1,1,94,0,0.479406," ","integrate((d*x+c)^m*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-\frac{d m \log\left(\frac{2 i \, b}{d}\right) - 2 i \, b c + 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, b d x + 2 i \, b c}{d}\right) + e^{\left(-\frac{d m \log\left(-\frac{2 i \, b}{d}\right) + 2 i \, b c - 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, b d x - 2 i \, b c}{d}\right)}{8 \, b}"," ",0,"-1/8*(e^(-(d*m*log(2*I*b/d) - 2*I*b*c + 2*I*a*d)/d)*gamma(m + 1, (2*I*b*d*x + 2*I*b*c)/d) + e^(-(d*m*log(-2*I*b/d) + 2*I*b*c - 2*I*a*d)/d)*gamma(m + 1, (-2*I*b*d*x - 2*I*b*c)/d))/b","A",0
2,1,255,0,0.656118," ","integrate((d*x+c)^4*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} - {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} - 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x}{4 \, b^{5}}"," ",0,"1/4*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 3*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 - (2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 - 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(2*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)^2 + 2*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d - 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)*sin(b*x + a) + 2*(2*b^4*c^3*d - 3*b^2*c*d^3)*x)/b^5","A",0
3,1,166,0,0.439608," ","integrate((d*x+c)^3*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} - 2 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x}{8 \, b^{4}}"," ",0,"1/8*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 - 2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 - 3*b*c*d^2 + 3*(2*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^2 + 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)*sin(b*x + a) + 3*(2*b^3*c^2*d - b*d^3)*x)/b^4","A",0
4,1,92,0,0.495159," ","integrate((d*x+c)^2*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x - {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{4 \, b^{3}}"," ",0,"1/4*(b^2*d^2*x^2 + 2*b^2*c*d*x - (2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 - d^2)*cos(b*x + a)^2 + 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a))/b^3","A",0
5,1,42,0,0.633769," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{b d x - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + d \cos\left(b x + a\right) \sin\left(b x + a\right)}{4 \, b^{2}}"," ",0,"1/4*(b*d*x - 2*(b*d*x + b*c)*cos(b*x + a)^2 + d*cos(b*x + a)*sin(b*x + a))/b^2","A",0
6,1,80,0,0.611355," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right)}{4 \, d}"," ",0,"1/4*((cos_integral(2*(b*d*x + b*c)/d) + cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) + 2*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d))/d","A",0
7,1,132,0,0.713807," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*d*cos(b*x + a)*sin(b*x + a) + 2*(b*d*x + b*c)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - ((b*d*x + b*c)*cos_integral(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
8,1,230,0,0.805130," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","\frac{b d^{2} x - d^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) + b c d - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*(b*d^2*x - d^2*cos(b*x + a)*sin(b*x + a) + b*c*d - 2*(b*d^2*x + b*c*d)*cos(b*x + a)^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
9,1,320,0,0.608796," ","integrate(cos(b*x+a)*sin(b*x+a)/(d*x+c)^4,x, algorithm=""fricas"")","\frac{b d^{3} x + b c d^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{6 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/6*(b*d^3*x + b*c*d^2 - 2*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2 + 2*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)*sin(b*x + a) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
10,1,6,0,0.721186," ","integrate(cos(x)*sin(x)/x,x, algorithm=""fricas"")","\frac{1}{2} \, \operatorname{Si}\left(2 \, x\right)"," ",0,"1/2*sin_integral(2*x)","A",0
11,1,24,0,0.763431," ","integrate(cos(x)*sin(x)/x^2,x, algorithm=""fricas"")","\frac{x \operatorname{Ci}\left(2 \, x\right) + x \operatorname{Ci}\left(-2 \, x\right) - 2 \, \cos\left(x\right) \sin\left(x\right)}{2 \, x}"," ",0,"1/2*(x*cos_integral(2*x) + x*cos_integral(-2*x) - 2*cos(x)*sin(x))/x","A",0
12,1,30,0,0.505636," ","integrate(cos(x)*sin(x)/x^3,x, algorithm=""fricas"")","-\frac{2 \, x \cos\left(x\right)^{2} + 2 \, x^{2} \operatorname{Si}\left(2 \, x\right) + \cos\left(x\right) \sin\left(x\right) - x}{2 \, x^{2}}"," ",0,"-1/2*(2*x*cos(x)^2 + 2*x^2*sin_integral(2*x) + cos(x)*sin(x) - x)/x^2","A",0
13,1,186,0,0.614902," ","integrate((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{-i \, e^{\left(-\frac{d m \log\left(\frac{3 i \, b}{d}\right) - 3 i \, b c + 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, b d x + 3 i \, b c}{d}\right) + 3 i \, e^{\left(-\frac{d m \log\left(\frac{i \, b}{d}\right) - i \, b c + i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{i \, b d x + i \, b c}{d}\right) - 3 i \, e^{\left(-\frac{d m \log\left(-\frac{i \, b}{d}\right) + i \, b c - i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-i \, b d x - i \, b c}{d}\right) + i \, e^{\left(-\frac{d m \log\left(-\frac{3 i \, b}{d}\right) + 3 i \, b c - 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, b d x - 3 i \, b c}{d}\right)}{24 \, b}"," ",0,"1/24*(-I*e^(-(d*m*log(3*I*b/d) - 3*I*b*c + 3*I*a*d)/d)*gamma(m + 1, (3*I*b*d*x + 3*I*b*c)/d) + 3*I*e^(-(d*m*log(I*b/d) - I*b*c + I*a*d)/d)*gamma(m + 1, (I*b*d*x + I*b*c)/d) - 3*I*e^(-(d*m*log(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d) + I*e^(-(d*m*log(-3*I*b/d) + 3*I*b*c - 3*I*a*d)/d)*gamma(m + 1, (-3*I*b*d*x - 3*I*b*c)/d))/b","A",0
14,1,352,0,0.544354," ","integrate((d*x+c)^4*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d - 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{3} - 36 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d - 14 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} - 14 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right) - {\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} - 252 \, b^{2} c^{2} d^{2} + 488 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} - 14 \, b^{2} d^{4}\right)} x^{2} - {\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} - 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d - 2 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 36 \, {\left(3 \, b^{4} c^{3} d - 14 \, b^{2} c d^{3}\right)} x\right)} \sin\left(b x + a\right)}{81 \, b^{5}}"," ",0,"-1/81*(12*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d - 2*b*c*d^3 + (9*b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^3 - 36*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d - 14*b*c*d^3 + (9*b^3*c^2*d^2 - 14*b*d^4)*x)*cos(b*x + a) - (27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 - 252*b^2*c^2*d^2 + 488*d^4 + 18*(9*b^4*c^2*d^2 - 14*b^2*d^4)*x^2 - (27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 - 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d - 2*b^2*c*d^3)*x)*cos(b*x + a)^2 + 36*(3*b^4*c^3*d - 14*b^2*c*d^3)*x)*sin(b*x + a))/b^5","A",0
15,1,227,0,0.494465," ","integrate((d*x+c)^3*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 14 \, d^{3}\right)} \cos\left(b x + a\right) - 3 \, {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} - 14 \, b c d^{2} - {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} - 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + {\left(9 \, b^{3} c^{2} d - 14 \, b d^{3}\right)} x\right)} \sin\left(b x + a\right)}{27 \, b^{4}}"," ",0,"-1/27*((9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 2*d^3)*cos(b*x + a)^3 - 3*(9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 14*d^3)*cos(b*x + a) - 3*(3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 - 14*b*c*d^2 - (3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 - 2*b*c*d^2 + (9*b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + (9*b^3*c^2*d - 14*b*d^3)*x)*sin(b*x + a))/b^4","A",0
16,1,130,0,0.485242," ","integrate((d*x+c)^2*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} - 18 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} - {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - 14 \, d^{2}\right)} \sin\left(b x + a\right)}{27 \, b^{3}}"," ",0,"-1/27*(6*(b*d^2*x + b*c*d)*cos(b*x + a)^3 - 18*(b*d^2*x + b*c*d)*cos(b*x + a) - (9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 - (9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 - 2*d^2)*cos(b*x + a)^2 - 14*d^2)*sin(b*x + a))/b^3","A",0
17,1,59,0,0.800908," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{d \cos\left(b x + a\right)^{3} - 3 \, d \cos\left(b x + a\right) - 3 \, {\left(b d x - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + b c\right)} \sin\left(b x + a\right)}{9 \, b^{2}}"," ",0,"-1/9*(d*cos(b*x + a)^3 - 3*d*cos(b*x + a) - 3*(b*d*x - (b*d*x + b*c)*cos(b*x + a)^2 + b*c)*sin(b*x + a))/b^2","A",0
18,1,153,0,0.493299," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - {\left(\operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 2 \, \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right)}{8 \, d}"," ",0,"1/8*((cos_integral((b*d*x + b*c)/d) + cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) - (cos_integral(3*(b*d*x + b*c)/d) + cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) + 2*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 2*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
19,1,236,0,0.596694," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{8 \, d \cos\left(b x + a\right)^{3} + 6 \, {\left(b d x + b c\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left(b d x + b c\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 8 \, d \cos\left(b x + a\right) - {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/8*(8*d*cos(b*x + a)^3 + 6*(b*d*x + b*c)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 2*(b*d*x + b*c)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - 8*d*cos(b*x + a) - ((b*d*x + b*c)*cos_integral((b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + 3*((b*d*x + b*c)*cos_integral(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
20,1,399,0,0.546010," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{8 \, d^{2} \cos\left(b x + a\right)^{3} - 8 \, d^{2} \cos\left(b x + a\right) - 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 8 \, {\left(b d^{2} x + b c d - 3 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{16 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/16*(8*d^2*cos(b*x + a)^3 - 8*d^2*cos(b*x + a) - 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) + 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) + 8*(b*d^2*x + b*c*d - 3*(b*d^2*x + b*c*d)*cos(b*x + a)^2)*sin(b*x + a))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
21,1,564,0,0.725908," ","integrate(cos(b*x+a)*sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{8 \, {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{3} + 54 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 8 \, {\left(7 \, b^{2} d^{3} x^{2} + 14 \, b^{2} c d^{2} x + 7 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) - 8 \, {\left(b d^{3} x + b c d^{2} - 3 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right) - {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + 27 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{48 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/48*(8*(9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 2*d^3)*cos(b*x + a)^3 + 54*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - 8*(7*b^2*d^3*x^2 + 14*b^2*c*d^2*x + 7*b^2*c^2*d - 2*d^3)*cos(b*x + a) - 8*(b*d^3*x + b*c*d^2 - 3*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*sin(b*x + a) - ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral((b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + 27*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(3*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
22,1,184,0,0.495058," ","integrate((d*x+c)^m*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{e^{\left(-\frac{d m \log\left(\frac{4 i \, b}{d}\right) - 4 i \, b c + 4 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{4 i \, b d x + 4 i \, b c}{d}\right) - 4 \, e^{\left(-\frac{d m \log\left(\frac{2 i \, b}{d}\right) - 2 i \, b c + 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, b d x + 2 i \, b c}{d}\right) - 4 \, e^{\left(-\frac{d m \log\left(-\frac{2 i \, b}{d}\right) + 2 i \, b c - 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, b d x - 2 i \, b c}{d}\right) + e^{\left(-\frac{d m \log\left(-\frac{4 i \, b}{d}\right) + 4 i \, b c - 4 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-4 i \, b d x - 4 i \, b c}{d}\right)}{64 \, b}"," ",0,"1/64*(e^(-(d*m*log(4*I*b/d) - 4*I*b*c + 4*I*a*d)/d)*gamma(m + 1, (4*I*b*d*x + 4*I*b*c)/d) - 4*e^(-(d*m*log(2*I*b/d) - 2*I*b*c + 2*I*a*d)/d)*gamma(m + 1, (2*I*b*d*x + 2*I*b*c)/d) - 4*e^(-(d*m*log(-2*I*b/d) + 2*I*b*c - 2*I*a*d)/d)*gamma(m + 1, (-2*I*b*d*x - 2*I*b*c)/d) + e^(-(d*m*log(-4*I*b/d) + 4*I*b*c - 4*I*a*d)/d)*gamma(m + 1, (-4*I*b*d*x - 4*I*b*c)/d))/b","A",0
23,1,434,0,0.593611," ","integrate((d*x+c)^4*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{20 \, b^{4} d^{4} x^{4} + 80 \, b^{4} c d^{3} x^{3} + {\left(32 \, b^{4} d^{4} x^{4} + 128 \, b^{4} c d^{3} x^{3} + 32 \, b^{4} c^{4} - 24 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 24 \, {\left(8 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 16 \, {\left(8 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} + 3 \, {\left(40 \, b^{4} c^{2} d^{2} - 17 \, b^{2} d^{4}\right)} x^{2} - {\left(64 \, b^{4} d^{4} x^{4} + 256 \, b^{4} c d^{3} x^{3} + 64 \, b^{4} c^{4} - 120 \, b^{2} c^{2} d^{2} + 51 \, d^{4} + 24 \, {\left(16 \, b^{4} c^{2} d^{2} - 5 \, b^{2} d^{4}\right)} x^{2} + 16 \, {\left(16 \, b^{4} c^{3} d - 15 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(40 \, b^{4} c^{3} d - 51 \, b^{2} c d^{3}\right)} x - 2 \, {\left(2 \, {\left(8 \, b^{3} d^{4} x^{3} + 24 \, b^{3} c d^{3} x^{2} + 8 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(8 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(40 \, b^{3} d^{4} x^{3} + 120 \, b^{3} c d^{3} x^{2} + 40 \, b^{3} c^{3} d - 51 \, b c d^{3} + 3 \, {\left(40 \, b^{3} c^{2} d^{2} - 17 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{128 \, b^{5}}"," ",0,"1/128*(20*b^4*d^4*x^4 + 80*b^4*c*d^3*x^3 + (32*b^4*d^4*x^4 + 128*b^4*c*d^3*x^3 + 32*b^4*c^4 - 24*b^2*c^2*d^2 + 3*d^4 + 24*(8*b^4*c^2*d^2 - b^2*d^4)*x^2 + 16*(8*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)^4 + 3*(40*b^4*c^2*d^2 - 17*b^2*d^4)*x^2 - (64*b^4*d^4*x^4 + 256*b^4*c*d^3*x^3 + 64*b^4*c^4 - 120*b^2*c^2*d^2 + 51*d^4 + 24*(16*b^4*c^2*d^2 - 5*b^2*d^4)*x^2 + 16*(16*b^4*c^3*d - 15*b^2*c*d^3)*x)*cos(b*x + a)^2 + 2*(40*b^4*c^3*d - 51*b^2*c*d^3)*x - 2*(2*(8*b^3*d^4*x^3 + 24*b^3*c*d^3*x^2 + 8*b^3*c^3*d - 3*b*c*d^3 + 3*(8*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^3 - (40*b^3*d^4*x^3 + 120*b^3*c*d^3*x^2 + 40*b^3*c^3*d - 51*b*c*d^3 + 3*(40*b^3*c^2*d^2 - 17*b*d^4)*x)*cos(b*x + a))*sin(b*x + a))/b^5","A",0
24,1,283,0,0.486260," ","integrate((d*x+c)^3*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{40 \, b^{3} d^{3} x^{3} + 120 \, b^{3} c d^{2} x^{2} + 8 \, {\left(8 \, b^{3} d^{3} x^{3} + 24 \, b^{3} c d^{2} x^{2} + 8 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(8 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - 8 \, {\left(16 \, b^{3} d^{3} x^{3} + 48 \, b^{3} c d^{2} x^{2} + 16 \, b^{3} c^{3} - 15 \, b c d^{2} + 3 \, {\left(16 \, b^{3} c^{2} d - 5 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(40 \, b^{3} c^{2} d - 17 \, b d^{3}\right)} x - 3 \, {\left(2 \, {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(40 \, b^{2} d^{3} x^{2} + 80 \, b^{2} c d^{2} x + 40 \, b^{2} c^{2} d - 17 \, d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{256 \, b^{4}}"," ",0,"1/256*(40*b^3*d^3*x^3 + 120*b^3*c*d^2*x^2 + 8*(8*b^3*d^3*x^3 + 24*b^3*c*d^2*x^2 + 8*b^3*c^3 - 3*b*c*d^2 + 3*(8*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^4 - 8*(16*b^3*d^3*x^3 + 48*b^3*c*d^2*x^2 + 16*b^3*c^3 - 15*b*c*d^2 + 3*(16*b^3*c^2*d - 5*b*d^3)*x)*cos(b*x + a)^2 + 3*(40*b^3*c^2*d - 17*b*d^3)*x - 3*(2*(8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^3 - (40*b^2*d^3*x^2 + 80*b^2*c*d^2*x + 40*b^2*c^2*d - 17*d^3)*cos(b*x + a))*sin(b*x + a))/b^4","A",0
25,1,159,0,0.455034," ","integrate((d*x+c)^2*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{5 \, b^{2} d^{2} x^{2} + 10 \, b^{2} c d x + {\left(8 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c d x + 8 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(16 \, b^{2} d^{2} x^{2} + 32 \, b^{2} c d x + 16 \, b^{2} c^{2} - 5 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - 2 \, {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} - 5 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{32 \, b^{3}}"," ",0,"1/32*(5*b^2*d^2*x^2 + 10*b^2*c*d*x + (8*b^2*d^2*x^2 + 16*b^2*c*d*x + 8*b^2*c^2 - d^2)*cos(b*x + a)^4 - (16*b^2*d^2*x^2 + 32*b^2*c*d*x + 16*b^2*c^2 - 5*d^2)*cos(b*x + a)^2 - 2*(2*(b*d^2*x + b*c*d)*cos(b*x + a)^3 - 5*(b*d^2*x + b*c*d)*cos(b*x + a))*sin(b*x + a))/b^3","A",0
26,1,76,0,0.438867," ","integrate((d*x+c)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{4} + 5 \, b d x - 16 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - {\left(2 \, d \cos\left(b x + a\right)^{3} - 5 \, d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{32 \, b^{2}}"," ",0,"1/32*(8*(b*d*x + b*c)*cos(b*x + a)^4 + 5*b*d*x - 16*(b*d*x + b*c)*cos(b*x + a)^2 - (2*d*cos(b*x + a)^3 - 5*d*cos(b*x + a))*sin(b*x + a))/b^2","A",0
27,1,156,0,0.486906," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(\operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(\operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + 4 \, \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right)}{16 \, d}"," ",0,"1/16*(2*(cos_integral(2*(b*d*x + b*c)/d) + cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) - (cos_integral(4*(b*d*x + b*c)/d) + cos_integral(-4*(b*d*x + b*c)/d))*sin(-4*(b*c - a*d)/d) - 2*cos(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + 4*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d))/d","A",0
28,1,245,0,0.512942," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b d x + b c\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left(b d x + b c\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left(d \cos\left(b x + a\right)^{3} - d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{4 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/4*(2*(b*d*x + b*c)*sin(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) - 2*(b*d*x + b*c)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + ((b*d*x + b*c)*cos_integral(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) - ((b*d*x + b*c)*cos_integral(4*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-4*(b*d*x + b*c)/d))*cos(-4*(b*c - a*d)/d) + 4*(d*cos(b*x + a)^3 - d*cos(b*x + a))*sin(b*x + a))/(d^3*x + c*d^2)","A",0
29,1,423,0,0.648696," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{4} + 2 \, b d^{2} x + 2 \, b c d - 10 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{3} - d^{2} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/4*(8*(b*d^2*x + b*c*d)*cos(b*x + a)^4 + 2*b*d^2*x + 2*b*c*d - 10*(b*d^2*x + b*c*d)*cos(b*x + a)^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + 2*(d^2*cos(b*x + a)^3 - d^2*cos(b*x + a))*sin(b*x + a) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) + 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(4*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-4*(b*d*x + b*c)/d))*sin(-4*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
30,1,588,0,0.695482," ","integrate(cos(b*x+a)*sin(b*x+a)^3/(d*x+c)^4,x, algorithm=""fricas"")","\frac{b d^{3} x + 4 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} + b c d^{2} - 5 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} - 8 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left({\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(5 \, b^{2} d^{3} x^{2} + 10 \, b^{2} c d^{2} x + 5 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{6 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/6*(b*d^3*x + 4*(b*d^3*x + b*c*d^2)*cos(b*x + a)^4 + b*c*d^2 - 5*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2 - 8*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) + 4*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(4*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-4*(b*d*x + b*c)/d))*cos(-4*(b*c - a*d)/d) - 2*((8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^3 - (5*b^2*d^3*x^2 + 10*b^2*c*d^2*x + 5*b^2*c^2*d - d^3)*cos(b*x + a))*sin(b*x + a))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
31,0,0,0,0.479231," ","integrate((d*x+c)^m*cos(b*x+a)*csc(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cos\left(b x + a\right) \csc\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*cos(b*x + a)*csc(b*x + a), x)","F",0
32,1,1204,0,0.602105," ","integrate((d*x+c)^4*cos(b*x+a)*csc(b*x+a),x, algorithm=""fricas"")","-\frac{24 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, b^{5}}"," ",0,"-1/2*(24*d^4*polylog(5, cos(b*x + a) + I*sin(b*x + a)) + 24*d^4*polylog(5, cos(b*x + a) - I*sin(b*x + a)) + 24*d^4*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) + 24*d^4*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/b^5","C",0
33,1,814,0,0.579529," ","integrate((d*x+c)^3*cos(b*x+a)*csc(b*x+a),x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, b^{4}}"," ",0,"1/2*(6*I*d^3*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - 6*I*d^3*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + 6*I*d^3*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 6*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/b^4","C",0
34,1,498,0,0.496444," ","integrate((d*x+c)^2*cos(b*x+a)*csc(b*x+a),x, algorithm=""fricas"")","\frac{2 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right)}{2 \, b^{3}}"," ",0,"1/2*(2*d^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 2*d^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1))/b^3","C",0
35,1,250,0,0.504815," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a),x, algorithm=""fricas"")","\frac{-i \, d {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right)}{2 \, b^{2}}"," ",0,"1/2*(-I*d*dilog(cos(b*x + a) + I*sin(b*x + a)) + I*d*dilog(cos(b*x + a) - I*sin(b*x + a)) + I*d*dilog(-cos(b*x + a) + I*sin(b*x + a)) - I*d*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b*d*x + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b*d*x + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b*c - a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b*c - a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b*d*x + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b*d*x + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1))/b^2","B",0
36,0,0,0,0.513079," ","integrate(cos(b*x+a)*csc(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \csc\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(cos(b*x + a)*csc(b*x + a)/(d*x + c), x)","F",0
37,0,0,0,0.440717," ","integrate(cos(b*x+a)*csc(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \csc\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cos(b*x + a)*csc(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
38,0,0,0,0.450575," ","integrate((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cos\left(b x + a\right) \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*cos(b*x + a)*csc(b*x + a)^2, x)","F",0
39,1,1021,0,0.553471," ","integrate((d*x+c)^4*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} - 12 i \, d^{4} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 i \, d^{4} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 i \, d^{4} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 i \, d^{4} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b^{2} d^{4} x^{2} - 12 i \, b^{2} c d^{3} x - 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b^{2} d^{4} x^{2} + 12 i \, b^{2} c d^{3} x + 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b^{2} d^{4} x^{2} - 12 i \, b^{2} c d^{3} x - 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b^{2} d^{4} x^{2} + 12 i \, b^{2} c d^{3} x + 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right)}{b^{5} \sin\left(b x + a\right)}"," ",0,"-(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 - 12*I*d^4*polylog(4, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*I*d^4*polylog(4, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 12*I*d^4*polylog(4, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*I*d^4*polylog(4, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b^2*d^4*x^2 - 12*I*b^2*c*d^3*x - 6*I*b^2*c^2*d^2)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b^2*d^4*x^2 + 12*I*b^2*c*d^3*x + 6*I*b^2*c^2*d^2)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b^2*d^4*x^2 - 12*I*b^2*c*d^3*x - 6*I*b^2*c^2*d^2)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b^2*d^4*x^2 + 12*I*b^2*c*d^3*x + 6*I*b^2*c^2*d^2)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 12*(b*d^4*x + b*c*d^3)*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 12*(b*d^4*x + b*c*d^3)*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 12*(b*d^4*x + b*c*d^3)*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*(b*d^4*x + b*c*d^3)*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a))/(b^5*sin(b*x + a))","C",0
40,1,669,0,0.547075," ","integrate((d*x+c)^3*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right)}{2 \, b^{4} \sin\left(b x + a\right)}"," ",0,"-1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 - 6*d^3*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 6*d^3*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 6*d^3*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 6*d^3*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a))/(b^4*sin(b*x + a))","C",0
41,1,375,0,0.531720," ","integrate((d*x+c)^2*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + i \, d^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(b d^{2} x + b c d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d^{2} x + b c d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right)}{b^{3} \sin\left(b x + a\right)}"," ",0,"-(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + I*d^2*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - I*d^2*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + I*d^2*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - I*d^2*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + (b*d^2*x + b*c*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + (b*d^2*x + b*c*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - (b*c*d - a*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - (b*c*d - a*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - (b*d^2*x + a*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - (b*d^2*x + a*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a))/(b^3*sin(b*x + a))","B",0
42,1,62,0,0.472777," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b d x + d \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - d \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 2 \, b c}{2 \, b^{2} \sin\left(b x + a\right)}"," ",0,"-1/2*(2*b*d*x + d*log(1/2*cos(b*x + a) + 1/2)*sin(b*x + a) - d*log(-1/2*cos(b*x + a) + 1/2)*sin(b*x + a) + 2*b*c)/(b^2*sin(b*x + a))","B",0
43,0,0,0,0.492916," ","integrate(cos(b*x+a)*csc(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \csc\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(cos(b*x + a)*csc(b*x + a)^2/(d*x + c), x)","F",0
44,0,0,0,0.534747," ","integrate(cos(b*x+a)*csc(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \csc\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cos(b*x + a)*csc(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
45,0,0,0,0.492208," ","integrate((d*x+c)^m*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cos\left(b x + a\right) \csc\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*x + c)^m*cos(b*x + a)*csc(b*x + a)^3, x)","F",0
46,1,1071,0,0.698790," ","integrate((d*x+c)^4*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} + 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(12 i \, b d^{4} x + 12 i \, b c d^{3} + {\left(-12 i \, b d^{4} x - 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-12 i \, b d^{4} x - 12 i \, b c d^{3} + {\left(12 i \, b d^{4} x + 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-12 i \, b d^{4} x - 12 i \, b c d^{3} + {\left(12 i \, b d^{4} x + 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(12 i \, b d^{4} x + 12 i \, b c d^{3} + {\left(-12 i \, b d^{4} x - 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4} - {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4} - {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 12 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, {\left(b^{5} \cos\left(b x + a\right)^{2} - b^{5}\right)}}"," ",0,"1/2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 + 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*cos(b*x + a)*sin(b*x + a) + (12*I*b*d^4*x + 12*I*b*c*d^3 + (-12*I*b*d^4*x - 12*I*b*c*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (-12*I*b*d^4*x - 12*I*b*c*d^3 + (12*I*b*d^4*x + 12*I*b*c*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-12*I*b*d^4*x - 12*I*b*c*d^3 + (12*I*b*d^4*x + 12*I*b*c*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (12*I*b*d^4*x + 12*I*b*c*d^3 + (-12*I*b*d^4*x - 12*I*b*c*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4 - (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4 - (b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 12*(d^4*cos(b*x + a)^2 - d^4)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 12*(d^4*cos(b*x + a)^2 - d^4)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 12*(d^4*cos(b*x + a)^2 - d^4)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 12*(d^4*cos(b*x + a)^2 - d^4)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^5*cos(b*x + a)^2 - b^5)","C",0
47,1,587,0,0.746057," ","integrate((d*x+c)^3*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3} + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(-3 i \, d^{3} \cos\left(b x + a\right)^{2} + 3 i \, d^{3}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, d^{3} \cos\left(b x + a\right)^{2} - 3 i \, d^{3}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(3 i \, d^{3} \cos\left(b x + a\right)^{2} - 3 i \, d^{3}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, d^{3} \cos\left(b x + a\right)^{2} + 3 i \, d^{3}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b c d^{2} - a d^{3} - {\left(b c d^{2} - a d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left(b c d^{2} - a d^{3} - {\left(b c d^{2} - a d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left(b d^{3} x + a d^{3} - {\left(b d^{3} x + a d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b d^{3} x + a d^{3} - {\left(b d^{3} x + a d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right)}{2 \, {\left(b^{4} \cos\left(b x + a\right)^{2} - b^{4}\right)}}"," ",0,"1/2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a) + (-3*I*d^3*cos(b*x + a)^2 + 3*I*d^3)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*d^3*cos(b*x + a)^2 - 3*I*d^3)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (3*I*d^3*cos(b*x + a)^2 - 3*I*d^3)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-3*I*d^3*cos(b*x + a)^2 + 3*I*d^3)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 3*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 3*(b*c*d^2 - a*d^3 - (b*c*d^2 - a*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 3*(b*c*d^2 - a*d^3 - (b*c*d^2 - a*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 3*(b*d^3*x + a*d^3 - (b*d^3*x + a*d^3)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b*d^3*x + a*d^3 - (b*d^3*x + a*d^3)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1))/(b^4*cos(b*x + a)^2 - b^4)","B",0
48,1,102,0,0.717047," ","integrate((d*x+c)^2*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right)}{2 \, {\left(b^{3} \cos\left(b x + a\right)^{2} - b^{3}\right)}}"," ",0,"1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) + 2*(d^2*cos(b*x + a)^2 - d^2)*log(1/2*sin(b*x + a)))/(b^3*cos(b*x + a)^2 - b^3)","A",0
49,1,44,0,0.583557," ","integrate((d*x+c)*cos(b*x+a)*csc(b*x+a)^3,x, algorithm=""fricas"")","\frac{b d x + d \cos\left(b x + a\right) \sin\left(b x + a\right) + b c}{2 \, {\left(b^{2} \cos\left(b x + a\right)^{2} - b^{2}\right)}}"," ",0,"1/2*(b*d*x + d*cos(b*x + a)*sin(b*x + a) + b*c)/(b^2*cos(b*x + a)^2 - b^2)","A",0
50,0,0,0,1.244688," ","integrate(cos(b*x+a)*csc(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \csc\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(cos(b*x + a)*csc(b*x + a)^3/(d*x + c), x)","F",0
51,0,0,0,0.878592," ","integrate(cos(b*x+a)*csc(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \csc\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cos(b*x + a)*csc(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
52,1,222,0,0.804992," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left(16 \, b^{3} d^{2} x^{2} + 32 \, b^{3} c d x + 16 \, b^{3} c^{2} - 15 \, b d^{2} - 2 \, {\left(16 \, b^{3} d^{2} x^{2} + 32 \, b^{3} c d x + 16 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right)^{2} + 40 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{128 \, b^{4}}"," ",0,"-1/128*(15*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 2*(16*b^3*d^2*x^2 + 32*b^3*c*d*x + 16*b^3*c^2 - 15*b*d^2 - 2*(16*b^3*d^2*x^2 + 32*b^3*c*d*x + 16*b^3*c^2 - 15*b*d^2)*cos(b*x + a)^2 + 40*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
53,1,167,0,0.803219," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(2 \, b^{2} d x + 3 \, b d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, b^{2} c - 4 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sqrt{d x + c}}{32 \, b^{3}}"," ",0,"-1/32*(3*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(2*b^2*d*x + 3*b*d*cos(b*x + a)*sin(b*x + a) + 2*b^2*c - 4*(b^2*d*x + b^2*c)*cos(b*x + a)^2)*sqrt(d*x + c))/b^3","A",0
54,1,125,0,0.749102," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{\pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left(2 \, b \cos\left(b x + a\right)^{2} - b\right)} \sqrt{d x + c}}{8 \, b^{2}}"," ",0,"1/8*(pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 2*(2*b*cos(b*x + a)^2 - b)*sqrt(d*x + c))/b^2","A",0
55,1,125,0,0.468689," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{\pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left(2 \, b \cos\left(b x + a\right)^{2} - b\right)} \sqrt{d x + c}}{8 \, b^{2}}"," ",0,"1/8*(pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 2*(2*b*cos(b*x + a)^2 - b)*sqrt(d*x + c))/b^2","A",0
56,1,167,0,0.501437," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(2 \, b^{2} d x + 3 \, b d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, b^{2} c - 4 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sqrt{d x + c}}{32 \, b^{3}}"," ",0,"-1/32*(3*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(2*b^2*d*x + 3*b*d*cos(b*x + a)*sin(b*x + a) + 2*b^2*c - 4*(b^2*d*x + b^2*c)*cos(b*x + a)^2)*sqrt(d*x + c))/b^3","A",0
57,1,222,0,0.677121," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left(16 \, b^{3} d^{2} x^{2} + 32 \, b^{3} c d x + 16 \, b^{3} c^{2} - 15 \, b d^{2} - 2 \, {\left(16 \, b^{3} d^{2} x^{2} + 32 \, b^{3} c d x + 16 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right)^{2} + 40 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{128 \, b^{4}}"," ",0,"-1/128*(15*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 2*(16*b^3*d^2*x^2 + 32*b^3*c*d*x + 16*b^3*c^2 - 15*b*d^2 - 2*(16*b^3*d^2*x^2 + 32*b^3*c*d*x + 16*b^3*c^2 - 15*b*d^2)*cos(b*x + a)^2 + 40*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
58,1,370,0,0.590991," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 24 \, {\left(10 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 30 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) - {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 35 \, b d^{2} - {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{864 \, b^{4}}"," ",0,"-1/864*(5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 24*(10*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 30*(b^2*d^2*x + b^2*c*d)*cos(b*x + a) - (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 35*b*d^2 - (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
59,1,298,0,0.632224," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(b d \cos\left(b x + a\right)^{3} - 3 \, b d \cos\left(b x + a\right) - 2 \, {\left(b^{2} d x + b^{2} c - {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{144 \, b^{3}}"," ",0,"1/144*(sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(b*d*cos(b*x + a)^3 - 3*b*d*cos(b*x + a) - 2*(b^2*d*x + b^2*c - (b^2*d*x + b^2*c)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
60,1,245,0,0.560867," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sqrt{d x + c} \sin\left(b x + a\right)}{72 \, b^{2}}"," ",0,"1/72*(sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(b*cos(b*x + a)^2 - b)*sqrt(d*x + c)*sin(b*x + a))/b^2","A",0
61,1,245,0,0.629015," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)} \sqrt{d x + c} \sin\left(b x + a\right)}{72 \, b^{2}}"," ",0,"1/72*(sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(b*cos(b*x + a)^2 - b)*sqrt(d*x + c)*sin(b*x + a))/b^2","A",0
62,1,298,0,0.823747," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{\sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(b d \cos\left(b x + a\right)^{3} - 3 \, b d \cos\left(b x + a\right) - 2 \, {\left(b^{2} d x + b^{2} c - {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{144 \, b^{3}}"," ",0,"1/144*(sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(b*d*cos(b*x + a)^3 - 3*b*d*cos(b*x + a) - 2*(b^2*d*x + b^2*c - (b^2*d*x + b^2*c)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
63,1,370,0,0.692205," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 24 \, {\left(10 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 30 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) - {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 35 \, b d^{2} - {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{864 \, b^{4}}"," ",0,"-1/864*(5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 24*(10*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 30*(b^2*d^2*x + b^2*c*d)*cos(b*x + a) - (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 35*b*d^2 - (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
64,1,406,0,0.879714," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left(320 \, b^{3} d^{2} x^{2} + 640 \, b^{3} c d x + 320 \, b^{3} c^{2} + 8 \, {\left(64 \, b^{3} d^{2} x^{2} + 128 \, b^{3} c d x + 64 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 255 \, b d^{2} - 8 \, {\left(128 \, b^{3} d^{2} x^{2} + 256 \, b^{3} c d x + 128 \, b^{3} c^{2} - 75 \, b d^{2}\right)} \cos\left(b x + a\right)^{2} - 160 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 5 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{8192 \, b^{4}}"," ",0,"1/8192*(15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 480*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 480*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 4*(320*b^3*d^2*x^2 + 640*b^3*c*d*x + 320*b^3*c^2 + 8*(64*b^3*d^2*x^2 + 128*b^3*c*d*x + 64*b^3*c^2 - 15*b*d^2)*cos(b*x + a)^4 - 255*b*d^2 - 8*(128*b^3*d^2*x^2 + 256*b^3*c*d*x + 128*b^3*c^2 - 75*b*d^2)*cos(b*x + a)^2 - 160*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 5*(b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
65,1,316,0,0.583374," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 16 \, {\left(16 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} + 10 \, b^{2} d x + 10 \, b^{2} c - 32 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2} - 3 \, {\left(2 \, b d \cos\left(b x + a\right)^{3} - 5 \, b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{1024 \, b^{3}}"," ",0,"1/1024*(3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 48*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 48*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 16*(16*(b^2*d*x + b^2*c)*cos(b*x + a)^4 + 10*b^2*d*x + 10*b^2*c - 32*(b^2*d*x + b^2*c)*cos(b*x + a)^2 - 3*(2*b*d*cos(b*x + a)^3 - 5*b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
66,1,244,0,0.807363," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 8 \, \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 8 \, \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(8 \, b \cos\left(b x + a\right)^{4} - 16 \, b \cos\left(b x + a\right)^{2} + 5 \, b\right)} \sqrt{d x + c}}{128 \, b^{2}}"," ",0,"-1/128*(sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 8*pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 8*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(8*b*cos(b*x + a)^4 - 16*b*cos(b*x + a)^2 + 5*b)*sqrt(d*x + c))/b^2","A",0
