1,1,170,0,1.048716," ","integrate((d*x+c)^4*sin(b*x+a),x, algorithm=""fricas"")","-\frac{{\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) - 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)} \sin\left(b x + a\right)}{b^{5}}"," ",0,"-((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*(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","A",0
2,1,110,0,0.728780," ","integrate((d*x+c)^3*sin(b*x+a),x, algorithm=""fricas"")","-\frac{{\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) - 3 \, {\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)}{b^{4}}"," ",0,"-((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*(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","A",0
3,1,63,0,1.008988," ","integrate((d*x+c)^2*sin(b*x+a),x, algorithm=""fricas"")","-\frac{{\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 d^{2} x + b c d\right)} \sin\left(b x + a\right)}{b^{3}}"," ",0,"-((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*d^2*x + b*c*d)*sin(b*x + a))/b^3","A",0
4,1,30,0,1.104979," ","integrate((d*x+c)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{{\left(b d x + b c\right)} \cos\left(b x + a\right) - d \sin\left(b x + a\right)}{b^{2}}"," ",0,"-((b*d*x + b*c)*cos(b*x + a) - d*sin(b*x + a))/b^2","A",0
5,1,78,0,1.135561," ","integrate(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) + 2 \, \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right)}{2 \, d}"," ",0,"1/2*((cos_integral((b*d*x + b*c)/d) + cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d) + 2*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
6,1,124,0,1.072304," ","integrate(sin(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{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) + 2 \, d \sin\left(b x + a\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(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) + 2*d*sin(b*x + a))/(d^3*x + c*d^2)","A",0
7,1,209,0,0.975228," ","integrate(sin(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \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(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 2 \, {\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)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*d^2*sin(b*x + a) + 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) + 2*(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))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
8,1,286,0,1.010684," ","integrate((d*x+c)^4*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{5} d^{4} x^{5} + 10 \, b^{5} c d^{3} x^{4} + 10 \, {\left(2 \, b^{5} c^{2} d^{2} + b^{3} d^{4}\right)} x^{3} + 10 \, {\left(2 \, 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(2 \, b^{5} c^{4} + 6 \, b^{3} c^{2} d^{2} - 3 \, b d^{4}\right)} x}{20 \, b^{5}}"," ",0,"1/20*(2*b^5*d^4*x^5 + 10*b^5*c*d^3*x^4 + 10*(2*b^5*c^2*d^2 + b^3*d^4)*x^3 + 10*(2*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*(2*b^5*c^4 + 6*b^3*c^2*d^2 - 3*b*d^4)*x)/b^5","A",0
9,1,189,0,1.097657," ","integrate((d*x+c)^3*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{4} d^{3} x^{4} + 4 \, b^{4} c d^{2} x^{3} + 3 \, {\left(2 \, b^{4} c^{2} d + b^{2} d^{3}\right)} x^{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)^{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) \sin\left(b x + a\right) + 2 \, {\left(2 \, b^{4} c^{3} + 3 \, b^{2} c d^{2}\right)} x}{8 \, b^{4}}"," ",0,"1/8*(b^4*d^3*x^4 + 4*b^4*c*d^2*x^3 + 3*(2*b^4*c^2*d + b^2*d^3)*x^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)^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)*sin(b*x + a) + 2*(2*b^4*c^3 + 3*b^2*c*d^2)*x)/b^4","A",0
10,1,112,0,1.026153," ","integrate((d*x+c)^2*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{2} x^{3} + 6 \, 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(2 \, b^{3} c^{2} + b d^{2}\right)} x}{12 \, b^{3}}"," ",0,"1/12*(2*b^3*d^2*x^3 + 6*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*(2*b^3*c^2 + b*d^2)*x)/b^3","A",0
11,1,54,0,1.264312," ","integrate((d*x+c)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{b^{2} d x^{2} + 2 \, b^{2} c x - d \cos\left(b x + a\right)^{2} - 2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)}{4 \, b^{2}}"," ",0,"1/4*(b^2*d*x^2 + 2*b^2*c*x - d*cos(b*x + a)^2 - 2*(b*d*x + b*c)*cos(b*x + a)*sin(b*x + a))/b^2","A",0
12,1,88,0,0.944934," ","integrate(sin(b*x+a)^2/(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) - 2 \, \log\left(d x + c\right)}{4 \, d}"," ",0,"-1/4*((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) - 2*log(d*x + c))/d","A",0
13,1,130,0,0.913289," ","integrate(sin(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, d \cos\left(b x + a\right)^{2} + 2 \, {\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) + {\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) - 2 \, d}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/2*(2*d*cos(b*x + a)^2 + 2*(b*d*x + b*c)*cos(-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))*sin(-2*(b*c - a*d)/d) - 2*d)/(d^3*x + c*d^2)","A",0
14,1,223,0,1.147673," ","integrate(sin(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{d^{2} \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) - 2 \, {\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} + {\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*(d^2*cos(b*x + a)^2 - 2*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - 2*(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 + ((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)","B",0
15,1,341,0,0.879467," ","integrate(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 - d^{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)^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right) \sin\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)} \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^{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*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - d^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)^2 - (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(-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))*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)","B",0
16,1,351,0,0.977500," ","integrate((d*x+c)^4*sin(b*x+a)^3,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} - 3 \, {\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} + 36 \, {\left(3 \, b^{4} c^{3} d - 14 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right) + 12 \, {\left(21 \, b^{3} d^{4} x^{3} + 63 \, b^{3} c d^{3} x^{2} + 21 \, b^{3} c^{3} d - 122 \, 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} + {\left(63 \, b^{3} c^{2} d^{2} - 122 \, 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 - 3*(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 + 36*(3*b^4*c^3*d - 14*b^2*c*d^3)*x)*cos(b*x + a) + 12*(21*b^3*d^4*x^3 + 63*b^3*c*d^3*x^2 + 21*b^3*c^3*d - 122*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 + (63*b^3*c^2*d^2 - 122*b*d^4)*x)*sin(b*x + a))/b^5","A",0
17,1,227,0,1.155884," ","integrate((d*x+c)^3*sin(b*x+a)^3,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} - 9 \, {\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(9 \, b^{3} c^{2} d - 14 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right) + {\left(63 \, b^{2} d^{3} x^{2} + 126 \, b^{2} c d^{2} x + 63 \, b^{2} c^{2} d - 122 \, 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 - 9*(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 + (9*b^3*c^2*d - 14*b*d^3)*x)*cos(b*x + a) + (63*b^2*d^3*x^2 + 126*b^2*c*d^2*x + 63*b^2*c^2*d - 122*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
18,1,131,0,1.151843," ","integrate((d*x+c)^2*sin(b*x+a)^3,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} - 3 \, {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} - 14 \, d^{2}\right)} \cos\left(b x + a\right) + 6 \, {\left(7 \, b d^{2} x + 7 \, 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 - 3*(9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 - 14*d^2)*cos(b*x + a) + 6*(7*b*d^2*x + 7*b*c*d - (b*d^2*x + b*c*d)*cos(b*x + a)^2)*sin(b*x + a))/b^3","A",0
19,1,62,0,1.112373," ","integrate((d*x+c)*sin(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - 9 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) - {\left(d \cos\left(b x + a\right)^{2} - 7 \, 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 - 9*(b*d*x + b*c)*cos(b*x + a) - (d*cos(b*x + a)^2 - 7*d)*sin(b*x + a))/b^2","A",0
20,1,154,0,0.991461," ","integrate(sin(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\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) + 6 \, \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*(3*(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) + 6*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
