(3*f*x + 3*e)) - 6*(2*(3*(f*x + e)*sin(f*x + e) + cos(2*f*x + 2*e) + cos(f*x + e))*cos(3*f*x + 3*e) + 2*(9*(f*x + e)*sin(f*x + e) + 6*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 6*cos(2*f*x + 2*e)^2 + 6*cos(f*x + e)^2 - (2*(3*cos(2*f*x + 2*e) + 3*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + cos(3*f*x + 3*e)^2 + 6*(3*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)^2 + 9*cos(f*x + e)^2 + 6*(sin(2*f*x + 2*e) + sin(f*x + e))*sin(3*f*x + 3*e) + sin(3*f*x + 3*e)^2 + 9*sin(2*f*x + 2*e)^2 + 18*sin(2*f*x + 2*e)*sin(f*x + e) + 9*sin(f*x + e)^2 + 6*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 2*(f*x + 3*(f*x + e)*cos(f*x + e) + e - sin(2*f*x + 2*e) - sin(f*x + e))*sin(3*f*x + 3*e) - 6*(f*x + 3*(f*x + e)*cos(f*x + e) + e - 2*sin(f*x + e))*sin(2*f*x + 2*e) + 6*sin(2*f*x + 2*e)^2 + 6*sin(f*x + e)^2 + 2*cos(f*x + e))*c^2*d/(a^2*f*cos(3*f*x + 3*e)^2 + 9*a^2*f*cos(2*f*x + 2*e)^2 + 9*a^2*f*cos(f*x + e)^2 + a^2*f*sin(3*f*x + 3*e)^2 + 9*a^2*f*sin(2*f*x + 2*e)^2 + 18*a^2*f*sin(2*f*x + 2*e)*sin(f*x + e) + 9*a^2*f*sin(f*x + e)^2 + 6*a^2*f*cos(f*x + e) + a^2*f + 2*(3*a^2*f*cos(2*f*x + 2*e) + 3*a^2*f*cos(f*x + e) + a^2*f)*cos(3*f*x + 3*e) + 6*(3*a^2*f*cos(f*x + e) + a^2*f)*cos(2*f*x + 2*e) + 6*(a^2*f*sin(2*f*x + 2*e) + a^2*f*sin(f*x + e))*sin(3*f*x + 3*e)) + c^3*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 + 3*c*d^2*e^2*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*f^2) - 3*c^2*d*e*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*f) - 6*(2*d^3*e^3 + 12*d^3*e - 12*c*d^2*f - (6*(f*x + e)^2*d^3 + 6*d^3*e^2 + 12*d^3 - 12*(d^3*e - c*d^2*f)*(f*x + e) + 6*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(3*f*x + 3*e) + 18*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + 18*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (6*I*(f*x + e)^2*d^3 + 6*I*d^3*e^2 + 12*I*d^3 + (-12*I*d^3*e + 12*I*c*d^2*f)*(f*x + e))*sin(3*f*x + 3*e) + (18*I*(f*x + e)^2*d^3 + 18*I*d^3*e^2 + 36*I*d^3 + (-36*I*d^3*e + 36*I*c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e) + (18*I*(f*x + e)^2*d^3 + 18*I*d^3*e^2 + 36*I*d^3 + (-36*I*d^3*e + 36*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) + 2*((f*x + e)^3*d^3 - 3*(d^3*e - c*d^2*f)*(f*x + e)^2 + 3*(d^3*e^2 + 2*d^3)*(f*x + e))*cos(3*f*x + 3*e) + (6*(f*x + e)^3*d^3 - 6*I*d^3*e^2 + 12*d^3*e - 12*c*d^2*f - 6*(3*d^3*e - 3*c*d^2*f + I*d^3)*(f*x + e)^2 + (18*d^3*e^2 + 12*I*d^3*e - 12*I*c*d^2*f + 24*d^3)*(f*x + e))*cos(2*f*x + 2*e) + (6*d^3*e^3 - 6*I*(f*x + e)^2*d^3 - 6*I*d^3*e^2 + 24*d^3*e - 24*c*d^2*f - (-12*I*d^3*e + 12*I*c*d^2*f - 12*d^3)*(f*x + e))*cos(f*x + e) + (12*(f*x + e)*d^3 - 12*d^3*e + 12*c*d^2*f + 12*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(3*f*x + 3*e) + 36*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(2*f*x + 2*e) + 36*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) - (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f)*sin(3*f*x + 3*e) - (-36*I*(f*x + e)*d^3 + 36*I*d^3*e - 36*I*c*d^2*f)*sin(2*f*x + 2*e) - (-36*I*(f*x + e)*d^3 + 36*I*d^3*e - 36*I*c*d^2*f)*sin(f*x + e))*dilog(-e^(I*f*x + I*e)) - (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 - 6*I*d^3 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e) + (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 - 6*I*d^3 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e))*cos(3*f*x + 3*e) + (-9*I*(f*x + e)^2*d^3 - 9*I*d^3*e^2 - 18*I*d^3 + (18*I*d^3*e - 18*I*c*d^2*f)*(f*x + e))*cos(2*f*x + 2*e) + (-9*I*(f*x + e)^2*d^3 - 9*I*d^3*e^2 - 18*I*d^3 + (18*I*d^3*e - 18*I*c*d^2*f)*(f*x + e))*cos(f*x + e) + 3*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(3*f*x + 3*e) + 9*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(2*f*x + 2*e) + 9*((f*x + e)^2*d^3 + d^3*e^2 + 2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - (-12*I*d^3*cos(3*f*x + 3*e) - 36*I*d^3*cos(2*f*x + 2*e) - 36*I*d^3*cos(f*x + e) + 12*d^3*sin(3*f*x + 3*e) + 36*d^3*sin(2*f*x + 2*e) + 36*d^3*sin(f*x + e) - 12*I*d^3)*polylog(3, -e^(I*f*x + I*e)) - (-2*I*(f*x + e)^3*d^3 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e)^2 + (-6*I*d^3*e^2 - 12*I*d^3)*(f*x + e))*sin(3*f*x + 3*e) - (-6*I*(f*x + e)^3*d^3 - 6*d^3*e^2 - 12*I*d^3*e + 12*I*c*d^2*f + (18*I*d^3*e - 18*I*c*d^2*f - 6*d^3)*(f*x + e)^2 + (-18*I*d^3*e^2 + 12*d^3*e - 12*c*d^2*f - 24*I*d^3)*(f*x + e))*sin(2*f*x + 2*e) - (-6*I*d^3*e^3 - 6*(f*x + e)^2*d^3 - 6*d^3*e^2 - 24*I*d^3*e + 24*I*c*d^2*f + 12*(d^3*e - c*d^2*f - I*d^3)*(f*x + e))*sin(f*x + e))/(-3*I*a^2*f^3*cos(3*f*x + 3*e) - 9*I*a^2*f^3*cos(2*f*x + 2*e) - 9*I*a^2*f^3*cos(f*x + e) + 3*a^2*f^3*sin(3*f*x + 3*e) + 9*a^2*f^3*sin(2*f*x + 2*e) + 9*a^2*f^3*sin(f*x + e) - 3*I*a^2*f^3))/f","B",0
134,1,772,0,2.469954," ","integrate((d*x+c)^2/(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{2 \, c^{2} f^{2} + 4 \, d^{2} + {\left(4 \, d^{2} f x + 4 \, c d f + 4 \, {\left(d^{2} f x + c d f\right)} \cos\left(3 \, f x + 3 \, e\right) + 12 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + 12 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + {\left(4 i \, d^{2} f x + 4 i \, c d f\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(12 i \, d^{2} f x + 12 i \, c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(12 i \, d^{2} f x + 12 i \, c d f\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x\right)} \cos\left(3 \, f x + 3 \, e\right) - {\left(6 \, d^{2} f^{2} x^{2} - 4 i \, c d f - 4 \, d^{2} + 4 \, {\left(3 \, c d f^{2} - i \, d^{2} f\right)} x\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(6 \, c^{2} f^{2} + 4 i \, d^{2} f x + 4 i \, c d f + 8 \, d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, d^{2} \cos\left(3 \, f x + 3 \, e\right) + 12 \, d^{2} \cos\left(2 \, f x + 2 \, e\right) + 12 \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} \sin\left(3 \, f x + 3 \, e\right) + 12 i \, d^{2} \sin\left(2 \, f x + 2 \, e\right) + 12 i \, d^{2} \sin\left(f x + e\right) + 4 \, d^{2}\right)} {\rm Li}_2\left(-e^{\left(i \, f x + i \, e\right)}\right) + {\left(-2 i \, d^{2} f x - 2 i \, c d f + {\left(-2 i \, d^{2} f x - 2 i \, c d f\right)} \cos\left(3 \, f x + 3 \, e\right) + {\left(-6 i \, d^{2} f x - 6 i \, c d f\right)} \cos\left(2 \, f x + 2 \, e\right) + {\left(-6 i \, d^{2} f x - 6 i \, c d f\right)} \cos\left(f x + e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x\right)} \sin\left(3 \, f x + 3 \, e\right) + {\left(-6 i \, d^{2} f^{2} x^{2} - 4 \, c d f + 4 i \, d^{2} + {\left(-12 i \, c d f^{2} - 4 \, d^{2} f\right)} x\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(6 i \, c^{2} f^{2} - 4 \, d^{2} f x - 4 \, c d f + 8 i \, d^{2}\right)} \sin\left(f x + e\right)}{-3 i \, a^{2} f^{3} \cos\left(3 \, f x + 3 \, e\right) - 9 i \, a^{2} f^{3} \cos\left(2 \, f x + 2 \, e\right) - 9 i \, a^{2} f^{3} \cos\left(f x + e\right) + 3 \, a^{2} f^{3} \sin\left(3 \, f x + 3 \, e\right) + 9 \, a^{2} f^{3} \sin\left(2 \, f x + 2 \, e\right) + 9 \, a^{2} f^{3} \sin\left(f x + e\right) - 3 i \, a^{2} f^{3}}"," ",0,"(2*c^2*f^2 + 4*d^2 + (4*d^2*f*x + 4*c*d*f + 4*(d^2*f*x + c*d*f)*cos(3*f*x + 3*e) + 12*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e) + 12*(d^2*f*x + c*d*f)*cos(f*x + e) + (4*I*d^2*f*x + 4*I*c*d*f)*sin(3*f*x + 3*e) + (12*I*d^2*f*x + 12*I*c*d*f)*sin(2*f*x + 2*e) + (12*I*d^2*f*x + 12*I*c*d*f)*sin(f*x + e))*arctan2(sin(f*x + e), cos(f*x + e) + 1) - 2*(d^2*f^2*x^2 + 2*c*d*f^2*x)*cos(3*f*x + 3*e) - (6*d^2*f^2*x^2 - 4*I*c*d*f - 4*d^2 + 4*(3*c*d*f^2 - I*d^2*f)*x)*cos(2*f*x + 2*e) + (6*c^2*f^2 + 4*I*d^2*f*x + 4*I*c*d*f + 8*d^2)*cos(f*x + e) - (4*d^2*cos(3*f*x + 3*e) + 12*d^2*cos(2*f*x + 2*e) + 12*d^2*cos(f*x + e) + 4*I*d^2*sin(3*f*x + 3*e) + 12*I*d^2*sin(2*f*x + 2*e) + 12*I*d^2*sin(f*x + e) + 4*d^2)*dilog(-e^(I*f*x + I*e)) + (-2*I*d^2*f*x - 2*I*c*d*f + (-2*I*d^2*f*x - 2*I*c*d*f)*cos(3*f*x + 3*e) + (-6*I*d^2*f*x - 6*I*c*d*f)*cos(2*f*x + 2*e) + (-6*I*d^2*f*x - 6*I*c*d*f)*cos(f*x + e) + 2*(d^2*f*x + c*d*f)*sin(3*f*x + 3*e) + 6*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e) + 6*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) + (-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x)*sin(3*f*x + 3*e) + (-6*I*d^2*f^2*x^2 - 4*c*d*f + 4*I*d^2 + (-12*I*c*d*f^2 - 4*d^2*f)*x)*sin(2*f*x + 2*e) + (6*I*c^2*f^2 - 4*d^2*f*x - 4*c*d*f + 8*I*d^2)*sin(f*x + e))/(-3*I*a^2*f^3*cos(3*f*x + 3*e) - 9*I*a^2*f^3*cos(2*f*x + 2*e) - 9*I*a^2*f^3*cos(f*x + e) + 3*a^2*f^3*sin(3*f*x + 3*e) + 9*a^2*f^3*sin(2*f*x + 2*e) + 9*a^2*f^3*sin(f*x + e) - 3*I*a^2*f^3)","B",0
135,1,763,0,0.989476," ","integrate((d*x+c)/(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(2 \, {\left(3 \, {\left(f x + e\right)} \sin\left(f x + e\right) + \cos\left(2 \, f x + 2 \, e\right) + \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(9 \, {\left(f x + e\right)} \sin\left(f x + e\right) + 6 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(3 \, \cos\left(2 \, f x + 2 \, e\right) + 3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(3 \, f x + 3 \, e\right) + \cos\left(3 \, f x + 3 \, e\right)^{2} + 6 \, {\left(3 \, \cos\left(f x + e\right) + 1\right)} \cos\left(2 \, f x + 2 \, e\right) + 9 \, \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, \cos\left(f x + e\right)^{2} + 6 \, {\left(\sin\left(2 \, f x + 2 \, e\right) + \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, \sin\left(f x + e\right)^{2} + 6 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(f x + 3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - \sin\left(2 \, f x + 2 \, e\right) - \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) - 6 \, {\left(f x + 3 \, {\left(f x + e\right)} \cos\left(f x + e\right) + e - 2 \, \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right) + 6 \, \sin\left(2 \, f x + 2 \, e\right)^{2} + 6 \, \sin\left(f x + e\right)^{2} + 2 \, \cos\left(f x + e\right)\right)} d}{a^{2} f \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, a^{2} f \cos\left(f x + e\right)^{2} + a^{2} f \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, a^{2} f \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, a^{2} f \sin\left(f x + e\right)^{2} + 6 \, a^{2} f \cos\left(f x + e\right) + a^{2} f + 2 \, {\left(3 \, a^{2} f \cos\left(2 \, f x + 2 \, e\right) + 3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(3 \, a^{2} f \cos\left(f x + e\right) + a^{2} f\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} f \sin\left(2 \, f x + 2 \, e\right) + a^{2} f \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)} - \frac{c {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2}} + \frac{d e {\left(\frac{3 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a^{2} f}}{6 \, f}"," ",0,"-1/6*(2*(2*(3*(f*x + e)*sin(f*x + e) + cos(2*f*x + 2*e) + cos(f*x + e))*cos(3*f*x + 3*e) + 2*(9*(f*x + e)*sin(f*x + e) + 6*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 6*cos(2*f*x + 2*e)^2 + 6*cos(f*x + e)^2 - (2*(3*cos(2*f*x + 2*e) + 3*cos(f*x + e) + 1)*cos(3*f*x + 3*e) + cos(3*f*x + 3*e)^2 + 6*(3*cos(f*x + e) + 1)*cos(2*f*x + 2*e) + 9*cos(2*f*x + 2*e)^2 + 9*cos(f*x + e)^2 + 6*(sin(2*f*x + 2*e) + sin(f*x + e))*sin(3*f*x + 3*e) + sin(3*f*x + 3*e)^2 + 9*sin(2*f*x + 2*e)^2 + 18*sin(2*f*x + 2*e)*sin(f*x + e) + 9*sin(f*x + e)^2 + 6*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 + 2*cos(f*x + e) + 1) - 2*(f*x + 3*(f*x + e)*cos(f*x + e) + e - sin(2*f*x + 2*e) - sin(f*x + e))*sin(3*f*x + 3*e) - 6*(f*x + 3*(f*x + e)*cos(f*x + e) + e - 2*sin(f*x + e))*sin(2*f*x + 2*e) + 6*sin(2*f*x + 2*e)^2 + 6*sin(f*x + e)^2 + 2*cos(f*x + e))*d/(a^2*f*cos(3*f*x + 3*e)^2 + 9*a^2*f*cos(2*f*x + 2*e)^2 + 9*a^2*f*cos(f*x + e)^2 + a^2*f*sin(3*f*x + 3*e)^2 + 9*a^2*f*sin(2*f*x + 2*e)^2 + 18*a^2*f*sin(2*f*x + 2*e)*sin(f*x + e) + 9*a^2*f*sin(f*x + e)^2 + 6*a^2*f*cos(f*x + e) + a^2*f + 2*(3*a^2*f*cos(2*f*x + 2*e) + 3*a^2*f*cos(f*x + e) + a^2*f)*cos(3*f*x + 3*e) + 6*(3*a^2*f*cos(f*x + e) + a^2*f)*cos(2*f*x + 2*e) + 6*(a^2*f*sin(2*f*x + 2*e) + a^2*f*sin(f*x + e))*sin(3*f*x + 3*e)) - c*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/a^2 + d*e*(3*sin(f*x + e)/(cos(f*x + e) + 1) + sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a^2*f))/f","B",0