67,1,244,0,0.847471," ","integrate((d*x+c)^(1/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 8 \, \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 8 \, \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(8 \, b \cos\left(b x + a\right)^{4} - 16 \, b \cos\left(b x + a\right)^{2} + 5 \, b\right)} \sqrt{d x + c}}{128 \, b^{2}}"," ",0,"-1/128*(sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 8*pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 8*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(8*b*cos(b*x + a)^4 - 16*b*cos(b*x + a)^2 + 5*b)*sqrt(d*x + c))/b^2","A",0
68,1,316,0,0.678797," ","integrate((d*x+c)^(3/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 16 \, {\left(16 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} + 10 \, b^{2} d x + 10 \, b^{2} c - 32 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2} - 3 \, {\left(2 \, b d \cos\left(b x + a\right)^{3} - 5 \, b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{1024 \, b^{3}}"," ",0,"1/1024*(3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 48*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 48*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 16*(16*(b^2*d*x + b^2*c)*cos(b*x + a)^4 + 10*b^2*d*x + 10*b^2*c - 32*(b^2*d*x + b^2*c)*cos(b*x + a)^2 - 3*(2*b*d*cos(b*x + a)^3 - 5*b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
69,1,406,0,0.911481," ","integrate((d*x+c)^(5/2)*cos(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left(320 \, b^{3} d^{2} x^{2} + 640 \, b^{3} c d x + 320 \, b^{3} c^{2} + 8 \, {\left(64 \, b^{3} d^{2} x^{2} + 128 \, b^{3} c d x + 64 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 255 \, b d^{2} - 8 \, {\left(128 \, b^{3} d^{2} x^{2} + 256 \, b^{3} c d x + 128 \, b^{3} c^{2} - 75 \, b d^{2}\right)} \cos\left(b x + a\right)^{2} - 160 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 5 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{8192 \, b^{4}}"," ",0,"1/8192*(15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 480*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 480*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 4*(320*b^3*d^2*x^2 + 640*b^3*c*d*x + 320*b^3*c^2 + 8*(64*b^3*d^2*x^2 + 128*b^3*c*d*x + 64*b^3*c^2 - 15*b*d^2)*cos(b*x + a)^4 - 255*b*d^2 - 8*(128*b^3*d^2*x^2 + 256*b^3*c*d*x + 128*b^3*c^2 - 75*b*d^2)*cos(b*x + a)^2 - 160*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 5*(b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
70,1,184,0,0.682679," ","integrate((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-\frac{d m \log\left(\frac{3 i \, b}{d}\right) - 3 i \, b c + 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, b d x + 3 i \, b c}{d}\right) + 3 \, e^{\left(-\frac{d m \log\left(\frac{i \, b}{d}\right) - i \, b c + i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{i \, b d x + i \, b c}{d}\right) + 3 \, e^{\left(-\frac{d m \log\left(-\frac{i \, b}{d}\right) + i \, b c - i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-i \, b d x - i \, b c}{d}\right) + e^{\left(-\frac{d m \log\left(-\frac{3 i \, b}{d}\right) + 3 i \, b c - 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, b d x - 3 i \, b c}{d}\right)}{24 \, b}"," ",0,"-1/24*(e^(-(d*m*log(3*I*b/d) - 3*I*b*c + 3*I*a*d)/d)*gamma(m + 1, (3*I*b*d*x + 3*I*b*c)/d) + 3*e^(-(d*m*log(I*b/d) - I*b*c + I*a*d)/d)*gamma(m + 1, (I*b*d*x + I*b*c)/d) + 3*e^(-(d*m*log(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d) + e^(-(d*m*log(-3*I*b/d) + 3*I*b*c - 3*I*a*d)/d)*gamma(m + 1, (-3*I*b*d*x - 3*I*b*c)/d))/b","A",0
71,1,294,0,0.486642," ","integrate((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{{\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} - 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d - 2 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - 24 \, {\left(9 \, b^{2} d^{4} x^{2} + 18 \, b^{2} c d^{3} x + 9 \, b^{2} c^{2} d^{2} - 20 \, d^{4}\right)} \cos\left(b x + a\right) - 12 \, {\left(6 \, b^{3} d^{4} x^{3} + 18 \, b^{3} c d^{3} x^{2} + 6 \, b^{3} c^{3} d - 40 \, b c d^{3} + {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d - 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(9 \, b^{3} c^{2} d^{2} - 20 \, b d^{4}\right)} x\right)} \sin\left(b x + a\right)}{81 \, b^{5}}"," ",0,"-1/81*((27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 - 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d - 2*b^2*c*d^3)*x)*cos(b*x + a)^3 - 24*(9*b^2*d^4*x^2 + 18*b^2*c*d^3*x + 9*b^2*c^2*d^2 - 20*d^4)*cos(b*x + a) - 12*(6*b^3*d^4*x^3 + 18*b^3*c*d^3*x^2 + 6*b^3*c^3*d - 40*b*c*d^3 + (3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d - 2*b*c*d^3 + (9*b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^2 + 2*(9*b^3*c^2*d^2 - 20*b*d^4)*x)*sin(b*x + a))/b^5","A",0
72,1,183,0,0.701868," ","integrate((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} - 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - 36 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) - {\left(18 \, b^{2} d^{3} x^{2} + 36 \, b^{2} c d^{2} x + 18 \, b^{2} c^{2} d - 40 \, d^{3} + {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{27 \, b^{4}}"," ",0,"-1/27*(3*(3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 - 2*b*c*d^2 + (9*b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^3 - 36*(b*d^3*x + b*c*d^2)*cos(b*x + a) - (18*b^2*d^3*x^2 + 36*b^2*c*d^2*x + 18*b^2*c^2*d - 40*d^3 + (9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 2*d^3)*cos(b*x + a)^2)*sin(b*x + a))/b^4","A",0
73,1,100,0,0.718935," ","integrate((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{3} - 12 \, d^{2} \cos\left(b x + a\right) - 6 \, {\left(2 \, b d^{2} x + 2 \, b c d + {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{27 \, b^{3}}"," ",0,"-1/27*((9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 - 2*d^2)*cos(b*x + a)^3 - 12*d^2*cos(b*x + a) - 6*(2*b*d^2*x + 2*b*c*d + (b*d^2*x + b*c*d)*cos(b*x + a)^2)*sin(b*x + a))/b^3","A",0
74,1,46,0,0.681410," ","integrate((d*x+c)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - {\left(d \cos\left(b x + a\right)^{2} + 2 \, d\right)} \sin\left(b x + a\right)}{9 \, b^{2}}"," ",0,"-1/9*(3*(b*d*x + b*c)*cos(b*x + a)^3 - (d*cos(b*x + a)^2 + 2*d)*sin(b*x + a))/b^2","A",0
75,1,152,0,0.617096," ","integrate(cos(b*x+a)^2*sin(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + {\left(\operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 2 \, \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right)}{8 \, d}"," ",0,"1/8*((cos_integral((b*d*x + b*c)/d) + cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + (cos_integral(3*(b*d*x + b*c)/d) + cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d) + 2*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 2*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
76,1,233,0,0.826955," ","integrate(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{8 \, d \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + 6 \, {\left(b d x + b c\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(b d x + b c\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/8*(8*d*cos(b*x + a)^2*sin(b*x + a) + 6*(b*d*x + b*c)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 2*(b*d*x + b*c)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - ((b*d*x + b*c)*cos_integral((b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) - 3*((b*d*x + b*c)*cos_integral(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
77,1,393,0,0.526170," ","integrate(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{8 \, d^{2} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) + 24 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} + 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 16 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/16*(8*d^2*cos(b*x + a)^2*sin(b*x + a) + 24*(b*d^2*x + b*c*d)*cos(b*x + a)^3 + 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - 16*(b*d^2*x + b*c*d)*cos(b*x + a) + ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
78,1,558,0,0.666142," ","integrate(cos(b*x+a)^2*sin(b*x+a)/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{24 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - 54 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 16 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) + {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 27 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 8 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{48 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/48*(24*(b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - 54*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - 16*(b*d^3*x + b*c*d^2)*cos(b*x + a) + ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral((b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) + 27*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(3*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) + 8*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - (9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 2*d^3)*cos(b*x + a)^2)*sin(b*x + a))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
79,1,134,0,0.590600," ","integrate((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, d m - i \, d\right)} e^{\left(-\frac{d m \log\left(\frac{4 i \, b}{d}\right) - 4 i \, b c + 4 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{4 i \, b d x + 4 i \, b c}{d}\right) + {\left(i \, d m + i \, d\right)} e^{\left(-\frac{d m \log\left(-\frac{4 i \, b}{d}\right) + 4 i \, b c - 4 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-4 i \, b d x - 4 i \, b c}{d}\right) + 8 \, {\left(b d x + b c\right)} {\left(d x + c\right)}^{m}}{64 \, {\left(b d m + b d\right)}}"," ",0,"1/64*((-I*d*m - I*d)*e^(-(d*m*log(4*I*b/d) - 4*I*b*c + 4*I*a*d)/d)*gamma(m + 1, (4*I*b*d*x + 4*I*b*c)/d) + (I*d*m + I*d)*e^(-(d*m*log(-4*I*b/d) + 4*I*b*c - 4*I*a*d)/d)*gamma(m + 1, (-4*I*b*d*x - 4*I*b*c)/d) + 8*(b*d*x + b*c)*(d*x + c)^m)/(b*d*m + b*d)","A",0
80,1,466,0,0.618454," ","integrate((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{32 \, b^{5} d^{4} x^{5} + 160 \, b^{5} c d^{3} x^{4} - 40 \, {\left(8 \, b^{3} d^{4} x^{3} + 24 \, b^{3} c d^{3} x^{2} + 8 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(8 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{4} + 40 \, {\left(8 \, b^{5} c^{2} d^{2} - b^{3} d^{4}\right)} x^{3} + 40 \, {\left(8 \, b^{5} c^{3} d - 3 \, b^{3} c d^{3}\right)} x^{2} + 40 \, {\left(8 \, b^{3} d^{4} x^{3} + 24 \, b^{3} c d^{3} x^{2} + 8 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(8 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} + 5 \, {\left(32 \, b^{5} c^{4} - 24 \, b^{3} c^{2} d^{2} + 3 \, b d^{4}\right)} x - 5 \, {\left(2 \, {\left(32 \, b^{4} d^{4} x^{4} + 128 \, b^{4} c d^{3} x^{3} + 32 \, b^{4} c^{4} - 24 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 24 \, {\left(8 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 16 \, {\left(8 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(32 \, b^{4} d^{4} x^{4} + 128 \, b^{4} c d^{3} x^{3} + 32 \, b^{4} c^{4} - 24 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 24 \, {\left(8 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 16 \, {\left(8 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{1280 \, b^{5}}"," ",0,"1/1280*(32*b^5*d^4*x^5 + 160*b^5*c*d^3*x^4 - 40*(8*b^3*d^4*x^3 + 24*b^3*c*d^3*x^2 + 8*b^3*c^3*d - 3*b*c*d^3 + 3*(8*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^4 + 40*(8*b^5*c^2*d^2 - b^3*d^4)*x^3 + 40*(8*b^5*c^3*d - 3*b^3*c*d^3)*x^2 + 40*(8*b^3*d^4*x^3 + 24*b^3*c*d^3*x^2 + 8*b^3*c^3*d - 3*b*c*d^3 + 3*(8*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^2 + 5*(32*b^5*c^4 - 24*b^3*c^2*d^2 + 3*b*d^4)*x - 5*(2*(32*b^4*d^4*x^4 + 128*b^4*c*d^3*x^3 + 32*b^4*c^4 - 24*b^2*c^2*d^2 + 3*d^4 + 24*(8*b^4*c^2*d^2 - b^2*d^4)*x^2 + 16*(8*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)^3 - (32*b^4*d^4*x^4 + 128*b^4*c*d^3*x^3 + 32*b^4*c^4 - 24*b^2*c^2*d^2 + 3*d^4 + 24*(8*b^4*c^2*d^2 - b^2*d^4)*x^2 + 16*(8*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a))*sin(b*x + a))/b^5","B",0
81,1,308,0,0.500222," ","integrate((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b^{4} d^{3} x^{4} + 16 \, b^{4} c d^{2} x^{3} - 3 \, {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{4} + 3 \, {\left(8 \, b^{4} c^{2} d - b^{2} d^{3}\right)} x^{2} + 3 \, {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(8 \, b^{4} c^{3} - 3 \, b^{2} c d^{2}\right)} x - 2 \, {\left(2 \, {\left(8 \, b^{3} d^{3} x^{3} + 24 \, b^{3} c d^{2} x^{2} + 8 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(8 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(8 \, b^{3} d^{3} x^{3} + 24 \, b^{3} c d^{2} x^{2} + 8 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(8 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{128 \, b^{4}}"," ",0,"1/128*(4*b^4*d^3*x^4 + 16*b^4*c*d^2*x^3 - 3*(8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^4 + 3*(8*b^4*c^2*d - b^2*d^3)*x^2 + 3*(8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^2 + 2*(8*b^4*c^3 - 3*b^2*c*d^2)*x - 2*(2*(8*b^3*d^3*x^3 + 24*b^3*c*d^2*x^2 + 8*b^3*c^3 - 3*b*c*d^2 + 3*(8*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^3 - (8*b^3*d^3*x^3 + 24*b^3*c*d^2*x^2 + 8*b^3*c^3 - 3*b*c*d^2 + 3*(8*b^3*c^2*d - b*d^3)*x)*cos(b*x + a))*sin(b*x + a))/b^4","B",0
82,1,180,0,0.436447," ","integrate((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{8 \, b^{3} d^{2} x^{3} + 24 \, b^{3} c d x^{2} - 24 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{4} + 24 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(8 \, b^{3} c^{2} - b d^{2}\right)} x - 3 \, {\left(2 \, {\left(8 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c d x + 8 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(8 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c d x + 8 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{192 \, b^{3}}"," ",0,"1/192*(8*b^3*d^2*x^3 + 24*b^3*c*d*x^2 - 24*(b*d^2*x + b*c*d)*cos(b*x + a)^4 + 24*(b*d^2*x + b*c*d)*cos(b*x + a)^2 + 3*(8*b^3*c^2 - b*d^2)*x - 3*(2*(8*b^2*d^2*x^2 + 16*b^2*c*d*x + 8*b^2*c^2 - d^2)*cos(b*x + a)^3 - (8*b^2*d^2*x^2 + 16*b^2*c*d*x + 8*b^2*c^2 - d^2)*cos(b*x + a))*sin(b*x + a))/b^3","B",0
83,1,85,0,0.594372," ","integrate((d*x+c)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d x^{2} - d \cos\left(b x + a\right)^{4} + 2 \, b^{2} c x + d \cos\left(b x + a\right)^{2} - 2 \, {\left(2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - {\left(b d x + b c\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{16 \, b^{2}}"," ",0,"1/16*(b^2*d*x^2 - d*cos(b*x + a)^4 + 2*b^2*c*x + d*cos(b*x + a)^2 - 2*(2*(b*d*x + b*c)*cos(b*x + a)^3 - (b*d*x + b*c)*cos(b*x + a))*sin(b*x + a))/b^2","A",0
84,1,88,0,0.493792," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(\operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, \log\left(d x + c\right)}{16 \, d}"," ",0,"-1/16*((cos_integral(4*(b*d*x + b*c)/d) + cos_integral(-4*(b*d*x + b*c)/d))*cos(-4*(b*c - a*d)/d) - 2*sin(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) - 2*log(d*x + c))/d","A",0
85,1,138,0,0.548308," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{4 \, d \cos\left(b x + a\right)^{4} - 4 \, d \cos\left(b x + a\right)^{2} + 2 \, {\left(b d x + b c\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/4*(4*d*cos(b*x + a)^4 - 4*d*cos(b*x + a)^2 + 2*(b*d*x + b*c)*cos(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + ((b*d*x + b*c)*cos_integral(4*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-4*(b*d*x + b*c)/d))*sin(-4*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
86,1,255,0,0.470722," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(4*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-4*(b*d*x + b*c)/d))*cos(-4*(b*c - a*d)/d) - 2*(2*(b*d^2*x + b*c*d)*cos(b*x + a)^3 - (b*d^2*x + b*c*d)*cos(b*x + a))*sin(b*x + a))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
87,1,406,0,0.543151," ","integrate(cos(b*x+a)^2*sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d + {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(2 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right) + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{3 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d + (8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^4 - (8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^2 + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + (2*(b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cos(b*x + a))*sin(b*x + a) + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(4*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-4*(b*d*x + b*c)/d))*sin(-4*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
88,1,276,0,0.721384," ","integrate((d*x+c)^m*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, e^{\left(-\frac{d m \log\left(\frac{5 i \, b}{d}\right) - 5 i \, b c + 5 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{5 i \, b d x + 5 i \, b c}{d}\right) - 5 \, e^{\left(-\frac{d m \log\left(\frac{3 i \, b}{d}\right) - 3 i \, b c + 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, b d x + 3 i \, b c}{d}\right) - 30 \, e^{\left(-\frac{d m \log\left(\frac{i \, b}{d}\right) - i \, b c + i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{i \, b d x + i \, b c}{d}\right) - 30 \, e^{\left(-\frac{d m \log\left(-\frac{i \, b}{d}\right) + i \, b c - i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-i \, b d x - i \, b c}{d}\right) - 5 \, e^{\left(-\frac{d m \log\left(-\frac{3 i \, b}{d}\right) + 3 i \, b c - 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, b d x - 3 i \, b c}{d}\right) + 3 \, e^{\left(-\frac{d m \log\left(-\frac{5 i \, b}{d}\right) + 5 i \, b c - 5 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-5 i \, b d x - 5 i \, b c}{d}\right)}{480 \, b}"," ",0,"1/480*(3*e^(-(d*m*log(5*I*b/d) - 5*I*b*c + 5*I*a*d)/d)*gamma(m + 1, (5*I*b*d*x + 5*I*b*c)/d) - 5*e^(-(d*m*log(3*I*b/d) - 3*I*b*c + 3*I*a*d)/d)*gamma(m + 1, (3*I*b*d*x + 3*I*b*c)/d) - 30*e^(-(d*m*log(I*b/d) - I*b*c + I*a*d)/d)*gamma(m + 1, (I*b*d*x + I*b*c)/d) - 30*e^(-(d*m*log(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d) - 5*e^(-(d*m*log(-3*I*b/d) + 3*I*b*c - 3*I*a*d)/d)*gamma(m + 1, (-3*I*b*d*x - 3*I*b*c)/d) + 3*e^(-(d*m*log(-5*I*b/d) + 5*I*b*c - 5*I*a*d)/d)*gamma(m + 1, (-5*I*b*d*x - 5*I*b*c)/d))/b","A",0
89,1,471,0,0.810528," ","integrate((d*x+c)^4*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{81 \, {\left(625 \, b^{4} d^{4} x^{4} + 2500 \, b^{4} c d^{3} x^{3} + 625 \, b^{4} c^{4} - 300 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 150 \, {\left(25 \, b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 100 \, {\left(25 \, b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{5} - 5 \, {\left(16875 \, b^{4} d^{4} x^{4} + 67500 \, b^{4} c d^{3} x^{3} + 16875 \, b^{4} c^{4} - 11700 \, b^{2} c^{2} d^{2} + 1736 \, d^{4} + 450 \, {\left(225 \, b^{4} c^{2} d^{2} - 26 \, b^{2} d^{4}\right)} x^{2} + 900 \, {\left(75 \, b^{4} c^{3} d - 26 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} + 120 \, {\left(2925 \, b^{2} d^{4} x^{2} + 5850 \, b^{2} c d^{3} x + 2925 \, b^{2} c^{2} d^{2} - 6284 \, d^{4}\right)} \cos\left(b x + a\right) + 60 \, {\left(1950 \, b^{3} d^{4} x^{3} + 5850 \, b^{3} c d^{3} x^{2} + 1950 \, b^{3} c^{3} d - 12568 \, b c d^{3} - 27 \, {\left(25 \, b^{3} d^{4} x^{3} + 75 \, b^{3} c d^{3} x^{2} + 25 \, b^{3} c^{3} d - 6 \, b c d^{3} + 3 \, {\left(25 \, b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{4} + {\left(975 \, b^{3} d^{4} x^{3} + 2925 \, b^{3} c d^{3} x^{2} + 975 \, b^{3} c^{3} d - 434 \, b c d^{3} + {\left(2925 \, b^{3} c^{2} d^{2} - 434 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(2925 \, b^{3} c^{2} d^{2} - 6284 \, b d^{4}\right)} x\right)} \sin\left(b x + a\right)}{253125 \, b^{5}}"," ",0,"1/253125*(81*(625*b^4*d^4*x^4 + 2500*b^4*c*d^3*x^3 + 625*b^4*c^4 - 300*b^2*c^2*d^2 + 24*d^4 + 150*(25*b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 100*(25*b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^5 - 5*(16875*b^4*d^4*x^4 + 67500*b^4*c*d^3*x^3 + 16875*b^4*c^4 - 11700*b^2*c^2*d^2 + 1736*d^4 + 450*(225*b^4*c^2*d^2 - 26*b^2*d^4)*x^2 + 900*(75*b^4*c^3*d - 26*b^2*c*d^3)*x)*cos(b*x + a)^3 + 120*(2925*b^2*d^4*x^2 + 5850*b^2*c*d^3*x + 2925*b^2*c^2*d^2 - 6284*d^4)*cos(b*x + a) + 60*(1950*b^3*d^4*x^3 + 5850*b^3*c*d^3*x^2 + 1950*b^3*c^3*d - 12568*b*c*d^3 - 27*(25*b^3*d^4*x^3 + 75*b^3*c*d^3*x^2 + 25*b^3*c^3*d - 6*b*c*d^3 + 3*(25*b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^4 + (975*b^3*d^4*x^3 + 2925*b^3*c*d^3*x^2 + 975*b^3*c^3*d - 434*b*c*d^3 + (2925*b^3*c^2*d^2 - 434*b*d^4)*x)*cos(b*x + a)^2 + 2*(2925*b^3*c^2*d^2 - 6284*b*d^4)*x)*sin(b*x + a))/b^5","A",0
90,1,296,0,0.532955," ","integrate((d*x+c)^3*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{135 \, {\left(25 \, b^{3} d^{3} x^{3} + 75 \, b^{3} c d^{2} x^{2} + 25 \, b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(25 \, b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{5} - 75 \, {\left(75 \, b^{3} d^{3} x^{3} + 225 \, b^{3} c d^{2} x^{2} + 75 \, b^{3} c^{3} - 26 \, b c d^{2} + {\left(225 \, b^{3} c^{2} d - 26 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} + 11700 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) + {\left(5850 \, b^{2} d^{3} x^{2} + 11700 \, b^{2} c d^{2} x + 5850 \, b^{2} c^{2} d - 81 \, {\left(25 \, b^{2} d^{3} x^{2} + 50 \, b^{2} c d^{2} x + 25 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{4} - 12568 \, d^{3} + {\left(2925 \, b^{2} d^{3} x^{2} + 5850 \, b^{2} c d^{2} x + 2925 \, b^{2} c^{2} d - 434 \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{16875 \, b^{4}}"," ",0,"1/16875*(135*(25*b^3*d^3*x^3 + 75*b^3*c*d^2*x^2 + 25*b^3*c^3 - 6*b*c*d^2 + 3*(25*b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^5 - 75*(75*b^3*d^3*x^3 + 225*b^3*c*d^2*x^2 + 75*b^3*c^3 - 26*b*c*d^2 + (225*b^3*c^2*d - 26*b*d^3)*x)*cos(b*x + a)^3 + 11700*(b*d^3*x + b*c*d^2)*cos(b*x + a) + (5850*b^2*d^3*x^2 + 11700*b^2*c*d^2*x + 5850*b^2*c^2*d - 81*(25*b^2*d^3*x^2 + 50*b^2*c*d^2*x + 25*b^2*c^2*d - 2*d^3)*cos(b*x + a)^4 - 12568*d^3 + (2925*b^2*d^3*x^2 + 5850*b^2*c*d^2*x + 2925*b^2*c^2*d - 434*d^3)*cos(b*x + a)^2)*sin(b*x + a))/b^4","A",0
91,1,166,0,0.470898," ","integrate((d*x+c)^2*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{27 \, {\left(25 \, b^{2} d^{2} x^{2} + 50 \, b^{2} c d x + 25 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{5} - 5 \, {\left(225 \, b^{2} d^{2} x^{2} + 450 \, b^{2} c d x + 225 \, b^{2} c^{2} - 26 \, d^{2}\right)} \cos\left(b x + a\right)^{3} + 780 \, d^{2} \cos\left(b x + a\right) - 30 \, {\left(9 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{4} - 26 \, b d^{2} x - 26 \, b c d - 13 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{3375 \, b^{3}}"," ",0,"1/3375*(27*(25*b^2*d^2*x^2 + 50*b^2*c*d*x + 25*b^2*c^2 - 2*d^2)*cos(b*x + a)^5 - 5*(225*b^2*d^2*x^2 + 450*b^2*c*d*x + 225*b^2*c^2 - 26*d^2)*cos(b*x + a)^3 + 780*d^2*cos(b*x + a) - 30*(9*(b*d^2*x + b*c*d)*cos(b*x + a)^4 - 26*b*d^2*x - 26*b*c*d - 13*(b*d^2*x + b*c*d)*cos(b*x + a)^2)*sin(b*x + a))/b^3","A",0
92,1,76,0,0.930999," ","integrate((d*x+c)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{45 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{5} - 75 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - {\left(9 \, d \cos\left(b x + a\right)^{4} - 13 \, d \cos\left(b x + a\right)^{2} - 26 \, d\right)} \sin\left(b x + a\right)}{225 \, b^{2}}"," ",0,"1/225*(45*(b*d*x + b*c)*cos(b*x + a)^5 - 75*(b*d*x + b*c)*cos(b*x + a)^3 - (9*d*cos(b*x + a)^4 - 13*d*cos(b*x + a)^2 - 26*d)*sin(b*x + a))/b^2","A",0
93,1,228,0,0.646821," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(\operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + {\left(\operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(\operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 4 \, \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right)}{32 \, d}"," ",0,"1/32*(2*(cos_integral((b*d*x + b*c)/d) + cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + (cos_integral(3*(b*d*x + b*c)/d) + cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d) - (cos_integral(5*(b*d*x + b*c)/d) + cos_integral(-5*(b*d*x + b*c)/d))*sin(-5*(b*c - a*d)/d) - 2*cos(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) + 2*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 4*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
94,1,347,0,0.909712," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","\frac{10 \, {\left(b d x + b c\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) - 6 \, {\left(b d x + b c\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 4 \, {\left(b d x + b c\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 2 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 5 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 32 \, {\left(d \cos\left(b x + a\right)^{4} - d \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{32 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/32*(10*(b*d*x + b*c)*sin(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) - 6*(b*d*x + b*c)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 4*(b*d*x + b*c)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 2*((b*d*x + b*c)*cos_integral((b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) + 3*((b*d*x + b*c)*cos_integral(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) - 5*((b*d*x + b*c)*cos_integral(5*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-5*(b*d*x + b*c)/d))*cos(-5*(b*c - a*d)/d) + 32*(d*cos(b*x + a)^4 - d*cos(b*x + a)^2)*sin(b*x + a))/(d^3*x + c*d^2)","A",0
95,1,585,0,0.825969," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{160 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{5} - 224 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} + 50 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) - 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 64 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + 32 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right) - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) - 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 25 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{64 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/64*(160*(b*d^2*x + b*c*d)*cos(b*x + a)^5 - 224*(b*d^2*x + b*c*d)*cos(b*x + a)^3 + 50*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) - 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 64*(b*d^2*x + b*c*d)*cos(b*x + a) + 32*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*sin(b*x + a) - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) - 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d) + 25*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(5*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-5*(b*d*x + b*c)/d))*sin(-5*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
96,1,824,0,0.618378," ","integrate(cos(b*x+a)^2*sin(b*x+a)^3/(d*x+c)^4,x, algorithm=""fricas"")","\frac{160 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{5} - 224 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - 250 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + 54 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 64 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) - 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - 27 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 125 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 32 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + {\left(25 \, b^{2} d^{3} x^{2} + 50 \, b^{2} c d^{2} x + 25 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(21 \, b^{2} d^{3} x^{2} + 42 \, b^{2} c d^{2} x + 21 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{192 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/192*(160*(b*d^3*x + b*c*d^2)*cos(b*x + a)^5 - 224*(b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - 250*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) + 54*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 64*(b*d^3*x + b*c*d^2)*cos(b*x + a) - 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral((b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) - 27*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(3*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) + 125*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(5*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-5*(b*d*x + b*c)/d))*cos(-5*(b*c - a*d)/d) - 32*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + (25*b^2*d^3*x^2 + 50*b^2*c*d^2*x + 25*b^2*c^2*d - 2*d^3)*cos(b*x + a)^4 - (21*b^2*d^3*x^2 + 42*b^2*c*d^2*x + 21*b^2*c^2*d - 2*d^3)*cos(b*x + a)^2)*sin(b*x + a))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
97,0,0,0,0.532411," ","integrate((d*x+c)^m*cos(b*x+a)*cot(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cos\left(b x + a\right) \cot\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*cos(b*x + a)*cot(b*x + a), x)","F",0
98,1,1367,0,0.749636," ","integrate((d*x+c)^4*cos(b*x+a)*cot(b*x+a),x, algorithm=""fricas"")","-\frac{24 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 8 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + b^{3} c^{3} d - 6 \, b c d^{3} + 3 \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \sin\left(b x + a\right)}{2 \, b^{5}}"," ",0,"-1/2*(24*d^4*polylog(5, cos(b*x + a) + I*sin(b*x + a)) + 24*d^4*polylog(5, cos(b*x + a) - I*sin(b*x + a)) - 24*d^4*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) - 24*d^4*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) - 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 - 12*b^2*c^2*d^2 + 24*d^4 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 8*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + b^3*c^3*d - 6*b*c*d^3 + 3*(b^3*c^2*d^2 - 2*b*d^4)*x)*sin(b*x + a))/b^5","C",0
99,1,921,0,0.785470," ","integrate((d*x+c)^3*cos(b*x+a)*cot(b*x+a),x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \sin\left(b x + a\right)}{2 \, b^{4}}"," ",0,"1/2*(6*I*d^3*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + 6*I*d^3*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 6*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*sin(b*x + a))/b^4","C",0
100,1,558,0,1.544142," ","integrate((d*x+c)^2*cos(b*x+a)*cot(b*x+a),x, algorithm=""fricas"")","\frac{2 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(2*d^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 2*d^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 2*d^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 4*(b*d^2*x + b*c*d)*sin(b*x + a))/b^3","C",0
101,1,277,0,0.647812," ","integrate((d*x+c)*cos(b*x+a)*cot(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) - i \, d {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 2 \, d \sin\left(b x + a\right)}{2 \, b^{2}}"," ",0,"1/2*(2*(b*d*x + b*c)*cos(b*x + a) - I*d*dilog(cos(b*x + a) + I*sin(b*x + a)) + I*d*dilog(cos(b*x + a) - I*sin(b*x + a)) - I*d*dilog(-cos(b*x + a) + I*sin(b*x + a)) + I*d*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b*d*x + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b*d*x + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b*c - a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b*c - a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b*d*x + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b*d*x + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 2*d*sin(b*x + a))/b^2","B",0
102,0,0,0,0.538538," ","integrate(cos(b*x+a)*cot(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \cot\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(cos(b*x + a)*cot(b*x + a)/(d*x + c), x)","F",0
103,0,0,0,0.691325," ","integrate(cos(b*x+a)*cot(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \cot\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cos(b*x + a)*cot(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
104,0,0,0,0.712646," ","integrate((d*x+c)^m*cot(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cot\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*cot(b*x + a)^2, x)","F",0
105,1,856,0,0.948336," ","integrate((d*x+c)^4*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{10 \, b^{4} d^{4} x^{4} + 40 \, b^{4} c d^{3} x^{3} + 60 \, b^{4} c^{2} d^{2} x^{2} + 40 \, b^{4} c^{3} d x + 10 \, b^{4} c^{4} - 15 i \, d^{4} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) + 15 i \, d^{4} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(-30 i \, b^{2} d^{4} x^{2} - 60 i \, b^{2} c d^{3} x - 30 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(30 i \, b^{2} d^{4} x^{2} + 60 i \, b^{2} c d^{3} x + 30 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 20 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 20 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 20 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 20 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 30 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 30 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) + 10 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b^{5} d^{4} x^{5} + 5 \, b^{5} c d^{3} x^{4} + 10 \, b^{5} c^{2} d^{2} x^{3} + 10 \, b^{5} c^{3} d x^{2} + 5 \, b^{5} c^{4} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{10 \, b^{5} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/10*(10*b^4*d^4*x^4 + 40*b^4*c*d^3*x^3 + 60*b^4*c^2*d^2*x^2 + 40*b^4*c^3*d*x + 10*b^4*c^4 - 15*I*d^4*polylog(4, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) + 15*I*d^4*polylog(4, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - (-30*I*b^2*d^4*x^2 - 60*I*b^2*c*d^3*x - 30*I*b^2*c^2*d^2)*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - (30*I*b^2*d^4*x^2 + 60*I*b^2*c*d^3*x + 30*I*b^2*c^2*d^2)*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 20*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 20*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 20*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 20*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 30*(b*d^4*x + b*c*d^3)*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 30*(b*d^4*x + b*c*d^3)*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) + 10*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*cos(2*b*x + 2*a) + 2*(b^5*d^4*x^5 + 5*b^5*c*d^3*x^4 + 10*b^5*c^2*d^2*x^3 + 10*b^5*c^3*d*x^2 + 5*b^5*c^4*x)*sin(2*b*x + 2*a))/(b^5*sin(2*b*x + 2*a))","C",0
106,1,599,0,0.781790," ","integrate((d*x+c)^3*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b^{3} d^{3} x^{3} + 12 \, b^{3} c d^{2} x^{2} + 12 \, b^{3} c^{2} d x + 4 \, b^{3} c^{3} - 3 \, d^{3} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 3 \, d^{3} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(2 \, b x + 2 \, a\right) + {\left(b^{4} d^{3} x^{4} + 4 \, b^{4} c d^{2} x^{3} + 6 \, b^{4} c^{2} d x^{2} + 4 \, b^{4} c^{3} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{4 \, b^{4} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/4*(4*b^3*d^3*x^3 + 12*b^3*c*d^2*x^2 + 12*b^3*c^2*d*x + 4*b^3*c^3 - 3*d^3*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 3*d^3*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(2*b*x + 2*a) + (b^4*d^3*x^4 + 4*b^4*c*d^2*x^3 + 6*b^4*c^2*d*x^2 + 4*b^4*c^3*x)*sin(2*b*x + 2*a))/(b^4*sin(2*b*x + 2*a))","C",0
107,1,384,0,0.724135," ","integrate((d*x+c)^2*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{6 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c d x + 6 \, b^{2} c^{2} + 3 i \, d^{2} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 3 i \, d^{2} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) - 6 \, {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) \sin\left(2 \, b x + 2 \, a\right) + 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(2 \, b x + 2 \, a\right) + 2 \, {\left(b^{3} d^{2} x^{3} + 3 \, b^{3} c d x^{2} + 3 \, b^{3} c^{2} x\right)} \sin\left(2 \, b x + 2 \, a\right)}{6 \, b^{3} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/6*(6*b^2*d^2*x^2 + 12*b^2*c*d*x + 6*b^2*c^2 + 3*I*d^2*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 3*I*d^2*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a))*sin(2*b*x + 2*a) - 6*(b*c*d - a*d^2)*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*(b*c*d - a*d^2)*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) - 6*(b*d^2*x + a*d^2)*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) - 6*(b*d^2*x + a*d^2)*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1)*sin(2*b*x + 2*a) + 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(2*b*x + 2*a) + 2*(b^3*d^2*x^3 + 3*b^3*c*d*x^2 + 3*b^3*c^2*x)*sin(2*b*x + 2*a))/(b^3*sin(2*b*x + 2*a))","B",0
108,1,97,0,0.587282," ","integrate((d*x+c)*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b d x - d \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\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) + {\left(b^{2} d x^{2} + 2 \, b^{2} c x\right)} \sin\left(2 \, b x + 2 \, a\right)}{2 \, b^{2} \sin\left(2 \, b x + 2 \, a\right)}"," ",0,"-1/2*(2*b*d*x - d*log(-1/2*cos(2*b*x + 2*a) + 1/2)*sin(2*b*x + 2*a) + 2*b*c + 2*(b*d*x + b*c)*cos(2*b*x + 2*a) + (b^2*d*x^2 + 2*b^2*c*x)*sin(2*b*x + 2*a))/(b^2*sin(2*b*x + 2*a))","B",0
109,0,0,0,0.797018," ","integrate(cot(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(cot(b*x + a)^2/(d*x + c), x)","F",0
110,0,0,0,0.560787," ","integrate(cot(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cot(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
111,0,0,0,0.635772," ","integrate((d*x+c)^m*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cot\left(b x + a\right)^{2} \csc\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*cot(b*x + a)^2*csc(b*x + a), x)","F",0
112,1,2762,0,2.057588," ","integrate((d*x+c)^4*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \cos\left(b x + a\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d + 24 i \, b c d^{3} + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d - 24 i \, b c d^{3} + 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} - 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d - 24 i \, b c d^{3} + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d + 24 i \, b c d^{3} - 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} + 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d + 24 i \, b c d^{3} + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d - 24 i \, b c d^{3} + 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} - 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d - 24 i \, b c d^{3} + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d + 24 i \, b c d^{3} - 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} + 12 i \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 2\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} + {\left(a^{4} - 12 \, a^{2}\right)} d^{4} - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 2\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} + {\left(a^{4} - 12 \, a^{2}\right)} d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 2\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} + {\left(a^{4} - 12 \, a^{2}\right)} d^{4} - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 2\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} + {\left(a^{4} - 12 \, a^{2}\right)} d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} - {\left(a^{4} - 12 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} - {\left(a^{4} - 12 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} - {\left(a^{4} - 12 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 6 \, a\right)} b c d^{3} - {\left(a^{4} - 12 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 24 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, {\left(d^{4} \cos\left(b x + a\right)^{2} - d^{4}\right)} {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3} + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3} + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3} + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3} + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - 2 \, d^{4}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 8 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \sin\left(b x + a\right)}{4 \, {\left(b^{5} \cos\left(b x + a\right)^{2} - b^{5}\right)}}"," ",0,"1/4*(2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*cos(b*x + a) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d + 24*I*b*c*d^3 + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d - 24*I*b*c*d^3 + 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^2 - 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d - 24*I*b*c*d^3 + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d + 24*I*b*c*d^3 - 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^2 + 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d + 24*I*b*c*d^3 + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d - 24*I*b*c*d^3 + 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^2 - 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d - 24*I*b*c*d^3 + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d + 24*I*b*c*d^3 - 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^2 + 12*I*(b^3*c^2*d^2 - 2*b*d^4)*x)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 - 12*b^2*c^2*d^2 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 - 12*b^2*c^2*d^2 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 - 12*b^2*c^2*d^2 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 - 12*b^2*c^2*d^2 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 2)*b^2*c^2*d^2 - 4*(a^3 - 6*a)*b*c*d^3 + (a^4 - 12*a^2)*d^4 - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 2)*b^2*c^2*d^2 - 4*(a^3 - 6*a)*b*c*d^3 + (a^4 - 12*a^2)*d^4)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 2)*b^2*c^2*d^2 - 4*(a^3 - 6*a)*b*c*d^3 + (a^4 - 12*a^2)*d^4 - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 2)*b^2*c^2*d^2 - 4*(a^3 - 6*a)*b*c*d^3 + (a^4 - 12*a^2)*d^4)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 6*a)*b*c*d^3 - (a^4 - 12*a^2)*d^4 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 6*a)*b*c*d^3 - (a^4 - 12*a^2)*d^4 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 6*a)*b*c*d^3 - (a^4 - 12*a^2)*d^4 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 6*a)*b*c*d^3 - (a^4 - 12*a^2)*d^4 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 24*(d^4*cos(b*x + a)^2 - d^4)*polylog(5, cos(b*x + a) + I*sin(b*x + a)) + 24*(d^4*cos(b*x + a)^2 - d^4)*polylog(5, cos(b*x + a) - I*sin(b*x + a)) - 24*(d^4*cos(b*x + a)^2 - d^4)*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) - 24*(d^4*cos(b*x + a)^2 - d^4)*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3 + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)^2)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3 + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)^2)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3 + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)^2)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3 + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)^2)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - 2*d^4)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 8*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*sin(b*x + a))/(b^5*cos(b*x + a)^2 - b^5)","C",0