21,1,238,0,1.244384," ","integrate(sin(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","\frac{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) - 6 \, {\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) + 3 \, {\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 \cos\left(b x + a\right)^{2} - d\right)} \sin\left(b x + a\right)}{8 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/8*(6*(b*d*x + b*c)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 6*(b*d*x + b*c)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 3*((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) + 8*(d*cos(b*x + a)^2 - d)*sin(b*x + a))/(d^3*x + c*d^2)","A",0
22,1,401,0,0.957039," ","integrate(sin(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","\frac{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) - 6 \, {\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) - 24 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + 8 \, {\left(d^{2} \cos\left(b x + a\right)^{2} - d^{2}\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{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*(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) - 6*(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) - 24*(b*d^2*x + b*c*d)*cos(b*x + a) + 8*(d^2*cos(b*x + a)^2 - d^2)*sin(b*x + a) - 3*((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)","B",0
23,1,816,0,1.307496," ","integrate((d*x+c)^3*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
24,1,500,0,1.133063," ","integrate((d*x+c)^2*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
25,1,252,0,1.295343," ","integrate((d*x+c)*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
26,0,0,0,1.156494," ","integrate(csc(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)/(d*x + c), x)","F",0
27,0,0,0,1.316386," ","integrate(csc(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csc(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
28,1,672,0,1.448555," ","integrate((d*x+c)^3*csc(b*x+a)^2,x, algorithm=""fricas"")","\frac{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 \, {\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 \, b^{4} \sin\left(b x + a\right)}"," ",0,"1/2*(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) - 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))/(b^4*sin(b*x + a))","C",0
29,1,379,0,1.148664," ","integrate((d*x+c)^2*csc(b*x+a)^2,x, algorithm=""fricas"")","\frac{-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) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(b x + a\right)}{b^{3} \sin\left(b x + a\right)}"," ",0,"(-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^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(b*x + a))/(b^3*sin(b*x + a))","B",0
30,1,46,0,1.034517," ","integrate((d*x+c)*csc(b*x+a)^2,x, algorithm=""fricas"")","\frac{d \log\left(\frac{1}{2} \, \sin\left(b x + a\right)\right) \sin\left(b x + a\right) - {\left(b d x + b c\right)} \cos\left(b x + a\right)}{b^{2} \sin\left(b x + a\right)}"," ",0,"(d*log(1/2*sin(b*x + a))*sin(b*x + a) - (b*d*x + b*c)*cos(b*x + a))/(b^2*sin(b*x + a))","A",0
31,0,0,0,1.453805," ","integrate(csc(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^2/(d*x + c), x)","F",0
32,0,0,0,0.971206," ","integrate(csc(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\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/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
33,1,1736,0,1.265151," ","integrate((d*x+c)^3*csc(b*x+a)^3,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
34,1,968,0,1.677109," ","integrate((d*x+c)^2*csc(b*x+a)^3,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
35,1,452,0,1.065915," ","integrate((d*x+c)*csc(b*x+a)^3,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
36,0,0,0,1.168707," ","integrate(csc(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(csc(b*x + a)^3/(d*x + c), x)","F",0
37,0,0,0,1.122182," ","integrate(csc(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\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/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
38,1,190,0,1.149044," ","integrate((d*x+c)^(5/2)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \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) - 15 \, \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) + 2 \, \sqrt{d x + c} {\left({\left(4 \, b^{3} d^{2} x^{2} + 8 \, b^{3} c d x + 4 \, b^{3} c^{2} - 15 \, b d^{2}\right)} \cos\left(b x + a\right) - 10 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \sin\left(b x + a\right)\right)}}{8 \, b^{4}}"," ",0,"-1/8*(15*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))) - 15*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) + 2*sqrt(d*x + c)*((4*b^3*d^2*x^2 + 8*b^3*c*d*x + 4*b^3*c^2 - 15*b*d^2)*cos(b*x + a) - 10*(b^2*d^2*x + b^2*c*d)*sin(b*x + a)))/b^4","A",0
39,1,156,0,1.281751," ","integrate((d*x+c)^(3/2)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \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) + 3 \, \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) - 2 \, {\left(3 \, b d \sin\left(b x + a\right) - 2 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)\right)} \sqrt{d x + c}}{4 \, b^{3}}"," ",0,"-1/4*(3*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))) + 3*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) - 2*(3*b*d*sin(b*x + a) - 2*(b^2*d*x + b^2*c)*cos(b*x + a))*sqrt(d*x + c))/b^3","A",0
40,1,127,0,1.230622," ","integrate((d*x+c)^(1/2)*sin(b*x+a),x, algorithm=""fricas"")","\frac{\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) - \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) - 2 \, \sqrt{d x + c} b \cos\left(b x + a\right)}{2 \, b^{2}}"," ",0,"1/2*(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))) - 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) - 2*sqrt(d*x + c)*b*cos(b*x + a))/b^2","A",0
41,1,107,0,0.950362," ","integrate(sin(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \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) + \sqrt{2} \pi \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)}{b}"," ",0,"(sqrt(2)*pi*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + sqrt(2)*pi*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d))/b","A",0
42,1,146,0,1.219278," ","integrate(sin(b*x+a)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{2} {\left(\pi d x + \pi c\right)} \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) - \sqrt{2} {\left(\pi d x + \pi c\right)} \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{d x + c} \sin\left(b x + a\right)\right)}}{d^{2} x + c d}"," ",0,"2*(sqrt(2)*(pi*d*x + pi*c)*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(2)*(pi*d*x + pi*c)*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - sqrt(d*x + c)*sin(b*x + a))/(d^2*x + c*d)","A",0
43,1,208,0,1.334881," ","integrate(sin(b*x+a)/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \sqrt{2} {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) + 2 \, \sqrt{2} {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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{d x + c} {\left(2 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) + d \sin\left(b x + a\right)\right)}\right)}}{3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}"," ",0,"-2/3*(2*sqrt(2)*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 2*sqrt(2)*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(d*x + c)*(2*(b*d*x + b*c)*cos(b*x + a) + d*sin(b*x + a)))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
44,1,297,0,1.393618," ","integrate(sin(b*x+a)/(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, \sqrt{2} {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) - 4 \, \sqrt{2} {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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{d x + c} {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - {\left(4 \, b^{2} d^{2} x^{2} + 8 \, b^{2} c d x + 4 \, b^{2} c^{2} - 3 \, d^{2}\right)} \sin\left(b x + a\right)\right)}\right)}}{15 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)}}"," ",0,"-2/15*(4*sqrt(2)*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 4*sqrt(2)*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(d*x + c)*(2*(b*d^2*x + b*c*d)*cos(b*x + a) - (4*b^2*d^2*x^2 + 8*b^2*c*d*x + 4*b^2*c^2 - 3*d^2)*sin(b*x + a)))/(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)","A",0
45,1,258,0,0.811597," ","integrate((d*x+c)^(5/2)*sin(b*x+a)^2,x, algorithm=""fricas"")","-\frac{105 \, \pi d^{4} \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) + 105 \, \pi d^{4} \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(32 \, b^{4} d^{3} x^{3} + 96 \, b^{4} c d^{2} x^{2} + 32 \, b^{4} c^{3} + 70 \, b^{2} c d^{2} - 140 \, {\left(b^{2} d^{3} x + b^{2} c d^{2}\right)} \cos\left(b x + a\right)^{2} - 7 \, {\left(16 \, b^{3} d^{3} x^{2} + 32 \, b^{3} c d^{2} x + 16 \, b^{3} c^{2} d - 15 \, b d^{3}\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 2 \, {\left(48 \, b^{4} c^{2} d + 35 \, b^{2} d^{3}\right)} x\right)} \sqrt{d x + c}}{896 \, b^{4} d}"," ",0,"-1/896*(105*pi*d^4*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 105*pi*d^4*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - 4*(32*b^4*d^3*x^3 + 96*b^4*c*d^2*x^2 + 32*b^4*c^3 + 70*b^2*c*d^2 - 140*(b^2*d^3*x + b^2*c*d^2)*cos(b*x + a)^2 - 7*(16*b^3*d^3*x^2 + 32*b^3*c*d^2*x + 16*b^3*c^2*d - 15*b*d^3)*cos(b*x + a)*sin(b*x + a) + 2*(48*b^4*c^2*d + 35*b^2*d^3)*x)*sqrt(d*x + c))/(b^4*d)","A",0