136,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{6 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 6 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 4 \, d^{2} \sin\left(f x + e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(2 \, d^{2} \sin\left(2 \, f x + 2 \, e\right) - {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) - {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 4 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(d^{2} f x + c d f + 6 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) - 3 \, {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 2 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \int \frac{{\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 6 \, d^{3}\right)} \sin\left(f x + e\right)}{a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)}\,{d x} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2} \cos\left(2 \, f x + 2 \, e\right) + 2 \, d^{2} + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 4 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 2 \, {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 4 \, d^{2} + 3 \, {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d f^{2} x + 3 \, c^{2} f^{2} + 2 \, d^{2}\right)} \cos\left(f x + e\right) + 6 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)}}"," ",0,"1/3*(6*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 + 6*(d^2*f*x + c*d*f)*cos(f*x + e)^2 + 6*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 4*d^2*sin(f*x + e) + 6*(d^2*f*x + c*d*f)*sin(f*x + e)^2 - 2*(2*d^2*sin(2*f*x + 2*e) - (d^2*f*x + c*d*f)*cos(2*f*x + 2*e) - (d^2*f*x + c*d*f)*cos(f*x + e) + (3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 4*d^2)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(d^2*f*x + c*d*f + 6*(d^2*f*x + c*d*f)*cos(f*x + e) - 3*(3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 2*d^2)*sin(f*x + e))*cos(2*f*x + 2*e) + 2*(d^2*f*x + c*d*f)*cos(f*x + e) + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e)^2 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e)^2 + 2*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e) + 6*((a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e) + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))*integrate(2/3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 6*d^3)*sin(f*x + e)/(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)), x) + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2*cos(2*f*x + 2*e) + 2*d^2 + (3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 4*d^2)*cos(f*x + e) + (d^2*f*x + c*d*f)*sin(2*f*x + 2*e) + (d^2*f*x + c*d*f)*sin(f*x + e))*sin(3*f*x + 3*e) + 2*(3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 4*d^2 + 3*(3*d^2*f^2*x^2 + 6*c*d*f^2*x + 3*c^2*f^2 + 2*d^2)*cos(f*x + e) + 6*(d^2*f*x + c*d*f)*sin(f*x + e))*sin(2*f*x + 2*e))/(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e)^2 + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e)^2 + 2*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*cos(f*x + e) + 6*((a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(2*f*x + 2*e) + (a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))","F",0
137,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*cos(f*x+e))^2,x, algorithm=""maxima"")","\frac{12 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 12 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 12 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 12 \, d^{2} \sin\left(f x + e\right) + 12 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(6 \, d^{2} \sin\left(2 \, f x + 2 \, e\right) - 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(2 \, f x + 2 \, e\right) - 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 4 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 2 \, {\left(2 \, d^{2} f x + 2 \, c d f + 12 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) - 9 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 4 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) + 4 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)} \int \frac{{\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 12 \, d^{3}\right)} \sin\left(f x + e\right)}{a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3} + {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} \cos\left(f x + e\right)}\,{d x} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 6 \, d^{2} \cos\left(2 \, f x + 2 \, e\right) + 6 \, d^{2} + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 4 \, d^{2}\right)} \cos\left(f x + e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(2 \, f x + 2 \, e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right) + 6 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 4 \, d^{2} + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2}\right)} \cos\left(f x + e\right) + 4 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \sin\left(2 \, f x + 2 \, e\right)}{3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(3 \, f x + 3 \, e\right)^{2} + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right)^{2} + 18 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) \sin\left(f x + e\right) + 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(2 \, f x + 2 \, e\right) + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(3 \, f x + 3 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right)\right)} \cos\left(2 \, f x + 2 \, e\right) + 6 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \cos\left(f x + e\right) + 6 \, {\left({\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(2 \, f x + 2 \, e\right) + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} \sin\left(f x + e\right)\right)} \sin\left(3 \, f x + 3 \, e\right)\right)}}"," ",0,"1/3*(12*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e)^2 + 12*(d^2*f*x + c*d*f)*cos(f*x + e)^2 + 12*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e)^2 + 12*d^2*sin(f*x + e) + 12*(d^2*f*x + c*d*f)*sin(f*x + e)^2 - 2*(6*d^2*sin(2*f*x + 2*e) - 2*(d^2*f*x + c*d*f)*cos(2*f*x + 2*e) - 2*(d^2*f*x + c*d*f)*cos(f*x + e) + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 4*d^2)*sin(f*x + e))*cos(3*f*x + 3*e) + 2*(2*d^2*f*x + 2*c*d*f + 12*(d^2*f*x + c*d*f)*cos(f*x + e) - 9*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2)*sin(f*x + e))*cos(2*f*x + 2*e) + 4*(d^2*f*x + c*d*f)*cos(f*x + e) + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e) + 6*((a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e) + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))*integrate(4/3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 12*d^3)*sin(f*x + e)/(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3 + (a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*cos(f*x + e)^2 + (a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*sin(f*x + e)^2 + 2*(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*cos(f*x + e)), x) + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 6*d^2*cos(2*f*x + 2*e) + 6*d^2 + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 4*d^2)*cos(f*x + e) + 2*(d^2*f*x + c*d*f)*sin(2*f*x + 2*e) + 2*(d^2*f*x + c*d*f)*sin(f*x + e))*sin(3*f*x + 3*e) + 6*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 4*d^2 + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2)*cos(f*x + e) + 4*(d^2*f*x + c*d*f)*sin(f*x + e))*sin(2*f*x + 2*e))/(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e)^2 + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(3*f*x + 3*e)^2 + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e)^2 + 18*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e)*sin(f*x + e) + 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e)^2 + 2*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(2*f*x + 2*e) + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e))*cos(3*f*x + 3*e) + 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e))*cos(2*f*x + 2*e) + 6*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*cos(f*x + e) + 6*((a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(2*f*x + 2*e) + (a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*sin(f*x + e))*sin(3*f*x + 3*e))","F",0
138,1,959,0,1.339562," ","integrate((d*x+c)^3/(a-a*cos(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{6 \, {\left({\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c d^{2} e}{a f^{2} \cos\left(f x + e\right)^{2} + a f^{2} \sin\left(f x + e\right)^{2} - 2 \, a f^{2} \cos\left(f x + e\right) + a f^{2}} - \frac{3 \, {\left({\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} c^{2} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} - 2 \, a f \cos\left(f x + e\right) + a f} + \frac{c^{3} {\left(\cos\left(f x + e\right) + 1\right)}}{a \sin\left(f x + e\right)} + \frac{3 \, c d^{2} e^{2} {\left(\cos\left(f x + e\right) + 1\right)}}{a f^{2} \sin\left(f x + e\right)} - \frac{3 \, c^{2} d e {\left(\cos\left(f x + e\right) + 1\right)}}{a f \sin\left(f x + e\right)} - \frac{2 \, d^{3} e^{3} + {\left(6 \, d^{3} e^{2} \cos\left(f x + e\right) + 6 i \, d^{3} e^{2} \sin\left(f x + e\right) - 6 \, d^{3} e^{2}\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + {\left(6 \, {\left(f x + e\right)}^{2} d^{3} - 12 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)} - 6 \, {\left({\left(f x + e\right)}^{2} d^{3} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + {\left(-6 i \, {\left(f x + e\right)}^{2} d^{3} + {\left(12 i \, d^{3} e - 12 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) - 2 \, {\left({\left(f x + e\right)}^{3} d^{3} + 3 \, {\left(f x + e\right)} d^{3} e^{2} - 3 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \cos\left(f x + e\right) + {\left(12 \, {\left(f x + e\right)} d^{3} - 12 \, d^{3} e + 12 \, c d^{2} f - 12 \, {\left({\left(f x + e\right)} d^{3} - d^{3} e + c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-12 i \, {\left(f x + e\right)} d^{3} + 12 i \, d^{3} e - 12 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) + {\left(3 i \, {\left(f x + e\right)}^{2} d^{3} + 3 i \, d^{3} e^{2} + {\left(-6 i \, d^{3} e + 6 i \, c d^{2} f\right)} {\left(f x + e\right)} + {\left(-3 i \, {\left(f x + e\right)}^{2} d^{3} - 3 i \, d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}\right)} \cos\left(f x + e\right) + 3 \, {\left({\left(f x + e\right)}^{2} d^{3} + d^{3} e^{2} - 2 \, {\left(d^{3} e - c d^{2} f\right)} {\left(f x + e\right)}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right) + {\left(-12 i \, d^{3} \cos\left(f x + e\right) + 12 \, d^{3} \sin\left(f x + e\right) + 12 i \, d^{3}\right)} {\rm Li}_{3}(e^{\left(i \, f x + i \, e\right)}) + {\left(-2 i \, {\left(f x + e\right)}^{3} d^{3} - 6 i \, {\left(f x + e\right)} d^{3} e^{2} + {\left(6 i \, d^{3} e - 6 i \, c d^{2} f\right)} {\left(f x + e\right)}^{2}\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) + i \, a f^{3}}}{f}"," ",0,"-(6*((cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) - 2*(f*x + e)*sin(f*x + e))*c*d^2*e/(a*f^2*cos(f*x + e)^2 + a*f^2*sin(f*x + e)^2 - 2*a*f^2*cos(f*x + e) + a*f^2) - 3*((cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) - 2*(f*x + e)*sin(f*x + e))*c^2*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 - 2*a*f*cos(f*x + e) + a*f) + c^3*(cos(f*x + e) + 1)/(a*sin(f*x + e)) + 3*c*d^2*e^2*(cos(f*x + e) + 1)/(a*f^2*sin(f*x + e)) - 3*c^2*d*e*(cos(f*x + e) + 1)/(a*f*sin(f*x + e)) - (2*d^3*e^3 + (6*d^3*e^2*cos(f*x + e) + 6*I*d^3*e^2*sin(f*x + e) - 6*d^3*e^2)*arctan2(sin(f*x + e), cos(f*x + e) - 1) + (6*(f*x + e)^2*d^3 - 12*(d^3*e - c*d^2*f)*(f*x + e) - 6*((f*x + e)^2*d^3 - 2*(d^3*e - c*d^2*f)*(f*x + e))*cos(f*x + e) + (-6*I*(f*x + e)^2*d^3 + (12*I*d^3*e - 12*I*c*d^2*f)*(f*x + e))*sin(f*x + e))*arctan2(sin(f*x + e), -cos(f*x + e) + 1) - 2*((f*x + e)^3*d^3 + 3*(f*x + e)*d^3*e^2 - 3*(d^3*e - c*d^2*f)*(f*x + e)^2)*cos(f*x + e) + (12*(f*x + e)*d^3 - 12*d^3*e + 12*c*d^2*f - 12*((f*x + e)*d^3 - d^3*e + c*d^2*f)*cos(f*x + e) + (-12*I*(f*x + e)*d^3 + 12*I*d^3*e - 12*I*c*d^2*f)*sin(f*x + e))*dilog(e^(I*f*x + I*e)) + (3*I*(f*x + e)^2*d^3 + 3*I*d^3*e^2 + (-6*I*d^3*e + 6*I*c*d^2*f)*(f*x + e) + (-3*I*(f*x + e)^2*d^3 - 3*I*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e))*cos(f*x + e) + 3*((f*x + e)^2*d^3 + d^3*e^2 - 2*(d^3*e - c*d^2*f)*(f*x + e))*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) + (-12*I*d^3*cos(f*x + e) + 12*d^3*sin(f*x + e) + 12*I*d^3)*polylog(3, e^(I*f*x + I*e)) + (-2*I*(f*x + e)^3*d^3 - 6*I*(f*x + e)*d^3*e^2 + (6*I*d^3*e - 6*I*c*d^2*f)*(f*x + e)^2)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) + I*a*f^3))/f","B",0