113,1,1734,0,1.190433," ","integrate((d*x+c)^3*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3} + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3} + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3} + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3} + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(-6 i \, d^{3} \cos\left(b x + a\right)^{2} + 6 i \, d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, d^{3} \cos\left(b x + a\right)^{2} - 6 i \, d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-6 i \, d^{3} \cos\left(b x + a\right)^{2} + 6 i \, d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, d^{3} \cos\left(b x + a\right)^{2} - 6 i \, d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \sin\left(b x + a\right)}{4 \, {\left(b^{4} \cos\left(b x + a\right)^{2} - b^{4}\right)}}"," ",0,"1/4*(2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3 + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3 + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3 + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3 + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + (-6*I*d^3*cos(b*x + a)^2 + 6*I*d^3)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + (6*I*d^3*cos(b*x + a)^2 - 6*I*d^3)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + (-6*I*d^3*cos(b*x + a)^2 + 6*I*d^3)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + (6*I*d^3*cos(b*x + a)^2 - 6*I*d^3)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*sin(b*x + a))/(b^4*cos(b*x + a)^2 - b^4)","C",0
114,1,966,0,0.705757," ","integrate((d*x+c)^2*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - 2 \, d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - 2 \, d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 4 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)}{4 \, {\left(b^{3} \cos\left(b x + a\right)^{2} - b^{3}\right)}}"," ",0,"1/4*(2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a) + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a)^2 - 2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a)^2 - 2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2 - (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2 - (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 4*(b*d^2*x + b*c*d)*sin(b*x + a))/(b^3*cos(b*x + a)^2 - b^3)","C",0
115,1,454,0,0.573180," ","integrate((d*x+c)*cot(b*x+a)^2*csc(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) + {\left(i \, d \cos\left(b x + a\right)^{2} - i \, d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-i \, d \cos\left(b x + a\right)^{2} + i \, d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(i \, d \cos\left(b x + a\right)^{2} - i \, d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-i \, d \cos\left(b x + a\right)^{2} + i \, d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b d x - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b d x - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 2 \, d \sin\left(b x + a\right)}{4 \, {\left(b^{2} \cos\left(b x + a\right)^{2} - b^{2}\right)}}"," ",0,"1/4*(2*(b*d*x + b*c)*cos(b*x + a) + (I*d*cos(b*x + a)^2 - I*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (-I*d*cos(b*x + a)^2 + I*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (I*d*cos(b*x + a)^2 - I*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-I*d*cos(b*x + a)^2 + I*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b*d*x - (b*d*x + b*c)*cos(b*x + a)^2 + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b*d*x - (b*d*x + b*c)*cos(b*x + a)^2 + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 2*d*sin(b*x + a))/(b^2*cos(b*x + a)^2 - b^2)","B",0
116,0,0,0,0.732577," ","integrate(cot(b*x+a)^2*csc(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{2} \csc\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(cot(b*x + a)^2*csc(b*x + a)/(d*x + c), x)","F",0
117,0,0,0,0.557089," ","integrate(cot(b*x+a)^2*csc(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{2} \csc\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cot(b*x + a)^2*csc(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
118,1,341,0,0.544412," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(30 \, b d^{2} \cos\left(b x + a\right) - {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{3} + 10 \, {\left(2 \, b^{2} d^{2} x + 2 \, b^{2} c d + {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{864 \, b^{4}}"," ",0,"-1/864*(5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(30*b*d^2*cos(b*x + a) - (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^3 + 10*(2*b^2*d^2*x + 2*b^2*c*d + (b^2*d^2*x + b^2*c*d)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
119,1,280,0,0.695183," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 24 \, {\left(2 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{3} - {\left(b d \cos\left(b x + a\right)^{2} + 2 \, b d\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{144 \, b^{3}}"," ",0,"-1/144*(sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 24*(2*(b^2*d*x + b^2*c)*cos(b*x + a)^3 - (b*d*cos(b*x + a)^2 + 2*b*d)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
120,1,235,0,0.727330," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, \sqrt{d x + c} b \cos\left(b x + a\right)^{3}}{72 \, b^{2}}"," ",0,"1/72*(sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*sqrt(d*x + c)*b*cos(b*x + a)^3)/b^2","A",0
121,1,235,0,0.720351," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, \sqrt{d x + c} b \cos\left(b x + a\right)^{3}}{72 \, b^{2}}"," ",0,"1/72*(sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*sqrt(d*x + c)*b*cos(b*x + a)^3)/b^2","A",0
122,1,280,0,0.723734," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{\sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 24 \, {\left(2 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{3} - {\left(b d \cos\left(b x + a\right)^{2} + 2 \, b d\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{144 \, b^{3}}"," ",0,"-1/144*(sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 24*(2*(b^2*d*x + b^2*c)*cos(b*x + a)^3 - (b*d*cos(b*x + a)^2 + 2*b*d)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
123,1,341,0,0.523457," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 405 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(30 \, b d^{2} \cos\left(b x + a\right) - {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{3} + 10 \, {\left(2 \, b^{2} d^{2} x + 2 \, b^{2} c d + {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{864 \, b^{4}}"," ",0,"-1/864*(5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 405*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(30*b*d^2*cos(b*x + a) - (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^3 + 10*(2*b^2*d^2*x + 2*b^2*c*d + (b^2*d^2*x + b^2*c*d)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
124,1,347,0,0.508194," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} \pi d^{4} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 105 \, \sqrt{2} \pi d^{4} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 16 \, {\left(128 \, b^{4} d^{3} x^{3} + 384 \, b^{4} c d^{2} x^{2} + 128 \, b^{4} c^{3} - 70 \, b^{2} c d^{2} - 560 \, {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \cos\left(b x + a\right)^{4} + 560 \, {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(192 \, b^{4} c^{2} d - 35 \, b^{2} d^{3}\right)} x - 7 \, {\left(2 \, {\left(64 \, b^{3} d^{3} x^{2} + 128 \, b^{3} c d^{2} x + 64 \, b^{3} c^{2} d - 15 \, b d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(64 \, b^{3} d^{3} x^{2} + 128 \, b^{3} c d^{2} x + 64 \, b^{3} c^{2} d - 15 \, b d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{57344 \, b^{4} d}"," ",0,"-1/57344*(105*sqrt(2)*pi*d^4*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 105*sqrt(2)*pi*d^4*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 16*(128*b^4*d^3*x^3 + 384*b^4*c*d^2*x^2 + 128*b^4*c^3 - 70*b^2*c*d^2 - 560*(b^2*d^3*x + b^2*c*d^2)*cos(b*x + a)^4 + 560*(b^2*d^3*x + b^2*c*d^2)*cos(b*x + a)^2 + 2*(192*b^4*c^2*d - 35*b^2*d^3)*x - 7*(2*(64*b^3*d^3*x^2 + 128*b^3*c*d^2*x + 64*b^3*c^2*d - 15*b*d^3)*cos(b*x + a)^3 - (64*b^3*d^3*x^2 + 128*b^3*c*d^2*x + 64*b^3*c^2*d - 15*b*d^3)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/(b^4*d)","A",0
125,1,249,0,0.744722," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left(64 \, b^{3} d^{2} x^{2} - 120 \, b d^{2} \cos\left(b x + a\right)^{4} + 128 \, b^{3} c d x + 64 \, b^{3} c^{2} + 120 \, b d^{2} \cos\left(b x + a\right)^{2} - 15 \, b d^{2} - 160 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{5120 \, b^{3} d}"," ",0,"1/5120*(15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 4*(64*b^3*d^2*x^2 - 120*b*d^2*cos(b*x + a)^4 + 128*b^3*c*d*x + 64*b^3*c^2 + 120*b*d^2*cos(b*x + a)^2 - 15*b*d^2 - 160*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - (b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/(b^3*d)","A",0
126,1,175,0,0.518548," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 16 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, {\left(2 \, b d \cos\left(b x + a\right)^{3} - b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{384 \, b^{2} d}"," ",0,"1/384*(3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 16*(2*b^2*d*x + 2*b^2*c - 3*(2*b*d*cos(b*x + a)^3 - b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/(b^2*d)","A",0
127,1,175,0,0.750554," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 16 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, {\left(2 \, b d \cos\left(b x + a\right)^{3} - b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{384 \, b^{2} d}"," ",0,"1/384*(3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 16*(2*b^2*d*x + 2*b^2*c - 3*(2*b*d*cos(b*x + a)^3 - b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/(b^2*d)","A",0
128,1,249,0,0.515923," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left(64 \, b^{3} d^{2} x^{2} - 120 \, b d^{2} \cos\left(b x + a\right)^{4} + 128 \, b^{3} c d x + 64 \, b^{3} c^{2} + 120 \, b d^{2} \cos\left(b x + a\right)^{2} - 15 \, b d^{2} - 160 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{5120 \, b^{3} d}"," ",0,"1/5120*(15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 4*(64*b^3*d^2*x^2 - 120*b*d^2*cos(b*x + a)^4 + 128*b^3*c*d*x + 64*b^3*c^2 + 120*b*d^2*cos(b*x + a)^2 - 15*b*d^2 - 160*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - (b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/(b^3*d)","A",0
129,1,347,0,0.607788," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{105 \, \sqrt{2} \pi d^{4} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 105 \, \sqrt{2} \pi d^{4} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 16 \, {\left(128 \, b^{4} d^{3} x^{3} + 384 \, b^{4} c d^{2} x^{2} + 128 \, b^{4} c^{3} - 70 \, b^{2} c d^{2} - 560 \, {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \cos\left(b x + a\right)^{4} + 560 \, {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(192 \, b^{4} c^{2} d - 35 \, b^{2} d^{3}\right)} x - 7 \, {\left(2 \, {\left(64 \, b^{3} d^{3} x^{2} + 128 \, b^{3} c d^{2} x + 64 \, b^{3} c^{2} d - 15 \, b d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(64 \, b^{3} d^{3} x^{2} + 128 \, b^{3} c d^{2} x + 64 \, b^{3} c^{2} d - 15 \, b d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{57344 \, b^{4} d}"," ",0,"-1/57344*(105*sqrt(2)*pi*d^4*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 105*sqrt(2)*pi*d^4*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) - 16*(128*b^4*d^3*x^3 + 384*b^4*c*d^2*x^2 + 128*b^4*c^3 - 70*b^2*c*d^2 - 560*(b^2*d^3*x + b^2*c*d^2)*cos(b*x + a)^4 + 560*(b^2*d^3*x + b^2*c*d^2)*cos(b*x + a)^2 + 2*(192*b^4*c^2*d - 35*b^2*d^3)*x - 7*(2*(64*b^3*d^3*x^2 + 128*b^3*c*d^2*x + 64*b^3*c^2*d - 15*b*d^3)*cos(b*x + a)^3 - (64*b^3*d^3*x^2 + 128*b^3*c*d^2*x + 64*b^3*c^2*d - 15*b*d^3)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/(b^4*d)","A",0
130,1,521,0,1.012893," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 480 \, {\left(9 \, {\left(20 \, b^{3} d^{2} x^{2} + 40 \, b^{3} c d x + 20 \, b^{3} c^{2} - 3 \, b d^{2}\right)} \cos\left(b x + a\right)^{5} + 390 \, b d^{2} \cos\left(b x + a\right) - 5 \, {\left(60 \, b^{3} d^{2} x^{2} + 120 \, b^{3} c d x + 60 \, b^{3} c^{2} - 13 \, b d^{2}\right)} \cos\left(b x + a\right)^{3} + 10 \, {\left(26 \, b^{2} d^{2} x - 9 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{4} + 26 \, b^{2} c d + 13 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{432000 \, b^{4}}"," ",0,"1/432000*(81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) + 480*(9*(20*b^3*d^2*x^2 + 40*b^3*c*d*x + 20*b^3*c^2 - 3*b*d^2)*cos(b*x + a)^5 + 390*b*d^2*cos(b*x + a) - 5*(60*b^3*d^2*x^2 + 120*b^3*c*d*x + 60*b^3*c^2 - 13*b*d^2)*cos(b*x + a)^3 + 10*(26*b^2*d^2*x - 9*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^4 + 26*b^2*c*d + 13*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
131,1,427,0,0.991964," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 480 \, {\left(30 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{5} - 50 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{3} - {\left(9 \, b d \cos\left(b x + a\right)^{4} - 13 \, b d \cos\left(b x + a\right)^{2} - 26 \, b d\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{72000 \, b^{3}}"," ",0,"1/72000*(27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) + 480*(30*(b^2*d*x + b^2*c)*cos(b*x + a)^5 - 50*(b^2*d*x + b^2*c)*cos(b*x + a)^3 - (9*b*d*cos(b*x + a)^4 - 13*b*d*cos(b*x + a)^2 - 26*b*d)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
132,1,356,0,1.012746," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 480 \, {\left(3 \, b \cos\left(b x + a\right)^{5} - 5 \, b \cos\left(b x + a\right)^{3}\right)} \sqrt{d x + c}}{7200 \, b^{2}}"," ",0,"-1/7200*(9*sqrt(10)*pi*d*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 9*sqrt(10)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) - 480*(3*b*cos(b*x + a)^5 - 5*b*cos(b*x + a)^3)*sqrt(d*x + c))/b^2","A",0
133,1,356,0,0.670578," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 480 \, {\left(3 \, b \cos\left(b x + a\right)^{5} - 5 \, b \cos\left(b x + a\right)^{3}\right)} \sqrt{d x + c}}{7200 \, b^{2}}"," ",0,"-1/7200*(9*sqrt(10)*pi*d*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 9*sqrt(10)*pi*d*sqrt(b/(pi*d))*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) - 480*(3*b*cos(b*x + a)^5 - 5*b*cos(b*x + a)^3)*sqrt(d*x + c))/b^2","A",0
134,1,427,0,0.625954," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 480 \, {\left(30 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{5} - 50 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{3} - {\left(9 \, b d \cos\left(b x + a\right)^{4} - 13 \, b d \cos\left(b x + a\right)^{2} - 26 \, b d\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{72000 \, b^{3}}"," ",0,"1/72000*(27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) + 480*(30*(b^2*d*x + b^2*c)*cos(b*x + a)^5 - 50*(b^2*d*x + b^2*c)*cos(b*x + a)^3 - (9*b*d*cos(b*x + a)^4 - 13*b*d*cos(b*x + a)^2 - 26*b*d)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
135,1,521,0,0.821547," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 480 \, {\left(9 \, {\left(20 \, b^{3} d^{2} x^{2} + 40 \, b^{3} c d x + 20 \, b^{3} c^{2} - 3 \, b d^{2}\right)} \cos\left(b x + a\right)^{5} + 390 \, b d^{2} \cos\left(b x + a\right) - 5 \, {\left(60 \, b^{3} d^{2} x^{2} + 120 \, b^{3} c d x + 60 \, b^{3} c^{2} - 13 \, b d^{2}\right)} \cos\left(b x + a\right)^{3} + 10 \, {\left(26 \, b^{2} d^{2} x - 9 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{4} + 26 \, b^{2} c d + 13 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{432000 \, b^{4}}"," ",0,"1/432000*(81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) + 480*(9*(20*b^3*d^2*x^2 + 40*b^3*c*d*x + 20*b^3*c^2 - 3*b*d^2)*cos(b*x + a)^5 + 390*b*d^2*cos(b*x + a) - 5*(60*b^3*d^2*x^2 + 120*b^3*c*d*x + 60*b^3*c^2 - 13*b*d^2)*cos(b*x + a)^3 + 10*(26*b^2*d^2*x - 9*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^4 + 26*b^2*c*d + 13*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
136,1,184,0,0.601178," ","integrate((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-\frac{d m \log\left(\frac{4 i \, b}{d}\right) - 4 i \, b c + 4 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{4 i \, b d x + 4 i \, b c}{d}\right) + 4 \, e^{\left(-\frac{d m \log\left(\frac{2 i \, b}{d}\right) - 2 i \, b c + 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, b d x + 2 i \, b c}{d}\right) + 4 \, e^{\left(-\frac{d m \log\left(-\frac{2 i \, b}{d}\right) + 2 i \, b c - 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, b d x - 2 i \, b c}{d}\right) + e^{\left(-\frac{d m \log\left(-\frac{4 i \, b}{d}\right) + 4 i \, b c - 4 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-4 i \, b d x - 4 i \, b c}{d}\right)}{64 \, b}"," ",0,"-1/64*(e^(-(d*m*log(4*I*b/d) - 4*I*b*c + 4*I*a*d)/d)*gamma(m + 1, (4*I*b*d*x + 4*I*b*c)/d) + 4*e^(-(d*m*log(2*I*b/d) - 2*I*b*c + 2*I*a*d)/d)*gamma(m + 1, (2*I*b*d*x + 2*I*b*c)/d) + 4*e^(-(d*m*log(-2*I*b/d) + 2*I*b*c - 2*I*a*d)/d)*gamma(m + 1, (-2*I*b*d*x - 2*I*b*c)/d) + e^(-(d*m*log(-4*I*b/d) + 4*I*b*c - 4*I*a*d)/d)*gamma(m + 1, (-4*I*b*d*x - 4*I*b*c)/d))/b","A",0
137,1,378,0,0.699124," ","integrate((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{12 \, b^{4} d^{4} x^{4} + 48 \, b^{4} c d^{3} x^{3} - {\left(32 \, b^{4} d^{4} x^{4} + 128 \, b^{4} c d^{3} x^{3} + 32 \, b^{4} c^{4} - 24 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 24 \, {\left(8 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 16 \, {\left(8 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} + 9 \, {\left(8 \, b^{4} c^{2} d^{2} - 5 \, b^{2} d^{4}\right)} x^{2} + 9 \, {\left(8 \, b^{2} d^{4} x^{2} + 16 \, b^{2} c d^{3} x + 8 \, b^{2} c^{2} d^{2} - 5 \, d^{4}\right)} \cos\left(b x + a\right)^{2} + 6 \, {\left(8 \, b^{4} c^{3} d - 15 \, b^{2} c d^{3}\right)} x + 2 \, {\left(2 \, {\left(8 \, b^{3} d^{4} x^{3} + 24 \, b^{3} c d^{3} x^{2} + 8 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(8 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(8 \, b^{3} d^{4} x^{3} + 24 \, b^{3} c d^{3} x^{2} + 8 \, b^{3} c^{3} d - 15 \, b c d^{3} + 3 \, {\left(8 \, b^{3} c^{2} d^{2} - 5 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{128 \, b^{5}}"," ",0,"1/128*(12*b^4*d^4*x^4 + 48*b^4*c*d^3*x^3 - (32*b^4*d^4*x^4 + 128*b^4*c*d^3*x^3 + 32*b^4*c^4 - 24*b^2*c^2*d^2 + 3*d^4 + 24*(8*b^4*c^2*d^2 - b^2*d^4)*x^2 + 16*(8*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)^4 + 9*(8*b^4*c^2*d^2 - 5*b^2*d^4)*x^2 + 9*(8*b^2*d^4*x^2 + 16*b^2*c*d^3*x + 8*b^2*c^2*d^2 - 5*d^4)*cos(b*x + a)^2 + 6*(8*b^4*c^3*d - 15*b^2*c*d^3)*x + 2*(2*(8*b^3*d^4*x^3 + 24*b^3*c*d^3*x^2 + 8*b^3*c^3*d - 3*b*c*d^3 + 3*(8*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^3 + 3*(8*b^3*d^4*x^3 + 24*b^3*c*d^3*x^2 + 8*b^3*c^3*d - 15*b*c*d^3 + 3*(8*b^3*c^2*d^2 - 5*b*d^4)*x)*cos(b*x + a))*sin(b*x + a))/b^5","A",0
138,1,238,0,0.669933," ","integrate((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{24 \, b^{3} d^{3} x^{3} + 72 \, b^{3} c d^{2} x^{2} - 8 \, {\left(8 \, b^{3} d^{3} x^{3} + 24 \, b^{3} c d^{2} x^{2} + 8 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(8 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} + 72 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} + 9 \, {\left(8 \, b^{3} c^{2} d - 5 \, b d^{3}\right)} x + 3 \, {\left(2 \, {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - 5 \, d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{256 \, b^{4}}"," ",0,"1/256*(24*b^3*d^3*x^3 + 72*b^3*c*d^2*x^2 - 8*(8*b^3*d^3*x^3 + 24*b^3*c*d^2*x^2 + 8*b^3*c^3 - 3*b*c*d^2 + 3*(8*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^4 + 72*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2 + 9*(8*b^3*c^2*d - 5*b*d^3)*x + 3*(2*(8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^3 + 3*(8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - 5*d^3)*cos(b*x + a))*sin(b*x + a))/b^4","A",0
139,1,130,0,0.640295," ","integrate((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x - {\left(8 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c d x + 8 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{4} + 3 \, d^{2} \cos\left(b x + a\right)^{2} + 2 \, {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{32 \, b^{3}}"," ",0,"1/32*(3*b^2*d^2*x^2 + 6*b^2*c*d*x - (8*b^2*d^2*x^2 + 16*b^2*c*d*x + 8*b^2*c^2 - d^2)*cos(b*x + a)^4 + 3*d^2*cos(b*x + a)^2 + 2*(2*(b*d^2*x + b*c*d)*cos(b*x + a)^3 + 3*(b*d^2*x + b*c*d)*cos(b*x + a))*sin(b*x + a))/b^3","A",0
140,1,58,0,0.615594," ","integrate((d*x+c)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{8 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{4} - 3 \, b d x - {\left(2 \, d \cos\left(b x + a\right)^{3} + 3 \, d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{32 \, b^{2}}"," ",0,"-1/32*(8*(b*d*x + b*c)*cos(b*x + a)^4 - 3*b*d*x - (2*d*cos(b*x + a)^3 + 3*d*cos(b*x + a))*sin(b*x + a))/b^2","A",0
141,1,155,0,0.423174," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(\operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(\operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 2 \, \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + 4 \, \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right)}{16 \, d}"," ",0,"1/16*(2*(cos_integral(2*(b*d*x + b*c)/d) + cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) + (cos_integral(4*(b*d*x + b*c)/d) + cos_integral(-4*(b*d*x + b*c)/d))*sin(-4*(b*c - a*d)/d) + 2*cos(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + 4*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d))/d","A",0
142,1,235,0,0.743561," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{4 \, d \cos\left(b x + a\right)^{3} \sin\left(b x + a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(b d x + b c\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/4*(4*d*cos(b*x + a)^3*sin(b*x + a) + 2*(b*d*x + b*c)*sin(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + 2*(b*d*x + b*c)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - ((b*d*x + b*c)*cos_integral(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) - ((b*d*x + b*c)*cos_integral(4*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-4*(b*d*x + b*c)/d))*cos(-4*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
143,1,397,0,0.751927," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \cos\left(b x + a\right)^{3} \sin\left(b x + a\right) + 8 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{4} - 6 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*d^2*cos(b*x + a)^3*sin(b*x + a) + 8*(b*d^2*x + b*c*d)*cos(b*x + a)^4 - 6*(b*d^2*x + b*c*d)*cos(b*x + a)^2 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) + 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(4*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-4*(b*d*x + b*c)/d))*sin(-4*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
144,1,568,0,0.704934," ","integrate(cos(b*x+a)^3*sin(b*x+a)/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{4 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - 3 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} - 8 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 4 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{4 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{4 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left({\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{6 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/6*(4*(b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - 3*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2 - 8*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-4*(b*c - a*d)/d)*sin_integral(4*(b*d*x + b*c)/d) - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) + 4*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(4*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-4*(b*d*x + b*c)/d))*cos(-4*(b*c - a*d)/d) - 2*((8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - d^3)*cos(b*x + a)^3 - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a))*sin(b*x + a))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
145,1,276,0,0.872440," ","integrate((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{-3 i \, e^{\left(-\frac{d m \log\left(\frac{5 i \, b}{d}\right) - 5 i \, b c + 5 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{5 i \, b d x + 5 i \, b c}{d}\right) - 5 i \, e^{\left(-\frac{d m \log\left(\frac{3 i \, b}{d}\right) - 3 i \, b c + 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, b d x + 3 i \, b c}{d}\right) + 30 i \, e^{\left(-\frac{d m \log\left(\frac{i \, b}{d}\right) - i \, b c + i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{i \, b d x + i \, b c}{d}\right) - 30 i \, e^{\left(-\frac{d m \log\left(-\frac{i \, b}{d}\right) + i \, b c - i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-i \, b d x - i \, b c}{d}\right) + 5 i \, e^{\left(-\frac{d m \log\left(-\frac{3 i \, b}{d}\right) + 3 i \, b c - 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, b d x - 3 i \, b c}{d}\right) + 3 i \, e^{\left(-\frac{d m \log\left(-\frac{5 i \, b}{d}\right) + 5 i \, b c - 5 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-5 i \, b d x - 5 i \, b c}{d}\right)}{480 \, b}"," ",0,"1/480*(-3*I*e^(-(d*m*log(5*I*b/d) - 5*I*b*c + 5*I*a*d)/d)*gamma(m + 1, (5*I*b*d*x + 5*I*b*c)/d) - 5*I*e^(-(d*m*log(3*I*b/d) - 3*I*b*c + 3*I*a*d)/d)*gamma(m + 1, (3*I*b*d*x + 3*I*b*c)/d) + 30*I*e^(-(d*m*log(I*b/d) - I*b*c + I*a*d)/d)*gamma(m + 1, (I*b*d*x + I*b*c)/d) - 30*I*e^(-(d*m*log(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d) + 5*I*e^(-(d*m*log(-3*I*b/d) + 3*I*b*c - 3*I*a*d)/d)*gamma(m + 1, (-3*I*b*d*x - 3*I*b*c)/d) + 3*I*e^(-(d*m*log(-5*I*b/d) + 5*I*b*c - 5*I*a*d)/d)*gamma(m + 1, (-5*I*b*d*x - 5*I*b*c)/d))/b","A",0
146,1,527,0,1.198737," ","integrate((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{1620 \, {\left(25 \, b^{3} d^{4} x^{3} + 75 \, b^{3} c d^{3} x^{2} + 25 \, b^{3} c^{3} d - 6 \, b c d^{3} + 3 \, {\left(25 \, b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{5} - 300 \, {\left(75 \, b^{3} d^{4} x^{3} + 225 \, b^{3} c d^{3} x^{2} + 75 \, b^{3} c^{3} d + 22 \, b c d^{3} + {\left(225 \, b^{3} c^{2} d^{2} + 22 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{3} - 1800 \, {\left(75 \, b^{3} d^{4} x^{3} + 225 \, b^{3} c d^{3} x^{2} + 75 \, b^{3} c^{3} d - 428 \, b c d^{3} + {\left(225 \, b^{3} c^{2} d^{2} - 428 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right) - {\left(33750 \, b^{4} d^{4} x^{4} + 135000 \, b^{4} c d^{3} x^{3} + 33750 \, b^{4} c^{4} - 385200 \, b^{2} c^{2} d^{2} - 81 \, {\left(625 \, b^{4} d^{4} x^{4} + 2500 \, b^{4} c d^{3} x^{3} + 625 \, b^{4} c^{4} - 300 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 150 \, {\left(25 \, b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 100 \, {\left(25 \, b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} + 760816 \, d^{4} + 900 \, {\left(225 \, b^{4} c^{2} d^{2} - 428 \, b^{2} d^{4}\right)} x^{2} + {\left(16875 \, b^{4} d^{4} x^{4} + 67500 \, b^{4} c d^{3} x^{3} + 16875 \, b^{4} c^{4} + 9900 \, b^{2} c^{2} d^{2} - 4792 \, d^{4} + 450 \, {\left(225 \, b^{4} c^{2} d^{2} + 22 \, b^{2} d^{4}\right)} x^{2} + 900 \, {\left(75 \, b^{4} c^{3} d + 22 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 1800 \, {\left(75 \, b^{4} c^{3} d - 428 \, b^{2} c d^{3}\right)} x\right)} \sin\left(b x + a\right)}{253125 \, b^{5}}"," ",0,"-1/253125*(1620*(25*b^3*d^4*x^3 + 75*b^3*c*d^3*x^2 + 25*b^3*c^3*d - 6*b*c*d^3 + 3*(25*b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^5 - 300*(75*b^3*d^4*x^3 + 225*b^3*c*d^3*x^2 + 75*b^3*c^3*d + 22*b*c*d^3 + (225*b^3*c^2*d^2 + 22*b*d^4)*x)*cos(b*x + a)^3 - 1800*(75*b^3*d^4*x^3 + 225*b^3*c*d^3*x^2 + 75*b^3*c^3*d - 428*b*c*d^3 + (225*b^3*c^2*d^2 - 428*b*d^4)*x)*cos(b*x + a) - (33750*b^4*d^4*x^4 + 135000*b^4*c*d^3*x^3 + 33750*b^4*c^4 - 385200*b^2*c^2*d^2 - 81*(625*b^4*d^4*x^4 + 2500*b^4*c*d^3*x^3 + 625*b^4*c^4 - 300*b^2*c^2*d^2 + 24*d^4 + 150*(25*b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 100*(25*b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^4 + 760816*d^4 + 900*(225*b^4*c^2*d^2 - 428*b^2*d^4)*x^2 + (16875*b^4*d^4*x^4 + 67500*b^4*c*d^3*x^3 + 16875*b^4*c^4 + 9900*b^2*c^2*d^2 - 4792*d^4 + 450*(225*b^4*c^2*d^2 + 22*b^2*d^4)*x^2 + 900*(75*b^4*c^3*d + 22*b^2*c*d^3)*x)*cos(b*x + a)^2 + 1800*(75*b^4*c^3*d - 428*b^2*c*d^3)*x)*sin(b*x + a))/b^5","A",0
147,1,342,0,0.765413," ","integrate((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{81 \, {\left(25 \, b^{2} d^{3} x^{2} + 50 \, b^{2} c d^{2} x + 25 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{5} - 5 \, {\left(225 \, b^{2} d^{3} x^{2} + 450 \, b^{2} c d^{2} x + 225 \, b^{2} c^{2} d + 22 \, d^{3}\right)} \cos\left(b x + a\right)^{3} - 30 \, {\left(225 \, b^{2} d^{3} x^{2} + 450 \, b^{2} c d^{2} x + 225 \, b^{2} c^{2} d - 428 \, d^{3}\right)} \cos\left(b x + a\right) - 15 \, {\left(150 \, b^{3} d^{3} x^{3} + 450 \, b^{3} c d^{2} x^{2} + 150 \, b^{3} c^{3} - 9 \, {\left(25 \, b^{3} d^{3} x^{3} + 75 \, b^{3} c d^{2} x^{2} + 25 \, b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(25 \, b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - 856 \, b c d^{2} + {\left(75 \, b^{3} d^{3} x^{3} + 225 \, b^{3} c d^{2} x^{2} + 75 \, b^{3} c^{3} + 22 \, b c d^{2} + {\left(225 \, b^{3} c^{2} d + 22 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(225 \, b^{3} c^{2} d - 428 \, b d^{3}\right)} x\right)} \sin\left(b x + a\right)}{16875 \, b^{4}}"," ",0,"-1/16875*(81*(25*b^2*d^3*x^2 + 50*b^2*c*d^2*x + 25*b^2*c^2*d - 2*d^3)*cos(b*x + a)^5 - 5*(225*b^2*d^3*x^2 + 450*b^2*c*d^2*x + 225*b^2*c^2*d + 22*d^3)*cos(b*x + a)^3 - 30*(225*b^2*d^3*x^2 + 450*b^2*c*d^2*x + 225*b^2*c^2*d - 428*d^3)*cos(b*x + a) - 15*(150*b^3*d^3*x^3 + 450*b^3*c*d^2*x^2 + 150*b^3*c^3 - 9*(25*b^3*d^3*x^3 + 75*b^3*c*d^2*x^2 + 25*b^3*c^3 - 6*b*c*d^2 + 3*(25*b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^4 - 856*b*c*d^2 + (75*b^3*d^3*x^3 + 225*b^3*c*d^2*x^2 + 75*b^3*c^3 + 22*b*c*d^2 + (225*b^3*c^2*d + 22*b*d^3)*x)*cos(b*x + a)^2 + 2*(225*b^3*c^2*d - 428*b*d^3)*x)*sin(b*x + a))/b^4","A",0
148,1,193,0,0.506746," ","integrate((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{270 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{5} - 150 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} - 900 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - {\left(450 \, b^{2} d^{2} x^{2} + 900 \, b^{2} c d x - 27 \, {\left(25 \, b^{2} d^{2} x^{2} + 50 \, b^{2} c d x + 25 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{4} + 450 \, b^{2} c^{2} + {\left(225 \, b^{2} d^{2} x^{2} + 450 \, b^{2} c d x + 225 \, b^{2} c^{2} + 22 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - 856 \, d^{2}\right)} \sin\left(b x + a\right)}{3375 \, b^{3}}"," ",0,"-1/3375*(270*(b*d^2*x + b*c*d)*cos(b*x + a)^5 - 150*(b*d^2*x + b*c*d)*cos(b*x + a)^3 - 900*(b*d^2*x + b*c*d)*cos(b*x + a) - (450*b^2*d^2*x^2 + 900*b^2*c*d*x - 27*(25*b^2*d^2*x^2 + 50*b^2*c*d*x + 25*b^2*c^2 - 2*d^2)*cos(b*x + a)^4 + 450*b^2*c^2 + (225*b^2*d^2*x^2 + 450*b^2*c*d*x + 225*b^2*c^2 + 22*d^2)*cos(b*x + a)^2 - 856*d^2)*sin(b*x + a))/b^3","A",0
149,1,91,0,0.759872," ","integrate((d*x+c)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{9 \, d \cos\left(b x + a\right)^{5} - 5 \, d \cos\left(b x + a\right)^{3} - 30 \, d \cos\left(b x + a\right) + 15 \, {\left(3 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{4} - 2 \, b d x - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - 2 \, b c\right)} \sin\left(b x + a\right)}{225 \, b^{2}}"," ",0,"-1/225*(9*d*cos(b*x + a)^5 - 5*d*cos(b*x + a)^3 - 30*d*cos(b*x + a) + 15*(3*(b*d*x + b*c)*cos(b*x + a)^4 - 2*b*d*x - (b*d*x + b*c)*cos(b*x + a)^2 - 2*b*c)*sin(b*x + a))/b^2","A",0
150,1,229,0,0.607152," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(\operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - {\left(\operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(\operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 2 \, \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 4 \, \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right)}{32 \, d}"," ",0,"1/32*(2*(cos_integral((b*d*x + b*c)/d) + cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) - (cos_integral(3*(b*d*x + b*c)/d) + cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) - (cos_integral(5*(b*d*x + b*c)/d) + cos_integral(-5*(b*d*x + b*c)/d))*cos(-5*(b*c - a*d)/d) + 2*sin(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) + 2*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 4*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
151,1,339,0,0.507568," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{32 \, d \cos\left(b x + a\right)^{5} - 32 \, d \cos\left(b x + a\right)^{3} + 10 \, {\left(b d x + b c\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + 6 \, {\left(b d x + b c\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 4 \, {\left(b d x + b c\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 2 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 5 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{32 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/32*(32*d*cos(b*x + a)^5 - 32*d*cos(b*x + a)^3 + 10*(b*d*x + b*c)*cos(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) + 6*(b*d*x + b*c)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 4*(b*d*x + b*c)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - 2*((b*d*x + b*c)*cos_integral((b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + 3*((b*d*x + b*c)*cos_integral(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d) + 5*((b*d*x + b*c)*cos_integral(5*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-5*(b*d*x + b*c)/d))*sin(-5*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
152,1,567,0,0.540652," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{32 \, d^{2} \cos\left(b x + a\right)^{5} - 32 \, d^{2} \cos\left(b x + a\right)^{3} - 50 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) - 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) + 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 25 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 32 \, {\left(5 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{4} - 3 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)}{64 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/64*(32*d^2*cos(b*x + a)^5 - 32*d^2*cos(b*x + a)^3 - 50*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) - 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) + 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) + 25*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(5*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-5*(b*d*x + b*c)/d))*cos(-5*(b*c - a*d)/d) - 32*(5*(b*d^2*x + b*c*d)*cos(b*x + a)^4 - 3*(b*d^2*x + b*c*d)*cos(b*x + a)^2)*sin(b*x + a))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
153,1,811,0,0.627904," ","integrate(cos(b*x+a)^3*sin(b*x+a)^2/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{32 \, {\left(25 \, b^{2} d^{3} x^{2} + 50 \, b^{2} c d^{2} x + 25 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{5} - 32 \, {\left(29 \, b^{2} d^{3} x^{2} + 58 \, b^{2} c d^{2} x + 29 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{3} + 250 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + 54 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 192 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) + 32 \, {\left(5 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - 3 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right) - 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right) + 27 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 125 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{5 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{5 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right)}{192 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/192*(32*(25*b^2*d^3*x^2 + 50*b^2*c*d^2*x + 25*b^2*c^2*d - 2*d^3)*cos(b*x + a)^5 - 32*(29*b^2*d^3*x^2 + 58*b^2*c*d^2*x + 29*b^2*c^2*d - 2*d^3)*cos(b*x + a)^3 + 250*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-5*(b*c - a*d)/d)*sin_integral(5*(b*d*x + b*c)/d) + 54*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 192*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a) + 32*(5*(b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - 3*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*sin(b*x + a) - 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral((b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + 27*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(3*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d) + 125*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(5*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-5*(b*d*x + b*c)/d))*sin(-5*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
154,1,184,0,0.497494," ","integrate((d*x+c)^m*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{e^{\left(-\frac{d m \log\left(\frac{6 i \, b}{d}\right) - 6 i \, b c + 6 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{6 i \, b d x + 6 i \, b c}{d}\right) - 9 \, e^{\left(-\frac{d m \log\left(\frac{2 i \, b}{d}\right) - 2 i \, b c + 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, b d x + 2 i \, b c}{d}\right) - 9 \, e^{\left(-\frac{d m \log\left(-\frac{2 i \, b}{d}\right) + 2 i \, b c - 2 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, b d x - 2 i \, b c}{d}\right) + e^{\left(-\frac{d m \log\left(-\frac{6 i \, b}{d}\right) + 6 i \, b c - 6 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-6 i \, b d x - 6 i \, b c}{d}\right)}{384 \, b}"," ",0,"1/384*(e^(-(d*m*log(6*I*b/d) - 6*I*b*c + 6*I*a*d)/d)*gamma(m + 1, (6*I*b*d*x + 6*I*b*c)/d) - 9*e^(-(d*m*log(2*I*b/d) - 2*I*b*c + 2*I*a*d)/d)*gamma(m + 1, (2*I*b*d*x + 2*I*b*c)/d) - 9*e^(-(d*m*log(-2*I*b/d) + 2*I*b*c - 2*I*a*d)/d)*gamma(m + 1, (-2*I*b*d*x - 2*I*b*c)/d) + e^(-(d*m*log(-6*I*b/d) + 6*I*b*c - 6*I*a*d)/d)*gamma(m + 1, (-6*I*b*d*x - 6*I*b*c)/d))/b","A",0