46,1,195,0,0.909652," ","integrate((d*x+c)^(3/2)*sin(b*x+a)^2,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} - 30 \, b d^{2} \cos\left(b x + a\right)^{2} + 15 \, b d^{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}}{160 \, b^{3} d}"," ",0,"1/160*(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 - 30*b*d^2*cos(b*x + a)^2 + 15*b*d^2 - 40*(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
47,1,148,0,1.312983," ","integrate((d*x+c)^(1/2)*sin(b*x+a)^2,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\right)} \sqrt{d x + c}}{24 \, b^{2} d}"," ",0,"1/24*(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)*sqrt(d*x + c))/(b^2*d)","A",0
48,1,114,0,1.184764," ","integrate(sin(b*x+a)^2/(d*x+c)^(1/2),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 \, \sqrt{d x + c} b}{2 \, b d}"," ",0,"-1/2*(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*sqrt(d*x + c)*b)/(b*d)","A",0
49,1,138,0,1.039469," ","integrate(sin(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(\pi d x + \pi c\right)} \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) + {\left(\pi d x + \pi c\right)} \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) + \sqrt{d x + c} {\left(\cos\left(b x + a\right)^{2} - 1\right)}\right)}}{d^{2} x + c d}"," ",0,"2*((pi*d*x + pi*c)*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + (pi*d*x + pi*c)*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + sqrt(d*x + c)*(cos(b*x + a)^2 - 1))/(d^2*x + c*d)","A",0
50,1,209,0,0.990761," ","integrate(sin(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) - 4 \, {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) + {\left(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) - d\right)} \sqrt{d x + c}\right)}}{3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}"," ",0,"2/3*(4*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 4*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) + (d*cos(b*x + a)^2 - 4*(b*d*x + b*c)*cos(b*x + a)*sin(b*x + a) - d)*sqrt(d*x + c))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
51,1,328,0,1.082628," ","integrate(sin(b*x+a)^2/(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(16 \, {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) + 16 \, {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) - {\left(8 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c d x + 8 \, b^{2} c^{2} - {\left(16 \, b^{2} d^{2} x^{2} + 32 \, b^{2} c d x + 16 \, b^{2} c^{2} - 3 \, d^{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) - 3 \, d^{2}\right)} \sqrt{d x + c}\right)}}{15 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)}}"," ",0,"-2/15*(16*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d))) + 16*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - (8*b^2*d^2*x^2 + 16*b^2*c*d*x + 8*b^2*c^2 - (16*b^2*d^2*x^2 + 32*b^2*c*d*x + 16*b^2*c^2 - 3*d^2)*cos(b*x + a)^2 - 4*(b*d^2*x + b*c*d)*cos(b*x + a)*sin(b*x + a) - 3*d^2)*sqrt(d*x + c))/(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)","A",0
52,1,422,0,1.258142," ","integrate(sin(b*x+a)^2/(d*x+c)^(9/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(64 \, {\left(\pi b^{3} d^{4} x^{4} + 4 \, \pi b^{3} c d^{3} x^{3} + 6 \, \pi b^{3} c^{2} d^{2} x^{2} + 4 \, \pi b^{3} c^{3} d x + \pi b^{3} c^{4}\right)} \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) - 64 \, {\left(\pi b^{3} d^{4} x^{4} + 4 \, \pi b^{3} c d^{3} x^{3} + 6 \, \pi b^{3} c^{2} d^{2} x^{2} + 4 \, \pi b^{3} c^{3} d x + \pi b^{3} c^{4}\right)} \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) - {\left(8 \, b^{2} d^{3} x^{2} + 16 \, b^{2} c d^{2} x + 8 \, b^{2} c^{2} d - 15 \, d^{3} - {\left(16 \, b^{2} d^{3} x^{2} + 32 \, b^{2} c d^{2} x + 16 \, b^{2} c^{2} d - 15 \, d^{3}\right)} \cos\left(b x + a\right)^{2} + 4 \, {\left(16 \, b^{3} d^{3} x^{3} + 48 \, b^{3} c d^{2} x^{2} + 16 \, b^{3} c^{3} - 3 \, b c d^{2} + 3 \, {\left(16 \, b^{3} c^{2} d - b d^{3}\right)} x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \sqrt{d x + c}\right)}}{105 \, {\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)}}"," ",0,"-2/105*(64*(pi*b^3*d^4*x^4 + 4*pi*b^3*c*d^3*x^3 + 6*pi*b^3*c^2*d^2*x^2 + 4*pi*b^3*c^3*d*x + pi*b^3*c^4)*sqrt(b/(pi*d))*cos(-2*(b*c - a*d)/d)*fresnel_cos(2*sqrt(d*x + c)*sqrt(b/(pi*d))) - 64*(pi*b^3*d^4*x^4 + 4*pi*b^3*c*d^3*x^3 + 6*pi*b^3*c^2*d^2*x^2 + 4*pi*b^3*c^3*d*x + pi*b^3*c^4)*sqrt(b/(pi*d))*fresnel_sin(2*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-2*(b*c - a*d)/d) - (8*b^2*d^3*x^2 + 16*b^2*c*d^2*x + 8*b^2*c^2*d - 15*d^3 - (16*b^2*d^3*x^2 + 32*b^2*c*d^2*x + 16*b^2*c^2*d - 15*d^3)*cos(b*x + a)^2 + 4*(16*b^3*d^3*x^3 + 48*b^3*c*d^2*x^2 + 16*b^3*c^3 - 3*b*c*d^2 + 3*(16*b^3*c^2*d - b*d^3)*x)*cos(b*x + a)*sin(b*x + a))*sqrt(d*x + c))/(d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)","B",0
53,1,371,0,1.118373," ","integrate((d*x+c)^(5/2)*sin(b*x+a)^3,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) - 1215 \, \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) + 1215 \, \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({\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} - 3 \, {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 35 \, b d^{2}\right)} \cos\left(b x + a\right) + 10 \, {\left(7 \, b^{2} d^{2} x + 7 \, 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))) - 1215*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))) + 1215*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*((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 - 3*(12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 35*b*d^2)*cos(b*x + a) + 10*(7*b^2*d^2*x + 7*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
54,1,300,0,1.297473," ","integrate((d*x+c)^(3/2)*sin(b*x+a)^3,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) - 81 \, \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) - 81 \, \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} - 6 \, {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right) - {\left(b d \cos\left(b x + a\right)^{2} - 7 \, 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))) - 81*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))) - 81*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 - 6*(b^2*d*x + b^2*c)*cos(b*x + a) - (b*d*cos(b*x + a)^2 - 7*b*d)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
55,1,246,0,1.061582," ","integrate((d*x+c)^(1/2)*sin(b*x+a)^3,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) - 27 \, \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) + 27 \, \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 \, {\left(b \cos\left(b x + a\right)^{3} - 3 \, b \cos\left(b x + a\right)\right)} \sqrt{d x + c}}{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))) - 27*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))) + 27*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*(b*cos(b*x + a)^3 - 3*b*cos(b*x + a))*sqrt(d*x + c))/b^2","A",0
56,1,212,0,1.223826," ","integrate(sin(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{6} \pi \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 \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 \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 \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)}{12 \, b}"," ",0,"-1/12*(sqrt(6)*pi*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*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*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*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d))/b","A",0
57,1,274,0,1.197886," ","integrate(sin(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{6} {\left(\pi d x + \pi c\right)} \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) - 3 \, \sqrt{2} {\left(\pi d x + \pi c\right)} \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) + 3 \, \sqrt{2} {\left(\pi d x + \pi c\right)} \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} {\left(\pi d x + \pi c\right)} \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) - 4 \, \sqrt{d x + c} {\left(\cos\left(b x + a\right)^{2} - 1\right)} \sin\left(b x + a\right)}{2 \, {\left(d^{2} x + c d\right)}}"," ",0,"-1/2*(sqrt(6)*(pi*d*x + pi*c)*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 3*sqrt(2)*(pi*d*x + pi*c)*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*(pi*d*x + pi*c)*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*x + pi*c)*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 4*sqrt(d*x + c)*(cos(b*x + a)^2 - 1)*sin(b*x + a))/(d^2*x + c*d)","A",0