139,1,314,0,0.677298," ","integrate((d*x+c)^2/(a-a*cos(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, c^{2} f^{2} - 4 \, {\left(c d f \cos\left(f x + e\right) + i \, c d f \sin\left(f x + e\right) - c d f\right)} \arctan\left(\sin\left(f x + e\right), \cos\left(f x + e\right) - 1\right) + {\left(4 \, d^{2} f x \cos\left(f x + e\right) + 4 i \, d^{2} f x \sin\left(f x + e\right) - 4 \, d^{2} f x\right)} \arctan\left(\sin\left(f x + e\right), -\cos\left(f x + e\right) + 1\right) + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x\right)} \cos\left(f x + e\right) + {\left(4 \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} \sin\left(f x + e\right) - 4 \, d^{2}\right)} {\rm Li}_2\left(e^{\left(i \, f x + i \, e\right)}\right) - {\left(2 i \, d^{2} f x + 2 i \, c d f + {\left(-2 i \, d^{2} f x - 2 i \, c d f\right)} \cos\left(f x + e\right) + 2 \, {\left(d^{2} f x + c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right) - {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x\right)} \sin\left(f x + e\right)}{-i \, a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) + i \, a f^{3}}"," ",0,"-(2*c^2*f^2 - 4*(c*d*f*cos(f*x + e) + I*c*d*f*sin(f*x + e) - c*d*f)*arctan2(sin(f*x + e), cos(f*x + e) - 1) + (4*d^2*f*x*cos(f*x + e) + 4*I*d^2*f*x*sin(f*x + e) - 4*d^2*f*x)*arctan2(sin(f*x + e), -cos(f*x + e) + 1) + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x)*cos(f*x + e) + (4*d^2*cos(f*x + e) + 4*I*d^2*sin(f*x + e) - 4*d^2)*dilog(e^(I*f*x + I*e)) - (2*I*d^2*f*x + 2*I*c*d*f + (-2*I*d^2*f*x - 2*I*c*d*f)*cos(f*x + e) + 2*(d^2*f*x + c*d*f)*sin(f*x + e))*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) - (-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x)*sin(f*x + e))/(-I*a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) + I*a*f^3)","B",0
140,1,160,0,0.864115," ","integrate((d*x+c)/(a-a*cos(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)} \log\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right) - 2 \, {\left(f x + e\right)} \sin\left(f x + e\right)\right)} d}{a f \cos\left(f x + e\right)^{2} + a f \sin\left(f x + e\right)^{2} - 2 \, a f \cos\left(f x + e\right) + a f} - \frac{c {\left(\cos\left(f x + e\right) + 1\right)}}{a \sin\left(f x + e\right)} + \frac{d e {\left(\cos\left(f x + e\right) + 1\right)}}{a f \sin\left(f x + e\right)}}{f}"," ",0,"(((cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1)*log(cos(f*x + e)^2 + sin(f*x + e)^2 - 2*cos(f*x + e) + 1) - 2*(f*x + e)*sin(f*x + e))*d/(a*f*cos(f*x + e)^2 + a*f*sin(f*x + e)^2 - 2*a*f*cos(f*x + e) + a*f) - c*(cos(f*x + e) + 1)/(a*sin(f*x + e)) + d*e*(cos(f*x + e) + 1)/(a*f*sin(f*x + e)))/f","B",0
141,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a-a*cos(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{{\left(a d^{2} f x + a c d f + {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)^{2} + {\left(a d^{2} f x + a c d f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)\right)} \int \frac{\sin\left(f x + e\right)}{{\left(d x + c\right)}^{2} {\left(\cos\left(f x + e\right)^{2} + \sin\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) + 1\right)}}\,{d x}}{a f} + \sin\left(f x + e\right)\right)}}{a d f x + a c f + {\left(a d f x + a c f\right)} \cos\left(f x + e\right)^{2} + {\left(a d f x + a c f\right)} \sin\left(f x + e\right)^{2} - 2 \, {\left(a d f x + a c f\right)} \cos\left(f x + e\right)}"," ",0,"-2*((a*d^2*f*x + a*c*d*f + (a*d^2*f*x + a*c*d*f)*cos(f*x + e)^2 + (a*d^2*f*x + a*c*d*f)*sin(f*x + e)^2 - 2*(a*d^2*f*x + a*c*d*f)*cos(f*x + e))*integrate(sin(f*x + e)/(a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*cos(f*x + e)^2 + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*sin(f*x + e)^2 - 2*(a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*cos(f*x + e)), x) + sin(f*x + e))/(a*d*f*x + a*c*f + (a*d*f*x + a*c*f)*cos(f*x + e)^2 + (a*d*f*x + a*c*f)*sin(f*x + e)^2 - 2*(a*d*f*x + a*c*f)*cos(f*x + e))","F",0
142,-1,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a-a*cos(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,1,206,0,1.713362," ","integrate(x^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} \sqrt{a} c^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 3 \, {\left(\sqrt{2} {\left(d x + c\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a} c^{2} + 3 \, {\left(\sqrt{2} {\left(d x + c\right)}^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, \sqrt{2} {\left(d x + c\right)} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a} c - {\left(\sqrt{2} {\left(d x + c\right)}^{3} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 6 \, \sqrt{2} {\left(d x + c\right)}^{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, \sqrt{2} {\left(d x + c\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 48 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}\right)}}{d^{4}}"," ",0,"-2*(sqrt(2)*sqrt(a)*c^3*sin(1/2*d*x + 1/2*c) - 3*(sqrt(2)*(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*cos(1/2*d*x + 1/2*c))*sqrt(a)*c^2 + 3*(sqrt(2)*(d*x + c)^2*sin(1/2*d*x + 1/2*c) + 4*sqrt(2)*(d*x + c)*cos(1/2*d*x + 1/2*c) - 8*sqrt(2)*sin(1/2*d*x + 1/2*c))*sqrt(a)*c - (sqrt(2)*(d*x + c)^3*sin(1/2*d*x + 1/2*c) + 6*sqrt(2)*(d*x + c)^2*cos(1/2*d*x + 1/2*c) - 24*sqrt(2)*(d*x + c)*sin(1/2*d*x + 1/2*c) - 48*sqrt(2)*cos(1/2*d*x + 1/2*c))*sqrt(a))/d^4","B",0