155,1,546,0,0.503274," ","integrate((d*x+c)^4*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 2 \, {\left(54 \, b^{4} d^{4} x^{4} + 216 \, b^{4} c d^{3} x^{3} + 54 \, b^{4} c^{4} - 18 \, b^{2} c^{2} d^{2} + d^{4} + 18 \, {\left(18 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 36 \, {\left(6 \, b^{4} c^{3} d - b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{6} - 3 \, {\left(54 \, b^{4} d^{4} x^{4} + 216 \, b^{4} c d^{3} x^{3} + 54 \, b^{4} c^{4} - 18 \, b^{2} c^{2} d^{2} + d^{4} + 18 \, {\left(18 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 36 \, {\left(6 \, b^{4} c^{3} d - b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} - 5 \, b^{2} d^{4}\right)} x^{2} + 18 \, {\left(9 \, b^{2} d^{4} x^{2} + 18 \, b^{2} c d^{3} x + 9 \, b^{2} c^{2} d^{2} - 5 \, d^{4}\right)} \cos\left(b x + a\right)^{2} + 36 \, {\left(3 \, b^{4} c^{3} d - 5 \, b^{2} c d^{3}\right)} x - 12 \, {\left({\left(6 \, b^{3} d^{4} x^{3} + 18 \, b^{3} c d^{3} x^{2} + 6 \, b^{3} c^{3} d - b c d^{3} + {\left(18 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{5} - {\left(6 \, b^{3} d^{4} x^{3} + 18 \, b^{3} c d^{3} x^{2} + 6 \, b^{3} c^{3} d - b c d^{3} + {\left(18 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d - 5 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} - 5 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{648 \, b^{5}}"," ",0,"1/648*(27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 2*(54*b^4*d^4*x^4 + 216*b^4*c*d^3*x^3 + 54*b^4*c^4 - 18*b^2*c^2*d^2 + d^4 + 18*(18*b^4*c^2*d^2 - b^2*d^4)*x^2 + 36*(6*b^4*c^3*d - b^2*c*d^3)*x)*cos(b*x + a)^6 - 3*(54*b^4*d^4*x^4 + 216*b^4*c*d^3*x^3 + 54*b^4*c^4 - 18*b^2*c^2*d^2 + d^4 + 18*(18*b^4*c^2*d^2 - b^2*d^4)*x^2 + 36*(6*b^4*c^3*d - b^2*c*d^3)*x)*cos(b*x + a)^4 + 18*(9*b^4*c^2*d^2 - 5*b^2*d^4)*x^2 + 18*(9*b^2*d^4*x^2 + 18*b^2*c*d^3*x + 9*b^2*c^2*d^2 - 5*d^4)*cos(b*x + a)^2 + 36*(3*b^4*c^3*d - 5*b^2*c*d^3)*x - 12*((6*b^3*d^4*x^3 + 18*b^3*c*d^3*x^2 + 6*b^3*c^3*d - b*c*d^3 + (18*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^5 - (6*b^3*d^4*x^3 + 18*b^3*c*d^3*x^2 + 6*b^3*c^3*d - b*c*d^3 + (18*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^3 - 3*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d - 5*b*c*d^3 + (9*b^3*c^2*d^2 - 5*b*d^4)*x)*cos(b*x + a))*sin(b*x + a))/b^5","B",0
156,1,349,0,0.458484," ","integrate((d*x+c)^3*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{9 \, b^{3} d^{3} x^{3} + 27 \, b^{3} c d^{2} x^{2} + 6 \, {\left(6 \, b^{3} d^{3} x^{3} + 18 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{3} - b c d^{2} + {\left(18 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{6} - 9 \, {\left(6 \, b^{3} d^{3} x^{3} + 18 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{3} - b c d^{2} + {\left(18 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} + 27 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(9 \, b^{3} c^{2} d - 5 \, b d^{3}\right)} x - {\left({\left(18 \, b^{2} d^{3} x^{2} + 36 \, b^{2} c d^{2} x + 18 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{5} - {\left(18 \, b^{2} d^{3} x^{2} + 36 \, b^{2} c d^{2} x + 18 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 5 \, d^{3}\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{216 \, b^{4}}"," ",0,"1/216*(9*b^3*d^3*x^3 + 27*b^3*c*d^2*x^2 + 6*(6*b^3*d^3*x^3 + 18*b^3*c*d^2*x^2 + 6*b^3*c^3 - b*c*d^2 + (18*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^6 - 9*(6*b^3*d^3*x^3 + 18*b^3*c*d^2*x^2 + 6*b^3*c^3 - b*c*d^2 + (18*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^4 + 27*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2 + 3*(9*b^3*c^2*d - 5*b*d^3)*x - ((18*b^2*d^3*x^2 + 36*b^2*c*d^2*x + 18*b^2*c^2*d - d^3)*cos(b*x + a)^5 - (18*b^2*d^3*x^2 + 36*b^2*c*d^2*x + 18*b^2*c^2*d - d^3)*cos(b*x + a)^3 - 3*(9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 5*d^3)*cos(b*x + a))*sin(b*x + a))/b^4","B",0
157,1,194,0,0.468442," ","integrate((d*x+c)^2*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(18 \, b^{2} d^{2} x^{2} + 36 \, b^{2} c d x + 18 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{6} + 9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x - 3 \, {\left(18 \, b^{2} d^{2} x^{2} + 36 \, b^{2} c d x + 18 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{4} + 9 \, d^{2} \cos\left(b x + a\right)^{2} - 6 \, {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{5} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{216 \, b^{3}}"," ",0,"1/216*(2*(18*b^2*d^2*x^2 + 36*b^2*c*d*x + 18*b^2*c^2 - d^2)*cos(b*x + a)^6 + 9*b^2*d^2*x^2 + 18*b^2*c*d*x - 3*(18*b^2*d^2*x^2 + 36*b^2*c*d*x + 18*b^2*c^2 - d^2)*cos(b*x + a)^4 + 9*d^2*cos(b*x + a)^2 - 6*(2*(b*d^2*x + b*c*d)*cos(b*x + a)^5 - 2*(b*d^2*x + b*c*d)*cos(b*x + a)^3 - 3*(b*d^2*x + b*c*d)*cos(b*x + a))*sin(b*x + a))/b^3","A",0
158,1,87,0,0.441405," ","integrate((d*x+c)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{6} - 18 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{4} + 3 \, b d x - {\left(2 \, d \cos\left(b x + a\right)^{5} - 2 \, d \cos\left(b x + a\right)^{3} - 3 \, d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{72 \, b^{2}}"," ",0,"1/72*(12*(b*d*x + b*c)*cos(b*x + a)^6 - 18*(b*d*x + b*c)*cos(b*x + a)^4 + 3*b*d*x - (2*d*cos(b*x + a)^5 - 2*d*cos(b*x + a)^3 - 3*d*cos(b*x + a))*sin(b*x + a))/b^2","A",0
159,1,156,0,0.439732," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left(\operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(\operatorname{Ci}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{6 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) + 6 \, \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right)}{64 \, d}"," ",0,"1/64*(3*(cos_integral(2*(b*d*x + b*c)/d) + cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) - (cos_integral(6*(b*d*x + b*c)/d) + cos_integral(-6*(b*d*x + b*c)/d))*sin(-6*(b*c - a*d)/d) - 2*cos(-6*(b*c - a*d)/d)*sin_integral(6*(b*d*x + b*c)/d) + 6*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d))/d","A",0
160,1,248,0,0.482917," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","\frac{6 \, {\left(b d x + b c\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) - 6 \, {\left(b d x + b c\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{6 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) + 32 \, {\left(d \cos\left(b x + a\right)^{5} - d \cos\left(b x + a\right)^{3}\right)} \sin\left(b x + a\right)}{32 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/32*(6*(b*d*x + b*c)*sin(-6*(b*c - a*d)/d)*sin_integral(6*(b*d*x + b*c)/d) - 6*(b*d*x + b*c)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + 3*((b*d*x + b*c)*cos_integral(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) - 3*((b*d*x + b*c)*cos_integral(6*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-6*(b*d*x + b*c)/d))*cos(-6*(b*c - a*d)/d) + 32*(d*cos(b*x + a)^5 - d*cos(b*x + a)^3)*sin(b*x + a))/(d^3*x + c*d^2)","A",0
161,1,434,0,0.538551," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{96 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{6} - 144 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{4} + 48 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} + 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + 16 \, {\left(d^{2} \cos\left(b x + a\right)^{5} - d^{2} \cos\left(b x + a\right)^{3}\right)} \sin\left(b x + a\right) - 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{6 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right)}{32 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/32*(96*(b*d^2*x + b*c*d)*cos(b*x + a)^6 - 144*(b*d^2*x + b*c*d)*cos(b*x + a)^4 + 48*(b*d^2*x + b*c*d)*cos(b*x + a)^2 + 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-6*(b*c - a*d)/d)*sin_integral(6*(b*d*x + b*c)/d) - 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + 16*(d^2*cos(b*x + a)^5 - d^2*cos(b*x + a)^3)*sin(b*x + a) - 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) + 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(6*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-6*(b*d*x + b*c)/d))*sin(-6*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
162,1,638,0,0.561038," ","integrate(cos(b*x+a)^3*sin(b*x+a)^3/(d*x+c)^4,x, algorithm=""fricas"")","\frac{48 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{6} - 72 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} + 24 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} - 54 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) + 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - 3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 27 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{6 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{6 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 16 \, {\left({\left(18 \, b^{2} d^{3} x^{2} + 36 \, b^{2} c d^{2} x + 18 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{5} - {\left(18 \, b^{2} d^{3} x^{2} + 36 \, b^{2} c d^{2} x + 18 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{48 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/48*(48*(b*d^3*x + b*c*d^2)*cos(b*x + a)^6 - 72*(b*d^3*x + b*c*d^2)*cos(b*x + a)^4 + 24*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2 - 54*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-6*(b*c - a*d)/d)*sin_integral(6*(b*d*x + b*c)/d) + 6*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - 3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) + 27*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(6*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-6*(b*d*x + b*c)/d))*cos(-6*(b*c - a*d)/d) - 16*((18*b^2*d^3*x^2 + 36*b^2*c*d^2*x + 18*b^2*c^2*d - d^3)*cos(b*x + a)^5 - (18*b^2*d^3*x^2 + 36*b^2*c*d^2*x + 18*b^2*c^2*d - d^3)*cos(b*x + a)^3 + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a))*sin(b*x + a))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
163,0,0,0,0.458778," ","integrate((d*x+c)^m*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{2} \cot\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*cos(b*x + a)^2*cot(b*x + a), x)","F",0
164,1,1453,0,0.660895," ","integrate((d*x+c)^4*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""fricas"")","-\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 48 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 48 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 48 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 48 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 3 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} - {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} - 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x - {\left(-8 i \, b^{3} d^{4} x^{3} - 24 i \, b^{3} c d^{3} x^{2} - 24 i \, b^{3} c^{2} d^{2} x - 8 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(8 i \, b^{3} d^{4} x^{3} + 24 i \, b^{3} c d^{3} x^{2} + 24 i \, b^{3} c^{2} d^{2} x + 8 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(8 i \, b^{3} d^{4} x^{3} + 24 i \, b^{3} c d^{3} x^{2} + 24 i \, b^{3} c^{2} d^{2} x + 8 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-8 i \, b^{3} d^{4} x^{3} - 24 i \, b^{3} c d^{3} x^{2} - 24 i \, b^{3} c^{2} d^{2} x - 8 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(48 i \, b d^{4} x + 48 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-48 i \, b d^{4} x - 48 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-48 i \, b d^{4} x - 48 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(48 i \, b d^{4} x + 48 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{4 \, b^{5}}"," ",0,"-1/4*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 48*d^4*polylog(5, cos(b*x + a) + I*sin(b*x + a)) + 48*d^4*polylog(5, cos(b*x + a) - I*sin(b*x + a)) + 48*d^4*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) + 48*d^4*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) + 3*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 - (2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 - 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(2*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)^2 + 2*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d - 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)*sin(b*x + a) + 2*(2*b^4*c^3*d - 3*b^2*c*d^3)*x - (-8*I*b^3*d^4*x^3 - 24*I*b^3*c*d^3*x^2 - 24*I*b^3*c^2*d^2*x - 8*I*b^3*c^3*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (8*I*b^3*d^4*x^3 + 24*I*b^3*c*d^3*x^2 + 24*I*b^3*c^2*d^2*x + 8*I*b^3*c^3*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (8*I*b^3*d^4*x^3 + 24*I*b^3*c*d^3*x^2 + 24*I*b^3*c^2*d^2*x + 8*I*b^3*c^3*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (-8*I*b^3*d^4*x^3 - 24*I*b^3*c*d^3*x^2 - 24*I*b^3*c^2*d^2*x - 8*I*b^3*c^3*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 2*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 2*(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (48*I*b*d^4*x + 48*I*b*c*d^3)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - (-48*I*b*d^4*x - 48*I*b*c*d^3)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - (-48*I*b*d^4*x - 48*I*b*c*d^3)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - (48*I*b*d^4*x + 48*I*b*c*d^3)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 24*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 24*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 24*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 24*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/b^5","C",0
165,1,984,0,0.585041," ","integrate((d*x+c)^3*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} - 24 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 24 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x - {\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{8 \, b^{4}}"," ",0,"-1/8*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 - 24*I*d^3*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + 24*I*d^3*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + 24*I*d^3*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - 24*I*d^3*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 - 3*b*c*d^2 + 3*(2*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^2 + 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)*sin(b*x + a) + 3*(2*b^3*c^2*d - b*d^3)*x - (-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 24*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 24*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 24*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 24*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/b^4","C",0
166,1,594,0,0.561732," ","integrate((d*x+c)^2*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x - {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{2} - 4 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 4 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 4 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 4 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right)}{4 \, b^{3}}"," ",0,"-1/4*(b^2*d^2*x^2 + 2*b^2*c*d*x - (2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 - d^2)*cos(b*x + a)^2 - 4*d^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 4*d^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 4*d^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 4*d^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - (-4*I*b*d^2*x - 4*I*b*c*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (4*I*b*d^2*x + 4*I*b*c*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (4*I*b*d^2*x + 4*I*b*c*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (-4*I*b*d^2*x - 4*I*b*c*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1))/b^3","C",0
167,1,292,0,0.587548," ","integrate((d*x+c)*cos(b*x+a)^2*cot(b*x+a),x, algorithm=""fricas"")","-\frac{b d x - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 i \, d {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 2 i \, d {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right)}{4 \, b^{2}}"," ",0,"-1/4*(b*d*x - 2*(b*d*x + b*c)*cos(b*x + a)^2 + d*cos(b*x + a)*sin(b*x + a) + 2*I*d*dilog(cos(b*x + a) + I*sin(b*x + a)) - 2*I*d*dilog(cos(b*x + a) - I*sin(b*x + a)) - 2*I*d*dilog(-cos(b*x + a) + I*sin(b*x + a)) + 2*I*d*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 2*(b*d*x + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b*d*x + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 2*(b*c - a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 2*(b*c - a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 2*(b*d*x + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b*d*x + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1))/b^2","B",0
168,0,0,0,0.462049," ","integrate(cos(b*x+a)^2*cot(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right)^{2} \cot\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(cos(b*x + a)^2*cot(b*x + a)/(d*x + c), x)","F",0
169,0,0,0,0.457730," ","integrate(cos(b*x+a)^2*cot(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right)^{2} \cot\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cos(b*x + a)^2*cot(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
170,0,0,0,0.427281," ","integrate((d*x+c)^m*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cos\left(b x + a\right) \cot\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*cos(b*x + a)*cot(b*x + a)^2, x)","F",0
171,1,1233,0,0.634300," ","integrate((d*x+c)^4*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} - 12 i \, d^{4} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 i \, d^{4} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 i \, d^{4} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 i \, d^{4} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 24 \, d^{4} + 12 \, {\left(b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} - 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 6 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + b^{3} c^{3} d - 6 \, b c d^{3} + 3 \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(-6 i \, b^{2} d^{4} x^{2} - 12 i \, b^{2} c d^{3} x - 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b^{2} d^{4} x^{2} + 12 i \, b^{2} c d^{3} x + 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b^{2} d^{4} x^{2} - 12 i \, b^{2} c d^{3} x - 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b^{2} d^{4} x^{2} + 12 i \, b^{2} c d^{3} x + 6 i \, b^{2} c^{2} d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 \, {\left(b d^{4} x + b c d^{3}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 8 \, {\left(b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x}{b^{5} \sin\left(b x + a\right)}"," ",0,"-(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 - 12*b^2*c^2*d^2 - 12*I*d^4*polylog(4, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*I*d^4*polylog(4, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 12*I*d^4*polylog(4, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*I*d^4*polylog(4, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 24*d^4 + 12*(b^4*c^2*d^2 - b^2*d^4)*x^2 - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 - 12*b^2*c^2*d^2 + 24*d^4 + 6*(b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d - 6*b^2*c*d^3)*x)*cos(b*x + a)^2 + 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + b^3*c^3*d - 6*b*c*d^3 + 3*(b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)*sin(b*x + a) - (-6*I*b^2*d^4*x^2 - 12*I*b^2*c*d^3*x - 6*I*b^2*c^2*d^2)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b^2*d^4*x^2 + 12*I*b^2*c*d^3*x + 6*I*b^2*c^2*d^2)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b^2*d^4*x^2 - 12*I*b^2*c*d^3*x - 6*I*b^2*c^2*d^2)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b^2*d^4*x^2 + 12*I*b^2*c*d^3*x + 6*I*b^2*c^2*d^2)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 12*(b*d^4*x + b*c*d^3)*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 12*(b*d^4*x + b*c*d^3)*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 12*(b*d^4*x + b*c*d^3)*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*(b*d^4*x + b*c*d^3)*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 8*(b^4*c^3*d - 3*b^2*c*d^3)*x)/(b^5*sin(b*x + a))","C",0
172,1,797,0,0.559226," ","integrate((d*x+c)^3*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b^{3} d^{3} x^{3} + 12 \, b^{3} c d^{2} x^{2} + 4 \, b^{3} c^{3} - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 \, b c d^{2} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 12 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x}{2 \, b^{4} \sin\left(b x + a\right)}"," ",0,"-1/2*(4*b^3*d^3*x^3 + 12*b^3*c*d^2*x^2 + 4*b^3*c^3 - 6*d^3*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 6*d^3*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 6*d^3*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 6*d^3*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 12*b*c*d^2 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cos(b*x + a)*sin(b*x + a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + 12*(b^3*c^2*d - b*d^3)*x)/(b^4*sin(b*x + a))","C",0
173,1,448,0,0.496770," ","integrate((d*x+c)^2*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + i \, d^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(b d^{2} x + b c d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d^{2} x + b c d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2 \, d^{2}}{b^{3} \sin\left(b x + a\right)}"," ",0,"-(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + I*d^2*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - I*d^2*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + I*d^2*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - I*d^2*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a)^2 + 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) + (b*d^2*x + b*c*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + (b*d^2*x + b*c*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - (b*c*d - a*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - (b*c*d - a*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - (b*d^2*x + a*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - (b*d^2*x + a*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 2*d^2)/(b^3*sin(b*x + a))","B",0
174,1,95,0,0.464049," ","integrate((d*x+c)*cos(b*x+a)*cot(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b d x - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + 2 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + d \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - d \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 4 \, b c}{2 \, b^{2} \sin\left(b x + a\right)}"," ",0,"-1/2*(4*b*d*x - 2*(b*d*x + b*c)*cos(b*x + a)^2 + 2*d*cos(b*x + a)*sin(b*x + a) + d*log(1/2*cos(b*x + a) + 1/2)*sin(b*x + a) - d*log(-1/2*cos(b*x + a) + 1/2)*sin(b*x + a) + 4*b*c)/(b^2*sin(b*x + a))","A",0
175,0,0,0,0.441569," ","integrate(cos(b*x+a)*cot(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \cot\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(cos(b*x + a)*cot(b*x + a)^2/(d*x + c), x)","F",0
176,0,0,0,0.450025," ","integrate(cos(b*x+a)*cot(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(b x + a\right) \cot\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cos(b*x + a)*cot(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
177,0,0,0,0.439400," ","integrate((d*x+c)^m*cot(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \cot\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*x + c)^m*cot(b*x + a)^3, x)","F",0
178,1,1747,0,0.582750," ","integrate((d*x+c)^4*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b^{4} d^{4} x^{4} + 16 \, b^{4} c d^{3} x^{3} + 24 \, b^{4} c^{2} d^{2} x^{2} + 16 \, b^{4} c^{3} d x + 4 \, b^{4} c^{4} + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d + 12 i \, b c d^{3} - 12 i \, {\left(b^{3} c^{2} d^{2} - b d^{4}\right)} x + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d - 12 i \, b c d^{3} + 12 i \, {\left(b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d - 12 i \, b c d^{3} + 12 i \, {\left(b^{3} c^{2} d^{2} - b d^{4}\right)} x + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d + 12 i \, b c d^{3} - 12 i \, {\left(b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} + {\left(a^{4} - 6 \, a^{2}\right)} d^{4} - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} + {\left(a^{4} - 6 \, a^{2}\right)} d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} + {\left(a^{4} - 6 \, a^{2}\right)} d^{4} - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} - 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} + {\left(a^{4} - 6 \, a^{2}\right)} d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} - {\left(a^{4} - 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} - {\left(a^{4} - 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} - {\left(a^{4} - 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} - 3 \, a\right)} b c d^{3} - {\left(a^{4} - 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 3 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) - d^{4}\right)} {\rm polylog}\left(5, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 3 \, {\left(d^{4} \cos\left(2 \, b x + 2 \, a\right) - d^{4}\right)} {\rm polylog}\left(5, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b d^{4} x + 6 i \, b c d^{3} + {\left(-6 i \, b d^{4} x - 6 i \, b c d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-6 i \, b d^{4} x - 6 i \, b c d^{3} + {\left(6 i \, b d^{4} x + 6 i \, b c d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - d^{4} - {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} - d^{4}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 8 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \sin\left(2 \, b x + 2 \, a\right)}{4 \, {\left(b^{5} \cos\left(2 \, b x + 2 \, a\right) - b^{5}\right)}}"," ",0,"1/4*(4*b^4*d^4*x^4 + 16*b^4*c*d^3*x^3 + 24*b^4*c^2*d^2*x^2 + 16*b^4*c^3*d*x + 4*b^4*c^4 + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d + 12*I*b*c*d^3 - 12*I*(b^3*c^2*d^2 - b*d^4)*x + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d - 12*I*b*c*d^3 + 12*I*(b^3*c^2*d^2 - b*d^4)*x)*cos(2*b*x + 2*a))*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d - 12*I*b*c*d^3 + 12*I*(b^3*c^2*d^2 - b*d^4)*x + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d + 12*I*b*c*d^3 - 12*I*(b^3*c^2*d^2 - b*d^4)*x)*cos(2*b*x + 2*a))*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 2*(b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 1)*b^2*c^2*d^2 - 4*(a^3 - 3*a)*b*c*d^3 + (a^4 - 6*a^2)*d^4 - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 1)*b^2*c^2*d^2 - 4*(a^3 - 3*a)*b*c*d^3 + (a^4 - 6*a^2)*d^4)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 1)*b^2*c^2*d^2 - 4*(a^3 - 3*a)*b*c*d^3 + (a^4 - 6*a^2)*d^4 - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 - 1)*b^2*c^2*d^2 - 4*(a^3 - 3*a)*b*c*d^3 + (a^4 - 6*a^2)*d^4)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 3*a)*b*c*d^3 - (a^4 - 6*a^2)*d^4 + 6*(b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(b^4*c^3*d - 3*b^2*c*d^3)*x - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 3*a)*b*c*d^3 - (a^4 - 6*a^2)*d^4 + 6*(b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 3*a)*b*c*d^3 - (a^4 - 6*a^2)*d^4 + 6*(b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(b^4*c^3*d - 3*b^2*c*d^3)*x - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 - 3*a)*b*c*d^3 - (a^4 - 6*a^2)*d^4 + 6*(b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + 3*(d^4*cos(2*b*x + 2*a) - d^4)*polylog(5, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + 3*(d^4*cos(2*b*x + 2*a) - d^4)*polylog(5, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + (6*I*b*d^4*x + 6*I*b*c*d^3 + (-6*I*b*d^4*x - 6*I*b*c*d^3)*cos(2*b*x + 2*a))*polylog(4, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (-6*I*b*d^4*x - 6*I*b*c*d^3 + (6*I*b*d^4*x + 6*I*b*c*d^3)*cos(2*b*x + 2*a))*polylog(4, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - d^4)*cos(2*b*x + 2*a))*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - d^4 - (b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 - d^4)*cos(2*b*x + 2*a))*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 8*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*sin(2*b*x + 2*a))/(b^5*cos(2*b*x + 2*a) - b^5)","C",0
179,1,1135,0,0.550494," ","integrate((d*x+c)^3*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{8 \, b^{3} d^{3} x^{3} + 24 \, b^{3} c d^{2} x^{2} + 24 \, b^{3} c^{2} d x + 8 \, b^{3} c^{3} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d + 6 i \, d^{3} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d - 6 i \, d^{3} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 1\right)} b c d^{2} - {\left(a^{3} - 3 \, a\right)} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 1\right)} b c d^{2} - {\left(a^{3} - 3 \, a\right)} d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 1\right)} b c d^{2} - {\left(a^{3} - 3 \, a\right)} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 1\right)} b c d^{2} - {\left(a^{3} - 3 \, a\right)} d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + {\left(-3 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) + 3 i \, d^{3}\right)} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(3 i \, d^{3} \cos\left(2 \, b x + 2 \, a\right) - 3 i \, d^{3}\right)} {\rm polylog}\left(4, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 12 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \sin\left(2 \, b x + 2 \, a\right)}{8 \, {\left(b^{4} \cos\left(2 \, b x + 2 \, a\right) - b^{4}\right)}}"," ",0,"1/8*(8*b^3*d^3*x^3 + 24*b^3*c*d^2*x^2 + 24*b^3*c^2*d*x + 8*b^3*c^3 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d + 6*I*d^3 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d - 6*I*d^3)*cos(2*b*x + 2*a))*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d - 6*I*d^3 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d + 6*I*d^3)*cos(2*b*x + 2*a))*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 1)*b*c*d^2 - (a^3 - 3*a)*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 1)*b*c*d^2 - (a^3 - 3*a)*d^3)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 1)*b*c*d^2 - (a^3 - 3*a)*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 1)*b*c*d^2 - (a^3 - 3*a)*d^3)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 3*a)*d^3 + 3*(b^3*c^2*d - b*d^3)*x - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 3*a)*d^3 + 3*(b^3*c^2*d - b*d^3)*x)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 3*a)*d^3 + 3*(b^3*c^2*d - b*d^3)*x - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 3*a)*d^3 + 3*(b^3*c^2*d - b*d^3)*x)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + (-3*I*d^3*cos(2*b*x + 2*a) + 3*I*d^3)*polylog(4, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (3*I*d^3*cos(2*b*x + 2*a) - 3*I*d^3)*polylog(4, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a))*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(2*b*x + 2*a))*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 12*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*sin(2*b*x + 2*a))/(b^4*cos(2*b*x + 2*a) - b^4)","C",0
180,1,655,0,0.473702," ","integrate((d*x+c)^2*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b^{2} d^{2} x^{2} + 8 \, b^{2} c d x + 4 \, b^{2} c^{2} + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 1\right)} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 1\right)} d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 1\right)} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 1\right)} d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) - {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) - {\left(d^{2} \cos\left(2 \, b x + 2 \, a\right) - d^{2}\right)} {\rm polylog}\left(3, \cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 4 \, {\left(b d^{2} x + b c d\right)} \sin\left(2 \, b x + 2 \, a\right)}{4 \, {\left(b^{3} \cos\left(2 \, b x + 2 \, a\right) - b^{3}\right)}}"," ",0,"1/4*(4*b^2*d^2*x^2 + 8*b^2*c*d*x + 4*b^2*c^2 + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(2*b*x + 2*a))*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(2*b*x + 2*a))*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 2*(b^2*c^2 - 2*a*b*c*d + (a^2 - 1)*d^2 - (b^2*c^2 - 2*a*b*c*d + (a^2 - 1)*d^2)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b^2*c^2 - 2*a*b*c*d + (a^2 - 1)*d^2 - (b^2*c^2 - 2*a*b*c*d + (a^2 - 1)*d^2)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) - (d^2*cos(2*b*x + 2*a) - d^2)*polylog(3, cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) - (d^2*cos(2*b*x + 2*a) - d^2)*polylog(3, cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 4*(b*d^2*x + b*c*d)*sin(2*b*x + 2*a))/(b^3*cos(2*b*x + 2*a) - b^3)","C",0
181,1,339,0,0.458647," ","integrate((d*x+c)*cot(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b d x + 4 \, b c + {\left(i \, d \cos\left(2 \, b x + 2 \, a\right) - i \, d\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right)\right) + {\left(-i \, d \cos\left(2 \, b x + 2 \, a\right) + i \, d\right)} {\rm Li}_2\left(\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right)\right) + 2 \, {\left(b c - a d - {\left(b c - a d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) + \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b c - a d - {\left(b c - a d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(2 \, b x + 2 \, a\right) - \frac{1}{2} i \, \sin\left(2 \, b x + 2 \, a\right) + \frac{1}{2}\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) + i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, {\left(b d x + a d - {\left(b d x + a d\right)} \cos\left(2 \, b x + 2 \, a\right)\right)} \log\left(-\cos\left(2 \, b x + 2 \, a\right) - i \, \sin\left(2 \, b x + 2 \, a\right) + 1\right) + 2 \, d \sin\left(2 \, b x + 2 \, a\right)}{4 \, {\left(b^{2} \cos\left(2 \, b x + 2 \, a\right) - b^{2}\right)}}"," ",0,"1/4*(4*b*d*x + 4*b*c + (I*d*cos(2*b*x + 2*a) - I*d)*dilog(cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a)) + (-I*d*cos(2*b*x + 2*a) + I*d)*dilog(cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a)) + 2*(b*c - a*d - (b*c - a*d)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) + 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b*c - a*d - (b*c - a*d)*cos(2*b*x + 2*a))*log(-1/2*cos(2*b*x + 2*a) - 1/2*I*sin(2*b*x + 2*a) + 1/2) + 2*(b*d*x + a*d - (b*d*x + a*d)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) + I*sin(2*b*x + 2*a) + 1) + 2*(b*d*x + a*d - (b*d*x + a*d)*cos(2*b*x + 2*a))*log(-cos(2*b*x + 2*a) - I*sin(2*b*x + 2*a) + 1) + 2*d*sin(2*b*x + 2*a))/(b^2*cos(2*b*x + 2*a) - b^2)","B",0
182,0,0,0,0.438329," ","integrate(cot(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(cot(b*x + a)^3/(d*x + c), x)","F",0
183,0,0,0,0.471157," ","integrate(cot(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cot\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(cot(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
184,1,376,0,0.566700," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(192 \, b^{3} d^{2} x^{2} + 384 \, b^{3} c d x + 192 \, b^{3} c^{2} + 360 \, b d^{2} \cos\left(b x + a\right)^{2} - 8 \, {\left(64 \, b^{3} d^{2} x^{2} + 128 \, b^{3} c d x + 64 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 225 \, b d^{2} + 160 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{8192 \, b^{4}}"," ",0,"-1/8192*(15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 480*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 480*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(192*b^3*d^2*x^2 + 384*b^3*c*d*x + 192*b^3*c^2 + 360*b*d^2*cos(b*x + a)^2 - 8*(64*b^3*d^2*x^2 + 128*b^3*c*d*x + 64*b^3*c^2 - 15*b*d^2)*cos(b*x + a)^4 - 225*b*d^2 + 160*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 + 3*(b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
185,1,294,0,0.502920," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 16 \, {\left(16 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} - 6 \, b^{2} d x - 6 \, b^{2} c - 3 \, {\left(2 \, b d \cos\left(b x + a\right)^{3} + 3 \, b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{1024 \, b^{3}}"," ",0,"-1/1024*(3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 48*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 48*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 16*(16*(b^2*d*x + b^2*c)*cos(b*x + a)^4 - 6*b^2*d*x - 6*b^2*c - 3*(2*b*d*cos(b*x + a)^3 + 3*b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
186,1,233,0,0.509812," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 8 \, \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 8 \, \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(8 \, b \cos\left(b x + a\right)^{4} - 3 \, b\right)} \sqrt{d x + c}}{128 \, b^{2}}"," ",0,"1/128*(sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 8*pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 8*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(8*b*cos(b*x + a)^4 - 3*b)*sqrt(d*x + c))/b^2","A",0
187,1,233,0,0.545601," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 8 \, \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 8 \, \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(8 \, b \cos\left(b x + a\right)^{4} - 3 \, b\right)} \sqrt{d x + c}}{128 \, b^{2}}"," ",0,"1/128*(sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 8*pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 8*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(8*b*cos(b*x + a)^4 - 3*b)*sqrt(d*x + c))/b^2","A",0
188,1,294,0,0.506821," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 48 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 16 \, {\left(16 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} - 6 \, b^{2} d x - 6 \, b^{2} c - 3 \, {\left(2 \, b d \cos\left(b x + a\right)^{3} + 3 \, b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{1024 \, b^{3}}"," ",0,"-1/1024*(3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 48*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 48*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 16*(16*(b^2*d*x + b^2*c)*cos(b*x + a)^4 - 6*b^2*d*x - 6*b^2*c - 3*(2*b*d*cos(b*x + a)^3 + 3*b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
189,1,376,0,0.534978," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 15 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{4 \, {\left(b c - a d\right)}}{d}\right) + 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 480 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 4 \, {\left(192 \, b^{3} d^{2} x^{2} + 384 \, b^{3} c d x + 192 \, b^{3} c^{2} + 360 \, b d^{2} \cos\left(b x + a\right)^{2} - 8 \, {\left(64 \, b^{3} d^{2} x^{2} + 128 \, b^{3} c d x + 64 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 225 \, b d^{2} + 160 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{8192 \, b^{4}}"," ",0,"-1/8192*(15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-4*(b*c - a*d)/d)*fresnel_cos(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-4*(b*c - a*d)/d) + 480*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 480*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(192*b^3*d^2*x^2 + 384*b^3*c*d*x + 192*b^3*c^2 + 360*b*d^2*cos(b*x + a)^2 - 8*(64*b^3*d^2*x^2 + 128*b^3*c*d*x + 64*b^3*c^2 - 15*b*d^2)*cos(b*x + a)^4 - 225*b*d^2 + 160*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 + 3*(b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
190,1,548,0,0.578966," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 480 \, {\left(90 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{5} - 50 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 300 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) - {\left(120 \, b^{3} d^{2} x^{2} + 240 \, b^{3} c d x + 120 \, b^{3} c^{2} - 9 \, {\left(20 \, b^{3} d^{2} x^{2} + 40 \, b^{3} c d x + 20 \, b^{3} c^{2} - 3 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 428 \, b d^{2} + {\left(60 \, b^{3} d^{2} x^{2} + 120 \, b^{3} c d x + 60 \, b^{3} c^{2} + 11 \, b d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{432000 \, b^{4}}"," ",0,"-1/432000*(81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) + 480*(90*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^5 - 50*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 300*(b^2*d^2*x + b^2*c*d)*cos(b*x + a) - (120*b^3*d^2*x^2 + 240*b^3*c*d*x + 120*b^3*c^2 - 9*(20*b^3*d^2*x^2 + 40*b^3*c*d*x + 20*b^3*c^2 - 3*b*d^2)*cos(b*x + a)^4 - 428*b*d^2 + (60*b^3*d^2*x^2 + 120*b^3*c*d*x + 60*b^3*c^2 + 11*b*d^2)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
191,1,446,0,0.559615," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 480 \, {\left(9 \, b d \cos\left(b x + a\right)^{5} - 5 \, b d \cos\left(b x + a\right)^{3} - 30 \, b d \cos\left(b x + a\right) + 10 \, {\left(3 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} - 2 \, b^{2} d x - 2 \, b^{2} c - {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{72000 \, b^{3}}"," ",0,"1/72000*(27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) - 480*(9*b*d*cos(b*x + a)^5 - 5*b*d*cos(b*x + a)^3 - 30*b*d*cos(b*x + a) + 10*(3*(b^2*d*x + b^2*c)*cos(b*x + a)^4 - 2*b^2*d*x - 2*b^2*c - (b^2*d*x + b^2*c)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
192,1,365,0,0.540964," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 480 \, {\left(3 \, b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2} - 2 \, b\right)} \sqrt{d x + c} \sin\left(b x + a\right)}{7200 \, b^{2}}"," ",0,"1/7200*(9*sqrt(10)*pi*d*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 9*sqrt(10)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) - 480*(3*b*cos(b*x + a)^4 - b*cos(b*x + a)^2 - 2*b)*sqrt(d*x + c)*sin(b*x + a))/b^2","A",0