58,1,388,0,1.600196," ","integrate(sin(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{6} {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) - 3 \, \sqrt{2} {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) - 3 \, \sqrt{2} {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) + 3 \, \sqrt{6} {\left(\pi b d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\right)} \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) + 2 \, {\left(6 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{3} - 6 \, {\left(b d x + b c\right)} \cos\left(b x + a\right) + {\left(d \cos\left(b x + a\right)^{2} - d\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}"," ",0,"1/3*(3*sqrt(6)*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 3*sqrt(2)*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 3*sqrt(2)*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 3*sqrt(6)*(pi*b*d^2*x^2 + 2*pi*b*c*d*x + pi*b*c^2)*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 2*(6*(b*d*x + b*c)*cos(b*x + a)^3 - 6*(b*d*x + b*c)*cos(b*x + a) + (d*cos(b*x + a)^2 - d)*sin(b*x + a))*sqrt(d*x + c))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
59,1,549,0,1.214947," ","integrate(sin(b*x+a)^3/(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, \sqrt{6} {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) - \sqrt{2} {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) + \sqrt{2} {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) - 3 \, \sqrt{6} {\left(\pi b^{2} d^{3} x^{3} + 3 \, \pi b^{2} c d^{2} x^{2} + 3 \, \pi b^{2} c^{2} d x + \pi b^{2} c^{3}\right)} \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) + {\left(2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} - 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + {\left(4 \, b^{2} d^{2} x^{2} + 8 \, b^{2} c d x + 4 \, b^{2} c^{2} - {\left(12 \, b^{2} d^{2} x^{2} + 24 \, b^{2} c d x + 12 \, b^{2} c^{2} - d^{2}\right)} \cos\left(b x + a\right)^{2} - d^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}\right)}}{5 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)}}"," ",0,"2/5*(3*sqrt(6)*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) - sqrt(2)*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + sqrt(2)*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 3*sqrt(6)*(pi*b^2*d^3*x^3 + 3*pi*b^2*c*d^2*x^2 + 3*pi*b^2*c^2*d*x + pi*b^2*c^3)*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + (2*(b*d^2*x + b*c*d)*cos(b*x + a)^3 - 2*(b*d^2*x + b*c*d)*cos(b*x + a) + (4*b^2*d^2*x^2 + 8*b^2*c*d*x + 4*b^2*c^2 - (12*b^2*d^2*x^2 + 24*b^2*c*d*x + 12*b^2*c^2 - d^2)*cos(b*x + a)^2 - d^2)*sin(b*x + a))*sqrt(d*x + c))/(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)","A",0
60,1,72,0,0.989885," ","integrate((d*x)^(3/2)*sin(f*x),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} \pi d^{2} \sqrt{\frac{f}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x} \sqrt{\frac{f}{\pi d}}\right) + 2 \, {\left(2 \, d f^{2} x \cos\left(f x\right) - 3 \, d f \sin\left(f x\right)\right)} \sqrt{d x}}{4 \, f^{3}}"," ",0,"-1/4*(3*sqrt(2)*pi*d^2*sqrt(f/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x)*sqrt(f/(pi*d))) + 2*(2*d*f^2*x*cos(f*x) - 3*d*f*sin(f*x))*sqrt(d*x))/f^3","A",0
61,1,54,0,1.216910," ","integrate((d*x)^(1/2)*sin(f*x),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi d \sqrt{\frac{f}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x} \sqrt{\frac{f}{\pi d}}\right) - 2 \, \sqrt{d x} f \cos\left(f x\right)}{2 \, f^{2}}"," ",0,"1/2*(sqrt(2)*pi*d*sqrt(f/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x)*sqrt(f/(pi*d))) - 2*sqrt(d*x)*f*cos(f*x))/f^2","A",0
62,1,38,0,1.222792," ","integrate(sin(f*x)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{f}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x} \sqrt{\frac{f}{\pi d}}\right)}{f}"," ",0,"sqrt(2)*pi*sqrt(f/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x)*sqrt(f/(pi*d)))/f","A",0
63,1,57,0,1.126726," ","integrate(sin(f*x)/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{2} \pi d x \sqrt{\frac{f}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x} \sqrt{\frac{f}{\pi d}}\right) - \sqrt{d x} \sin\left(f x\right)\right)}}{d^{2} x}"," ",0,"2*(sqrt(2)*pi*d*x*sqrt(f/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x)*sqrt(f/(pi*d))) - sqrt(d*x)*sin(f*x))/(d^2*x)","A",0
64,1,69,0,1.212540," ","integrate(sin(f*x)/(d*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, \sqrt{2} \pi d f x^{2} \sqrt{\frac{f}{\pi d}} \operatorname{S}\left(\sqrt{2} \sqrt{d x} \sqrt{\frac{f}{\pi d}}\right) + {\left(2 \, f x \cos\left(f x\right) + \sin\left(f x\right)\right)} \sqrt{d x}\right)}}{3 \, d^{3} x^{2}}"," ",0,"-2/3*(2*sqrt(2)*pi*d*f*x^2*sqrt(f/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x)*sqrt(f/(pi*d))) + (2*f*x*cos(f*x) + sin(f*x))*sqrt(d*x))/(d^3*x^2)","A",0
65,0,0,0,0.930521," ","integrate(csc(b*x+a)*(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x + c} \csc\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*x + c)*csc(b*x + a), x)","F",0
66,0,0,0,1.084117," ","integrate(csc(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(b x + a\right)}{\sqrt{d x + c}}, x\right)"," ",0,"integral(csc(b*x + a)/sqrt(d*x + c), x)","F",0
67,-2,0,0,0.000000," ","integrate(x/sin(f*x+e)^(3/2)+x*sin(f*x+e)^(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
68,-2,0,0,0.000000," ","integrate(x^2/sin(f*x+e)^(3/2)+x^2*sin(f*x+e)^(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
69,1,48,0,1.156667," ","integrate(x/sin(f*x+e)^(5/2)-1/3*x/sin(f*x+e)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(f x \cos\left(f x + e\right) + 2 \, \sin\left(f x + e\right)\right)} \sqrt{\sin\left(f x + e\right)}}{3 \, {\left(f^{2} \cos\left(f x + e\right)^{2} - f^{2}\right)}}"," ",0,"2/3*(f*x*cos(f*x + e) + 2*sin(f*x + e))*sqrt(sin(f*x + e))/(f^2*cos(f*x + e)^2 - f^2)","A",0
70,-2,0,0,0.000000," ","integrate(x/sin(f*x+e)^(7/2)+3/5*x*sin(f*x+e)^(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
71,0,0,0,1.118030," ","integrate((d*x+c)^m*(b*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \left(b \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*sin(f*x + e))^n, x)","F",0
72,1,184,0,1.327037," ","integrate((d*x+c)^m*sin(b*x+a)^3,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) - 9 \, 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) - 9 \, 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) - 9*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) - 9*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
73,1,134,0,1.174176," ","integrate((d*x+c)^m*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, d m - i \, 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) + {\left(i \, d m + i \, 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) + 4 \, {\left(b d x + b c\right)} {\left(d x + c\right)}^{m}}{8 \, {\left(b d m + b d\right)}}"," ",0,"1/8*((-I*d*m - I*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) + (I*d*m + I*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) + 4*(b*d*x + b*c)*(d*x + c)^m)/(b*d*m + b*d)","A",0
74,1,94,0,1.223614," ","integrate((d*x+c)^m*sin(b*x+a),x, algorithm=""fricas"")","-\frac{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{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)}{2 \, b}"," ",0,"-1/2*(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(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d))/b","A",0
75,0,0,0,1.578628," ","integrate((d*x+c)^m*csc(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a), x)","F",0
76,0,0,0,1.192054," ","integrate((d*x+c)^m*csc(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \csc\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*csc(b*x + a)^2, x)","F",0
77,1,52,0,1.084781," ","integrate(x^(3+m)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-{\left(m + 3\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 4, i \, b x\right) + e^{\left(-{\left(m + 3\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m + 4, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-(m + 3)*log(I*b) - I*a)*gamma(m + 4, I*b*x) + e^(-(m + 3)*log(-I*b) + I*a)*gamma(m + 4, -I*b*x))/b","A",0
78,1,52,0,1.295740," ","integrate(x^(2+m)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-{\left(m + 2\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 3, i \, b x\right) + e^{\left(-{\left(m + 2\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m + 3, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-(m + 2)*log(I*b) - I*a)*gamma(m + 3, I*b*x) + e^(-(m + 2)*log(-I*b) + I*a)*gamma(m + 3, -I*b*x))/b","A",0
79,1,52,0,1.248768," ","integrate(x^(1+m)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-{\left(m + 1\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 2, i \, b x\right) + e^{\left(-{\left(m + 1\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m + 2, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-(m + 1)*log(I*b) - I*a)*gamma(m + 2, I*b*x) + e^(-(m + 1)*log(-I*b) + I*a)*gamma(m + 2, -I*b*x))/b","A",0
80,1,48,0,1.190016," ","integrate(x^m*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-m \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 1, i \, b x\right) + e^{\left(-m \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m + 1, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-m*log(I*b) - I*a)*gamma(m + 1, I*b*x) + e^(-m*log(-I*b) + I*a)*gamma(m + 1, -I*b*x))/b","A",0