144,1,122,0,1.556202," ","integrate(x^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, {\left(\sqrt{2} \sqrt{a} c^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, {\left(\sqrt{2} {\left(d x + c\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a} c + {\left(\sqrt{2} {\left(d x + c\right)}^{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, \sqrt{2} {\left(d x + c\right)} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, \sqrt{2} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}\right)}}{d^{3}}"," ",0,"2*(sqrt(2)*sqrt(a)*c^2*sin(1/2*d*x + 1/2*c) - 2*(sqrt(2)*(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*cos(1/2*d*x + 1/2*c))*sqrt(a)*c + (sqrt(2)*(d*x + c)^2*sin(1/2*d*x + 1/2*c) + 4*sqrt(2)*(d*x + c)*cos(1/2*d*x + 1/2*c) - 8*sqrt(2)*sin(1/2*d*x + 1/2*c))*sqrt(a))/d^3","A",0
145,1,61,0,1.486054," ","integrate(x*(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(\sqrt{2} \sqrt{a} c \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - {\left(\sqrt{2} {\left(d x + c\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} \sqrt{a}\right)}}{d^{2}}"," ",0,"-2*(sqrt(2)*sqrt(a)*c*sin(1/2*d*x + 1/2*c) - (sqrt(2)*(d*x + c)*sin(1/2*d*x + 1/2*c) + 2*sqrt(2)*cos(1/2*d*x + 1/2*c))*sqrt(a))/d^2","A",0
146,1,20,0,1.340250," ","integrate((a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{2 \, \sqrt{2} \sqrt{a} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sin(1/2*d*x + 1/2*c)/d","A",0
147,1,61,0,2.239202," ","integrate((a+a*cos(d*x+c))^(1/2)/x,x, algorithm=""maxima"")","-\frac{1}{2} \, {\left({\left(\sqrt{2} E_{1}\left(\frac{1}{2} i \, d x\right) + \sqrt{2} E_{1}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right) - {\left(i \, \sqrt{2} E_{1}\left(\frac{1}{2} i \, d x\right) - i \, \sqrt{2} E_{1}\left(-\frac{1}{2} i \, d x\right)\right)} \sin\left(\frac{1}{2} \, c\right)\right)} \sqrt{a}"," ",0,"-1/2*((sqrt(2)*exp_integral_e(1, 1/2*I*d*x) + sqrt(2)*exp_integral_e(1, -1/2*I*d*x))*cos(1/2*c) - (I*sqrt(2)*exp_integral_e(1, 1/2*I*d*x) - I*sqrt(2)*exp_integral_e(1, -1/2*I*d*x))*sin(1/2*c))*sqrt(a)","C",0
148,1,198,0,0.981555," ","integrate((a+a*cos(d*x+c))^(1/2)/x^2,x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(E_{2}\left(\frac{1}{2} i \, d x\right) + E_{2}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right)^{3} + 4 \, {\left(E_{2}\left(\frac{1}{2} i \, d x\right) + E_{2}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, c\right)^{2} - {\left(4 i \, E_{2}\left(\frac{1}{2} i \, d x\right) - 4 i \, E_{2}\left(-\frac{1}{2} i \, d x\right)\right)} \sin\left(\frac{1}{2} \, c\right)^{3} + 4 \, {\left(E_{2}\left(\frac{1}{2} i \, d x\right) + E_{2}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right) - {\left({\left(4 i \, E_{2}\left(\frac{1}{2} i \, d x\right) - 4 i \, E_{2}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right)^{2} + 4 i \, E_{2}\left(\frac{1}{2} i \, d x\right) - 4 i \, E_{2}\left(-\frac{1}{2} i \, d x\right)\right)} \sin\left(\frac{1}{2} \, c\right)\right)} \sqrt{a} d}{8 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, c\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, c\right)^{2}\right)} {\left(d x + c\right)} - {\left(\sqrt{2} \cos\left(\frac{1}{2} \, c\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, c\right)^{2}\right)} c\right)}}"," ",0,"-1/8*(4*(exp_integral_e(2, 1/2*I*d*x) + exp_integral_e(2, -1/2*I*d*x))*cos(1/2*c)^3 + 4*(exp_integral_e(2, 1/2*I*d*x) + exp_integral_e(2, -1/2*I*d*x))*cos(1/2*c)*sin(1/2*c)^2 - (4*I*exp_integral_e(2, 1/2*I*d*x) - 4*I*exp_integral_e(2, -1/2*I*d*x))*sin(1/2*c)^3 + 4*(exp_integral_e(2, 1/2*I*d*x) + exp_integral_e(2, -1/2*I*d*x))*cos(1/2*c) - ((4*I*exp_integral_e(2, 1/2*I*d*x) - 4*I*exp_integral_e(2, -1/2*I*d*x))*cos(1/2*c)^2 + 4*I*exp_integral_e(2, 1/2*I*d*x) - 4*I*exp_integral_e(2, -1/2*I*d*x))*sin(1/2*c))*sqrt(a)*d/((sqrt(2)*cos(1/2*c)^2 + sqrt(2)*sin(1/2*c)^2)*(d*x + c) - (sqrt(2)*cos(1/2*c)^2 + sqrt(2)*sin(1/2*c)^2)*c)","C",0
149,1,232,0,1.516339," ","integrate((a+a*cos(d*x+c))^(1/2)/x^3,x, algorithm=""maxima"")","-\frac{{\left(4 \, {\left(E_{3}\left(\frac{1}{2} i \, d x\right) + E_{3}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right)^{3} + 4 \, {\left(E_{3}\left(\frac{1}{2} i \, d x\right) + E_{3}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right) \sin\left(\frac{1}{2} \, c\right)^{2} - {\left(4 i \, E_{3}\left(\frac{1}{2} i \, d x\right) - 4 i \, E_{3}\left(-\frac{1}{2} i \, d x\right)\right)} \sin\left(\frac{1}{2} \, c\right)^{3} + 4 \, {\left(E_{3}\left(\frac{1}{2} i \, d x\right) + E_{3}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right) - {\left({\left(4 i \, E_{3}\left(\frac{1}{2} i \, d x\right) - 4 i \, E_{3}\left(-\frac{1}{2} i \, d x\right)\right)} \cos\left(\frac{1}{2} \, c\right)^{2} + 4 i \, E_{3}\left(\frac{1}{2} i \, d x\right) - 4 i \, E_{3}\left(-\frac{1}{2} i \, d x\right)\right)} \sin\left(\frac{1}{2} \, c\right)\right)} \sqrt{a} d^{2}}{8 \, {\left({\left(\sqrt{2} \cos\left(\frac{1}{2} \, c\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, c\right)^{2}\right)} {\left(d x + c\right)}^{2} - 2 \, {\left(\sqrt{2} \cos\left(\frac{1}{2} \, c\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, c\right)^{2}\right)} {\left(d x + c\right)} c + {\left(\sqrt{2} \cos\left(\frac{1}{2} \, c\right)^{2} + \sqrt{2} \sin\left(\frac{1}{2} \, c\right)^{2}\right)} c^{2}\right)}}"," ",0,"-1/8*(4*(exp_integral_e(3, 1/2*I*d*x) + exp_integral_e(3, -1/2*I*d*x))*cos(1/2*c)^3 + 4*(exp_integral_e(3, 1/2*I*d*x) + exp_integral_e(3, -1/2*I*d*x))*cos(1/2*c)*sin(1/2*c)^2 - (4*I*exp_integral_e(3, 1/2*I*d*x) - 4*I*exp_integral_e(3, -1/2*I*d*x))*sin(1/2*c)^3 + 4*(exp_integral_e(3, 1/2*I*d*x) + exp_integral_e(3, -1/2*I*d*x))*cos(1/2*c) - ((4*I*exp_integral_e(3, 1/2*I*d*x) - 4*I*exp_integral_e(3, -1/2*I*d*x))*cos(1/2*c)^2 + 4*I*exp_integral_e(3, 1/2*I*d*x) - 4*I*exp_integral_e(3, -1/2*I*d*x))*sin(1/2*c))*sqrt(a)*d^2/((sqrt(2)*cos(1/2*c)^2 + sqrt(2)*sin(1/2*c)^2)*(d*x + c)^2 - 2*(sqrt(2)*cos(1/2*c)^2 + sqrt(2)*sin(1/2*c)^2)*(d*x + c)*c + (sqrt(2)*cos(1/2*c)^2 + sqrt(2)*sin(1/2*c)^2)*c^2)","C",0
150,1,48,0,1.227898," ","integrate(x^3*(a+a*cos(x))^(1/2),x, algorithm=""maxima"")","2 \, {\left(\sqrt{2} x^{3} \sin\left(\frac{1}{2} \, x\right) + 6 \, \sqrt{2} x^{2} \cos\left(\frac{1}{2} \, x\right) - 24 \, \sqrt{2} x \sin\left(\frac{1}{2} \, x\right) - 48 \, \sqrt{2} \cos\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"2*(sqrt(2)*x^3*sin(1/2*x) + 6*sqrt(2)*x^2*cos(1/2*x) - 24*sqrt(2)*x*sin(1/2*x) - 48*sqrt(2)*cos(1/2*x))*sqrt(a)","A",0