193,1,365,0,0.538214," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 450 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 25 \, \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 9 \, \sqrt{10} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 480 \, {\left(3 \, b \cos\left(b x + a\right)^{4} - b \cos\left(b x + a\right)^{2} - 2 \, b\right)} \sqrt{d x + c} \sin\left(b x + a\right)}{7200 \, b^{2}}"," ",0,"1/7200*(9*sqrt(10)*pi*d*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 450*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 25*sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 9*sqrt(10)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) - 480*(3*b*cos(b*x + a)^4 - b*cos(b*x + a)^2 - 2*b)*sqrt(d*x + c)*sin(b*x + a))/b^2","A",0
194,1,446,0,0.585206," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 6750 \, \sqrt{2} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 125 \, \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 27 \, \sqrt{10} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) - 480 \, {\left(9 \, b d \cos\left(b x + a\right)^{5} - 5 \, b d \cos\left(b x + a\right)^{3} - 30 \, b d \cos\left(b x + a\right) + 10 \, {\left(3 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} - 2 \, b^{2} d x - 2 \, b^{2} c - {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{72000 \, b^{3}}"," ",0,"1/72000*(27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 6750*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 125*sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 27*sqrt(10)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) - 480*(9*b*d*cos(b*x + a)^5 - 5*b*d*cos(b*x + a)^3 - 30*b*d*cos(b*x + a) + 10*(3*(b^2*d*x + b^2*c)*cos(b*x + a)^4 - 2*b^2*d*x - 2*b^2*c - (b^2*d*x + b^2*c)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
195,1,548,0,0.570596," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 101250 \, \sqrt{2} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 625 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 81 \, \sqrt{10} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{10} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{5 \, {\left(b c - a d\right)}}{d}\right) + 480 \, {\left(90 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{5} - 50 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 300 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) - {\left(120 \, b^{3} d^{2} x^{2} + 240 \, b^{3} c d x + 120 \, b^{3} c^{2} - 9 \, {\left(20 \, b^{3} d^{2} x^{2} + 40 \, b^{3} c d x + 20 \, b^{3} c^{2} - 3 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 428 \, b d^{2} + {\left(60 \, b^{3} d^{2} x^{2} + 120 \, b^{3} c d x + 60 \, b^{3} c^{2} + 11 \, b d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{432000 \, b^{4}}"," ",0,"-1/432000*(81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*cos(-5*(b*c - a*d)/d)*fresnel_sin(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 101250*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 625*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 81*sqrt(10)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(10)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-5*(b*c - a*d)/d) + 480*(90*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^5 - 50*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 300*(b^2*d^2*x + b^2*c*d)*cos(b*x + a) - (120*b^3*d^2*x^2 + 240*b^3*c*d*x + 120*b^3*c^2 - 9*(20*b^3*d^2*x^2 + 40*b^3*c*d*x + 20*b^3*c^2 - 3*b*d^2)*cos(b*x + a)^4 - 428*b*d^2 + (60*b^3*d^2*x^2 + 120*b^3*c*d*x + 60*b^3*c^2 + 11*b*d^2)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
196,1,445,0,0.594221," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{5 \, \sqrt{3} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 5 \, \sqrt{3} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 1215 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 1215 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 96 \, {\left(24 \, b^{3} d^{2} x^{2} + 2 \, {\left(48 \, b^{3} d^{2} x^{2} + 96 \, b^{3} c d x + 48 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{6} + 48 \, b^{3} c d x + 24 \, b^{3} c^{2} + 45 \, b d^{2} \cos\left(b x + a\right)^{2} - 3 \, {\left(48 \, b^{3} d^{2} x^{2} + 96 \, b^{3} c d x + 48 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 25 \, b d^{2} - 20 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{5} - 2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{55296 \, b^{4}}"," ",0,"1/55296*(5*sqrt(3)*pi*d^3*sqrt(b/(pi*d))*cos(-6*(b*c - a*d)/d)*fresnel_cos(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 5*sqrt(3)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-6*(b*c - a*d)/d) - 1215*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 1215*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 96*(24*b^3*d^2*x^2 + 2*(48*b^3*d^2*x^2 + 96*b^3*c*d*x + 48*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^6 + 48*b^3*c*d*x + 24*b^3*c^2 + 45*b*d^2*cos(b*x + a)^2 - 3*(48*b^3*d^2*x^2 + 96*b^3*c*d*x + 48*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^4 - 25*b*d^2 - 20*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^5 - 2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 3*(b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
197,1,326,0,0.559127," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\sqrt{3} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + \sqrt{3} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 81 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 81 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 96 \, {\left(8 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{6} - 12 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} + 2 \, b^{2} d x + 2 \, b^{2} c - {\left(2 \, b d \cos\left(b x + a\right)^{5} - 2 \, b d \cos\left(b x + a\right)^{3} - 3 \, b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{4608 \, b^{3}}"," ",0,"1/4608*(sqrt(3)*pi*d^2*sqrt(b/(pi*d))*cos(-6*(b*c - a*d)/d)*fresnel_sin(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d))) + sqrt(3)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-6*(b*c - a*d)/d) - 81*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 81*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 96*(8*(b^2*d*x + b^2*c)*cos(b*x + a)^6 - 12*(b^2*d*x + b^2*c)*cos(b*x + a)^4 + 2*b^2*d*x + 2*b^2*c - (2*b*d*cos(b*x + a)^5 - 2*b*d*cos(b*x + a)^3 - 3*b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
198,1,242,0,0.510714," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{3} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{3} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 27 \, \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 48 \, {\left(4 \, b \cos\left(b x + a\right)^{6} - 6 \, b \cos\left(b x + a\right)^{4} + b\right)} \sqrt{d x + c}}{1152 \, b^{2}}"," ",0,"-1/1152*(sqrt(3)*pi*d*sqrt(b/(pi*d))*cos(-6*(b*c - a*d)/d)*fresnel_cos(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(3)*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-6*(b*c - a*d)/d) - 27*pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 48*(4*b*cos(b*x + a)^6 - 6*b*cos(b*x + a)^4 + b)*sqrt(d*x + c))/b^2","A",0
199,1,242,0,0.564399," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{3} \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{3} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 27 \, \pi d \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \pi d \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 48 \, {\left(4 \, b \cos\left(b x + a\right)^{6} - 6 \, b \cos\left(b x + a\right)^{4} + b\right)} \sqrt{d x + c}}{1152 \, b^{2}}"," ",0,"-1/1152*(sqrt(3)*pi*d*sqrt(b/(pi*d))*cos(-6*(b*c - a*d)/d)*fresnel_cos(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(3)*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-6*(b*c - a*d)/d) - 27*pi*d*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*pi*d*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 48*(4*b*cos(b*x + a)^6 - 6*b*cos(b*x + a)^4 + b)*sqrt(d*x + c))/b^2","A",0
200,1,326,0,0.580003," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{\sqrt{3} \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + \sqrt{3} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 81 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 81 \, \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 96 \, {\left(8 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{6} - 12 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{4} + 2 \, b^{2} d x + 2 \, b^{2} c - {\left(2 \, b d \cos\left(b x + a\right)^{5} - 2 \, b d \cos\left(b x + a\right)^{3} - 3 \, b d \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{4608 \, b^{3}}"," ",0,"1/4608*(sqrt(3)*pi*d^2*sqrt(b/(pi*d))*cos(-6*(b*c - a*d)/d)*fresnel_sin(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d))) + sqrt(3)*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-6*(b*c - a*d)/d) - 81*pi*d^2*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 81*pi*d^2*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 96*(8*(b^2*d*x + b^2*c)*cos(b*x + a)^6 - 12*(b^2*d*x + b^2*c)*cos(b*x + a)^4 + 2*b^2*d*x + 2*b^2*c - (2*b*d*cos(b*x + a)^5 - 2*b*d*cos(b*x + a)^3 - 3*b*d*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
201,1,445,0,0.605676," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{5 \, \sqrt{3} \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 5 \, \sqrt{3} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{6 \, {\left(b c - a d\right)}}{d}\right) - 1215 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{C}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 1215 \, \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(2 \, \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 96 \, {\left(24 \, b^{3} d^{2} x^{2} + 2 \, {\left(48 \, b^{3} d^{2} x^{2} + 96 \, b^{3} c d x + 48 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{6} + 48 \, b^{3} c d x + 24 \, b^{3} c^{2} + 45 \, b d^{2} \cos\left(b x + a\right)^{2} - 3 \, {\left(48 \, b^{3} d^{2} x^{2} + 96 \, b^{3} c d x + 48 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{4} - 25 \, b d^{2} - 20 \, {\left(2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{5} - 2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} - 3 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{55296 \, b^{4}}"," ",0,"1/55296*(5*sqrt(3)*pi*d^3*sqrt(b/(pi*d))*cos(-6*(b*c - a*d)/d)*fresnel_cos(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 5*sqrt(3)*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(3)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-6*(b*c - a*d)/d) - 1215*pi*d^3*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 1215*pi*d^3*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + 96*(24*b^3*d^2*x^2 + 2*(48*b^3*d^2*x^2 + 96*b^3*c*d*x + 48*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^6 + 48*b^3*c*d*x + 24*b^3*c^2 + 45*b*d^2*cos(b*x + a)^2 - 3*(48*b^3*d^2*x^2 + 96*b^3*c*d*x + 48*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^4 - 25*b*d^2 - 20*(2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^5 - 2*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 - 3*(b^2*d^2*x + b^2*c*d)*cos(b*x + a))*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
202,1,244,0,0.510401," ","integrate(x^3*cos(x)^2*cot(x)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{3} + 24 \, x^{2} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) \sin\left(x\right) + 24 \, x^{2} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) \sin\left(x\right) + 24 \, x^{2} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) \sin\left(x\right) + 24 \, x^{2} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) \sin\left(x\right) - 48 i \, x {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) \sin\left(x\right) + 48 i \, x {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) \sin\left(x\right) + 48 i \, x {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) \sin\left(x\right) - 48 i \, x {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) \sin\left(x\right) - 12 \, {\left(2 \, x^{3} - x\right)} \cos\left(x\right) - 3 \, {\left(2 \, x^{4} + 2 \, {\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{2} - 2 \, x^{2} + 1\right)} \sin\left(x\right) + 48 \, {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) \sin\left(x\right) + 48 \, {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) \sin\left(x\right) + 48 \, {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) \sin\left(x\right) + 48 \, {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) \sin\left(x\right)}{16 \, \sin\left(x\right)}"," ",0,"1/16*(4*(2*x^3 - 3*x)*cos(x)^3 + 24*x^2*log(cos(x) + I*sin(x) + 1)*sin(x) + 24*x^2*log(cos(x) - I*sin(x) + 1)*sin(x) + 24*x^2*log(-cos(x) + I*sin(x) + 1)*sin(x) + 24*x^2*log(-cos(x) - I*sin(x) + 1)*sin(x) - 48*I*x*dilog(cos(x) + I*sin(x))*sin(x) + 48*I*x*dilog(cos(x) - I*sin(x))*sin(x) + 48*I*x*dilog(-cos(x) + I*sin(x))*sin(x) - 48*I*x*dilog(-cos(x) - I*sin(x))*sin(x) - 12*(2*x^3 - x)*cos(x) - 3*(2*x^4 + 2*(2*x^2 - 1)*cos(x)^2 - 2*x^2 + 1)*sin(x) + 48*polylog(3, cos(x) + I*sin(x))*sin(x) + 48*polylog(3, cos(x) - I*sin(x))*sin(x) + 48*polylog(3, -cos(x) + I*sin(x))*sin(x) + 48*polylog(3, -cos(x) - I*sin(x))*sin(x))/sin(x)","C",0
203,1,162,0,0.483726," ","integrate(x^2*cos(x)^2*cot(x)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{3} + 4 \, x \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) \sin\left(x\right) + 4 \, x \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) \sin\left(x\right) + 4 \, x \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) \sin\left(x\right) + 4 \, x \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) \sin\left(x\right) - {\left(6 \, x^{2} - 1\right)} \cos\left(x\right) - {\left(2 \, x^{3} + 2 \, x \cos\left(x\right)^{2} - x\right)} \sin\left(x\right) - 4 i \, {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) \sin\left(x\right) + 4 i \, {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) \sin\left(x\right) + 4 i \, {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) \sin\left(x\right) - 4 i \, {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) \sin\left(x\right)}{4 \, \sin\left(x\right)}"," ",0,"1/4*((2*x^2 - 1)*cos(x)^3 + 4*x*log(cos(x) + I*sin(x) + 1)*sin(x) + 4*x*log(cos(x) - I*sin(x) + 1)*sin(x) + 4*x*log(-cos(x) + I*sin(x) + 1)*sin(x) + 4*x*log(-cos(x) - I*sin(x) + 1)*sin(x) - (6*x^2 - 1)*cos(x) - (2*x^3 + 2*x*cos(x)^2 - x)*sin(x) - 4*I*dilog(cos(x) + I*sin(x))*sin(x) + 4*I*dilog(cos(x) - I*sin(x))*sin(x) + 4*I*dilog(-cos(x) + I*sin(x))*sin(x) - 4*I*dilog(-cos(x) - I*sin(x))*sin(x))/sin(x)","B",0
204,1,45,0,0.461189," ","integrate(x*cos(x)^2*cot(x)^2,x, algorithm=""fricas"")","\frac{4 \, x \cos\left(x\right)^{3} - 12 \, x \cos\left(x\right) - {\left(6 \, x^{2} + 2 \, \cos\left(x\right)^{2} - 1\right)} \sin\left(x\right) + 8 \, \log\left(\frac{1}{2} \, \sin\left(x\right)\right) \sin\left(x\right)}{8 \, \sin\left(x\right)}"," ",0,"1/8*(4*x*cos(x)^3 - 12*x*cos(x) - (6*x^2 + 2*cos(x)^2 - 1)*sin(x) + 8*log(1/2*sin(x))*sin(x))/sin(x)","A",0
205,1,508,0,0.510423," ","integrate(x^3*cos(x)^2*cot(x)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{4} - 2 \, x^{3} - 3 \, {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{2} - {\left({\left(24 i \, x^{2} - 12 i\right)} \cos\left(x\right)^{2} - 24 i \, x^{2} + 12 i\right)} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left({\left(-24 i \, x^{2} + 12 i\right)} \cos\left(x\right)^{2} + 24 i \, x^{2} - 12 i\right)} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) - {\left({\left(-24 i \, x^{2} + 12 i\right)} \cos\left(x\right)^{2} + 24 i \, x^{2} - 12 i\right)} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left({\left(24 i \, x^{2} - 12 i\right)} \cos\left(x\right)^{2} - 24 i \, x^{2} + 12 i\right)} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) - 4 \, {\left(2 \, x^{3} - {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{2} - 3 \, x\right)} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - 4 \, {\left(2 \, x^{3} - {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{2} - 3 \, x\right)} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - 4 \, {\left(2 \, x^{3} - {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{2} - 3 \, x\right)} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) - 4 \, {\left(2 \, x^{3} - {\left(2 \, x^{3} - 3 \, x\right)} \cos\left(x\right)^{2} - 3 \, x\right)} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - {\left(-48 i \, \cos\left(x\right)^{2} + 48 i\right)} {\rm polylog}\left(4, \cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left(48 i \, \cos\left(x\right)^{2} - 48 i\right)} {\rm polylog}\left(4, \cos\left(x\right) - i \, \sin\left(x\right)\right) - {\left(48 i \, \cos\left(x\right)^{2} - 48 i\right)} {\rm polylog}\left(4, -\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left(-48 i \, \cos\left(x\right)^{2} + 48 i\right)} {\rm polylog}\left(4, -\cos\left(x\right) - i \, \sin\left(x\right)\right) + 48 \, {\left(x \cos\left(x\right)^{2} - x\right)} {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 48 \, {\left(x \cos\left(x\right)^{2} - x\right)} {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 48 \, {\left(x \cos\left(x\right)^{2} - x\right)} {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 48 \, {\left(x \cos\left(x\right)^{2} - x\right)} {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) - 3 \, {\left({\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{3} + {\left(2 \, x^{2} + 1\right)} \cos\left(x\right)\right)} \sin\left(x\right) - 3 \, x}{8 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/8*(2*(2*x^3 - 3*x)*cos(x)^4 - 2*x^3 - 3*(2*x^3 - 3*x)*cos(x)^2 - ((24*I*x^2 - 12*I)*cos(x)^2 - 24*I*x^2 + 12*I)*dilog(cos(x) + I*sin(x)) - ((-24*I*x^2 + 12*I)*cos(x)^2 + 24*I*x^2 - 12*I)*dilog(cos(x) - I*sin(x)) - ((-24*I*x^2 + 12*I)*cos(x)^2 + 24*I*x^2 - 12*I)*dilog(-cos(x) + I*sin(x)) - ((24*I*x^2 - 12*I)*cos(x)^2 - 24*I*x^2 + 12*I)*dilog(-cos(x) - I*sin(x)) - 4*(2*x^3 - (2*x^3 - 3*x)*cos(x)^2 - 3*x)*log(cos(x) + I*sin(x) + 1) - 4*(2*x^3 - (2*x^3 - 3*x)*cos(x)^2 - 3*x)*log(cos(x) - I*sin(x) + 1) - 4*(2*x^3 - (2*x^3 - 3*x)*cos(x)^2 - 3*x)*log(-cos(x) + I*sin(x) + 1) - 4*(2*x^3 - (2*x^3 - 3*x)*cos(x)^2 - 3*x)*log(-cos(x) - I*sin(x) + 1) - (-48*I*cos(x)^2 + 48*I)*polylog(4, cos(x) + I*sin(x)) - (48*I*cos(x)^2 - 48*I)*polylog(4, cos(x) - I*sin(x)) - (48*I*cos(x)^2 - 48*I)*polylog(4, -cos(x) + I*sin(x)) - (-48*I*cos(x)^2 + 48*I)*polylog(4, -cos(x) - I*sin(x)) + 48*(x*cos(x)^2 - x)*polylog(3, cos(x) + I*sin(x)) + 48*(x*cos(x)^2 - x)*polylog(3, cos(x) - I*sin(x)) + 48*(x*cos(x)^2 - x)*polylog(3, -cos(x) + I*sin(x)) + 48*(x*cos(x)^2 - x)*polylog(3, -cos(x) - I*sin(x)) - 3*((2*x^2 - 1)*cos(x)^3 + (2*x^2 + 1)*cos(x))*sin(x) - 3*x)/(cos(x)^2 - 1)","C",0
206,1,370,0,0.535807," ","integrate(x^2*cos(x)^2*cot(x)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{4} - 3 \, {\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{2} - 2 \, x^{2} - {\left(16 i \, x \cos\left(x\right)^{2} - 16 i \, x\right)} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left(-16 i \, x \cos\left(x\right)^{2} + 16 i \, x\right)} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) - {\left(-16 i \, x \cos\left(x\right)^{2} + 16 i \, x\right)} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left(16 i \, x \cos\left(x\right)^{2} - 16 i \, x\right)} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) + 4 \, {\left({\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{2} - 2 \, x^{2} + 1\right)} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + 4 \, {\left({\left(2 \, x^{2} - 1\right)} \cos\left(x\right)^{2} - 2 \, x^{2} + 1\right)} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - 4 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) + \frac{1}{2} i \, \sin\left(x\right) + \frac{1}{2}\right) - 4 \, {\left(\cos\left(x\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(x\right) - \frac{1}{2} i \, \sin\left(x\right) + \frac{1}{2}\right) + 8 \, {\left(x^{2} \cos\left(x\right)^{2} - x^{2}\right)} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + 8 \, {\left(x^{2} \cos\left(x\right)^{2} - x^{2}\right)} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + 16 \, {\left(\cos\left(x\right)^{2} - 1\right)} {\rm polylog}\left(3, \cos\left(x\right) + i \, \sin\left(x\right)\right) + 16 \, {\left(\cos\left(x\right)^{2} - 1\right)} {\rm polylog}\left(3, \cos\left(x\right) - i \, \sin\left(x\right)\right) + 16 \, {\left(\cos\left(x\right)^{2} - 1\right)} {\rm polylog}\left(3, -\cos\left(x\right) + i \, \sin\left(x\right)\right) + 16 \, {\left(\cos\left(x\right)^{2} - 1\right)} {\rm polylog}\left(3, -\cos\left(x\right) - i \, \sin\left(x\right)\right) - 4 \, {\left(x \cos\left(x\right)^{3} + x \cos\left(x\right)\right)} \sin\left(x\right) - 1}{8 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/8*(2*(2*x^2 - 1)*cos(x)^4 - 3*(2*x^2 - 1)*cos(x)^2 - 2*x^2 - (16*I*x*cos(x)^2 - 16*I*x)*dilog(cos(x) + I*sin(x)) - (-16*I*x*cos(x)^2 + 16*I*x)*dilog(cos(x) - I*sin(x)) - (-16*I*x*cos(x)^2 + 16*I*x)*dilog(-cos(x) + I*sin(x)) - (16*I*x*cos(x)^2 - 16*I*x)*dilog(-cos(x) - I*sin(x)) + 4*((2*x^2 - 1)*cos(x)^2 - 2*x^2 + 1)*log(cos(x) + I*sin(x) + 1) + 4*((2*x^2 - 1)*cos(x)^2 - 2*x^2 + 1)*log(cos(x) - I*sin(x) + 1) - 4*(cos(x)^2 - 1)*log(-1/2*cos(x) + 1/2*I*sin(x) + 1/2) - 4*(cos(x)^2 - 1)*log(-1/2*cos(x) - 1/2*I*sin(x) + 1/2) + 8*(x^2*cos(x)^2 - x^2)*log(-cos(x) + I*sin(x) + 1) + 8*(x^2*cos(x)^2 - x^2)*log(-cos(x) - I*sin(x) + 1) + 16*(cos(x)^2 - 1)*polylog(3, cos(x) + I*sin(x)) + 16*(cos(x)^2 - 1)*polylog(3, cos(x) - I*sin(x)) + 16*(cos(x)^2 - 1)*polylog(3, -cos(x) + I*sin(x)) + 16*(cos(x)^2 - 1)*polylog(3, -cos(x) - I*sin(x)) - 4*(x*cos(x)^3 + x*cos(x))*sin(x) - 1)/(cos(x)^2 - 1)","C",0
207,1,203,0,0.482478," ","integrate(x*cos(x)^2*cot(x)^3,x, algorithm=""fricas"")","-\frac{2 \, x \cos\left(x\right)^{4} - 3 \, x \cos\left(x\right)^{2} - {\left(4 i \, \cos\left(x\right)^{2} - 4 i\right)} {\rm Li}_2\left(\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left(-4 i \, \cos\left(x\right)^{2} + 4 i\right)} {\rm Li}_2\left(\cos\left(x\right) - i \, \sin\left(x\right)\right) - {\left(-4 i \, \cos\left(x\right)^{2} + 4 i\right)} {\rm Li}_2\left(-\cos\left(x\right) + i \, \sin\left(x\right)\right) - {\left(4 i \, \cos\left(x\right)^{2} - 4 i\right)} {\rm Li}_2\left(-\cos\left(x\right) - i \, \sin\left(x\right)\right) + 4 \, {\left(x \cos\left(x\right)^{2} - x\right)} \log\left(\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + 4 \, {\left(x \cos\left(x\right)^{2} - x\right)} \log\left(\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) + 4 \, {\left(x \cos\left(x\right)^{2} - x\right)} \log\left(-\cos\left(x\right) + i \, \sin\left(x\right) + 1\right) + 4 \, {\left(x \cos\left(x\right)^{2} - x\right)} \log\left(-\cos\left(x\right) - i \, \sin\left(x\right) + 1\right) - {\left(\cos\left(x\right)^{3} + \cos\left(x\right)\right)} \sin\left(x\right) - x}{4 \, {\left(\cos\left(x\right)^{2} - 1\right)}}"," ",0,"-1/4*(2*x*cos(x)^4 - 3*x*cos(x)^2 - (4*I*cos(x)^2 - 4*I)*dilog(cos(x) + I*sin(x)) - (-4*I*cos(x)^2 + 4*I)*dilog(cos(x) - I*sin(x)) - (-4*I*cos(x)^2 + 4*I)*dilog(-cos(x) + I*sin(x)) - (4*I*cos(x)^2 - 4*I)*dilog(-cos(x) - I*sin(x)) + 4*(x*cos(x)^2 - x)*log(cos(x) + I*sin(x) + 1) + 4*(x*cos(x)^2 - x)*log(cos(x) - I*sin(x) + 1) + 4*(x*cos(x)^2 - x)*log(-cos(x) + I*sin(x) + 1) + 4*(x*cos(x)^2 - x)*log(-cos(x) - I*sin(x) + 1) - (cos(x)^3 + cos(x))*sin(x) - x)/(cos(x)^2 - 1)","B",0
208,0,0,0,0.424072," ","integrate((d*x+c)^m*sec(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sec\left(b x + a\right) \sin\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*sec(b*x + a)*sin(b*x + a), x)","F",0
209,1,1402,0,0.568729," ","integrate((d*x+c)^4*sec(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{24 \, d^{4} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{2 \, b^{5}}"," ",0,"1/2*(24*d^4*polylog(5, I*cos(b*x + a) + sin(b*x + a)) + 24*d^4*polylog(5, I*cos(b*x + a) - sin(b*x + a)) + 24*d^4*polylog(5, -I*cos(b*x + a) + sin(b*x + a)) + 24*d^4*polylog(5, -I*cos(b*x + a) - sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/b^5","C",0
210,1,970,0,0.536565," ","integrate((d*x+c)^3*sec(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{2 \, b^{4}}"," ",0,"1/2*(6*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/b^4","C",0
211,1,594,0,0.495718," ","integrate((d*x+c)^2*sec(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{3}}"," ",0,"-1/2*(2*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 2*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 2*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^3","C",0
212,1,310,0,0.494432," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a),x, algorithm=""fricas"")","\frac{-i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{2}}"," ",0,"1/2*(-I*d*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d*dilog(I*cos(b*x + a) - sin(b*x + a)) + I*d*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^2","B",0
213,0,0,0,0.437531," ","integrate(sec(b*x+a)*sin(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \sin\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)*sin(b*x + a)/(d*x + c), x)","F",0
214,0,0,0,0.440477," ","integrate(sec(b*x+a)*sin(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \sin\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sec(b*x + a)*sin(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
215,0,0,0,0.430826," ","integrate((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} {\left(d x + c\right)}^{m} \sec\left(b x + a\right), x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*(d*x + c)^m*sec(b*x + a), x)","F",0
216,1,1071,0,0.555176," ","integrate((d*x+c)^3*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sin\left(b x + a\right)}{2 \, b^{4}}"," ",0,"1/2*(6*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cos(b*x + a) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*sin(b*x + a))/b^4","C",0
217,1,656,0,0.517816," ","integrate((d*x+c)^2*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \sin\left(b x + a\right)}{2 \, b^{3}}"," ",0,"-1/2*(2*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 4*(b*d^2*x + b*c*d)*cos(b*x + a) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*sin(b*x + a))/b^3","C",0
218,1,331,0,1.036498," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, d \cos\left(b x + a\right) + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b d x + b c\right)} \sin\left(b x + a\right)}{2 \, b^{2}}"," ",0,"-1/2*(2*d*cos(b*x + a) + I*d*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 2*(b*d*x + b*c)*sin(b*x + a))/b^2","B",0
219,0,0,0,0.434153," ","integrate(sec(b*x+a)*sin(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sec\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sec(b*x + a)/(d*x + c), x)","F",0
220,0,0,0,0.428137," ","integrate(sec(b*x+a)*sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sec\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sec(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
221,0,0,0,0.444497," ","integrate((d*x+c)^m*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x + a\right)^{2} - 1\right)} {\left(d x + c\right)}^{m} \sec\left(b x + a\right) \sin\left(b x + a\right), x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*(d*x + c)^m*sec(b*x + a)*sin(b*x + a), x)","F",0
222,1,1134,0,0.614748," ","integrate((d*x+c)^3*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} - 24 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x - {\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{8 \, b^{4}}"," ",0,"-1/8*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 - 24*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + 24*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + 24*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - 24*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - 2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 - 3*b*c*d^2 + 3*(2*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^2 + 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)*sin(b*x + a) + 3*(2*b^3*c^2*d - b*d^3)*x - (-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 24*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 24*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 24*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 24*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/b^4","C",0
223,1,688,0,0.542530," ","integrate((d*x+c)^2*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x - {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{2} + 4 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 4 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 4 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 4 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{4 \, b^{3}}"," ",0,"-1/4*(b^2*d^2*x^2 + 2*b^2*c*d*x - (2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 - d^2)*cos(b*x + a)^2 + 4*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 4*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 4*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 4*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - (-4*I*b*d^2*x - 4*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (4*I*b*d^2*x + 4*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (4*I*b*d^2*x + 4*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (-4*I*b*d^2*x - 4*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^3","C",0
224,1,346,0,0.494852," ","integrate((d*x+c)*sec(b*x+a)*sin(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b d x - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 2 i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{4 \, b^{2}}"," ",0,"-1/4*(b*d*x - 2*(b*d*x + b*c)*cos(b*x + a)^2 + d*cos(b*x + a)*sin(b*x + a) + 2*I*d*dilog(I*cos(b*x + a) + sin(b*x + a)) - 2*I*d*dilog(I*cos(b*x + a) - sin(b*x + a)) - 2*I*d*dilog(-I*cos(b*x + a) + sin(b*x + a)) + 2*I*d*dilog(-I*cos(b*x + a) - sin(b*x + a)) + 2*(b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 2*(b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) + 2*(b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 2*(b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + 2*(b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 2*(b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^2","B",0
225,0,0,0,0.437839," ","integrate(sec(b*x+a)*sin(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sec\left(b x + a\right) \sin\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sec(b*x + a)*sin(b*x + a)/(d*x + c), x)","F",0
226,0,0,0,0.422053," ","integrate(sec(b*x+a)*sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(b x + a\right)^{2} - 1\right)} \sec\left(b x + a\right) \sin\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(-(cos(b*x + a)^2 - 1)*sec(b*x + a)*sin(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
227,0,0,0,0.431289," ","integrate((d*x+c)^m*csc(b*x+a)*sec(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right) \sec\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)*sec(b*x + a), x)","F",0
228,1,2600,0,0.658469," ","integrate((d*x+c)^4*csc(b*x+a)*sec(b*x+a),x, algorithm=""fricas"")","-\frac{24 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, b^{5}}"," ",0,"-1/2*(24*d^4*polylog(5, cos(b*x + a) + I*sin(b*x + a)) + 24*d^4*polylog(5, cos(b*x + a) - I*sin(b*x + a)) - 24*d^4*polylog(5, I*cos(b*x + a) + sin(b*x + a)) - 24*d^4*polylog(5, I*cos(b*x + a) - sin(b*x + a)) - 24*d^4*polylog(5, -I*cos(b*x + a) + sin(b*x + a)) - 24*d^4*polylog(5, -I*cos(b*x + a) - sin(b*x + a)) + 24*d^4*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) + 24*d^4*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/b^5","C",0
229,1,1778,0,0.604277," ","integrate((d*x+c)^3*csc(b*x+a)*sec(b*x+a),x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, b^{4}}"," ",0,"1/2*(6*I*d^3*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + 6*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + 6*I*d^3*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 6*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/b^4","C",0
230,1,1090,0,0.558875," ","integrate((d*x+c)^2*csc(b*x+a)*sec(b*x+a),x, algorithm=""fricas"")","\frac{2 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{3}}"," ",0,"1/2*(2*d^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 2*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 2*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^3","C",0
231,1,554,0,0.516786," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a),x, algorithm=""fricas"")","\frac{-i \, d {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{2}}"," ",0,"1/2*(-I*d*dilog(cos(b*x + a) + I*sin(b*x + a)) + I*d*dilog(cos(b*x + a) - I*sin(b*x + a)) - I*d*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d*dilog(I*cos(b*x + a) - sin(b*x + a)) + I*d*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d*dilog(-I*cos(b*x + a) - sin(b*x + a)) + I*d*dilog(-cos(b*x + a) + I*sin(b*x + a)) - I*d*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b*d*x + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*d*x + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b*c - a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b*c - a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b*d*x + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*d*x + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^2","B",0
232,0,0,0,0.441334," ","integrate(csc(b*x+a)*sec(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right) \sec\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)*sec(b*x + a)/(d*x + c), x)","F",0
233,0,0,0,0.446194," ","integrate(csc(b*x+a)*sec(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right) \sec\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)*sec(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
234,0,0,0,0.458787," ","integrate((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2} \sec\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^2*sec(b*x + a), x)","F",0
235,1,1753,0,0.650915," ","integrate((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} - 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right)}{2 \, b^{4} \sin\left(b x + a\right)}"," ",0,"-1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 - 6*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 6*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 6*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 6*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - 6*d^3*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 6*d^3*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 6*d^3*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 6*d^3*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a))/(b^4*sin(b*x + a))","C",0
236,1,1067,0,0.560014," ","integrate((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + 2 i \, d^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 2 i \, d^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 i \, d^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 2 i \, d^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 \, {\left(b d^{2} x + b c d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 2 \, {\left(b d^{2} x + b c d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 2 \, {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 2 \, {\left(b c d - a d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - 2 \, {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 2 \, {\left(b d^{2} x + a d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right)}{2 \, b^{3} \sin\left(b x + a\right)}"," ",0,"-1/2*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + 2*I*d^2*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 2*I*d^2*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 2*I*d^2*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 2*I*d^2*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 2*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 2*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 2*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 2*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 2*(b*d^2*x + b*c*d)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + 2*(b*d^2*x + b*c*d)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) - 2*(b*c*d - a*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 2*(b*c*d - a*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) - 2*(b*d^2*x + a*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) - 2*(b*d^2*x + a*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a))/(b^3*sin(b*x + a))","C",0
237,1,434,0,0.504361," ","integrate((d*x+c)*csc(b*x+a)^2*sec(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b d x + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + d \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - d \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 2 \, b c}{2 \, b^{2} \sin\left(b x + a\right)}"," ",0,"-1/2*(2*b*d*x + I*d*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + I*d*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - I*d*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - I*d*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - (b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + (b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + d*log(1/2*cos(b*x + a) + 1/2)*sin(b*x + a) - (b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) - (b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) - d*log(-1/2*cos(b*x + a) + 1/2)*sin(b*x + a) - (b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + (b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 2*b*c)/(b^2*sin(b*x + a))","B",0
238,0,0,0,0.462410," ","integrate(csc(b*x+a)^2*sec(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sec\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^2*sec(b*x + a)/(d*x + c), x)","F",0
239,0,0,0,0.462818," ","integrate(csc(b*x+a)^2*sec(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sec\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^2*sec(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
240,0,0,0,0.421925," ","integrate((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^3*sec(b*x + a), x)","F",0
241,1,3459,0,0.771542," ","integrate((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3} + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 3 i \, d^{3} + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 3 i \, d^{3} + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 3 i \, d^{3} + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 3 i \, d^{3} + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 3 \, b c d^{2} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 3 \, b c d^{2} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(6 i \, d^{3} \cos\left(b x + a\right)^{2} - 6 i \, d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-6 i \, d^{3} \cos\left(b x + a\right)^{2} + 6 i \, d^{3}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(6 i \, d^{3} \cos\left(b x + a\right)^{2} - 6 i \, d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-6 i \, d^{3} \cos\left(b x + a\right)^{2} + 6 i \, d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, d^{3} \cos\left(b x + a\right)^{2} + 6 i \, d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(6 i \, d^{3} \cos\left(b x + a\right)^{2} - 6 i \, d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, d^{3} \cos\left(b x + a\right)^{2} + 6 i \, d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, d^{3} \cos\left(b x + a\right)^{2} - 6 i \, d^{3}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, {\left(b^{4} \cos\left(b x + a\right)^{2} - b^{4}\right)}}"," ",0,"1/2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 3*I*d^3 + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 3*I*d^3 + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 3*I*d^3 + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 3*I*d^3 + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 3*b*c*d^2 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 3*b*c*d^2 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d + b*d^3)*x)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 3*b*c*d^2 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 3*b*c*d^2 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d + b*d^3)*x)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d + b*d^3)*x)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2 + 3*(b^3*c^2*d + b*d^3)*x)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (6*I*d^3*cos(b*x + a)^2 - 6*I*d^3)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + (-6*I*d^3*cos(b*x + a)^2 + 6*I*d^3)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + (6*I*d^3*cos(b*x + a)^2 - 6*I*d^3)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + (-6*I*d^3*cos(b*x + a)^2 + 6*I*d^3)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + (-6*I*d^3*cos(b*x + a)^2 + 6*I*d^3)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + (6*I*d^3*cos(b*x + a)^2 - 6*I*d^3)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (-6*I*d^3*cos(b*x + a)^2 + 6*I*d^3)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + (6*I*d^3*cos(b*x + a)^2 - 6*I*d^3)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^4*cos(b*x + a)^2 - b^4)","C",0