81,1,48,0,1.077844," ","integrate(x^(-1+m)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-{\left(m - 1\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m, i \, b x\right) + e^{\left(-{\left(m - 1\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-(m - 1)*log(I*b) - I*a)*gamma(m, I*b*x) + e^(-(m - 1)*log(-I*b) + I*a)*gamma(m, -I*b*x))/b","A",0
82,1,52,0,1.119479," ","integrate(x^(-2+m)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-{\left(m - 2\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m - 1, i \, b x\right) + e^{\left(-{\left(m - 2\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m - 1, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-(m - 2)*log(I*b) - I*a)*gamma(m - 1, I*b*x) + e^(-(m - 2)*log(-I*b) + I*a)*gamma(m - 1, -I*b*x))/b","A",0
83,1,52,0,0.788345," ","integrate(x^(-3+m)*sin(b*x+a),x, algorithm=""fricas"")","-\frac{e^{\left(-{\left(m - 3\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m - 2, i \, b x\right) + e^{\left(-{\left(m - 3\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m - 2, -i \, b x\right)}{2 \, b}"," ",0,"-1/2*(e^(-(m - 3)*log(I*b) - I*a)*gamma(m - 2, I*b*x) + e^(-(m - 3)*log(-I*b) + I*a)*gamma(m - 2, -I*b*x))/b","A",0
84,1,77,0,1.322385," ","integrate(x^(3+m)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m + 3} + {\left(-i \, m - 4 i\right)} e^{\left(-{\left(m + 3\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m + 4, 2 i \, b x\right) + {\left(i \, m + 4 i\right)} e^{\left(-{\left(m + 3\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m + 4, -2 i \, b x\right)}{8 \, {\left(b m + 4 \, b\right)}}"," ",0,"1/8*(4*b*x*x^(m + 3) + (-I*m - 4*I)*e^(-(m + 3)*log(2*I*b) - 2*I*a)*gamma(m + 4, 2*I*b*x) + (I*m + 4*I)*e^(-(m + 3)*log(-2*I*b) + 2*I*a)*gamma(m + 4, -2*I*b*x))/(b*m + 4*b)","A",0
85,1,77,0,1.217893," ","integrate(x^(2+m)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m + 2} + {\left(-i \, m - 3 i\right)} e^{\left(-{\left(m + 2\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m + 3, 2 i \, b x\right) + {\left(i \, m + 3 i\right)} e^{\left(-{\left(m + 2\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m + 3, -2 i \, b x\right)}{8 \, {\left(b m + 3 \, b\right)}}"," ",0,"1/8*(4*b*x*x^(m + 2) + (-I*m - 3*I)*e^(-(m + 2)*log(2*I*b) - 2*I*a)*gamma(m + 3, 2*I*b*x) + (I*m + 3*I)*e^(-(m + 2)*log(-2*I*b) + 2*I*a)*gamma(m + 3, -2*I*b*x))/(b*m + 3*b)","A",0
86,1,77,0,1.064485," ","integrate(x^(1+m)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m + 1} + {\left(-i \, m - 2 i\right)} e^{\left(-{\left(m + 1\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m + 2, 2 i \, b x\right) + {\left(i \, m + 2 i\right)} e^{\left(-{\left(m + 1\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m + 2, -2 i \, b x\right)}{8 \, {\left(b m + 2 \, b\right)}}"," ",0,"1/8*(4*b*x*x^(m + 1) + (-I*m - 2*I)*e^(-(m + 1)*log(2*I*b) - 2*I*a)*gamma(m + 2, 2*I*b*x) + (I*m + 2*I)*e^(-(m + 1)*log(-2*I*b) + 2*I*a)*gamma(m + 2, -2*I*b*x))/(b*m + 2*b)","A",0
87,1,69,0,1.054435," ","integrate(x^m*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m} + {\left(-i \, m - i\right)} e^{\left(-m \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m + 1, 2 i \, b x\right) + {\left(i \, m + i\right)} e^{\left(-m \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m + 1, -2 i \, b x\right)}{8 \, {\left(b m + b\right)}}"," ",0,"1/8*(4*b*x*x^m + (-I*m - I)*e^(-m*log(2*I*b) - 2*I*a)*gamma(m + 1, 2*I*b*x) + (I*m + I)*e^(-m*log(-2*I*b) + 2*I*a)*gamma(m + 1, -2*I*b*x))/(b*m + b)","A",0
88,1,64,0,0.977916," ","integrate(x^(-1+m)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m - 1} - i \, m e^{\left(-{\left(m - 1\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m, 2 i \, b x\right) + i \, m e^{\left(-{\left(m - 1\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m, -2 i \, b x\right)}{8 \, b m}"," ",0,"1/8*(4*b*x*x^(m - 1) - I*m*e^(-(m - 1)*log(2*I*b) - 2*I*a)*gamma(m, 2*I*b*x) + I*m*e^(-(m - 1)*log(-2*I*b) + 2*I*a)*gamma(m, -2*I*b*x))/(b*m)","A",0
89,1,77,0,1.125815," ","integrate(x^(-2+m)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m - 2} + {\left(-i \, m + i\right)} e^{\left(-{\left(m - 2\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m - 1, 2 i \, b x\right) + {\left(i \, m - i\right)} e^{\left(-{\left(m - 2\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m - 1, -2 i \, b x\right)}{8 \, {\left(b m - b\right)}}"," ",0,"1/8*(4*b*x*x^(m - 2) + (-I*m + I)*e^(-(m - 2)*log(2*I*b) - 2*I*a)*gamma(m - 1, 2*I*b*x) + (I*m - I)*e^(-(m - 2)*log(-2*I*b) + 2*I*a)*gamma(m - 1, -2*I*b*x))/(b*m - b)","A",0
90,1,77,0,1.227555," ","integrate(x^(-3+m)*sin(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x x^{m - 3} + {\left(-i \, m + 2 i\right)} e^{\left(-{\left(m - 3\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m - 2, 2 i \, b x\right) + {\left(i \, m - 2 i\right)} e^{\left(-{\left(m - 3\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m - 2, -2 i \, b x\right)}{8 \, {\left(b m - 2 \, b\right)}}"," ",0,"1/8*(4*b*x*x^(m - 3) + (-I*m + 2*I)*e^(-(m - 3)*log(2*I*b) - 2*I*a)*gamma(m - 2, 2*I*b*x) + (I*m - 2*I)*e^(-(m - 3)*log(-2*I*b) + 2*I*a)*gamma(m - 2, -2*I*b*x))/(b*m - 2*b)","A",0
91,-2,0,0,0.000000," ","integrate(x/csc(f*x+e)^(3/2)-1/3*x*csc(f*x+e)^(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
92,-2,0,0,0.000000," ","integrate(x^2/csc(f*x+e)^(3/2)-1/3*x^2*csc(f*x+e)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
93,-2,0,0,0.000000," ","integrate(x/csc(f*x+e)^(5/2)-3/5*x/csc(f*x+e)^(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
94,-2,0,0,0.000000," ","integrate(x/csc(f*x+e)^(7/2)-5/21*x*csc(f*x+e)^(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
95,1,168,0,1.070223," ","integrate((d*x+c)^3*(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x - 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + a c^{3} f^{3} - 6 \, a c d^{2} f + 3 \, {\left(a c^{2} d f^{3} - 2 \, a d^{3} f\right)} x\right)} \cos\left(f x + e\right) + 12 \, {\left(a d^{3} f^{2} x^{2} + 2 \, a c d^{2} f^{2} x + a c^{2} d f^{2} - 2 \, a d^{3}\right)} \sin\left(f x + e\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x - 4*(a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + a*c^3*f^3 - 6*a*c*d^2*f + 3*(a*c^2*d*f^3 - 2*a*d^3*f)*x)*cos(f*x + e) + 12*(a*d^3*f^2*x^2 + 2*a*c*d^2*f^2*x + a*c^2*d*f^2 - 2*a*d^3)*sin(f*x + e))/f^4","A",0
96,1,102,0,0.550101," ","integrate((d*x+c)^2*(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{2} f^{3} x^{3} + 3 \, a c d f^{3} x^{2} + 3 \, a c^{2} f^{3} x - 3 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2} - 2 \, a d^{2}\right)} \cos\left(f x + e\right) + 6 \, {\left(a d^{2} f x + a c d f\right)} \sin\left(f x + e\right)}{3 \, f^{3}}"," ",0,"1/3*(a*d^2*f^3*x^3 + 3*a*c*d*f^3*x^2 + 3*a*c^2*f^3*x - 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2 - 2*a*d^2)*cos(f*x + e) + 6*(a*d^2*f*x + a*c*d*f)*sin(f*x + e))/f^3","A",0
97,1,51,0,0.772780," ","integrate((d*x+c)*(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x + 2 \, a d \sin\left(f x + e\right) - 2 \, {\left(a d f x + a c f\right)} \cos\left(f x + e\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x + 2*a*d*sin(f*x + e) - 2*(a*d*f*x + a*c*f)*cos(f*x + e))/f^2","A",0
98,1,93,0,0.961517," ","integrate((a+a*sin(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, a \log\left(d x + c\right) - {\left(a \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + a \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{2 \, d}"," ",0,"1/2*(2*a*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*a*log(d*x + c) - (a*cos_integral((d*f*x + c*f)/d) + a*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/d","A",0
99,1,135,0,1.059416," ","integrate((a+a*sin(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, a d \sin\left(f x + e\right) - 2 \, {\left(a d f x + a c f\right)} \sin\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, a d - {\left({\left(a d f x + a c f\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(a d f x + a c f\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*a*d*sin(f*x + e) - 2*(a*d*f*x + a*c*f)*sin(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*a*d - ((a*d*f*x + a*c*f)*cos_integral((d*f*x + c*f)/d) + (a*d*f*x + a*c*f)*cos_integral(-(d*f*x + c*f)/d))*cos(-(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
100,1,228,0,0.675973," ","integrate((a+a*sin(f*x+e))/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a d^{2} \sin\left(f x + e\right) + 2 \, a d^{2} + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right) - {\left({\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*a*d^2*sin(f*x + e) + 2*a*d^2 + 2*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*(a*d^2*f*x + a*c*d*f)*cos(f*x + e) - ((a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*cos_integral((d*f*x + c*f)/d) + (a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