151,1,36,0,1.287417," ","integrate(x^2*(a+a*cos(x))^(1/2),x, algorithm=""maxima"")","2 \, {\left(\sqrt{2} x^{2} \sin\left(\frac{1}{2} \, x\right) + 4 \, \sqrt{2} x \cos\left(\frac{1}{2} \, x\right) - 8 \, \sqrt{2} \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"2*(sqrt(2)*x^2*sin(1/2*x) + 4*sqrt(2)*x*cos(1/2*x) - 8*sqrt(2)*sin(1/2*x))*sqrt(a)","A",0
152,1,24,0,1.504989," ","integrate(x*(a+a*cos(x))^(1/2),x, algorithm=""maxima"")","2 \, {\left(\sqrt{2} x \sin\left(\frac{1}{2} \, x\right) + 2 \, \sqrt{2} \cos\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"2*(sqrt(2)*x*sin(1/2*x) + 2*sqrt(2)*cos(1/2*x))*sqrt(a)","A",0
153,1,12,0,1.482361," ","integrate((a+a*cos(x))^(1/2),x, algorithm=""maxima"")","2 \, \sqrt{2} \sqrt{a} \sin\left(\frac{1}{2} \, x\right)"," ",0,"2*sqrt(2)*sqrt(a)*sin(1/2*x)","A",0
154,1,17,0,1.517002," ","integrate((a+a*cos(x))^(1/2)/x,x, algorithm=""maxima"")","\frac{1}{2} \, \sqrt{2} \sqrt{a} {\left({\rm Ei}\left(\frac{1}{2} i \, x\right) + {\rm Ei}\left(-\frac{1}{2} i \, x\right)\right)}"," ",0,"1/2*sqrt(2)*sqrt(a)*(Ei(1/2*I*x) + Ei(-1/2*I*x))","C",0
155,1,23,0,0.896782," ","integrate((a+a*cos(x))^(1/2)/x^2,x, algorithm=""maxima"")","-\frac{1}{4} \, \sqrt{2} \sqrt{a} {\left(i \, \Gamma\left(-1, \frac{1}{2} i \, x\right) - i \, \Gamma\left(-1, -\frac{1}{2} i \, x\right)\right)}"," ",0,"-1/4*sqrt(2)*sqrt(a)*(I*gamma(-1, 1/2*I*x) - I*gamma(-1, -1/2*I*x))","C",0
156,1,19,0,1.405301," ","integrate((a+a*cos(x))^(1/2)/x^3,x, algorithm=""maxima"")","\frac{1}{8} \, \sqrt{2} \sqrt{a} {\left(\Gamma\left(-2, \frac{1}{2} i \, x\right) + \Gamma\left(-2, -\frac{1}{2} i \, x\right)\right)}"," ",0,"1/8*sqrt(2)*sqrt(a)*(gamma(-2, 1/2*I*x) + gamma(-2, -1/2*I*x))","C",0
157,1,129,0,1.145250," ","integrate(x^3*(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","-{\left({\left(6 \, \sqrt{2} x^{2} - 6 \, {\left(\sqrt{2} x^{2} - 8 \, \sqrt{2}\right)} \cos\left(x\right) - {\left(\sqrt{2} x^{3} - 24 \, \sqrt{2} x\right)} \sin\left(x\right) - 48 \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right) + {\left(\sqrt{2} x^{3} + {\left(\sqrt{2} x^{3} - 24 \, \sqrt{2} x\right)} \cos\left(x\right) - 6 \, {\left(\sqrt{2} x^{2} - 8 \, \sqrt{2}\right)} \sin\left(x\right) - 24 \, \sqrt{2} x\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)\right)} \sqrt{a}"," ",0,"-((6*sqrt(2)*x^2 - 6*(sqrt(2)*x^2 - 8*sqrt(2))*cos(x) - (sqrt(2)*x^3 - 24*sqrt(2)*x)*sin(x) - 48*sqrt(2))*cos(1/2*pi + 1/2*arctan2(sin(x), cos(x))) + (sqrt(2)*x^3 + (sqrt(2)*x^3 - 24*sqrt(2)*x)*cos(x) - 6*(sqrt(2)*x^2 - 8*sqrt(2))*sin(x) - 24*sqrt(2)*x)*sin(1/2*pi + 1/2*arctan2(sin(x), cos(x))))*sqrt(a)","B",0
158,1,100,0,1.382026," ","integrate(x^2*(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","{\left({\left(4 \, \sqrt{2} x \cos\left(x\right) + {\left(\sqrt{2} x^{2} - 8 \, \sqrt{2}\right)} \sin\left(x\right) - 4 \, \sqrt{2} x\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right) - {\left(\sqrt{2} x^{2} - 4 \, \sqrt{2} x \sin\left(x\right) + {\left(\sqrt{2} x^{2} - 8 \, \sqrt{2}\right)} \cos\left(x\right) - 8 \, \sqrt{2}\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)\right)} \sqrt{a}"," ",0,"((4*sqrt(2)*x*cos(x) + (sqrt(2)*x^2 - 8*sqrt(2))*sin(x) - 4*sqrt(2)*x)*cos(1/2*pi + 1/2*arctan2(sin(x), cos(x))) - (sqrt(2)*x^2 - 4*sqrt(2)*x*sin(x) + (sqrt(2)*x^2 - 8*sqrt(2))*cos(x) - 8*sqrt(2))*sin(1/2*pi + 1/2*arctan2(sin(x), cos(x))))*sqrt(a)","B",0
159,1,72,0,1.692634," ","integrate(x*(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","{\left({\left(\sqrt{2} x \sin\left(x\right) + 2 \, \sqrt{2} \cos\left(x\right) - 2 \, \sqrt{2}\right)} \cos\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right) - {\left(\sqrt{2} x \cos\left(x\right) + \sqrt{2} x - 2 \, \sqrt{2} \sin\left(x\right)\right)} \sin\left(\frac{1}{2} \, \pi + \frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)\right)} \sqrt{a}"," ",0,"((sqrt(2)*x*sin(x) + 2*sqrt(2)*cos(x) - 2*sqrt(2))*cos(1/2*pi + 1/2*arctan2(sin(x), cos(x))) - (sqrt(2)*x*cos(x) + sqrt(2)*x - 2*sqrt(2)*sin(x))*sin(1/2*pi + 1/2*arctan2(sin(x), cos(x))))*sqrt(a)","B",0
160,1,23,0,1.066833," ","integrate((a-a*cos(x))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, \sqrt{2} \sqrt{a}}{\sqrt{\frac{\sin\left(x\right)^{2}}{{\left(\cos\left(x\right) + 1\right)}^{2}} + 1}}"," ",0,"-2*sqrt(2)*sqrt(a)/sqrt(sin(x)^2/(cos(x) + 1)^2 + 1)","A",0
161,0,0,0,0.000000," ","integrate((a-a*cos(x))^(1/2)/x,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \cos\left(x\right) + a}}{x}\,{d x}"," ",0,"integrate(sqrt(-a*cos(x) + a)/x, x)","F",0
162,0,0,0,0.000000," ","integrate((a-a*cos(x))^(1/2)/x^2,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \cos\left(x\right) + a}}{x^{2}}\,{d x}"," ",0,"integrate(sqrt(-a*cos(x) + a)/x^2, x)","F",0
163,0,0,0,0.000000," ","integrate((a-a*cos(x))^(1/2)/x^3,x, algorithm=""maxima"")","\int \frac{\sqrt{-a \cos\left(x\right) + a}}{x^{3}}\,{d x}"," ",0,"integrate(sqrt(-a*cos(x) + a)/x^3, x)","F",0
164,1,98,0,0.815040," ","integrate(x^3*(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\frac{1}{27} \, {\left(81 \, \sqrt{2} a x^{3} \sin\left(\frac{1}{2} \, x\right) + 486 \, \sqrt{2} a x^{2} \cos\left(\frac{1}{2} \, x\right) - 1944 \, \sqrt{2} a x \sin\left(\frac{1}{2} \, x\right) - 3888 \, \sqrt{2} a \cos\left(\frac{1}{2} \, x\right) + 2 \, {\left(9 \, \sqrt{2} a x^{2} - 8 \, \sqrt{2} a\right)} \cos\left(\frac{3}{2} \, x\right) + 3 \, {\left(3 \, \sqrt{2} a x^{3} - 8 \, \sqrt{2} a x\right)} \sin\left(\frac{3}{2} \, x\right)\right)} \sqrt{a}"," ",0,"1/27*(81*sqrt(2)*a*x^3*sin(1/2*x) + 486*sqrt(2)*a*x^2*cos(1/2*x) - 1944*sqrt(2)*a*x*sin(1/2*x) - 3888*sqrt(2)*a*cos(1/2*x) + 2*(9*sqrt(2)*a*x^2 - 8*sqrt(2)*a)*cos(3/2*x) + 3*(3*sqrt(2)*a*x^3 - 8*sqrt(2)*a*x)*sin(3/2*x))*sqrt(a)","A",0