242,1,1987,0,0.641605," ","integrate((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + d^{2}\right)} \cos\left(b x + a\right)^{2} + d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + d^{2}\right)} \cos\left(b x + a\right)^{2} + d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, {\left(b^{3} \cos\left(b x + a\right)^{2} - b^{3}\right)}}"," ",0,"1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + d^2)*cos(b*x + a)^2 + d^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + d^2)*cos(b*x + a)^2 + d^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2 - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2 - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 2*(d^2*cos(b*x + a)^2 - d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^3*cos(b*x + a)^2 - b^3)","C",0
243,1,942,0,0.541075," ","integrate((d*x+c)*csc(b*x+a)^3*sec(b*x+a),x, algorithm=""fricas"")","\frac{b d x + d \cos\left(b x + a\right) \sin\left(b x + a\right) + b c + {\left(-i \, d \cos\left(b x + a\right)^{2} + i \, d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(i \, d \cos\left(b x + a\right)^{2} - i \, d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-i \, d \cos\left(b x + a\right)^{2} + i \, d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(i \, d \cos\left(b x + a\right)^{2} - i \, d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(i \, d \cos\left(b x + a\right)^{2} - i \, d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-i \, d \cos\left(b x + a\right)^{2} + i \, d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(i \, d \cos\left(b x + a\right)^{2} - i \, d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-i \, d \cos\left(b x + a\right)^{2} + i \, d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b d x - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b d x - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b d x - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{2} - b c + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, {\left(b^{2} \cos\left(b x + a\right)^{2} - b^{2}\right)}}"," ",0,"1/2*(b*d*x + d*cos(b*x + a)*sin(b*x + a) + b*c + (-I*d*cos(b*x + a)^2 + I*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (I*d*cos(b*x + a)^2 - I*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-I*d*cos(b*x + a)^2 + I*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (I*d*cos(b*x + a)^2 - I*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (I*d*cos(b*x + a)^2 - I*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-I*d*cos(b*x + a)^2 + I*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (I*d*cos(b*x + a)^2 - I*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-I*d*cos(b*x + a)^2 + I*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b*d*x - (b*d*x + b*c)*cos(b*x + a)^2 + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b*d*x - (b*d*x + b*c)*cos(b*x + a)^2 + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) - ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b*d*x - (b*d*x + a*d)*cos(b*x + a)^2 + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - ((b*c - a*d)*cos(b*x + a)^2 - b*c + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/(b^2*cos(b*x + a)^2 - b^2)","B",0
244,0,0,0,0.530023," ","integrate(csc(b*x+a)^3*sec(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)/(d*x + c), x)","F",0
245,0,0,0,0.638375," ","integrate(csc(b*x+a)^3*sec(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
246,0,0,0,0.439163," ","integrate((d*x+c)^m*sec(b*x+a)*tan(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sec\left(b x + a\right) \tan\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*sec(b*x + a)*tan(b*x + a), x)","F",0
247,1,1186,0,0.574718," ","integrate((d*x+c)^4*sec(b*x+a)*tan(b*x+a),x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} - 12 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(6 i \, b^{2} d^{4} x^{2} + 12 i \, b^{2} c d^{3} x + 6 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(6 i \, b^{2} d^{4} x^{2} + 12 i \, b^{2} c d^{3} x + 6 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, b^{2} d^{4} x^{2} - 12 i \, b^{2} c d^{3} x - 6 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-6 i \, b^{2} d^{4} x^{2} - 12 i \, b^{2} c d^{3} x - 6 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 12 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{b^{5} \cos\left(b x + a\right)}"," ",0,"(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 - 12*I*d^4*cos(b*x + a)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - 12*I*d^4*cos(b*x + a)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + 12*I*d^4*cos(b*x + a)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + 12*I*d^4*cos(b*x + a)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (6*I*b^2*d^4*x^2 + 12*I*b^2*c*d^3*x + 6*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (6*I*b^2*d^4*x^2 + 12*I*b^2*c*d^3*x + 6*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-6*I*b^2*d^4*x^2 - 12*I*b^2*c*d^3*x - 6*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-6*I*b^2*d^4*x^2 - 12*I*b^2*c*d^3*x - 6*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 2*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 12*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 12*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 12*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 12*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/(b^5*cos(b*x + a))","C",0
248,1,779,0,0.529510," ","integrate((d*x+c)^3*sec(b*x+a)*tan(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{4} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/(b^4*cos(b*x + a))","C",0
249,1,446,0,0.503504," ","integrate((d*x+c)^2*sec(b*x+a)*tan(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{b^{3} \cos\left(b x + a\right)}"," ",0,"(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/(b^3*cos(b*x + a))","B",0
250,1,60,0,0.474806," ","integrate((d*x+c)*sec(b*x+a)*tan(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b d x - d \cos\left(b x + a\right) \log\left(\sin\left(b x + a\right) + 1\right) + d \cos\left(b x + a\right) \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, b c}{2 \, b^{2} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b*d*x - d*cos(b*x + a)*log(sin(b*x + a) + 1) + d*cos(b*x + a)*log(-sin(b*x + a) + 1) + 2*b*c)/(b^2*cos(b*x + a))","B",0
251,0,0,0,0.441353," ","integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \tan\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)*tan(b*x + a)/(d*x + c), x)","F",0
252,0,0,0,0.433288," ","integrate(sec(b*x+a)*tan(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \tan\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sec(b*x + a)*tan(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
253,0,0,0,0.430066," ","integrate((d*x+c)^m*tan(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*tan(b*x + a)^2, x)","F",0
254,1,373,0,0.461705," ","integrate((d*x+c)^3*tan(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{4} d^{3} x^{4} + 4 \, b^{4} c d^{2} x^{3} + 6 \, b^{4} c^{2} d x^{2} + 4 \, b^{4} c^{3} x - 3 \, d^{3} {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 3 \, d^{3} {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \tan\left(b x + a\right)}{4 \, b^{4}}"," ",0,"-1/4*(b^4*d^3*x^4 + 4*b^4*c*d^2*x^3 + 6*b^4*c^2*d*x^2 + 4*b^4*c^3*x - 3*d^3*polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 3*d^3*polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - (6*I*b*d^3*x + 6*I*b*c*d^2)*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*tan(b*x + a))/b^4","C",0
255,1,210,0,0.465447," ","integrate((d*x+c)^2*tan(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{2} x^{3} + 6 \, b^{3} c d x^{2} + 6 \, b^{3} c^{2} x - 3 i \, d^{2} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 3 i \, d^{2} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - 6 \, {\left(b d^{2} x + b c d\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b d^{2} x + b c d\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \tan\left(b x + a\right)}{6 \, b^{3}}"," ",0,"-1/6*(2*b^3*d^2*x^3 + 6*b^3*c*d*x^2 + 6*b^3*c^2*x - 3*I*d^2*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 3*I*d^2*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - 6*(b*d^2*x + b*c*d)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 6*(b*d^2*x + b*c*d)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*tan(b*x + a))/b^3","B",0
256,1,53,0,0.436250," ","integrate((d*x+c)*tan(b*x+a)^2,x, algorithm=""fricas"")","-\frac{b^{2} d x^{2} + 2 \, b^{2} c x - d \log\left(\frac{1}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, {\left(b d x + b c\right)} \tan\left(b x + a\right)}{2 \, b^{2}}"," ",0,"-1/2*(b^2*d*x^2 + 2*b^2*c*x - d*log(1/(tan(b*x + a)^2 + 1)) - 2*(b*d*x + b*c)*tan(b*x + a))/b^2","A",0
257,0,0,0,0.439180," ","integrate(tan(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(tan(b*x + a)^2/(d*x + c), x)","F",0
258,0,0,0,0.458371," ","integrate(tan(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(tan(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
259,0,0,0,0.430654," ","integrate((d*x+c)^m*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sin\left(b x + a\right) \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*sin(b*x + a)*tan(b*x + a)^2, x)","F",0
260,1,892,0,0.565562," ","integrate((d*x+c)^3*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{4} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cos(b*x + a)*sin(b*x + a))/(b^4*cos(b*x + a))","C",0
261,1,511,0,0.532527," ","integrate((d*x+c)^2*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{b^{3} \cos\left(b x + a\right)}"," ",0,"(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a)^2 - (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a))/(b^3*cos(b*x + a))","B",0
262,1,93,0,0.480305," ","integrate((d*x+c)*sin(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b d x + 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - d \cos\left(b x + a\right) \log\left(\sin\left(b x + a\right) + 1\right) + d \cos\left(b x + a\right) \log\left(-\sin\left(b x + a\right) + 1\right) - 2 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, b c}{2 \, b^{2} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b*d*x + 2*(b*d*x + b*c)*cos(b*x + a)^2 - d*cos(b*x + a)*log(sin(b*x + a) + 1) + d*cos(b*x + a)*log(-sin(b*x + a) + 1) - 2*d*cos(b*x + a)*sin(b*x + a) + 2*b*c)/(b^2*cos(b*x + a))","A",0
263,0,0,0,0.457255," ","integrate(sin(b*x+a)*tan(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b x + a\right) \tan\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(sin(b*x + a)*tan(b*x + a)^2/(d*x + c), x)","F",0
264,0,0,0,0.491041," ","integrate(sin(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b x + a\right) \tan\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sin(b*x + a)*tan(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
265,0,0,0,0.435172," ","integrate((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right) \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)*sec(b*x + a)^2, x)","F",0
266,1,2507,0,0.814999," ","integrate((d*x+c)^4*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 12 \, b^{4} c^{2} d^{2} x^{2} + 8 \, b^{4} c^{3} d x + 2 \, b^{4} c^{4} - 24 \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 i \, d^{4} \cos\left(b x + a\right) {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(12 i \, b^{2} d^{4} x^{2} + 24 i \, b^{2} c d^{3} x + 12 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(12 i \, b^{2} d^{4} x^{2} + 24 i \, b^{2} c d^{3} x + 12 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-12 i \, b^{2} d^{4} x^{2} - 24 i \, b^{2} c d^{3} x - 12 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-12 i \, b^{2} d^{4} x^{2} - 24 i \, b^{2} c d^{3} x - 12 i \, b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + 3 \, a b^{2} c^{2} d^{2} - 3 \, a^{2} b c d^{3} + a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left(b^{3} c^{3} d - 3 \, a b^{2} c^{2} d^{2} + 3 \, a^{2} b c d^{3} - a^{3} d^{4}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 24 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 \, {\left(b d^{4} x + b c d^{3}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, b^{5} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 12*b^4*c^2*d^2*x^2 + 8*b^4*c^3*d*x + 2*b^4*c^4 - 24*d^4*cos(b*x + a)*polylog(5, cos(b*x + a) + I*sin(b*x + a)) - 24*d^4*cos(b*x + a)*polylog(5, cos(b*x + a) - I*sin(b*x + a)) + 24*d^4*cos(b*x + a)*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) + 24*d^4*cos(b*x + a)*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) - 24*I*d^4*cos(b*x + a)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - 24*I*d^4*cos(b*x + a)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + 24*I*d^4*cos(b*x + a)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + 24*I*d^4*cos(b*x + a)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*cos(b*x + a)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*cos(b*x + a)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (12*I*b^2*d^4*x^2 + 24*I*b^2*c*d^3*x + 12*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (12*I*b^2*d^4*x^2 + 24*I*b^2*c*d^3*x + 12*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-12*I*b^2*d^4*x^2 - 24*I*b^2*c*d^3*x - 12*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-12*I*b^2*d^4*x^2 - 24*I*b^2*c*d^3*x - 12*I*b^2*c^2*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*cos(b*x + a)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*cos(b*x + a)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + 3*a*b^2*c^2*d^2 - 3*a^2*b*c*d^3 + a^3*d^4)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*cos(b*x + a)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 4*(b^3*c^3*d - 3*a*b^2*c^2*d^2 + 3*a^2*b*c*d^3 - a^3*d^4)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 24*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 24*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 24*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 24*(b*d^4*x + b*c*d^3)*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^5*cos(b*x + a))","C",0
267,1,1697,0,0.650399," ","integrate((d*x+c)^3*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} + 6 i \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, b^{4} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 + 6*I*d^3*cos(b*x + a)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*cos(b*x + a)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + 6*I*d^3*cos(b*x + a)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*cos(b*x + a)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*cos(b*x + a)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*cos(b*x + a)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*cos(b*x + a)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*cos(b*x + a)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^4*cos(b*x + a))","C",0
268,1,1031,0,0.569166," ","integrate((d*x+c)^2*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + 2 i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 2 i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{3} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + 2*I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + 2*I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) - 2*I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - 2*I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*cos(b*x + a)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*cos(b*x + a)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 2*d^2*cos(b*x + a)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 2*d^2*cos(b*x + a)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 2*(b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 2*(b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 2*(b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 2*(b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 2*(b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 2*(b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/(b^3*cos(b*x + a))","C",0
269,1,366,0,0.470523," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b d x - i \, d \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(b d x + b c\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b d x + b c\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b c - a d\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - d \cos\left(b x + a\right) \log\left(\sin\left(b x + a\right) + 1\right) + d \cos\left(b x + a\right) \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, b c}{2 \, b^{2} \cos\left(b x + a\right)}"," ",0,"1/2*(2*b*d*x - I*d*cos(b*x + a)*dilog(cos(b*x + a) + I*sin(b*x + a)) + I*d*cos(b*x + a)*dilog(cos(b*x + a) - I*sin(b*x + a)) - I*d*cos(b*x + a)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + I*d*cos(b*x + a)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - (b*d*x + b*c)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b*d*x + b*c)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + (b*c - a*d)*cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b*c - a*d)*cos(b*x + a)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b*d*x + a*d)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + (b*d*x + a*d)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - d*cos(b*x + a)*log(sin(b*x + a) + 1) + d*cos(b*x + a)*log(-sin(b*x + a) + 1) + 2*b*c)/(b^2*cos(b*x + a))","B",0
270,0,0,0,0.438452," ","integrate(csc(b*x+a)*sec(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right) \sec\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)*sec(b*x + a)^2/(d*x + c), x)","F",0
271,0,0,0,0.446278," ","integrate(csc(b*x+a)*sec(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right) \sec\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)*sec(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
272,0,0,0,0.426933," ","integrate((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^2*sec(b*x + a)^2, x)","F",0
273,1,1627,0,0.618801," ","integrate((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right)^{2}}{2 \, b^{4} \cos\left(b x + a\right) \sin\left(b x + a\right)}"," ",0,"1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 + 6*d^3*cos(b*x + a)*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 6*d^3*cos(b*x + a)*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)^2)/(b^4*cos(b*x + a)*sin(b*x + a))","C",0
274,1,950,0,0.557659," ","integrate((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + b^{2} c^{2} + {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)^{2}}{b^{3} \cos\left(b x + a\right) \sin\left(b x + a\right)}"," ",0,"(b^2*d^2*x^2 + 2*b^2*c*d*x - I*d^2*cos(b*x + a)*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + I*d^2*cos(b*x + a)*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + I*d^2*cos(b*x + a)*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - I*d^2*cos(b*x + a)*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + b^2*c^2 + (b*d^2*x + b*c*d)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + (b*d^2*x + b*c*d)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + (b*c*d - a*d^2)*cos(b*x + a)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + (b*c*d - a*d^2)*cos(b*x + a)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)^2)/(b^3*cos(b*x + a)*sin(b*x + a))","B",0
275,1,75,0,0.447646," ","integrate((d*x+c)*csc(b*x+a)^2*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{d \cos\left(b x + a\right) \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + b d x - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + b c}{b^{2} \cos\left(b x + a\right) \sin\left(b x + a\right)}"," ",0,"(d*cos(b*x + a)*log(-1/2*cos(b*x + a)*sin(b*x + a))*sin(b*x + a) + b*d*x - 2*(b*d*x + b*c)*cos(b*x + a)^2 + b*c)/(b^2*cos(b*x + a)*sin(b*x + a))","B",0
276,0,0,0,0.431250," ","integrate(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^2*sec(b*x + a)^2/(d*x + c), x)","F",0
277,0,0,0,0.424591," ","integrate(csc(b*x+a)^2*sec(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^2*sec(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
278,0,0,0,0.432116," ","integrate((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^3*sec(b*x + a)^2, x)","F",0
279,1,3173,0,0.813103," ","integrate((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b^{3} d^{3} x^{3} + 12 \, b^{3} c d^{2} x^{2} + 12 \, b^{3} c^{2} d x + 4 \, b^{3} c^{3} - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right)^{2} - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left({\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{3} + {\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{3} + {\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left({\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{3} + {\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left({\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{3} + {\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{3} + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left({\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{3} + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{3} + {\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{3} + {\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 2 \, b c d^{2} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 2 \, b c d^{2} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 6 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 2 \, b c d^{2} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 2 \, b c d^{2} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 6 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 6 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 6 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 6 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left({\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(18 i \, d^{3} \cos\left(b x + a\right)^{3} - 18 i \, d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-18 i \, d^{3} \cos\left(b x + a\right)^{3} + 18 i \, d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(18 i \, d^{3} \cos\left(b x + a\right)^{3} - 18 i \, d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-18 i \, d^{3} \cos\left(b x + a\right)^{3} + 18 i \, d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 18 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 18 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(d^{3} \cos\left(b x + a\right)^{3} - d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left(d^{3} \cos\left(b x + a\right)^{3} - d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left(d^{3} \cos\left(b x + a\right)^{3} - d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left(d^{3} \cos\left(b x + a\right)^{3} - d^{3} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 18 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 18 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{4 \, {\left(b^{4} \cos\left(b x + a\right)^{3} - b^{4} \cos\left(b x + a\right)\right)}}"," ",0,"-1/4*(4*b^3*d^3*x^3 + 12*b^3*c*d^2*x^2 + 12*b^3*c^2*d*x + 4*b^3*c^3 - 6*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)^2 - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a) - ((-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^3 + (9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a))*dilog(cos(b*x + a) + I*sin(b*x + a)) - ((9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^3 + (-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a))*dilog(cos(b*x + a) - I*sin(b*x + a)) - ((12*I*b*d^3*x + 12*I*b*c*d^2)*cos(b*x + a)^3 + (-12*I*b*d^3*x - 12*I*b*c*d^2)*cos(b*x + a))*dilog(I*cos(b*x + a) + sin(b*x + a)) - ((12*I*b*d^3*x + 12*I*b*c*d^2)*cos(b*x + a)^3 + (-12*I*b*d^3*x - 12*I*b*c*d^2)*cos(b*x + a))*dilog(I*cos(b*x + a) - sin(b*x + a)) - ((-12*I*b*d^3*x - 12*I*b*c*d^2)*cos(b*x + a)^3 + (12*I*b*d^3*x + 12*I*b*c*d^2)*cos(b*x + a))*dilog(-I*cos(b*x + a) + sin(b*x + a)) - ((-12*I*b*d^3*x - 12*I*b*c*d^2)*cos(b*x + a)^3 + (12*I*b*d^3*x + 12*I*b*c*d^2)*cos(b*x + a))*dilog(-I*cos(b*x + a) - sin(b*x + a)) - ((-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^3 + (9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a))*dilog(-cos(b*x + a) + I*sin(b*x + a)) - ((9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^3 + (-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a))*dilog(-cos(b*x + a) - I*sin(b*x + a)) + 3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 2*b*c*d^2 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 2*b*c*d^2 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + 1) + 6*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)^3 - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + I) + 3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 2*b*c*d^2 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 2*b*c*d^2 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 6*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)^3 - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + I) + 6*((b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a))*log(I*cos(b*x + a) + sin(b*x + a) + 1) - 6*((b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a))*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 6*((b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a))*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - 6*((b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a))*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 3*((b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a)^3 - (b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 3*((b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a)^3 - (b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a))*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 6*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)^3 - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + I) - 3*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 6*((b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)^3 - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + I) - (18*I*d^3*cos(b*x + a)^3 - 18*I*d^3*cos(b*x + a))*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - (-18*I*d^3*cos(b*x + a)^3 + 18*I*d^3*cos(b*x + a))*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - (18*I*d^3*cos(b*x + a)^3 - 18*I*d^3*cos(b*x + a))*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - (-18*I*d^3*cos(b*x + a)^3 + 18*I*d^3*cos(b*x + a))*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 18*((b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cos(b*x + a))*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 18*((b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cos(b*x + a))*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 12*(d^3*cos(b*x + a)^3 - d^3*cos(b*x + a))*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 12*(d^3*cos(b*x + a)^3 - d^3*cos(b*x + a))*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 12*(d^3*cos(b*x + a)^3 - d^3*cos(b*x + a))*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 12*(d^3*cos(b*x + a)^3 - d^3*cos(b*x + a))*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 18*((b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cos(b*x + a))*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 18*((b*d^3*x + b*c*d^2)*cos(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cos(b*x + a))*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^4*cos(b*x + a)^3 - b^4*cos(b*x + a))","C",0
280,1,1801,0,0.655889," ","integrate((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b^{2} d^{2} x^{2} + 8 \, b^{2} c d x + 4 \, b^{2} c^{2} - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)^{2} - 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left({\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} \cos\left(b x + a\right)^{3} + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \cos\left(b x + a\right)^{3} + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(4 i \, d^{2} \cos\left(b x + a\right)^{3} - 4 i \, d^{2} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(4 i \, d^{2} \cos\left(b x + a\right)^{3} - 4 i \, d^{2} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-4 i \, d^{2} \cos\left(b x + a\right)^{3} + 4 i \, d^{2} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-4 i \, d^{2} \cos\left(b x + a\right)^{3} + 4 i \, d^{2} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} \cos\left(b x + a\right)^{3} + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \cos\left(b x + a\right)^{3} + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left({\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left({\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{2} d^{2} x^{2} + 6 \, b^{2} c d x + 3 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left({\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 4 \, {\left({\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 4 \, {\left({\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 4 \, {\left({\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left({\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left({\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left({\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(d^{2} \cos\left(b x + a\right)^{3} - d^{2} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(d^{2} \cos\left(b x + a\right)^{3} - d^{2} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 \, {\left(d^{2} \cos\left(b x + a\right)^{3} - d^{2} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(d^{2} \cos\left(b x + a\right)^{3} - d^{2} \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{4 \, {\left(b^{3} \cos\left(b x + a\right)^{3} - b^{3} \cos\left(b x + a\right)\right)}}"," ",0,"-1/4*(4*b^2*d^2*x^2 + 8*b^2*c*d*x + 4*b^2*c^2 - 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)^2 - 4*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - ((-6*I*b*d^2*x - 6*I*b*c*d)*cos(b*x + a)^3 + (6*I*b*d^2*x + 6*I*b*c*d)*cos(b*x + a))*dilog(cos(b*x + a) + I*sin(b*x + a)) - ((6*I*b*d^2*x + 6*I*b*c*d)*cos(b*x + a)^3 + (-6*I*b*d^2*x - 6*I*b*c*d)*cos(b*x + a))*dilog(cos(b*x + a) - I*sin(b*x + a)) - (4*I*d^2*cos(b*x + a)^3 - 4*I*d^2*cos(b*x + a))*dilog(I*cos(b*x + a) + sin(b*x + a)) - (4*I*d^2*cos(b*x + a)^3 - 4*I*d^2*cos(b*x + a))*dilog(I*cos(b*x + a) - sin(b*x + a)) - (-4*I*d^2*cos(b*x + a)^3 + 4*I*d^2*cos(b*x + a))*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (-4*I*d^2*cos(b*x + a)^3 + 4*I*d^2*cos(b*x + a))*dilog(-I*cos(b*x + a) - sin(b*x + a)) - ((-6*I*b*d^2*x - 6*I*b*c*d)*cos(b*x + a)^3 + (6*I*b*d^2*x + 6*I*b*c*d)*cos(b*x + a))*dilog(-cos(b*x + a) + I*sin(b*x + a)) - ((6*I*b*d^2*x + 6*I*b*c*d)*cos(b*x + a)^3 + (-6*I*b*d^2*x - 6*I*b*c*d)*cos(b*x + a))*dilog(-cos(b*x + a) - I*sin(b*x + a)) + ((3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*d^2)*cos(b*x + a)^3 - (3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*d^2)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + 1) + 4*((b*c*d - a*d^2)*cos(b*x + a)^3 - (b*c*d - a*d^2)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + I) + ((3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*d^2)*cos(b*x + a)^3 - (3*b^2*d^2*x^2 + 6*b^2*c*d*x + 3*b^2*c^2 + 2*d^2)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 4*((b*c*d - a*d^2)*cos(b*x + a)^3 - (b*c*d - a*d^2)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + I) + 4*((b*d^2*x + a*d^2)*cos(b*x + a)^3 - (b*d^2*x + a*d^2)*cos(b*x + a))*log(I*cos(b*x + a) + sin(b*x + a) + 1) - 4*((b*d^2*x + a*d^2)*cos(b*x + a)^3 - (b*d^2*x + a*d^2)*cos(b*x + a))*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 4*((b*d^2*x + a*d^2)*cos(b*x + a)^3 - (b*d^2*x + a*d^2)*cos(b*x + a))*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - 4*((b*d^2*x + a*d^2)*cos(b*x + a)^3 - (b*d^2*x + a*d^2)*cos(b*x + a))*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - ((3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a)^3 - (3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - ((3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a)^3 - (3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a))*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^3 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 4*((b*c*d - a*d^2)*cos(b*x + a)^3 - (b*c*d - a*d^2)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + I) - 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^3 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 4*((b*c*d - a*d^2)*cos(b*x + a)^3 - (b*c*d - a*d^2)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 6*(d^2*cos(b*x + a)^3 - d^2*cos(b*x + a))*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 6*(d^2*cos(b*x + a)^3 - d^2*cos(b*x + a))*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 6*(d^2*cos(b*x + a)^3 - d^2*cos(b*x + a))*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 6*(d^2*cos(b*x + a)^3 - d^2*cos(b*x + a))*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^3*cos(b*x + a)^3 - b^3*cos(b*x + a))","C",0
281,1,621,0,0.517421," ","integrate((d*x+c)*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b d x - 6 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - 2 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, b c - {\left(-3 i \, d \cos\left(b x + a\right)^{3} + 3 i \, d \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(3 i \, d \cos\left(b x + a\right)^{3} - 3 i \, d \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-3 i \, d \cos\left(b x + a\right)^{3} + 3 i \, d \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(3 i \, d \cos\left(b x + a\right)^{3} - 3 i \, d \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 3 \, {\left({\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - {\left(b d x + b c\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left({\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - {\left(b d x + b c\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{3} - {\left(b c - a d\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{3} - {\left(b c - a d\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{3} - {\left(b d x + a d\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{3} - {\left(b d x + a d\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left(d \cos\left(b x + a\right)^{3} - d \cos\left(b x + a\right)\right)} \log\left(\sin\left(b x + a\right) + 1\right) - 2 \, {\left(d \cos\left(b x + a\right)^{3} - d \cos\left(b x + a\right)\right)} \log\left(-\sin\left(b x + a\right) + 1\right)}{4 \, {\left(b^{2} \cos\left(b x + a\right)^{3} - b^{2} \cos\left(b x + a\right)\right)}}"," ",0,"-1/4*(4*b*d*x - 6*(b*d*x + b*c)*cos(b*x + a)^2 - 2*d*cos(b*x + a)*sin(b*x + a) + 4*b*c - (-3*I*d*cos(b*x + a)^3 + 3*I*d*cos(b*x + a))*dilog(cos(b*x + a) + I*sin(b*x + a)) - (3*I*d*cos(b*x + a)^3 - 3*I*d*cos(b*x + a))*dilog(cos(b*x + a) - I*sin(b*x + a)) - (-3*I*d*cos(b*x + a)^3 + 3*I*d*cos(b*x + a))*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (3*I*d*cos(b*x + a)^3 - 3*I*d*cos(b*x + a))*dilog(-cos(b*x + a) - I*sin(b*x + a)) + 3*((b*d*x + b*c)*cos(b*x + a)^3 - (b*d*x + b*c)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + 1) + 3*((b*d*x + b*c)*cos(b*x + a)^3 - (b*d*x + b*c)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 3*((b*c - a*d)*cos(b*x + a)^3 - (b*c - a*d)*cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 3*((b*c - a*d)*cos(b*x + a)^3 - (b*c - a*d)*cos(b*x + a))*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 3*((b*d*x + a*d)*cos(b*x + a)^3 - (b*d*x + a*d)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 3*((b*d*x + a*d)*cos(b*x + a)^3 - (b*d*x + a*d)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 2*(d*cos(b*x + a)^3 - d*cos(b*x + a))*log(sin(b*x + a) + 1) - 2*(d*cos(b*x + a)^3 - d*cos(b*x + a))*log(-sin(b*x + a) + 1))/(b^2*cos(b*x + a)^3 - b^2*cos(b*x + a))","B",0
282,0,0,0,0.505849," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)^2/(d*x + c), x)","F",0
283,0,0,0,0.584150," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
284,0,0,0,0.451920," ","integrate(x^m*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral(x^m*csc(b*x + a)^3*sec(b*x + a)^2, x)","F",0
285,1,1735,0,0.618855," ","integrate(x^3*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, b^{3} x^{3} \cos\left(b x + a\right)^{2} - 4 \, b^{3} x^{3} + 6 \, b^{2} x^{2} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left({\left(-9 i \, b^{2} x^{2} - 6 i\right)} \cos\left(b x + a\right)^{3} + {\left(9 i \, b^{2} x^{2} + 6 i\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left({\left(9 i \, b^{2} x^{2} + 6 i\right)} \cos\left(b x + a\right)^{3} + {\left(-9 i \, b^{2} x^{2} - 6 i\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(12 i \, b x \cos\left(b x + a\right)^{3} - 12 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(12 i \, b x \cos\left(b x + a\right)^{3} - 12 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-12 i \, b x \cos\left(b x + a\right)^{3} + 12 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-12 i \, b x \cos\left(b x + a\right)^{3} + 12 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left({\left(-9 i \, b^{2} x^{2} - 6 i\right)} \cos\left(b x + a\right)^{3} + {\left(9 i \, b^{2} x^{2} + 6 i\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left({\left(9 i \, b^{2} x^{2} + 6 i\right)} \cos\left(b x + a\right)^{3} + {\left(-9 i \, b^{2} x^{2} - 6 i\right)} \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left({\left(b^{3} x^{3} + 2 \, b x\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} x^{3} + 2 \, b x\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left(a^{2} \cos\left(b x + a\right)^{3} - a^{2} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left({\left(b^{3} x^{3} + 2 \, b x\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} x^{3} + 2 \, b x\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 6 \, {\left(a^{2} \cos\left(b x + a\right)^{3} - a^{2} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 6 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 6 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 6 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left({\left(a^{3} + 2 \, a\right)} \cos\left(b x + a\right)^{3} - {\left(a^{3} + 2 \, a\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left({\left(a^{3} + 2 \, a\right)} \cos\left(b x + a\right)^{3} - {\left(a^{3} + 2 \, a\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left({\left(b^{3} x^{3} + a^{3} + 2 \, b x + 2 \, a\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} x^{3} + a^{3} + 2 \, b x + 2 \, a\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 6 \, {\left(a^{2} \cos\left(b x + a\right)^{3} - a^{2} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left({\left(b^{3} x^{3} + a^{3} + 2 \, b x + 2 \, a\right)} \cos\left(b x + a\right)^{3} - {\left(b^{3} x^{3} + a^{3} + 2 \, b x + 2 \, a\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 6 \, {\left(a^{2} \cos\left(b x + a\right)^{3} - a^{2} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(18 i \, \cos\left(b x + a\right)^{3} - 18 i \, \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-18 i \, \cos\left(b x + a\right)^{3} + 18 i \, \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(18 i \, \cos\left(b x + a\right)^{3} - 18 i \, \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-18 i \, \cos\left(b x + a\right)^{3} + 18 i \, \cos\left(b x + a\right)\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 18 \, {\left(b x \cos\left(b x + a\right)^{3} - b x \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 18 \, {\left(b x \cos\left(b x + a\right)^{3} - b x \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 18 \, {\left(b x \cos\left(b x + a\right)^{3} - b x \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 18 \, {\left(b x \cos\left(b x + a\right)^{3} - b x \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{4 \, {\left(b^{4} \cos\left(b x + a\right)^{3} - b^{4} \cos\left(b x + a\right)\right)}}"," ",0,"1/4*(6*b^3*x^3*cos(b*x + a)^2 - 4*b^3*x^3 + 6*b^2*x^2*cos(b*x + a)*sin(b*x + a) + ((-9*I*b^2*x^2 - 6*I)*cos(b*x + a)^3 + (9*I*b^2*x^2 + 6*I)*cos(b*x + a))*dilog(cos(b*x + a) + I*sin(b*x + a)) + ((9*I*b^2*x^2 + 6*I)*cos(b*x + a)^3 + (-9*I*b^2*x^2 - 6*I)*cos(b*x + a))*dilog(cos(b*x + a) - I*sin(b*x + a)) + (12*I*b*x*cos(b*x + a)^3 - 12*I*b*x*cos(b*x + a))*dilog(I*cos(b*x + a) + sin(b*x + a)) + (12*I*b*x*cos(b*x + a)^3 - 12*I*b*x*cos(b*x + a))*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-12*I*b*x*cos(b*x + a)^3 + 12*I*b*x*cos(b*x + a))*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-12*I*b*x*cos(b*x + a)^3 + 12*I*b*x*cos(b*x + a))*dilog(-I*cos(b*x + a) - sin(b*x + a)) + ((-9*I*b^2*x^2 - 6*I)*cos(b*x + a)^3 + (9*I*b^2*x^2 + 6*I)*cos(b*x + a))*dilog(-cos(b*x + a) + I*sin(b*x + a)) + ((9*I*b^2*x^2 + 6*I)*cos(b*x + a)^3 + (-9*I*b^2*x^2 - 6*I)*cos(b*x + a))*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 3*((b^3*x^3 + 2*b*x)*cos(b*x + a)^3 - (b^3*x^3 + 2*b*x)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 6*(a^2*cos(b*x + a)^3 - a^2*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + I) - 3*((b^3*x^3 + 2*b*x)*cos(b*x + a)^3 - (b^3*x^3 + 2*b*x)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 6*(a^2*cos(b*x + a)^3 - a^2*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + I) - 6*((b^2*x^2 - a^2)*cos(b*x + a)^3 - (b^2*x^2 - a^2)*cos(b*x + a))*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 6*((b^2*x^2 - a^2)*cos(b*x + a)^3 - (b^2*x^2 - a^2)*cos(b*x + a))*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 6*((b^2*x^2 - a^2)*cos(b*x + a)^3 - (b^2*x^2 - a^2)*cos(b*x + a))*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 6*((b^2*x^2 - a^2)*cos(b*x + a)^3 - (b^2*x^2 - a^2)*cos(b*x + a))*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 3*((a^3 + 2*a)*cos(b*x + a)^3 - (a^3 + 2*a)*cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 3*((a^3 + 2*a)*cos(b*x + a)^3 - (a^3 + 2*a)*cos(b*x + a))*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + 3*((b^3*x^3 + a^3 + 2*b*x + 2*a)*cos(b*x + a)^3 - (b^3*x^3 + a^3 + 2*b*x + 2*a)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - 6*(a^2*cos(b*x + a)^3 - a^2*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 3*((b^3*x^3 + a^3 + 2*b*x + 2*a)*cos(b*x + a)^3 - (b^3*x^3 + a^3 + 2*b*x + 2*a)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 6*(a^2*cos(b*x + a)^3 - a^2*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (18*I*cos(b*x + a)^3 - 18*I*cos(b*x + a))*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + (-18*I*cos(b*x + a)^3 + 18*I*cos(b*x + a))*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + (18*I*cos(b*x + a)^3 - 18*I*cos(b*x + a))*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + (-18*I*cos(b*x + a)^3 + 18*I*cos(b*x + a))*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 18*(b*x*cos(b*x + a)^3 - b*x*cos(b*x + a))*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 18*(b*x*cos(b*x + a)^3 - b*x*cos(b*x + a))*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 12*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 12*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 12*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 12*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 18*(b*x*cos(b*x + a)^3 - b*x*cos(b*x + a))*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 18*(b*x*cos(b*x + a)^3 - b*x*cos(b*x + a))*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^4*cos(b*x + a)^3 - b^4*cos(b*x + a))","C",0