101,1,368,0,0.924693," ","integrate((d*x+c)^3*(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} d^{3} f^{4} x^{4} + 12 \, a^{2} c d^{2} f^{4} x^{3} + 3 \, {\left(6 \, a^{2} c^{2} d f^{4} + a^{2} d^{3} f^{2}\right)} x^{2} - 3 \, {\left(2 \, a^{2} d^{3} f^{2} x^{2} + 4 \, a^{2} c d^{2} f^{2} x + 2 \, a^{2} c^{2} d f^{2} - a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(2 \, a^{2} c^{3} f^{4} + a^{2} c d^{2} f^{2}\right)} x - 16 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + a^{2} c^{3} f^{3} - 6 \, a^{2} c d^{2} f + 3 \, {\left(a^{2} c^{2} d f^{3} - 2 \, a^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right) + 2 \, {\left(24 \, a^{2} d^{3} f^{2} x^{2} + 48 \, a^{2} c d^{2} f^{2} x + 24 \, a^{2} c^{2} d f^{2} - 48 \, a^{2} d^{3} - {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 6 \, a^{2} c d^{2} f^{3} x^{2} + 2 \, a^{2} c^{3} f^{3} - 3 \, a^{2} c d^{2} f + 3 \, {\left(2 \, a^{2} c^{2} d f^{3} - a^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{8 \, f^{4}}"," ",0,"1/8*(3*a^2*d^3*f^4*x^4 + 12*a^2*c*d^2*f^4*x^3 + 3*(6*a^2*c^2*d*f^4 + a^2*d^3*f^2)*x^2 - 3*(2*a^2*d^3*f^2*x^2 + 4*a^2*c*d^2*f^2*x + 2*a^2*c^2*d*f^2 - a^2*d^3)*cos(f*x + e)^2 + 6*(2*a^2*c^3*f^4 + a^2*c*d^2*f^2)*x - 16*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + a^2*c^3*f^3 - 6*a^2*c*d^2*f + 3*(a^2*c^2*d*f^3 - 2*a^2*d^3*f)*x)*cos(f*x + e) + 2*(24*a^2*d^3*f^2*x^2 + 48*a^2*c*d^2*f^2*x + 24*a^2*c^2*d*f^2 - 48*a^2*d^3 - (2*a^2*d^3*f^3*x^3 + 6*a^2*c*d^2*f^3*x^2 + 2*a^2*c^3*f^3 - 3*a^2*c*d^2*f + 3*(2*a^2*c^2*d*f^3 - a^2*d^3*f)*x)*cos(f*x + e))*sin(f*x + e))/f^4","A",0
102,1,212,0,0.972453," ","integrate((d*x+c)^2*(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{2} f^{3} x^{3} + 6 \, a^{2} c d f^{3} x^{2} - 2 \, {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, a^{2} c^{2} f^{3} + a^{2} d^{2} f\right)} x - 8 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2} - 2 \, a^{2} d^{2}\right)} \cos\left(f x + e\right) + {\left(16 \, a^{2} d^{2} f x + 16 \, a^{2} c d f - {\left(2 \, a^{2} d^{2} f^{2} x^{2} + 4 \, a^{2} c d f^{2} x + 2 \, a^{2} c^{2} f^{2} - a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, f^{3}}"," ",0,"1/4*(2*a^2*d^2*f^3*x^3 + 6*a^2*c*d*f^3*x^2 - 2*(a^2*d^2*f*x + a^2*c*d*f)*cos(f*x + e)^2 + (6*a^2*c^2*f^3 + a^2*d^2*f)*x - 8*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2 - 2*a^2*d^2)*cos(f*x + e) + (16*a^2*d^2*f*x + 16*a^2*c*d*f - (2*a^2*d^2*f^2*x^2 + 4*a^2*c*d*f^2*x + 2*a^2*c^2*f^2 - a^2*d^2)*cos(f*x + e))*sin(f*x + e))/f^3","A",0
103,1,101,0,0.911044," ","integrate((d*x+c)*(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} d f^{2} x^{2} + 6 \, a^{2} c f^{2} x - a^{2} d \cos\left(f x + e\right)^{2} - 8 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(f x + e\right) + 2 \, {\left(4 \, a^{2} d - {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, f^{2}}"," ",0,"1/4*(3*a^2*d*f^2*x^2 + 6*a^2*c*f^2*x - a^2*d*cos(f*x + e)^2 - 8*(a^2*d*f*x + a^2*c*f)*cos(f*x + e) + 2*(4*a^2*d - (a^2*d*f*x + a^2*c*f)*cos(f*x + e))*sin(f*x + e))/f^2","A",0
104,1,186,0,0.845396," ","integrate((a+a*sin(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, a^{2} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 \, a^{2} \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) - 6 \, a^{2} \log\left(d x + c\right) + {\left(a^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + a^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 4 \, {\left(a^{2} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + a^{2} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{4 \, d}"," ",0,"-1/4*(2*a^2*sin(-2*(d*e - c*f)/d)*sin_integral(2*(d*f*x + c*f)/d) - 8*a^2*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) - 6*a^2*log(d*x + c) + (a^2*cos_integral(2*(d*f*x + c*f)/d) + a^2*cos_integral(-2*(d*f*x + c*f)/d))*cos(-2*(d*e - c*f)/d) + 4*(a^2*cos_integral((d*f*x + c*f)/d) + a^2*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/d","A",0
105,1,284,0,0.667956," ","integrate((a+a*sin(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} d \cos\left(f x + e\right)^{2} - 4 \, a^{2} d \sin\left(f x + e\right) - 4 \, a^{2} d + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, {\left({\left(a^{2} d f x + a^{2} c f\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(a^{2} d f x + a^{2} c f\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) - {\left({\left(a^{2} d f x + a^{2} c f\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(a^{2} d f x + a^{2} c f\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/2*(2*a^2*d*cos(f*x + e)^2 - 4*a^2*d*sin(f*x + e) - 4*a^2*d + 2*(a^2*d*f*x + a^2*c*f)*cos(-2*(d*e - c*f)/d)*sin_integral(2*(d*f*x + c*f)/d) + 4*(a^2*d*f*x + a^2*c*f)*sin(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*((a^2*d*f*x + a^2*c*f)*cos_integral((d*f*x + c*f)/d) + (a^2*d*f*x + a^2*c*f)*cos_integral(-(d*f*x + c*f)/d))*cos(-(d*e - c*f)/d) - ((a^2*d*f*x + a^2*c*f)*cos_integral(2*(d*f*x + c*f)/d) + (a^2*d*f*x + a^2*c*f)*cos_integral(-2*(d*f*x + c*f)/d))*sin(-2*(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
106,1,475,0,1.467429," ","integrate((a+a*sin(f*x+e))^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{a^{2} d^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} d^{2} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) - 2 \, {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cos\left(f x + e\right) + {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(a^{2} d^{2} + {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) + {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*(a^2*d^2*cos(f*x + e)^2 - 2*a^2*d^2 + 2*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*sin(-2*(d*e - c*f)/d)*sin_integral(2*(d*f*x + c*f)/d) - 2*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) - 2*(a^2*d^2*f*x + a^2*c*d*f)*cos(f*x + e) + ((a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*cos_integral(2*(d*f*x + c*f)/d) + (a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*cos_integral(-2*(d*f*x + c*f)/d))*cos(-2*(d*e - c*f)/d) - 2*(a^2*d^2 + (a^2*d^2*f*x + a^2*c*d*f)*cos(f*x + e))*sin(f*x + e) + ((a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*cos_integral((d*f*x + c*f)/d) + (a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
107,1,915,0,0.950923," ","integrate((d*x+c)^3/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3}\right)} \cos\left(f x + e\right) - {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \cos\left(f x + e\right) + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 3 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \cos\left(f x + e\right) + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \sin\left(f x + e\right)\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \sin\left(f x + e\right)\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \cos\left(f x + e\right) + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 6 \, {\left(d^{3} \cos\left(f x + e\right) + d^{3} \sin\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 6 \, {\left(d^{3} \cos\left(f x + e\right) + d^{3} \sin\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3}\right)} \sin\left(f x + e\right)}{a f^{4} \cos\left(f x + e\right) + a f^{4} \sin\left(f x + e\right) + a f^{4}}"," ",0,"-(d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3 + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3)*cos(f*x + e) - (-6*I*d^3*f*x - 6*I*c*d^2*f + (-6*I*d^3*f*x - 6*I*c*d^2*f)*cos(f*x + e) + (-6*I*d^3*f*x - 6*I*c*d^2*f)*sin(f*x + e))*dilog(I*cos(f*x + e) - sin(f*x + e)) - (6*I*d^3*f*x + 6*I*c*d^2*f + (6*I*d^3*f*x + 6*I*c*d^2*f)*cos(f*x + e) + (6*I*d^3*f*x + 6*I*c*d^2*f)*sin(f*x + e))*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 3*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*cos(f*x + e) + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*sin(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + I) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e) + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*sin(f*x + e))*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e) + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*sin(f*x + e))*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*cos(f*x + e) + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*sin(f*x + e))*log(-cos(f*x + e) + I*sin(f*x + e) + I) - 6*(d^3*cos(f*x + e) + d^3*sin(f*x + e) + d^3)*polylog(3, I*cos(f*x + e) - sin(f*x + e)) - 6*(d^3*cos(f*x + e) + d^3*sin(f*x + e) + d^3)*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) - (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3)*sin(f*x + e))/(a*f^4*cos(f*x + e) + a*f^4*sin(f*x + e) + a*f^4)","C",0