165,1,72,0,1.081330," ","integrate(x^2*(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\frac{1}{27} \, {\left(81 \, \sqrt{2} a x^{2} \sin\left(\frac{1}{2} \, x\right) + 12 \, \sqrt{2} a x \cos\left(\frac{3}{2} \, x\right) + 324 \, \sqrt{2} a x \cos\left(\frac{1}{2} \, x\right) - 648 \, \sqrt{2} a \sin\left(\frac{1}{2} \, x\right) + {\left(9 \, \sqrt{2} a x^{2} - 8 \, \sqrt{2} a\right)} \sin\left(\frac{3}{2} \, x\right)\right)} \sqrt{a}"," ",0,"1/27*(81*sqrt(2)*a*x^2*sin(1/2*x) + 12*sqrt(2)*a*x*cos(3/2*x) + 324*sqrt(2)*a*x*cos(1/2*x) - 648*sqrt(2)*a*sin(1/2*x) + (9*sqrt(2)*a*x^2 - 8*sqrt(2)*a)*sin(3/2*x))*sqrt(a)","A",0
166,1,48,0,1.067402," ","integrate(x*(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\frac{1}{9} \, {\left(3 \, \sqrt{2} a x \sin\left(\frac{3}{2} \, x\right) + 27 \, \sqrt{2} a x \sin\left(\frac{1}{2} \, x\right) + 2 \, \sqrt{2} a \cos\left(\frac{3}{2} \, x\right) + 54 \, \sqrt{2} a \cos\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"1/9*(3*sqrt(2)*a*x*sin(3/2*x) + 27*sqrt(2)*a*x*sin(1/2*x) + 2*sqrt(2)*a*cos(3/2*x) + 54*sqrt(2)*a*cos(1/2*x))*sqrt(a)","A",0
167,1,29,0,1.175814," ","integrate((a+a*cos(x))^(3/2)/x,x, algorithm=""maxima"")","\frac{1}{4} \, \sqrt{2} a^{\frac{3}{2}} {\left({\rm Ei}\left(\frac{3}{2} i \, x\right) + 3 \, {\rm Ei}\left(\frac{1}{2} i \, x\right) + 3 \, {\rm Ei}\left(-\frac{1}{2} i \, x\right) + {\rm Ei}\left(-\frac{3}{2} i \, x\right)\right)}"," ",0,"1/4*sqrt(2)*a^(3/2)*(Ei(3/2*I*x) + 3*Ei(1/2*I*x) + 3*Ei(-1/2*I*x) + Ei(-3/2*I*x))","C",0
168,1,37,0,1.332917," ","integrate((a+a*cos(x))^(3/2)/x^2,x, algorithm=""maxima"")","-\frac{1}{8} \, \sqrt{2} a^{\frac{3}{2}} {\left(3 i \, \Gamma\left(-1, \frac{3}{2} i \, x\right) + 3 i \, \Gamma\left(-1, \frac{1}{2} i \, x\right) - 3 i \, \Gamma\left(-1, -\frac{1}{2} i \, x\right) - 3 i \, \Gamma\left(-1, -\frac{3}{2} i \, x\right)\right)}"," ",0,"-1/8*sqrt(2)*a^(3/2)*(3*I*gamma(-1, 3/2*I*x) + 3*I*gamma(-1, 1/2*I*x) - 3*I*gamma(-1, -1/2*I*x) - 3*I*gamma(-1, -3/2*I*x))","C",0
169,1,33,0,1.087260," ","integrate((a+a*cos(x))^(3/2)/x^3,x, algorithm=""maxima"")","\frac{3}{16} \, \sqrt{2} a^{\frac{3}{2}} {\left(3 \, \Gamma\left(-2, \frac{3}{2} i \, x\right) + \Gamma\left(-2, \frac{1}{2} i \, x\right) + \Gamma\left(-2, -\frac{1}{2} i \, x\right) + 3 \, \Gamma\left(-2, -\frac{3}{2} i \, x\right)\right)}"," ",0,"3/16*sqrt(2)*a^(3/2)*(3*gamma(-2, 3/2*I*x) + gamma(-2, 1/2*I*x) + gamma(-2, -1/2*I*x) + 3*gamma(-2, -3/2*I*x))","C",0
170,-1,0,0,0.000000," ","integrate(x^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(x^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(x/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,1,90,0,1.625175," ","integrate(1/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 1\right)}{2 \, \sqrt{a} d}"," ",0,"1/2*(sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 + 2*sin(1/2*d*x + 1/2*c) + 1) - sqrt(2)*log(cos(1/2*d*x + 1/2*c)^2 + sin(1/2*d*x + 1/2*c)^2 - 2*sin(1/2*d*x + 1/2*c) + 1))/(sqrt(a)*d)","B",0
174,0,0,0,0.000000," ","integrate(1/x/(a+a*cos(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \cos\left(d x + c\right) + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(a*cos(d*x + c) + a)*x), x)","F",0
175,0,0,0,0.000000," ","integrate(x^3/(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{3}}{\sqrt{-a \cos\left(x\right) + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(-a*cos(x) + a), x)","F",0
176,0,0,0,0.000000," ","integrate(x^2/(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","\int \frac{x^{2}}{\sqrt{-a \cos\left(x\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(-a*cos(x) + a), x)","F",0
177,0,0,0,0.000000," ","integrate(x/(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","\int \frac{x}{\sqrt{-a \cos\left(x\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(-a*cos(x) + a), x)","F",0
178,1,81,0,1.929309," ","integrate(1/(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","-\frac{\sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)^{2} + 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right) + 1\right) - \sqrt{2} \log\left(\cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)^{2} + \sin\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right)^{2} - 2 \, \cos\left(\frac{1}{2} \, \arctan\left(\sin\left(x\right), \cos\left(x\right)\right)\right) + 1\right)}{2 \, \sqrt{a}}"," ",0,"-1/2*(sqrt(2)*log(cos(1/2*arctan2(sin(x), cos(x)))^2 + sin(1/2*arctan2(sin(x), cos(x)))^2 + 2*cos(1/2*arctan2(sin(x), cos(x))) + 1) - sqrt(2)*log(cos(1/2*arctan2(sin(x), cos(x)))^2 + sin(1/2*arctan2(sin(x), cos(x)))^2 - 2*cos(1/2*arctan2(sin(x), cos(x))) + 1))/sqrt(a)","B",0
179,0,0,0,0.000000," ","integrate(1/x/(a-a*cos(x))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{-a \cos\left(x\right) + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(-a*cos(x) + a)*x), x)","F",0
180,-1,0,0,0.000000," ","integrate(x^3/(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate(x^2/(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(x/(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,0,0,0,0.000000," ","integrate(1/x/(a+a*cos(x))^(3/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(a \cos\left(x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((a*cos(x) + a)^(3/2)*x), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/3)/x,x, algorithm=""maxima"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(1/3)/x, x)","F",0
185,-2,0,0,0.000000," ","integrate(x^3/(a+b*cos(x)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*a^2-4*b^2>0)', see `assume?` for more details)Is 4*a^2-4*b^2 positive or negative?","F(-2)",0
186,-2,0,0,0.000000," ","integrate(x^2/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
187,-2,0,0,0.000000," ","integrate(x/(a+b*cos(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
188,0,0,0,0.000000," ","integrate(1/x/(a+b*cos(x)),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \cos\left(x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*cos(x) + a)*x), x)","F",0
189,-2,0,0,0.000000," ","integrate((f*x+e)/(a+b*cos(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