286,1,1229,0,0.562365," ","integrate(x^2*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, b^{2} x^{2} \cos\left(b x + a\right)^{2} - 4 \, b^{2} x^{2} + 4 \, b x \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(-6 i \, b x \cos\left(b x + a\right)^{3} + 6 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, b x \cos\left(b x + a\right)^{3} - 6 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(4 i \, \cos\left(b x + a\right)^{3} - 4 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(4 i \, \cos\left(b x + a\right)^{3} - 4 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-4 i \, \cos\left(b x + a\right)^{3} + 4 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-4 i \, \cos\left(b x + a\right)^{3} + 4 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, b x \cos\left(b x + a\right)^{3} + 6 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, b x \cos\left(b x + a\right)^{3} - 6 i \, b x \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left({\left(3 \, b^{2} x^{2} + 2\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{2} x^{2} + 2\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left(a \cos\left(b x + a\right)^{3} - a \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left({\left(3 \, b^{2} x^{2} + 2\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, b^{2} x^{2} + 2\right)} \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(a \cos\left(b x + a\right)^{3} - a \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 4 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} - {\left(b x + a\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} - {\left(b x + a\right)} \cos\left(b x + a\right)\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 4 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} - {\left(b x + a\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 4 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} - {\left(b x + a\right)} \cos\left(b x + a\right)\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left({\left(3 \, a^{2} + 2\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, a^{2} + 2\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left({\left(3 \, a^{2} + 2\right)} \cos\left(b x + a\right)^{3} - {\left(3 \, a^{2} + 2\right)} \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 4 \, {\left(a \cos\left(b x + a\right)^{3} - a \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left({\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)^{3} - {\left(b^{2} x^{2} - a^{2}\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 4 \, {\left(a \cos\left(b x + a\right)^{3} - a \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{4 \, {\left(b^{3} \cos\left(b x + a\right)^{3} - b^{3} \cos\left(b x + a\right)\right)}}"," ",0,"1/4*(6*b^2*x^2*cos(b*x + a)^2 - 4*b^2*x^2 + 4*b*x*cos(b*x + a)*sin(b*x + a) + (-6*I*b*x*cos(b*x + a)^3 + 6*I*b*x*cos(b*x + a))*dilog(cos(b*x + a) + I*sin(b*x + a)) + (6*I*b*x*cos(b*x + a)^3 - 6*I*b*x*cos(b*x + a))*dilog(cos(b*x + a) - I*sin(b*x + a)) + (4*I*cos(b*x + a)^3 - 4*I*cos(b*x + a))*dilog(I*cos(b*x + a) + sin(b*x + a)) + (4*I*cos(b*x + a)^3 - 4*I*cos(b*x + a))*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-4*I*cos(b*x + a)^3 + 4*I*cos(b*x + a))*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-4*I*cos(b*x + a)^3 + 4*I*cos(b*x + a))*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (-6*I*b*x*cos(b*x + a)^3 + 6*I*b*x*cos(b*x + a))*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (6*I*b*x*cos(b*x + a)^3 - 6*I*b*x*cos(b*x + a))*dilog(-cos(b*x + a) - I*sin(b*x + a)) - ((3*b^2*x^2 + 2)*cos(b*x + a)^3 - (3*b^2*x^2 + 2)*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + 1) + 4*(a*cos(b*x + a)^3 - a*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + I) - ((3*b^2*x^2 + 2)*cos(b*x + a)^3 - (3*b^2*x^2 + 2)*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 4*(a*cos(b*x + a)^3 - a*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + I) - 4*((b*x + a)*cos(b*x + a)^3 - (b*x + a)*cos(b*x + a))*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 4*((b*x + a)*cos(b*x + a)^3 - (b*x + a)*cos(b*x + a))*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 4*((b*x + a)*cos(b*x + a)^3 - (b*x + a)*cos(b*x + a))*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 4*((b*x + a)*cos(b*x + a)^3 - (b*x + a)*cos(b*x + a))*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + ((3*a^2 + 2)*cos(b*x + a)^3 - (3*a^2 + 2)*cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + ((3*a^2 + 2)*cos(b*x + a)^3 - (3*a^2 + 2)*cos(b*x + a))*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + 3*((b^2*x^2 - a^2)*cos(b*x + a)^3 - (b^2*x^2 - a^2)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 4*(a*cos(b*x + a)^3 - a*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 3*((b^2*x^2 - a^2)*cos(b*x + a)^3 - (b^2*x^2 - a^2)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 4*(a*cos(b*x + a)^3 - a*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 6*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 6*(cos(b*x + a)^3 - cos(b*x + a))*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^3*cos(b*x + a)^3 - b^3*cos(b*x + a))","C",0
287,1,527,0,0.511908," ","integrate(x*csc(b*x+a)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, b x \cos\left(b x + a\right)^{2} - 4 \, b x + {\left(-3 i \, \cos\left(b x + a\right)^{3} + 3 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, \cos\left(b x + a\right)^{3} - 3 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, \cos\left(b x + a\right)^{3} + 3 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, \cos\left(b x + a\right)^{3} - 3 i \, \cos\left(b x + a\right)\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left(b x \cos\left(b x + a\right)^{3} - b x \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b x \cos\left(b x + a\right)^{3} - b x \cos\left(b x + a\right)\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(a \cos\left(b x + a\right)^{3} - a \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 3 \, {\left(a \cos\left(b x + a\right)^{3} - a \cos\left(b x + a\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} - {\left(b x + a\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left({\left(b x + a\right)} \cos\left(b x + a\right)^{3} - {\left(b x + a\right)} \cos\left(b x + a\right)\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 2 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(\sin\left(b x + a\right) + 1\right) + 2 \, {\left(\cos\left(b x + a\right)^{3} - \cos\left(b x + a\right)\right)} \log\left(-\sin\left(b x + a\right) + 1\right) + 2 \, \cos\left(b x + a\right) \sin\left(b x + a\right)}{4 \, {\left(b^{2} \cos\left(b x + a\right)^{3} - b^{2} \cos\left(b x + a\right)\right)}}"," ",0,"1/4*(6*b*x*cos(b*x + a)^2 - 4*b*x + (-3*I*cos(b*x + a)^3 + 3*I*cos(b*x + a))*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*cos(b*x + a)^3 - 3*I*cos(b*x + a))*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-3*I*cos(b*x + a)^3 + 3*I*cos(b*x + a))*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (3*I*cos(b*x + a)^3 - 3*I*cos(b*x + a))*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 3*(b*x*cos(b*x + a)^3 - b*x*cos(b*x + a))*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b*x*cos(b*x + a)^3 - b*x*cos(b*x + a))*log(cos(b*x + a) - I*sin(b*x + a) + 1) - 3*(a*cos(b*x + a)^3 - a*cos(b*x + a))*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 3*(a*cos(b*x + a)^3 - a*cos(b*x + a))*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + 3*((b*x + a)*cos(b*x + a)^3 - (b*x + a)*cos(b*x + a))*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 3*((b*x + a)*cos(b*x + a)^3 - (b*x + a)*cos(b*x + a))*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 2*(cos(b*x + a)^3 - cos(b*x + a))*log(sin(b*x + a) + 1) + 2*(cos(b*x + a)^3 - cos(b*x + a))*log(-sin(b*x + a) + 1) + 2*cos(b*x + a)*sin(b*x + a))/(b^2*cos(b*x + a)^3 - b^2*cos(b*x + a))","B",0
288,0,0,0,0.438551," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}}{x}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)^2/x, x)","F",0
289,0,0,0,0.452226," ","integrate(csc(b*x+a)^3*sec(b*x+a)^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{2}}{x^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)^2/x^2, x)","F",0
290,0,0,0,0.447644," ","integrate((d*x+c)^m*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sec\left(b x + a\right)^{2} \tan\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*sec(b*x + a)^2*tan(b*x + a), x)","F",0
291,1,888,0,0.571568," ","integrate((d*x+c)^4*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} - 12 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-12 i \, b d^{4} x - 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(12 i \, b d^{4} x + 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(12 i \, b d^{4} x + 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-12 i \, b d^{4} x - 12 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + 2 \, a b c d^{3} - a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b^{2} c^{2} d^{2} - 2 \, a b c d^{3} + a^{2} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{5} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 - 12*d^4*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 12*d^4*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 12*d^4*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 12*d^4*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + (-12*I*b*d^4*x - 12*I*b*c*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (12*I*b*d^4*x + 12*I*b*c*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (12*I*b*d^4*x + 12*I*b*c*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-12*I*b*d^4*x - 12*I*b*c*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) - 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) - 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - 6*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + 2*a*b*c*d^3 - a^2*d^4)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) - 6*(b^2*c^2*d^2 - 2*a*b*c*d^3 + a^2*d^4)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*cos(b*x + a)*sin(b*x + a))/(b^5*cos(b*x + a)^2)","C",0
292,1,540,0,0.533341," ","integrate((d*x+c)^3*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3} - 3 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 3 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 3 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 3 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 3 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b d^{3} x + a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b d^{3} x + a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b d^{3} x + a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b d^{3} x + a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b c d^{2} - a d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{4} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 - 3*I*d^3*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + 3*I*d^3*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + 3*I*d^3*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) - 3*I*d^3*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) - 3*(b*c*d^2 - a*d^3)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) - 3*(b*c*d^2 - a*d^3)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - 3*(b*d^3*x + a*d^3)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - 3*(b*d^3*x + a*d^3)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b*d^3*x + a*d^3)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - 3*(b*d^3*x + a*d^3)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b*c*d^2 - a*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) - 3*(b*c*d^2 - a*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a))/(b^4*cos(b*x + a)^2)","B",0
293,1,86,0,0.451406," ","integrate((d*x+c)^2*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x - 2 \, d^{2} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right)\right) + b^{2} c^{2} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{3} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x - 2*d^2*cos(b*x + a)^2*log(-cos(b*x + a)) + b^2*c^2 - 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a))/(b^3*cos(b*x + a)^2)","A",0
294,1,36,0,0.408576," ","integrate((d*x+c)*sec(b*x+a)^2*tan(b*x+a),x, algorithm=""fricas"")","\frac{b d x - d \cos\left(b x + a\right) \sin\left(b x + a\right) + b c}{2 \, b^{2} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b*d*x - d*cos(b*x + a)*sin(b*x + a) + b*c)/(b^2*cos(b*x + a)^2)","A",0
295,0,0,0,0.487766," ","integrate(sec(b*x+a)^2*tan(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2} \tan\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)^2*tan(b*x + a)/(d*x + c), x)","F",0
296,0,0,0,0.448330," ","integrate(sec(b*x+a)^2*tan(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2} \tan\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sec(b*x + a)^2*tan(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
297,0,0,0,0.421631," ","integrate((d*x+c)^m*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sec\left(b x + a\right) \tan\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*sec(b*x + a)*tan(b*x + a)^2, x)","F",0
298,1,1311,0,0.638560," ","integrate((d*x+c)^3*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","\frac{-6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(b x + a\right)}{4 \, b^{4} \cos\left(b x + a\right)^{2}}"," ",0,"1/4*(-6*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + 6*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(b*x + a))/(b^4*cos(b*x + a)^2)","C",0
299,1,791,0,0.547658," ","integrate((d*x+c)^2*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(b x + a\right)}{4 \, b^{3} \cos\left(b x + a\right)^{2}}"," ",0,"1/4*(2*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 4*(b*d^2*x + b*c*d)*cos(b*x + a) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(b*x + a))/(b^3*cos(b*x + a)^2)","C",0
300,1,435,0,0.525211," ","integrate((d*x+c)*sec(b*x+a)*tan(b*x+a)^2,x, algorithm=""fricas"")","\frac{i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 2 \, d \cos\left(b x + a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(b x + a\right)}{4 \, b^{2} \cos\left(b x + a\right)^{2}}"," ",0,"1/4*(I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 2*d*cos(b*x + a) + 2*(b*d*x + b*c)*sin(b*x + a))/(b^2*cos(b*x + a)^2)","B",0
301,0,0,0,0.455982," ","integrate(sec(b*x+a)*tan(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \tan\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)*tan(b*x + a)^2/(d*x + c), x)","F",0
302,0,0,0,0.449400," ","integrate(sec(b*x+a)*tan(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \tan\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sec(b*x + a)*tan(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
303,0,0,0,0.421654," ","integrate((d*x+c)^m*tan(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \tan\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*x + c)^m*tan(b*x + a)^3, x)","F",0
304,1,590,0,0.453722," ","integrate((d*x+c)^3*tan(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, b^{3} d^{3} x^{3} + 12 \, b^{3} c d^{2} x^{2} + 12 \, b^{3} c^{2} d x - 3 i \, d^{3} {\rm polylog}\left(4, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 3 i \, d^{3} {\rm polylog}\left(4, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \tan\left(b x + a\right)^{2} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - b d^{3}\right)} x\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) - 12 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \tan\left(b x + a\right)}{8 \, b^{4}}"," ",0,"1/8*(4*b^3*d^3*x^3 + 12*b^3*c*d^2*x^2 + 12*b^3*c^2*d*x - 3*I*d^3*polylog(4, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 3*I*d^3*polylog(4, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*tan(b*x + a)^2 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d - 6*I*d^3)*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d + 6*I*d^3)*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 3*b*c*d^2 + 3*(b^3*c^2*d - b*d^3)*x)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 3*b*c*d^2 + 3*(b^3*c^2*d - b*d^3)*x)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 12*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*tan(b*x + a))/b^4","C",0
305,1,352,0,0.454554," ","integrate((d*x+c)^2*tan(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + d^{2} {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} + 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + d^{2} {\rm polylog}\left(3, \frac{\tan\left(b x + a\right)^{2} - 2 i \, \tan\left(b x + a\right) - 1}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \tan\left(b x + a\right)^{2} + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - d^{2}\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - d^{2}\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 4 \, {\left(b d^{2} x + b c d\right)} \tan\left(b x + a\right)}{4 \, b^{3}}"," ",0,"1/4*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + d^2*polylog(3, (tan(b*x + a)^2 + 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + d^2*polylog(3, (tan(b*x + a)^2 - 2*I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*tan(b*x + a)^2 + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - d^2)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - d^2)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 4*(b*d^2*x + b*c*d)*tan(b*x + a))/b^3","C",0
306,1,168,0,0.429608," ","integrate((d*x+c)*tan(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b d x + 2 \, {\left(b d x + b c\right)} \tan\left(b x + a\right)^{2} + i \, d {\rm Li}_2\left(\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) - i \, d {\rm Li}_2\left(\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1} + 1\right) + 2 \, {\left(b d x + b c\right)} \log\left(-\frac{2 \, {\left(i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) + 2 \, {\left(b d x + b c\right)} \log\left(-\frac{2 \, {\left(-i \, \tan\left(b x + a\right) - 1\right)}}{\tan\left(b x + a\right)^{2} + 1}\right) - 2 \, d \tan\left(b x + a\right)}{4 \, b^{2}}"," ",0,"1/4*(2*b*d*x + 2*(b*d*x + b*c)*tan(b*x + a)^2 + I*d*dilog(2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) - I*d*dilog(2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1) + 1) + 2*(b*d*x + b*c)*log(-2*(I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) + 2*(b*d*x + b*c)*log(-2*(-I*tan(b*x + a) - 1)/(tan(b*x + a)^2 + 1)) - 2*d*tan(b*x + a))/b^2","A",0
307,0,0,0,0.424525," ","integrate(tan(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(tan(b*x + a)^3/(d*x + c), x)","F",0
308,0,0,0,0.417166," ","integrate(tan(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tan\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(tan(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
309,0,0,0,0.415171," ","integrate((d*x+c)^m*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right) \sec\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)*sec(b*x + a)^3, x)","F",0
310,1,3308,0,1.046478," ","integrate((d*x+c)^4*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} - 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 24 \, d^{4} \cos\left(b x + a\right)^{2} {\rm polylog}\left(5, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d - 12 i \, b c d^{3} - 12 i \, {\left(b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d + 12 i \, b c d^{3} + 12 i \, {\left(b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 4 i \, b^{3} c^{3} d + 12 i \, b c d^{3} + 12 i \, {\left(b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 4 i \, b^{3} c^{3} d - 12 i \, b c d^{3} - 12 i \, {\left(b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} + 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} + {\left(a^{4} + 6 \, a^{2}\right)} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} + 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} + {\left(a^{4} + 6 \, a^{2}\right)} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} - {\left(a^{4} + 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} - {\left(a^{4} + 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} - {\left(a^{4} + 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} - {\left(a^{4} + 6 \, a^{2}\right)} d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} + 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} + {\left(a^{4} + 6 \, a^{2}\right)} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, {\left(a^{2} + 1\right)} b^{2} c^{2} d^{2} - 4 \, {\left(a^{3} + 3 \, a\right)} b c d^{3} + {\left(a^{4} + 6 \, a^{2}\right)} d^{4}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} + d^{4}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} + d^{4}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} + d^{4}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2} + d^{4}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{5} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 - 24*d^4*cos(b*x + a)^2*polylog(5, cos(b*x + a) + I*sin(b*x + a)) - 24*d^4*cos(b*x + a)^2*polylog(5, cos(b*x + a) - I*sin(b*x + a)) + 24*d^4*cos(b*x + a)^2*polylog(5, I*cos(b*x + a) + sin(b*x + a)) + 24*d^4*cos(b*x + a)^2*polylog(5, I*cos(b*x + a) - sin(b*x + a)) + 24*d^4*cos(b*x + a)^2*polylog(5, -I*cos(b*x + a) + sin(b*x + a)) + 24*d^4*cos(b*x + a)^2*polylog(5, -I*cos(b*x + a) - sin(b*x + a)) - 24*d^4*cos(b*x + a)^2*polylog(5, -cos(b*x + a) + I*sin(b*x + a)) - 24*d^4*cos(b*x + a)^2*polylog(5, -cos(b*x + a) - I*sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*cos(b*x + a)^2*dilog(cos(b*x + a) + I*sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*cos(b*x + a)^2*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d - 12*I*b*c*d^3 - 12*I*(b^3*c^2*d^2 + b*d^4)*x)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d + 12*I*b*c*d^3 + 12*I*(b^3*c^2*d^2 + b*d^4)*x)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 4*I*b^3*c^3*d + 12*I*b*c*d^3 + 12*I*(b^3*c^2*d^2 + b*d^4)*x)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 4*I*b^3*c^3*d - 12*I*b*c*d^3 - 12*I*(b^3*c^2*d^2 + b*d^4)*x)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*cos(b*x + a)^2*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*cos(b*x + a)^2*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 + 1)*b^2*c^2*d^2 - 4*(a^3 + 3*a)*b*c*d^3 + (a^4 + 6*a^2)*d^4)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 + 1)*b^2*c^2*d^2 - 4*(a^3 + 3*a)*b*c*d^3 + (a^4 + 6*a^2)*d^4)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 + 3*a)*b*c*d^3 - (a^4 + 6*a^2)*d^4 + 6*(b^4*c^2*d^2 + b^2*d^4)*x^2 + 4*(b^4*c^3*d + 3*b^2*c*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 + 3*a)*b*c*d^3 - (a^4 + 6*a^2)*d^4 + 6*(b^4*c^2*d^2 + b^2*d^4)*x^2 + 4*(b^4*c^3*d + 3*b^2*c*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 + 3*a)*b*c*d^3 - (a^4 + 6*a^2)*d^4 + 6*(b^4*c^2*d^2 + b^2*d^4)*x^2 + 4*(b^4*c^3*d + 3*b^2*c*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*(a^3 + 3*a)*b*c*d^3 - (a^4 + 6*a^2)*d^4 + 6*(b^4*c^2*d^2 + b^2*d^4)*x^2 + 4*(b^4*c^3*d + 3*b^2*c*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 + 1)*b^2*c^2*d^2 - 4*(a^3 + 3*a)*b*c*d^3 + (a^4 + 6*a^2)*d^4)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b^4*c^4 - 4*a*b^3*c^3*d + 6*(a^2 + 1)*b^2*c^2*d^2 - 4*(a^3 + 3*a)*b*c*d^3 + (a^4 + 6*a^2)*d^4)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, cos(b*x + a) + I*sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*cos(b*x + a)^2*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 + d^4)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 + d^4)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 + d^4)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2 + d^4)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*cos(b*x + a)^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) - 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d)*cos(b*x + a)*sin(b*x + a))/(b^5*cos(b*x + a)^2)","C",0
311,1,2260,0,0.830189," ","integrate((d*x+c)^3*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3} + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 1\right)} b c d^{2} - {\left(a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{4} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 + 6*I*d^3*cos(b*x + a)^2*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + 6*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) + 6*I*d^3*cos(b*x + a)^2*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*cos(b*x + a)^2*dilog(cos(b*x + a) + I*sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*cos(b*x + a)^2*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*cos(b*x + a)^2*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*cos(b*x + a)^2*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 3*a)*d^3 + 3*(b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 1)*b*c*d^2 - (a^3 + 3*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a))/(b^4*cos(b*x + a)^2)","C",0
312,1,1396,0,0.654475," ","integrate((d*x+c)^2*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + b^{2} c^{2} + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{3} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*d^2*cos(b*x + a)^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*cos(b*x + a)^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*cos(b*x + a)^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) + 2*d^2*cos(b*x + a)^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + b^2*c^2 + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(cos(b*x + a) + I*sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 1)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a))/(b^3*cos(b*x + a)^2)","C",0
313,1,760,0,0.558112," ","integrate((d*x+c)*csc(b*x+a)*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{-i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + b d x - d \cos\left(b x + a\right) \sin\left(b x + a\right) + b c}{2 \, b^{2} \cos\left(b x + a\right)^{2}}"," ",0,"1/2*(-I*d*cos(b*x + a)^2*dilog(cos(b*x + a) + I*sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(cos(b*x + a) - I*sin(b*x + a)) - I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(-cos(b*x + a) + I*sin(b*x + a)) - I*d*cos(b*x + a)^2*dilog(-cos(b*x + a) - I*sin(b*x + a)) + (b*d*x + b*c)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + 1) - (b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*d*x + b*c)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + 1) - (b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b*c - a*d)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + (b*c - a*d)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + (b*d*x + a*d)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + 1) - (b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*d*x + a*d)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - (b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) + b*d*x - d*cos(b*x + a)*sin(b*x + a) + b*c)/(b^2*cos(b*x + a)^2)","B",0
314,0,0,0,0.525388," ","integrate(csc(b*x+a)*sec(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right) \sec\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)*sec(b*x + a)^3/(d*x + c), x)","F",0
315,0,0,0,0.629373," ","integrate(csc(b*x+a)*sec(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right) \sec\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)*sec(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
316,0,0,0,0.462410," ","integrate((d*x+c)^m*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^2*sec(b*x + a)^3, x)","F",0
317,1,2218,0,0.837011," ","integrate((d*x+c)^3*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 18 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 18 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 18 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 18 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 12 \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 12 \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 2 \, b^{3} c^{3} + {\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 2 \, a\right)} d^{3} + {\left(3 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 6 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + {\left(3 \, a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 2 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 18 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 18 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 18 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 18 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right)^{2} - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{4 \, b^{4} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)}"," ",0,"1/4*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 18*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 18*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - 18*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 18*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 12*d^3*cos(b*x + a)^2*polylog(3, cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 12*d^3*cos(b*x + a)^2*polylog(3, cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 12*d^3*cos(b*x + a)^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) - 12*d^3*cos(b*x + a)^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + 2*b^3*c^3 + (-12*I*b*d^3*x - 12*I*b*c*d^2)*cos(b*x + a)^2*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + (12*I*b*d^3*x + 12*I*b*c*d^2)*cos(b*x + a)^2*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) + (-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + (-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + (9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + (9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + (-12*I*b*d^3*x - 12*I*b*c*d^2)*cos(b*x + a)^2*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + (12*I*b*d^3*x + 12*I*b*c*d^2)*cos(b*x + a)^2*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 2*a)*d^3 + (3*b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + 6*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^3*c^3 - 3*a*b^2*c^2*d + (3*a^2 + 2)*b*c*d^2 - (a^3 + 2*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) - 18*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 18*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - 18*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 18*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - 6*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)^2 - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a))/(b^4*cos(b*x + a)^2*sin(b*x + a))","C",0
318,1,1362,0,0.649156," ","integrate((d*x+c)^2*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{2} x^{2} - 4 i \, d^{2} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 4 i \, d^{2} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 4 i \, d^{2} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 4 i \, d^{2} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 6 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 6 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 4 \, b^{2} c d x + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 4 \, {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 4 \, {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 4 \, {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + {\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 4 \, {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - {\left(3 \, b^{2} c^{2} - 6 \, a b c d + {\left(3 \, a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 2 \, b^{2} c^{2} - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)^{2} - 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{4 \, b^{3} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)}"," ",0,"1/4*(2*b^2*d^2*x^2 - 4*I*d^2*cos(b*x + a)^2*dilog(cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 4*I*d^2*cos(b*x + a)^2*dilog(cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 4*I*d^2*cos(b*x + a)^2*dilog(-cos(b*x + a) + I*sin(b*x + a))*sin(b*x + a) + 4*I*d^2*cos(b*x + a)^2*dilog(-cos(b*x + a) - I*sin(b*x + a))*sin(b*x + a) - 6*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 6*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - 6*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 6*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 4*b^2*c*d*x + (-6*I*b*d^2*x - 6*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + (-6*I*b*d^2*x - 6*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + (6*I*b*d^2*x + 6*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + (6*I*b*d^2*x + 6*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) - 4*(b*d^2*x + b*c*d)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + (3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) - 4*(b*d^2*x + b*c*d)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - (3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 4*(b*c*d - a*d^2)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + 4*(b*c*d - a*d^2)*cos(b*x + a)^2*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2)*sin(b*x + a) + 4*(b*d^2*x + a*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + 1)*sin(b*x + a) + (3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) + 4*(b*d^2*x + a*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + 1)*sin(b*x + a) - (3*b^2*c^2 - 6*a*b*c*d + (3*a^2 + 2)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 2*b^2*c^2 - 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)^2 - 4*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a))/(b^3*cos(b*x + a)^2*sin(b*x + a))","C",0
319,1,592,0,0.536573," ","integrate((d*x+c)*csc(b*x+a)^2*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{-3 i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - 3 i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) \sin\left(b x + a\right) + 3 \, {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 3 \, {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 2 \, d \cos\left(b x + a\right)^{2} \log\left(\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 3 \, {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 3 \, {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) - 3 \, {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) \sin\left(b x + a\right) + 2 \, d \cos\left(b x + a\right)^{2} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2}\right) \sin\left(b x + a\right) + 3 \, {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) - 3 \, {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) \sin\left(b x + a\right) + 2 \, b d x - 6 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - 2 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, b c}{4 \, b^{2} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right)}"," ",0,"1/4*(-3*I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) - 3*I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 3*I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a))*sin(b*x + a) + 3*I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a))*sin(b*x + a) + 3*(b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) - 3*(b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) - 2*d*cos(b*x + a)^2*log(1/2*cos(b*x + a) + 1/2)*sin(b*x + a) + 3*(b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) - 3*(b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 3*(b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1)*sin(b*x + a) - 3*(b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1)*sin(b*x + a) + 2*d*cos(b*x + a)^2*log(-1/2*cos(b*x + a) + 1/2)*sin(b*x + a) + 3*(b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I)*sin(b*x + a) - 3*(b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I)*sin(b*x + a) + 2*b*d*x - 6*(b*d*x + b*c)*cos(b*x + a)^2 - 2*d*cos(b*x + a)*sin(b*x + a) + 2*b*c)/(b^2*cos(b*x + a)^2*sin(b*x + a))","B",0
320,0,0,0,0.527330," ","integrate(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^2*sec(b*x + a)^3/(d*x + c), x)","F",0
321,0,0,0,0.578291," ","integrate(csc(b*x+a)^2*sec(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sec\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^2*sec(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
322,0,0,0,0.430288," ","integrate((d*x+c)^m*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{3}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^3*sec(b*x + a)^3, x)","F",0