108,1,493,0,1.098351," ","integrate((d*x+c)^2/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} \cos\left(f x + e\right) - {\left(-2 i \, d^{2} \cos\left(f x + e\right) - 2 i \, d^{2} \sin\left(f x + e\right) - 2 i \, d^{2}\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(2 i \, d^{2} \cos\left(f x + e\right) + 2 i \, d^{2} \sin\left(f x + e\right) + 2 i \, d^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 2 \, {\left(d^{2} e - c d f + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right) + {\left(d^{2} e - c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 2 \, {\left(d^{2} f x + d^{2} e + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right) + {\left(d^{2} f x + d^{2} e\right)} \sin\left(f x + e\right)\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f x + d^{2} e + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right) + {\left(d^{2} f x + d^{2} e\right)} \sin\left(f x + e\right)\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) + 2 \, {\left(d^{2} e - c d f + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right) + {\left(d^{2} e - c d f\right)} \sin\left(f x + e\right)\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} \sin\left(f x + e\right)}{a f^{3} \cos\left(f x + e\right) + a f^{3} \sin\left(f x + e\right) + a f^{3}}"," ",0,"-(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*cos(f*x + e) - (-2*I*d^2*cos(f*x + e) - 2*I*d^2*sin(f*x + e) - 2*I*d^2)*dilog(I*cos(f*x + e) - sin(f*x + e)) - (2*I*d^2*cos(f*x + e) + 2*I*d^2*sin(f*x + e) + 2*I*d^2)*dilog(-I*cos(f*x + e) - sin(f*x + e)) + 2*(d^2*e - c*d*f + (d^2*e - c*d*f)*cos(f*x + e) + (d^2*e - c*d*f)*sin(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + I) - 2*(d^2*f*x + d^2*e + (d^2*f*x + d^2*e)*cos(f*x + e) + (d^2*f*x + d^2*e)*sin(f*x + e))*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(d^2*f*x + d^2*e + (d^2*f*x + d^2*e)*cos(f*x + e) + (d^2*f*x + d^2*e)*sin(f*x + e))*log(-I*cos(f*x + e) + sin(f*x + e) + 1) + 2*(d^2*e - c*d*f + (d^2*e - c*d*f)*cos(f*x + e) + (d^2*e - c*d*f)*sin(f*x + e))*log(-cos(f*x + e) + I*sin(f*x + e) + I) - (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*sin(f*x + e))/(a*f^3*cos(f*x + e) + a*f^3*sin(f*x + e) + a*f^3)","B",0
109,1,100,0,0.801357," ","integrate((d*x+c)/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{d f x + c f + {\left(d f x + c f\right)} \cos\left(f x + e\right) - {\left(d \cos\left(f x + e\right) + d \sin\left(f x + e\right) + d\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(d f x + c f\right)} \sin\left(f x + e\right)}{a f^{2} \cos\left(f x + e\right) + a f^{2} \sin\left(f x + e\right) + a f^{2}}"," ",0,"-(d*f*x + c*f + (d*f*x + c*f)*cos(f*x + e) - (d*cos(f*x + e) + d*sin(f*x + e) + d)*log(sin(f*x + e) + 1) - (d*f*x + c*f)*sin(f*x + e))/(a*f^2*cos(f*x + e) + a*f^2*sin(f*x + e) + a*f^2)","B",0
110,0,0,0,0.924731," ","integrate(1/(d*x+c)/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(a d x + a c\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (a*d*x + a*c)*sin(f*x + e)), x)","F",0
111,0,0,0,0.753909," ","integrate(1/(d*x+c)^2/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (a*d^2*x^2 + 2*a*c*d*x + a*c^2)*sin(f*x + e)), x)","F",0
112,1,1708,0,1.221890," ","integrate((d*x+c)^3/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{d^{3} f^{3} x^{3} + c^{3} f^{3} + 3 \, c^{2} d f^{2} + 3 \, {\left(c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + c^{3} f^{3} + 6 \, c d^{2} f + 3 \, {\left(c^{2} d f^{3} + 2 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(c^{2} d f^{3} + 2 \, c d^{2} f^{2}\right)} x + {\left(2 \, d^{3} f^{3} x^{3} + 2 \, c^{3} f^{3} + 3 \, c^{2} d f^{2} + 6 \, c d^{2} f + 3 \, {\left(2 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} + 6 \, {\left(c^{2} d f^{3} + c d^{2} f^{2} + d^{3} f\right)} x\right)} \cos\left(f x + e\right) - {\left(-12 i \, d^{3} f x - 12 i \, c d^{2} f + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \cos\left(f x + e\right)^{2} + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-12 i \, d^{3} f x - 12 i \, c d^{2} f + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(12 i \, d^{3} f x + 12 i \, c d^{2} f + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \cos\left(f x + e\right)^{2} + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \cos\left(f x + e\right) + {\left(12 i \, d^{3} f x + 12 i \, c d^{2} f + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - 3 \, {\left(2 \, d^{3} e^{2} - 4 \, c d^{2} e f + 2 \, c^{2} d f^{2} + 4 \, d^{3} - {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(2 \, d^{3} e^{2} - 4 \, c d^{2} e f + 2 \, c^{2} d f^{2} + 4 \, d^{3} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 3 \, {\left(2 \, d^{3} f^{2} x^{2} + 4 \, c d^{2} f^{2} x - 2 \, d^{3} e^{2} + 4 \, c d^{2} e f - {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right)^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(2 \, d^{3} f^{2} x^{2} + 4 \, c d^{2} f^{2} x - 2 \, d^{3} e^{2} + 4 \, c d^{2} e f + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(2 \, d^{3} f^{2} x^{2} + 4 \, c d^{2} f^{2} x - 2 \, d^{3} e^{2} + 4 \, c d^{2} e f - {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right)^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right) + {\left(2 \, d^{3} f^{2} x^{2} + 4 \, c d^{2} f^{2} x - 2 \, d^{3} e^{2} + 4 \, c d^{2} e f + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 3 \, {\left(2 \, d^{3} e^{2} - 4 \, c d^{2} e f + 2 \, c^{2} d f^{2} + 4 \, d^{3} - {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(2 \, d^{3} e^{2} - 4 \, c d^{2} e f + 2 \, c^{2} d f^{2} + 4 \, d^{3} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) + 6 \, {\left(d^{3} \cos\left(f x + e\right)^{2} - d^{3} \cos\left(f x + e\right) - 2 \, d^{3} - {\left(d^{3} \cos\left(f x + e\right) + 2 \, d^{3}\right)} \sin\left(f x + e\right)\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 6 \, {\left(d^{3} \cos\left(f x + e\right)^{2} - d^{3} \cos\left(f x + e\right) - 2 \, d^{3} - {\left(d^{3} \cos\left(f x + e\right) + 2 \, d^{3}\right)} \sin\left(f x + e\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(d^{3} f^{3} x^{3} + c^{3} f^{3} - 3 \, c^{2} d f^{2} + 3 \, {\left(c d^{2} f^{3} - d^{3} f^{2}\right)} x^{2} + 3 \, {\left(c^{2} d f^{3} - 2 \, c d^{2} f^{2}\right)} x - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + c^{3} f^{3} + 6 \, c d^{2} f + 3 \, {\left(c^{2} d f^{3} + 2 \, d^{3} f\right)} x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f^{4} \cos\left(f x + e\right)^{2} - a^{2} f^{4} \cos\left(f x + e\right) - 2 \, a^{2} f^{4} - {\left(a^{2} f^{4} \cos\left(f x + e\right) + 2 \, a^{2} f^{4}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(d^3*f^3*x^3 + c^3*f^3 + 3*c^2*d*f^2 + 3*(c*d^2*f^3 + d^3*f^2)*x^2 + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + c^3*f^3 + 6*c*d^2*f + 3*(c^2*d*f^3 + 2*d^3*f)*x)*cos(f*x + e)^2 + 3*(c^2*d*f^3 + 2*c*d^2*f^2)*x + (2*d^3*f^3*x^3 + 2*c^3*f^3 + 3*c^2*d*f^2 + 6*c*d^2*f + 3*(2*c*d^2*f^3 + d^3*f^2)*x^2 + 6*(c^2*d*f^3 + c*d^2*f^2 + d^3*f)*x)*cos(f*x + e) - (-12*I*d^3*f*x - 12*I*c*d^2*f + (6*I*d^3*f*x + 6*I*c*d^2*f)*cos(f*x + e)^2 + (-6*I*d^3*f*x - 6*I*c*d^2*f)*cos(f*x + e) + (-12*I*d^3*f*x - 12*I*c*d^2*f + (-6*I*d^3*f*x - 6*I*c*d^2*f)*cos(f*x + e))*sin(f*x + e))*dilog(I*cos(f*x + e) - sin(f*x + e)) - (12*I*d^3*f*x + 12*I*c*d^2*f + (-6*I*d^3*f*x - 6*I*c*d^2*f)*cos(f*x + e)^2 + (6*I*d^3*f*x + 6*I*c*d^2*f)*cos(f*x + e) + (12*I*d^3*f*x + 12*I*c*d^2*f + (6*I*d^3*f*x + 6*I*c*d^2*f)*cos(f*x + e))*sin(f*x + e))*dilog(-I*cos(f*x + e) - sin(f*x + e)) - 3*(2*d^3*e^2 - 4*c*d^2*e*f + 2*c^2*d*f^2 + 4*d^3 - (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + 2*d^3)*cos(f*x + e)^2 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + 2*d^3)*cos(f*x + e) + (2*d^3*e^2 - 4*c*d^2*e*f + 2*c^2*d*f^2 + 4*d^3 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + 2*d^3)*cos(f*x + e))*sin(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + I) - 3*(2*d^3*f^2*x^2 + 4*c*d^2*f^2*x - 2*d^3*e^2 + 4*c*d^2*e*f - (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e)^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e) + (2*d^3*f^2*x^2 + 4*c*d^2*f^2*x - 2*d^3*e^2 + 4*c*d^2*e*f + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e))*sin(f*x + e))*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(2*d^3*f^2*x^2 + 4*c*d^2*f^2*x - 2*d^3*e^2 + 4*c*d^2*e*f - (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e)^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e) + (2*d^3*f^2*x^2 + 4*c*d^2*f^2*x - 2*d^3*e^2 + 4*c*d^2*e*f + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e))*sin(f*x + e))*log(-I*cos(f*x + e) + sin(f*x + e) + 1) - 3*(2*d^3*e^2 - 4*c*d^2*e*f + 2*c^2*d*f^2 + 4*d^3 - (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + 2*d^3)*cos(f*x + e)^2 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + 2*d^3)*cos(f*x + e) + (2*d^3*e^2 - 4*c*d^2*e*f + 2*c^2*d*f^2 + 4*d^3 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + 2*d^3)*cos(f*x + e))*sin(f*x + e))*log(-cos(f*x + e) + I*sin(f*x + e) + I) + 6*(d^3*cos(f*x + e)^2 - d^3*cos(f*x + e) - 2*d^3 - (d^3*cos(f*x + e) + 2*d^3)*sin(f*x + e))*polylog(3, I*cos(f*x + e) - sin(f*x + e)) + 6*(d^3*cos(f*x + e)^2 - d^3*cos(f*x + e) - 2*d^3 - (d^3*cos(f*x + e) + 2*d^3)*sin(f*x + e))*polylog(3, -I*cos(f*x + e) - sin(f*x + e)) - (d^3*f^3*x^3 + c^3*f^3 - 3*c^2*d*f^2 + 3*(c*d^2*f^3 - d^3*f^2)*x^2 + 3*(c^2*d*f^3 - 2*c*d^2*f^2)*x - (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + c^3*f^3 + 6*c*d^2*f + 3*(c^2*d*f^3 + 2*d^3*f)*x)*cos(f*x + e))*sin(f*x + e))/(a^2*f^4*cos(f*x + e)^2 - a^2*f^4*cos(f*x + e) - 2*a^2*f^4 - (a^2*f^4*cos(f*x + e) + 2*a^2*f^4)*sin(f*x + e))","C",0