323,1,4193,0,0.945096," ","integrate((d*x+c)^3*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(b x + a\right)^{2} - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left({\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left({\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left({\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left({\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d - 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{4} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d + 3 i \, d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left({\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left({\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left({\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, a b^{2} c^{2} d - 6 \, a^{2} b c d^{2} + {\left(2 \, a^{3} + 3 \, a\right)} d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 3 \, {\left(2 \, a^{2} + 1\right)} b c d^{2} - {\left(2 \, a^{3} + 3 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(12 i \, d^{3} \cos\left(b x + a\right)^{4} - 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-12 i \, d^{3} \cos\left(b x + a\right)^{4} + 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(12 i \, d^{3} \cos\left(b x + a\right)^{4} - 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-12 i \, d^{3} \cos\left(b x + a\right)^{4} + 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-12 i \, d^{3} \cos\left(b x + a\right)^{4} + 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(12 i \, d^{3} \cos\left(b x + a\right)^{4} - 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-12 i \, d^{3} \cos\left(b x + a\right)^{4} + 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(12 i \, d^{3} \cos\left(b x + a\right)^{4} - 12 i \, d^{3} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 12 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, {\left(b^{4} \cos\left(b x + a\right)^{4} - b^{4} \cos\left(b x + a\right)^{2}\right)}}"," ",0,"-1/2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(b*x + a)^2 - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a)*sin(b*x + a) - ((-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^4 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) - ((6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^4 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) - ((-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^4 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) + sin(b*x + a)) - ((6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^4 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) - sin(b*x + a)) - ((6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^4 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - ((-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^4 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - ((6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^4 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - ((-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d - 3*I*d^3)*cos(b*x + a)^4 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d + 3*I*d^3)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 + 3*b*c*d^2 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 + 3*b*c*d^2 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + ((2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^4 - (2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) - ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 + 3*b*c*d^2 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 + 3*b*c*d^2 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + ((2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^4 - (2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - ((2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^4 - (2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - ((2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^4 - (2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + ((2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^4 - (2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - ((2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^4 - (2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*a*b^2*c^2*d - 6*a^2*b*c*d^2 + (2*a^3 + 3*a)*d^3 + 3*(2*b^3*c^2*d + b*d^3)*x)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + ((2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^4 - (2*b^3*c^3 - 6*a*b^2*c^2*d + 3*(2*a^2 + 1)*b*c*d^2 - (2*a^3 + 3*a)*d^3)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - (12*I*d^3*cos(b*x + a)^4 - 12*I*d^3*cos(b*x + a)^2)*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - (-12*I*d^3*cos(b*x + a)^4 + 12*I*d^3*cos(b*x + a)^2)*polylog(4, cos(b*x + a) - I*sin(b*x + a)) - (12*I*d^3*cos(b*x + a)^4 - 12*I*d^3*cos(b*x + a)^2)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) - (-12*I*d^3*cos(b*x + a)^4 + 12*I*d^3*cos(b*x + a)^2)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - (-12*I*d^3*cos(b*x + a)^4 + 12*I*d^3*cos(b*x + a)^2)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - (12*I*d^3*cos(b*x + a)^4 - 12*I*d^3*cos(b*x + a)^2)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - (-12*I*d^3*cos(b*x + a)^4 + 12*I*d^3*cos(b*x + a)^2)*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - (12*I*d^3*cos(b*x + a)^4 - 12*I*d^3*cos(b*x + a)^2)*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) - 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 12*((b*d^3*x + b*c*d^2)*cos(b*x + a)^4 - (b*d^3*x + b*c*d^2)*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^4*cos(b*x + a)^4 - b^4*cos(b*x + a)^2)","C",0
324,1,2387,0,0.700091," ","integrate((d*x+c)^2*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)^{2} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - {\left({\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left({\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left({\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left({\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left({\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left({\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cos\left(b x + a\right)^{4} + {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left({\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left({\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left({\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - {\left({\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + {\left({\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{4} - {\left(2 \, b^{2} c^{2} - 4 \, a b c d + {\left(2 \, a^{2} + 1\right)} d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 4 \, {\left(d^{2} \cos\left(b x + a\right)^{4} - d^{2} \cos\left(b x + a\right)^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right)}{2 \, {\left(b^{3} \cos\left(b x + a\right)^{4} - b^{3} \cos\left(b x + a\right)^{2}\right)}}"," ",0,"-1/2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a)^2 - 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - ((-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^4 + (4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) - ((4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^4 + (-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) - ((-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^4 + (4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) + sin(b*x + a)) - ((4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^4 + (-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^2)*dilog(I*cos(b*x + a) - sin(b*x + a)) - ((4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^4 + (-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - ((-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^4 + (4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - ((4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^4 + (-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - ((-4*I*b*d^2*x - 4*I*b*c*d)*cos(b*x + a)^4 + (4*I*b*d^2*x + 4*I*b*c*d)*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - ((2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + d^2)*cos(b*x + a)^4 - (2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + d^2)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + ((2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^4 - (2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) - ((2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + d^2)*cos(b*x + a)^4 - (2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + d^2)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + ((2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^4 - (2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^4 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^4 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^4 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^4 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - ((2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^4 - (2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - ((2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^4 - (2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^4 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + ((2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^4 - (2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^4 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + ((2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^4 - (2*b^2*c^2 - 4*a*b*c*d + (2*a^2 + 1)*d^2)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) - 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) + 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 4*(d^2*cos(b*x + a)^4 - d^2*cos(b*x + a)^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)))/(b^3*cos(b*x + a)^4 - b^3*cos(b*x + a)^2)","C",0
325,1,1193,0,0.596084," ","integrate((d*x+c)*csc(b*x+a)^3*sec(b*x+a)^3,x, algorithm=""fricas"")","-\frac{b d x - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - d \cos\left(b x + a\right) \sin\left(b x + a\right) + b c - {\left(-2 i \, d \cos\left(b x + a\right)^{4} + 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(2 i \, d \cos\left(b x + a\right)^{4} - 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - {\left(-2 i \, d \cos\left(b x + a\right)^{4} + 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(2 i \, d \cos\left(b x + a\right)^{4} - 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(2 i \, d \cos\left(b x + a\right)^{4} - 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-2 i \, d \cos\left(b x + a\right)^{4} + 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(2 i \, d \cos\left(b x + a\right)^{4} - 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - {\left(-2 i \, d \cos\left(b x + a\right)^{4} + 2 i \, d \cos\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 2 \, {\left({\left(b d x + b c\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{4} - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left({\left(b d x + b c\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{4} - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 2 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{4} - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{4} - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) - 2 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{4} - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - 2 \, {\left({\left(b d x + a d\right)} \cos\left(b x + a\right)^{4} - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 2 \, {\left({\left(b c - a d\right)} \cos\left(b x + a\right)^{4} - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, {\left(b^{2} \cos\left(b x + a\right)^{4} - b^{2} \cos\left(b x + a\right)^{2}\right)}}"," ",0,"-1/2*(b*d*x - 2*(b*d*x + b*c)*cos(b*x + a)^2 - d*cos(b*x + a)*sin(b*x + a) + b*c - (-2*I*d*cos(b*x + a)^4 + 2*I*d*cos(b*x + a)^2)*dilog(cos(b*x + a) + I*sin(b*x + a)) - (2*I*d*cos(b*x + a)^4 - 2*I*d*cos(b*x + a)^2)*dilog(cos(b*x + a) - I*sin(b*x + a)) - (-2*I*d*cos(b*x + a)^4 + 2*I*d*cos(b*x + a)^2)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (2*I*d*cos(b*x + a)^4 - 2*I*d*cos(b*x + a)^2)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (2*I*d*cos(b*x + a)^4 - 2*I*d*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (-2*I*d*cos(b*x + a)^4 + 2*I*d*cos(b*x + a)^2)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (2*I*d*cos(b*x + a)^4 - 2*I*d*cos(b*x + a)^2)*dilog(-cos(b*x + a) + I*sin(b*x + a)) - (-2*I*d*cos(b*x + a)^4 + 2*I*d*cos(b*x + a)^2)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 2*((b*d*x + b*c)*cos(b*x + a)^4 - (b*d*x + b*c)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) + 2*((b*c - a*d)*cos(b*x + a)^4 - (b*c - a*d)*cos(b*x + a)^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) - 2*((b*d*x + b*c)*cos(b*x + a)^4 - (b*d*x + b*c)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 2*((b*c - a*d)*cos(b*x + a)^4 - (b*c - a*d)*cos(b*x + a)^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + 2*((b*d*x + a*d)*cos(b*x + a)^4 - (b*d*x + a*d)*cos(b*x + a)^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 2*((b*d*x + a*d)*cos(b*x + a)^4 - (b*d*x + a*d)*cos(b*x + a)^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 2*((b*d*x + a*d)*cos(b*x + a)^4 - (b*d*x + a*d)*cos(b*x + a)^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 2*((b*d*x + a*d)*cos(b*x + a)^4 - (b*d*x + a*d)*cos(b*x + a)^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 2*((b*c - a*d)*cos(b*x + a)^4 - (b*c - a*d)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) - 2*((b*c - a*d)*cos(b*x + a)^4 - (b*c - a*d)*cos(b*x + a)^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) - 2*((b*d*x + a*d)*cos(b*x + a)^4 - (b*d*x + a*d)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 2*((b*c - a*d)*cos(b*x + a)^4 - (b*c - a*d)*cos(b*x + a)^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - 2*((b*d*x + a*d)*cos(b*x + a)^4 - (b*d*x + a*d)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 2*((b*c - a*d)*cos(b*x + a)^4 - (b*c - a*d)*cos(b*x + a)^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/(b^2*cos(b*x + a)^4 - b^2*cos(b*x + a)^2)","B",0
326,0,0,0,0.512319," ","integrate(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)^3/(d*x + c), x)","F",0
327,0,0,0,0.567566," ","integrate(csc(b*x+a)^3*sec(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3} \sec\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^3*sec(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
328,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)^(5/2)*sin(b*x+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
329,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2)*sin(b*x+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
330,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)*cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
331,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
332,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
333,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
334,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(7/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
335,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/cos(b*x+a)^(9/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
336,-2,0,0,0.000000," ","integrate(x*sec(b*x+a)^(9/2)*sin(b*x+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
337,-2,0,0,0.000000," ","integrate(x*sec(b*x+a)^(7/2)*sin(b*x+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
338,-2,0,0,0.000000," ","integrate(x*sec(b*x+a)^(5/2)*sin(b*x+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
339,-2,0,0,0.000000," ","integrate(x*sec(b*x+a)^(3/2)*sin(b*x+a),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
340,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)*sec(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
341,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
342,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
343,-2,0,0,0.000000," ","integrate(x*sin(b*x+a)/sec(b*x+a)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
344,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
345,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
346,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*sin(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
347,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
348,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
349,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
350,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(7/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
351,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/sin(b*x+a)^(9/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
352,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(9/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
353,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(7/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
354,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
355,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
356,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)*csc(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
357,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
358,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
359,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)/csc(b*x+a)^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
360,1,17,0,0.448521," ","integrate(x*csc(x)*sin(3*x),x, algorithm=""fricas"")","2 \, x \cos\left(x\right) \sin\left(x\right) + \frac{1}{2} \, x^{2} + \cos\left(x\right)^{2}"," ",0,"2*x*cos(x)*sin(x) + 1/2*x^2 + cos(x)^2","A",0
361,1,200,0,0.446956," ","integrate((d*x+c)^4*csc(x)*sin(3*x),x, algorithm=""fricas"")","\frac{1}{5} \, d^{4} x^{5} + c d^{3} x^{4} + 2 \, {\left(c^{2} d^{2} - d^{4}\right)} x^{3} + 2 \, {\left(c^{3} d - 3 \, c d^{3}\right)} x^{2} + 2 \, {\left(2 \, d^{4} x^{3} + 6 \, c d^{3} x^{2} + 2 \, c^{3} d - 3 \, c d^{3} + 3 \, {\left(2 \, c^{2} d^{2} - d^{4}\right)} x\right)} \cos\left(x\right)^{2} + {\left(2 \, d^{4} x^{4} + 8 \, c d^{3} x^{3} + 2 \, c^{4} - 6 \, c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, c^{2} d^{2} - d^{4}\right)} x^{2} + 4 \, {\left(2 \, c^{3} d - 3 \, c d^{3}\right)} x\right)} \cos\left(x\right) \sin\left(x\right) + {\left(c^{4} - 6 \, c^{2} d^{2} + 3 \, d^{4}\right)} x"," ",0,"1/5*d^4*x^5 + c*d^3*x^4 + 2*(c^2*d^2 - d^4)*x^3 + 2*(c^3*d - 3*c*d^3)*x^2 + 2*(2*d^4*x^3 + 6*c*d^3*x^2 + 2*c^3*d - 3*c*d^3 + 3*(2*c^2*d^2 - d^4)*x)*cos(x)^2 + (2*d^4*x^4 + 8*c*d^3*x^3 + 2*c^4 - 6*c^2*d^2 + 3*d^4 + 6*(2*c^2*d^2 - d^4)*x^2 + 4*(2*c^3*d - 3*c*d^3)*x)*cos(x)*sin(x) + (c^4 - 6*c^2*d^2 + 3*d^4)*x","A",0
362,1,127,0,0.471294," ","integrate((d*x+c)^3*csc(x)*sin(3*x),x, algorithm=""fricas"")","\frac{1}{4} \, d^{3} x^{4} + c d^{2} x^{3} + \frac{3}{2} \, {\left(c^{2} d - d^{3}\right)} x^{2} + \frac{3}{2} \, {\left(2 \, d^{3} x^{2} + 4 \, c d^{2} x + 2 \, c^{2} d - d^{3}\right)} \cos\left(x\right)^{2} + {\left(2 \, d^{3} x^{3} + 6 \, c d^{2} x^{2} + 2 \, c^{3} - 3 \, c d^{2} + 3 \, {\left(2 \, c^{2} d - d^{3}\right)} x\right)} \cos\left(x\right) \sin\left(x\right) + {\left(c^{3} - 3 \, c d^{2}\right)} x"," ",0,"1/4*d^3*x^4 + c*d^2*x^3 + 3/2*(c^2*d - d^3)*x^2 + 3/2*(2*d^3*x^2 + 4*c*d^2*x + 2*c^2*d - d^3)*cos(x)^2 + (2*d^3*x^3 + 6*c*d^2*x^2 + 2*c^3 - 3*c*d^2 + 3*(2*c^2*d - d^3)*x)*cos(x)*sin(x) + (c^3 - 3*c*d^2)*x","A",0
363,1,70,0,0.454990," ","integrate((d*x+c)^2*csc(x)*sin(3*x),x, algorithm=""fricas"")","\frac{1}{3} \, d^{2} x^{3} + c d x^{2} + 2 \, {\left(d^{2} x + c d\right)} \cos\left(x\right)^{2} + {\left(2 \, d^{2} x^{2} + 4 \, c d x + 2 \, c^{2} - d^{2}\right)} \cos\left(x\right) \sin\left(x\right) + {\left(c^{2} - d^{2}\right)} x"," ",0,"1/3*d^2*x^3 + c*d*x^2 + 2*(d^2*x + c*d)*cos(x)^2 + (2*d^2*x^2 + 4*c*d*x + 2*c^2 - d^2)*cos(x)*sin(x) + (c^2 - d^2)*x","A",0
364,1,27,0,0.439164," ","integrate((d*x+c)*csc(x)*sin(3*x),x, algorithm=""fricas"")","\frac{1}{2} \, d x^{2} + d \cos\left(x\right)^{2} + 2 \, {\left(d x + c\right)} \cos\left(x\right) \sin\left(x\right) + c x"," ",0,"1/2*d*x^2 + d*cos(x)^2 + 2*(d*x + c)*cos(x)*sin(x) + c*x","A",0
365,1,62,0,0.439839," ","integrate(csc(x)*sin(3*x)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(\frac{2 \, {\left(d x + c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(d x + c\right)}}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right) + 2 \, \sin\left(\frac{2 \, c}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d x + c\right)}}{d}\right) + \log\left(d x + c\right)}{d}"," ",0,"((cos_integral(2*(d*x + c)/d) + cos_integral(-2*(d*x + c)/d))*cos(2*c/d) + 2*sin(2*c/d)*sin_integral(2*(d*x + c)/d) + log(d*x + c))/d","A",0
366,1,95,0,0.479381," ","integrate(csc(x)*sin(3*x)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{4 \, d \cos\left(x\right)^{2} + 4 \, {\left(d x + c\right)} \cos\left(\frac{2 \, c}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d x + c\right)}}{d}\right) - 2 \, {\left({\left(d x + c\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d x + c\right)}}{d}\right) + {\left(d x + c\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d x + c\right)}}{d}\right)\right)} \sin\left(\frac{2 \, c}{d}\right) - d}{d^{3} x + c d^{2}}"," ",0,"-(4*d*cos(x)^2 + 4*(d*x + c)*cos(2*c/d)*sin_integral(2*(d*x + c)/d) - 2*((d*x + c)*cos_integral(2*(d*x + c)/d) + (d*x + c)*cos_integral(-2*(d*x + c)/d))*sin(2*c/d) - d)/(d^3*x + c*d^2)","A",0
367,1,158,0,0.443443," ","integrate(csc(x)*sin(3*x)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{4 \, d^{2} \cos\left(x\right)^{2} - 8 \, {\left(d^{2} x + c d\right)} \cos\left(x\right) \sin\left(x\right) + 8 \, {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \sin\left(\frac{2 \, c}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d x + c\right)}}{d}\right) - d^{2} + 4 \, {\left({\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d x + c\right)}}{d}\right) + {\left(d^{2} x^{2} + 2 \, c d x + c^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d x + c\right)}}{d}\right)\right)} \cos\left(\frac{2 \, c}{d}\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/2*(4*d^2*cos(x)^2 - 8*(d^2*x + c*d)*cos(x)*sin(x) + 8*(d^2*x^2 + 2*c*d*x + c^2)*sin(2*c/d)*sin_integral(2*(d*x + c)/d) - d^2 + 4*((d^2*x^2 + 2*c*d*x + c^2)*cos_integral(2*(d*x + c)/d) + (d^2*x^2 + 2*c*d*x + c^2)*cos_integral(-2*(d*x + c)/d))*cos(2*c/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
368,1,283,0,0.449447," ","integrate((d*x+c)^4*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{b^{5} d^{4} x^{5} + 5 \, b^{5} c d^{3} x^{4} + 10 \, {\left(b^{5} c^{2} d^{2} - b^{3} d^{4}\right)} x^{3} + 10 \, {\left(b^{5} c^{3} d - 3 \, b^{3} c d^{3}\right)} x^{2} + 10 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{2} + 5 \, {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} - 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 5 \, {\left(b^{5} c^{4} - 6 \, b^{3} c^{2} d^{2} + 3 \, b d^{4}\right)} x}{5 \, b^{5}}"," ",0,"1/5*(b^5*d^4*x^5 + 5*b^5*c*d^3*x^4 + 10*(b^5*c^2*d^2 - b^3*d^4)*x^3 + 10*(b^5*c^3*d - 3*b^3*c*d^3)*x^2 + 10*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d - 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)^2 + 5*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 - 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(2*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)*sin(b*x + a) + 5*(b^5*c^4 - 6*b^3*c^2*d^2 + 3*b*d^4)*x)/b^5","A",0
369,1,188,0,0.449035," ","integrate((d*x+c)^3*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{b^{4} d^{3} x^{4} + 4 \, b^{4} c d^{2} x^{3} + 6 \, {\left(b^{4} c^{2} d - b^{2} d^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(b^{4} c^{3} - 3 \, b^{2} c d^{2}\right)} x}{4 \, b^{4}}"," ",0,"1/4*(b^4*d^3*x^4 + 4*b^4*c*d^2*x^3 + 6*(b^4*c^2*d - b^2*d^3)*x^2 + 6*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)^2 + 4*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 - 3*b*c*d^2 + 3*(2*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)*sin(b*x + a) + 4*(b^4*c^3 - 3*b^2*c*d^2)*x)/b^4","A",0
370,1,111,0,0.445618," ","integrate((d*x+c)^2*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{b^{3} d^{2} x^{3} + 3 \, b^{3} c d x^{2} + 6 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 3 \, {\left(b^{3} c^{2} - b d^{2}\right)} x}{3 \, b^{3}}"," ",0,"1/3*(b^3*d^2*x^3 + 3*b^3*c*d*x^2 + 6*(b*d^2*x + b*c*d)*cos(b*x + a)^2 + 3*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 - d^2)*cos(b*x + a)*sin(b*x + a) + 3*(b^3*c^2 - b*d^2)*x)/b^3","A",0
371,1,54,0,0.435916," ","integrate((d*x+c)*csc(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{b^{2} d x^{2} + 2 \, b^{2} c x + 2 \, d \cos\left(b x + a\right)^{2} + 4 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{2}}"," ",0,"1/2*(b^2*d*x^2 + 2*b^2*c*x + 2*d*cos(b*x + a)^2 + 4*(b*d*x + b*c)*cos(b*x + a)*sin(b*x + a))/b^2","A",0
372,1,85,0,0.457374," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + \log\left(d x + c\right)}{d}"," ",0,"((cos_integral(2*(b*d*x + b*c)/d) + cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d) - 2*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + log(d*x + c))/d","A",0
373,1,131,0,0.445748," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{4 \, d \cos\left(b x + a\right)^{2} + 4 \, {\left(b d x + b c\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + 2 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d}{d^{3} x + c d^{2}}"," ",0,"-(4*d*cos(b*x + a)^2 + 4*(b*d*x + b*c)*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) + 2*((b*d*x + b*c)*cos_integral(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d) - d)/(d^3*x + c*d^2)","A",0
374,1,225,0,0.459818," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{4 \, d^{2} \cos\left(b x + a\right)^{2} - 8 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - 8 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - d^{2} + 4 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/2*(4*d^2*cos(b*x + a)^2 - 8*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - 8*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - d^2 + 4*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
375,1,343,0,0.494509," ","integrate(csc(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{4 \, b^{2} d^{3} x^{2} + 8 \, b^{2} c d^{2} x + 4 \, b^{2} c^{2} d - d^{3} - 4 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right)^{2} - 4 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - 8 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - 4 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{3 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/3*(4*b^2*d^3*x^2 + 8*b^2*c*d^2*x + 4*b^2*c^2*d - d^3 - 4*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)^2 - 4*(b*d^3*x + b*c*d^2)*cos(b*x + a)*sin(b*x + a) - 8*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-2*(b*c - a*d)/d)*sin_integral(2*(b*d*x + b*c)/d) - 4*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-2*(b*d*x + b*c)/d))*sin(-2*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","A",0
376,1,925,0,0.557626," ","integrate((d*x+c)^3*csc(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{18 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 18 i \, d^{3} {\rm polylog}\left(4, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 18 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 18 i \, d^{3} {\rm polylog}\left(4, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 8 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right) + {\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-9 i \, b^{2} d^{3} x^{2} - 18 i \, b^{2} c d^{2} x - 9 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(9 i \, b^{2} d^{3} x^{2} + 18 i \, b^{2} c d^{2} x + 9 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 18 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 18 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 18 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 18 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 24 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \sin\left(b x + a\right)}{2 \, b^{4}}"," ",0,"1/2*(18*I*d^3*polylog(4, cos(b*x + a) + I*sin(b*x + a)) - 18*I*d^3*polylog(4, cos(b*x + a) - I*sin(b*x + a)) + 18*I*d^3*polylog(4, -cos(b*x + a) + I*sin(b*x + a)) - 18*I*d^3*polylog(4, -cos(b*x + a) - I*sin(b*x + a)) + 8*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a) + (-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-9*I*b^2*d^3*x^2 - 18*I*b^2*c*d^2*x - 9*I*b^2*c^2*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (9*I*b^2*d^3*x^2 + 18*I*b^2*c*d^2*x + 9*I*b^2*c^2*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) + 18*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 18*(b*d^3*x + b*c*d^2)*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 18*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 18*(b*d^3*x + b*c*d^2)*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) - 24*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*sin(b*x + a))/b^4","C",0
377,1,562,0,0.541285," ","integrate((d*x+c)^2*csc(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{6 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 6 \, d^{2} {\rm polylog}\left(3, \cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 6 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) - 6 \, d^{2} {\rm polylog}\left(3, -\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + 8 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right) + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{2} x - 6 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{2} x + 6 i \, b c d\right)} {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 16 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)}{2 \, b^{3}}"," ",0,"1/2*(6*d^2*polylog(3, cos(b*x + a) + I*sin(b*x + a)) + 6*d^2*polylog(3, cos(b*x + a) - I*sin(b*x + a)) - 6*d^2*polylog(3, -cos(b*x + a) + I*sin(b*x + a)) - 6*d^2*polylog(3, -cos(b*x + a) - I*sin(b*x + a)) + 8*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a) + (-6*I*b*d^2*x - 6*I*b*c*d)*dilog(cos(b*x + a) + I*sin(b*x + a)) + (6*I*b*d^2*x + 6*I*b*c*d)*dilog(cos(b*x + a) - I*sin(b*x + a)) + (-6*I*b*d^2*x - 6*I*b*c*d)*dilog(-cos(b*x + a) + I*sin(b*x + a)) + (6*I*b*d^2*x + 6*I*b*c*d)*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + 3*(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 16*(b*d^2*x + b*c*d)*sin(b*x + a))/b^3","C",0
378,1,281,0,0.478002," ","integrate((d*x+c)*csc(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{8 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) - 3 i \, d {\rm Li}_2\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 3 i \, d {\rm Li}_2\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right)\right) + 3 i \, d {\rm Li}_2\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right)\right) - 3 \, {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b d x + b c\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) + \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(b c - a d\right)} \log\left(-\frac{1}{2} \, \cos\left(b x + a\right) - \frac{1}{2} i \, \sin\left(b x + a\right) + \frac{1}{2}\right) + 3 \, {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b d x + a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + 1\right) - 8 \, d \sin\left(b x + a\right)}{2 \, b^{2}}"," ",0,"1/2*(8*(b*d*x + b*c)*cos(b*x + a) - 3*I*d*dilog(cos(b*x + a) + I*sin(b*x + a)) + 3*I*d*dilog(cos(b*x + a) - I*sin(b*x + a)) - 3*I*d*dilog(-cos(b*x + a) + I*sin(b*x + a)) + 3*I*d*dilog(-cos(b*x + a) - I*sin(b*x + a)) - 3*(b*d*x + b*c)*log(cos(b*x + a) + I*sin(b*x + a) + 1) - 3*(b*d*x + b*c)*log(cos(b*x + a) - I*sin(b*x + a) + 1) + 3*(b*c - a*d)*log(-1/2*cos(b*x + a) + 1/2*I*sin(b*x + a) + 1/2) + 3*(b*c - a*d)*log(-1/2*cos(b*x + a) - 1/2*I*sin(b*x + a) + 1/2) + 3*(b*d*x + a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + 1) + 3*(b*d*x + a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + 1) - 8*d*sin(b*x + a))/b^2","B",0
379,0,0,0,0.434803," ","integrate(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sin\left(3 \, b x + 3 \, a\right)}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^2*sin(3*b*x + 3*a)/(d*x + c), x)","F",0
380,0,0,0,0.419573," ","integrate(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sin\left(3 \, b x + 3 \, a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)^2*sin(3*b*x + 3*a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
381,0,0,0,0.438385," ","integrate(csc(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2} \sin\left(3 \, b x + 3 \, a\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}, x\right)"," ",0,"integral(csc(b*x + a)^2*sin(3*b*x + 3*a)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x)","F",0
382,1,1644,0,0.643526," ","integrate((d*x+c)^4*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} - 24 \, d^{4} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 24 \, d^{4} {\rm polylog}\left(5, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} - 2 \, {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} - 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} - b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d - 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} - b d^{4}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 4 \, {\left(2 \, b^{4} c^{3} d - 3 \, b^{2} c d^{3}\right)} x + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-4 i \, b^{3} d^{4} x^{3} - 12 i \, b^{3} c d^{3} x^{2} - 12 i \, b^{3} c^{2} d^{2} x - 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(4 i \, b^{3} d^{4} x^{3} + 12 i \, b^{3} c d^{3} x^{2} + 12 i \, b^{3} c^{2} d^{2} x + 4 i \, b^{3} c^{3} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + 4 \, a b^{3} c^{3} d - 6 \, a^{2} b^{2} c^{2} d^{2} + 4 \, a^{3} b c d^{3} - a^{4} d^{4}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(24 i \, b d^{4} x + 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-24 i \, b d^{4} x - 24 i \, b c d^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 12 \, {\left(b^{2} d^{4} x^{2} + 2 \, b^{2} c d^{3} x + b^{2} c^{2} d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{2 \, b^{5}}"," ",0,"1/2*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 - 24*d^4*polylog(5, I*cos(b*x + a) + sin(b*x + a)) - 24*d^4*polylog(5, I*cos(b*x + a) - sin(b*x + a)) - 24*d^4*polylog(5, -I*cos(b*x + a) + sin(b*x + a)) - 24*d^4*polylog(5, -I*cos(b*x + a) - sin(b*x + a)) + 6*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 - 2*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 - 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 - b^2*d^4)*x^2 + 4*(2*b^4*c^3*d - 3*b^2*c*d^3)*x)*cos(b*x + a)^2 + 4*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d - 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 - b*d^4)*x)*cos(b*x + a)*sin(b*x + a) + 4*(2*b^4*c^3*d - 3*b^2*c*d^3)*x + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-4*I*b^3*d^4*x^3 - 12*I*b^3*c*d^3*x^2 - 12*I*b^3*c^2*d^2*x - 4*I*b^3*c^3*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (4*I*b^3*d^4*x^3 + 12*I*b^3*c*d^3*x^2 + 12*I*b^3*c^2*d^2*x + 4*I*b^3*c^3*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + 4*a*b^3*c^3*d - 6*a^2*b^2*c^2*d^2 + 4*a^3*b*c*d^3 - a^4*d^4)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + (24*I*b*d^4*x + 24*I*b*c*d^3)*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) + (-24*I*b*d^4*x - 24*I*b*c*d^3)*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 12*(b^2*d^4*x^2 + 2*b^2*c*d^3*x + b^2*c^2*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/b^5","C",0
383,1,1122,0,0.602841," ","integrate((d*x+c)^3*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} - 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 2 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d - d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 3 \, {\left(2 \, b^{3} c^{2} d - b d^{3}\right)} x + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{2 \, b^{4}}"," ",0,"1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 - 6*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a)) + 6*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) - 2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 - 3*b*c*d^2 + 3*(2*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)^2 + 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(b*x + a)*sin(b*x + a) + 3*(2*b^3*c^2*d - b*d^3)*x + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/b^4","C",0
384,1,677,0,0.554139," ","integrate((d*x+c)^2*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x - 2 \, {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{2} + 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{3}}"," ",0,"1/2*(2*b^2*d^2*x^2 + 4*b^2*c*d*x - 2*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 - d^2)*cos(b*x + a)^2 + 2*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 2*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 2*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 4*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^3","C",0
385,1,340,0,0.528035," ","integrate((d*x+c)*sec(b*x+a)*sin(3*b*x+3*a),x, algorithm=""fricas"")","\frac{2 \, b d x - 4 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + 2 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{2}}"," ",0,"1/2*(2*b*d*x - 4*(b*d*x + b*c)*cos(b*x + a)^2 + 2*d*cos(b*x + a)*sin(b*x + a) + I*d*dilog(I*cos(b*x + a) + sin(b*x + a)) - I*d*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d*dilog(-I*cos(b*x + a) + sin(b*x + a)) + I*d*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^2","B",0
386,0,0,0,0.435540," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \sin\left(3 \, b x + 3 \, a\right)}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)*sin(3*b*x + 3*a)/(d*x + c), x)","F",0
387,0,0,0,0.442284," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \sin\left(3 \, b x + 3 \, a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sec(b*x + a)*sin(3*b*x + 3*a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
388,0,0,0,0.442900," ","integrate(sec(b*x+a)*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right) \sin\left(3 \, b x + 3 \, a\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}, x\right)"," ",0,"integral(sec(b*x + a)*sin(3*b*x + 3*a)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x)","F",0
389,1,896,0,0.555340," ","integrate((d*x+c)^3*sec(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 8 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 24 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{2 \, b^{4} \cos\left(b x + a\right)}"," ",0,"-1/2*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + 8*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 - (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 24*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cos(b*x + a)*sin(b*x + a))/(b^4*cos(b*x + a))","C",0
390,1,513,0,0.535020," ","integrate((d*x+c)^2*sec(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 8 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{b^{3} \cos\left(b x + a\right)}"," ",0,"-(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cos(b*x + a)^2 - (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 8*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a))/(b^3*cos(b*x + a))","B",0
391,1,93,0,0.444066," ","integrate((d*x+c)*sec(b*x+a)^2*sin(3*b*x+3*a),x, algorithm=""fricas"")","-\frac{2 \, b d x + 8 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} - d \cos\left(b x + a\right) \log\left(\sin\left(b x + a\right) + 1\right) + d \cos\left(b x + a\right) \log\left(-\sin\left(b x + a\right) + 1\right) - 8 \, d \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, b c}{2 \, b^{2} \cos\left(b x + a\right)}"," ",0,"-1/2*(2*b*d*x + 8*(b*d*x + b*c)*cos(b*x + a)^2 - d*cos(b*x + a)*log(sin(b*x + a) + 1) + d*cos(b*x + a)*log(-sin(b*x + a) + 1) - 8*d*cos(b*x + a)*sin(b*x + a) + 2*b*c)/(b^2*cos(b*x + a))","A",0
392,0,0,0,0.453647," ","integrate(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2} \sin\left(3 \, b x + 3 \, a\right)}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)^2*sin(3*b*x + 3*a)/(d*x + c), x)","F",0
393,0,0,0,1.607163," ","integrate(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2} \sin\left(3 \, b x + 3 \, a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sec(b*x + a)^2*sin(3*b*x + 3*a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
394,0,0,0,0.513905," ","integrate(sec(b*x+a)^2*sin(3*b*x+3*a)/(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2} \sin\left(3 \, b x + 3 \, a\right)}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}, x\right)"," ",0,"integral(sec(b*x + a)^2*sin(3*b*x + 3*a)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3), x)","F",0
395,1,106,0,1.227115," ","integrate(x*cos(2*x)*sec(x),x, algorithm=""fricas"")","-\frac{1}{2} \, x \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) + \frac{1}{2} \, x \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - \frac{1}{2} \, x \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) + \frac{1}{2} \, x \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) + 2 \, x \sin\left(x\right) + 2 \, \cos\left(x\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) + \frac{1}{2} i \, {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) - \frac{1}{2} i \, {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) - \frac{1}{2} i \, {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right)"," ",0,"-1/2*x*log(I*cos(x) + sin(x) + 1) + 1/2*x*log(I*cos(x) - sin(x) + 1) - 1/2*x*log(-I*cos(x) + sin(x) + 1) + 1/2*x*log(-I*cos(x) - sin(x) + 1) + 2*x*sin(x) + 2*cos(x) + 1/2*I*dilog(I*cos(x) + sin(x)) + 1/2*I*dilog(I*cos(x) - sin(x)) - 1/2*I*dilog(-I*cos(x) + sin(x)) - 1/2*I*dilog(-I*cos(x) - sin(x))","B",0
396,1,26,0,0.563690," ","integrate(x*cos(2*x)*sec(x)^2,x, algorithm=""fricas"")","\frac{x^{2} \cos\left(x\right) - \cos\left(x\right) \log\left(-\cos\left(x\right)\right) - x \sin\left(x\right)}{\cos\left(x\right)}"," ",0,"(x^2*cos(x) - cos(x)*log(-cos(x)) - x*sin(x))/cos(x)","A",0
397,1,144,0,2.066880," ","integrate(x*cos(2*x)*sec(x)^3,x, algorithm=""fricas"")","\frac{3 \, x \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - 3 \, x \cos\left(x\right)^{2} \log\left(i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) + 3 \, x \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) + \sin\left(x\right) + 1\right) - 3 \, x \cos\left(x\right)^{2} \log\left(-i \, \cos\left(x\right) - \sin\left(x\right) + 1\right) - 3 i \, \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) + \sin\left(x\right)\right) - 3 i \, \cos\left(x\right)^{2} {\rm Li}_2\left(i \, \cos\left(x\right) - \sin\left(x\right)\right) + 3 i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) + \sin\left(x\right)\right) + 3 i \, \cos\left(x\right)^{2} {\rm Li}_2\left(-i \, \cos\left(x\right) - \sin\left(x\right)\right) - 2 \, x \sin\left(x\right) + 2 \, \cos\left(x\right)}{4 \, \cos\left(x\right)^{2}}"," ",0,"1/4*(3*x*cos(x)^2*log(I*cos(x) + sin(x) + 1) - 3*x*cos(x)^2*log(I*cos(x) - sin(x) + 1) + 3*x*cos(x)^2*log(-I*cos(x) + sin(x) + 1) - 3*x*cos(x)^2*log(-I*cos(x) - sin(x) + 1) - 3*I*cos(x)^2*dilog(I*cos(x) + sin(x)) - 3*I*cos(x)^2*dilog(I*cos(x) - sin(x)) + 3*I*cos(x)^2*dilog(-I*cos(x) + sin(x)) + 3*I*cos(x)^2*dilog(-I*cos(x) - sin(x)) - 2*x*sin(x) + 2*cos(x))/cos(x)^2","B",0