113,1,876,0,1.108619," ","integrate((d*x+c)^2/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{d^{2} f^{2} x^{2} + c^{2} f^{2} + 2 \, c d f + {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(c d f^{2} + d^{2} f\right)} x + 2 \, {\left(d^{2} f^{2} x^{2} + c^{2} f^{2} + c d f + d^{2} + {\left(2 \, c d f^{2} + d^{2} f\right)} x\right)} \cos\left(f x + e\right) - {\left(2 i \, d^{2} \cos\left(f x + e\right)^{2} - 2 i \, d^{2} \cos\left(f x + e\right) - 4 i \, d^{2} + {\left(-2 i \, d^{2} \cos\left(f x + e\right) - 4 i \, d^{2}\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) - {\left(-2 i \, d^{2} \cos\left(f x + e\right)^{2} + 2 i \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2} + {\left(2 i \, d^{2} \cos\left(f x + e\right) + 4 i \, d^{2}\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right)\right) + 2 \, {\left(2 \, d^{2} e - 2 \, c d f - {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right)^{2} + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right) + {\left(2 \, d^{2} e - 2 \, c d f + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - 2 \, {\left(2 \, d^{2} f x + 2 \, d^{2} e - {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right)^{2} + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right) + {\left(2 \, d^{2} f x + 2 \, d^{2} e + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) - 2 \, {\left(2 \, d^{2} f x + 2 \, d^{2} e - {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right)^{2} + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right) + {\left(2 \, d^{2} f x + 2 \, d^{2} e + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right) + 2 \, {\left(2 \, d^{2} e - 2 \, c d f - {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right)^{2} + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right) + {\left(2 \, d^{2} e - 2 \, c d f + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + i\right) - {\left(d^{2} f^{2} x^{2} + c^{2} f^{2} - 2 \, c d f + 2 \, {\left(c d f^{2} - d^{2} f\right)} x - {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f^{3} \cos\left(f x + e\right)^{2} - a^{2} f^{3} \cos\left(f x + e\right) - 2 \, a^{2} f^{3} - {\left(a^{2} f^{3} \cos\left(f x + e\right) + 2 \, a^{2} f^{3}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(d^2*f^2*x^2 + c^2*f^2 + 2*c*d*f + (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2)*cos(f*x + e)^2 + 2*(c*d*f^2 + d^2*f)*x + 2*(d^2*f^2*x^2 + c^2*f^2 + c*d*f + d^2 + (2*c*d*f^2 + d^2*f)*x)*cos(f*x + e) - (2*I*d^2*cos(f*x + e)^2 - 2*I*d^2*cos(f*x + e) - 4*I*d^2 + (-2*I*d^2*cos(f*x + e) - 4*I*d^2)*sin(f*x + e))*dilog(I*cos(f*x + e) - sin(f*x + e)) - (-2*I*d^2*cos(f*x + e)^2 + 2*I*d^2*cos(f*x + e) + 4*I*d^2 + (2*I*d^2*cos(f*x + e) + 4*I*d^2)*sin(f*x + e))*dilog(-I*cos(f*x + e) - sin(f*x + e)) + 2*(2*d^2*e - 2*c*d*f - (d^2*e - c*d*f)*cos(f*x + e)^2 + (d^2*e - c*d*f)*cos(f*x + e) + (2*d^2*e - 2*c*d*f + (d^2*e - c*d*f)*cos(f*x + e))*sin(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + I) - 2*(2*d^2*f*x + 2*d^2*e - (d^2*f*x + d^2*e)*cos(f*x + e)^2 + (d^2*f*x + d^2*e)*cos(f*x + e) + (2*d^2*f*x + 2*d^2*e + (d^2*f*x + d^2*e)*cos(f*x + e))*sin(f*x + e))*log(I*cos(f*x + e) + sin(f*x + e) + 1) - 2*(2*d^2*f*x + 2*d^2*e - (d^2*f*x + d^2*e)*cos(f*x + e)^2 + (d^2*f*x + d^2*e)*cos(f*x + e) + (2*d^2*f*x + 2*d^2*e + (d^2*f*x + d^2*e)*cos(f*x + e))*sin(f*x + e))*log(-I*cos(f*x + e) + sin(f*x + e) + 1) + 2*(2*d^2*e - 2*c*d*f - (d^2*e - c*d*f)*cos(f*x + e)^2 + (d^2*e - c*d*f)*cos(f*x + e) + (2*d^2*e - 2*c*d*f + (d^2*e - c*d*f)*cos(f*x + e))*sin(f*x + e))*log(-cos(f*x + e) + I*sin(f*x + e) + I) - (d^2*f^2*x^2 + c^2*f^2 - 2*c*d*f + 2*(c*d*f^2 - d^2*f)*x - (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*d^2)*cos(f*x + e))*sin(f*x + e))/(a^2*f^3*cos(f*x + e)^2 - a^2*f^3*cos(f*x + e) - 2*a^2*f^3 - (a^2*f^3*cos(f*x + e) + 2*a^2*f^3)*sin(f*x + e))","B",0
114,1,204,0,1.015029," ","integrate((d*x+c)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{d f x + {\left(d f x + c f\right)} \cos\left(f x + e\right)^{2} + c f + {\left(2 \, d f x + 2 \, c f + d\right)} \cos\left(f x + e\right) + {\left(d \cos\left(f x + e\right)^{2} - d \cos\left(f x + e\right) - {\left(d \cos\left(f x + e\right) + 2 \, d\right)} \sin\left(f x + e\right) - 2 \, d\right)} \log\left(\sin\left(f x + e\right) + 1\right) - {\left(d f x + c f - {\left(d f x + c f\right)} \cos\left(f x + e\right) - d\right)} \sin\left(f x + e\right) + d}{3 \, {\left(a^{2} f^{2} \cos\left(f x + e\right)^{2} - a^{2} f^{2} \cos\left(f x + e\right) - 2 \, a^{2} f^{2} - {\left(a^{2} f^{2} \cos\left(f x + e\right) + 2 \, a^{2} f^{2}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(d*f*x + (d*f*x + c*f)*cos(f*x + e)^2 + c*f + (2*d*f*x + 2*c*f + d)*cos(f*x + e) + (d*cos(f*x + e)^2 - d*cos(f*x + e) - (d*cos(f*x + e) + 2*d)*sin(f*x + e) - 2*d)*log(sin(f*x + e) + 1) - (d*f*x + c*f - (d*f*x + c*f)*cos(f*x + e) - d)*sin(f*x + e) + d)/(a^2*f^2*cos(f*x + e)^2 - a^2*f^2*cos(f*x + e) - 2*a^2*f^2 - (a^2*f^2*cos(f*x + e) + 2*a^2*f^2)*sin(f*x + e))","A",0
115,0,0,0,0.841777," ","integrate(1/(d*x+c)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{2 \, a^{2} d x + 2 \, a^{2} c - {\left(a^{2} d x + a^{2} c\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d x + a^{2} c\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(2*a^2*d*x + 2*a^2*c - (a^2*d*x + a^2*c)*cos(f*x + e)^2 + 2*(a^2*d*x + a^2*c)*sin(f*x + e)), x)","F",0
116,0,0,0,0.967460," ","integrate(1/(d*x+c)^2/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{2 \, a^{2} d^{2} x^{2} + 4 \, a^{2} c d x + 2 \, a^{2} c^{2} - {\left(a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(2*a^2*d^2*x^2 + 4*a^2*c*d*x + 2*a^2*c^2 - (a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2)*cos(f*x + e)^2 + 2*(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2)*sin(f*x + e)), x)","F",0
117,1,916,0,1.067111," ","integrate((d*x+c)^3/(a-a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3}\right)} \cos\left(f x + e\right) - {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \cos\left(f x + e\right) + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f + {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} \cos\left(f x + e\right) + {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} \sin\left(f x + e\right)\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 3 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \cos\left(f x + e\right) - {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right) - {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \sin\left(f x + e\right)\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \cos\left(f x + e\right) - {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} \sin\left(f x + e\right)\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 3 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} + {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \cos\left(f x + e\right) - {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 6 \, {\left(d^{3} \cos\left(f x + e\right) - d^{3} \sin\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + 6 \, {\left(d^{3} \cos\left(f x + e\right) - d^{3} \sin\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + c^{3} f^{3}\right)} \sin\left(f x + e\right)}{a f^{4} \cos\left(f x + e\right) - a f^{4} \sin\left(f x + e\right) + a f^{4}}"," ",0,"(d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3 + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3)*cos(f*x + e) - (-6*I*d^3*f*x - 6*I*c*d^2*f + (-6*I*d^3*f*x - 6*I*c*d^2*f)*cos(f*x + e) + (6*I*d^3*f*x + 6*I*c*d^2*f)*sin(f*x + e))*dilog(I*cos(f*x + e) + sin(f*x + e)) - (6*I*d^3*f*x + 6*I*c*d^2*f + (6*I*d^3*f*x + 6*I*c*d^2*f)*cos(f*x + e) + (-6*I*d^3*f*x - 6*I*c*d^2*f)*sin(f*x + e))*dilog(-I*cos(f*x + e) + sin(f*x + e)) + 3*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*cos(f*x + e) - (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*sin(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + I) + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e) - (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*sin(f*x + e))*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f + (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*cos(f*x + e) - (d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*sin(f*x + e))*log(-I*cos(f*x + e) - sin(f*x + e) + 1) + 3*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 + (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*cos(f*x + e) - (d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*sin(f*x + e))*log(-cos(f*x + e) - I*sin(f*x + e) + I) + 6*(d^3*cos(f*x + e) - d^3*sin(f*x + e) + d^3)*polylog(3, I*cos(f*x + e) + sin(f*x + e)) + 6*(d^3*cos(f*x + e) - d^3*sin(f*x + e) + d^3)*polylog(3, -I*cos(f*x + e) + sin(f*x + e)) + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + c^3*f^3)*sin(f*x + e))/(a*f^4*cos(f*x + e) - a*f^4*sin(f*x + e) + a*f^4)","C",0
118,1,496,0,0.895405," ","integrate((d*x+c)^2/(a-a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} \cos\left(f x + e\right) - {\left(-2 i \, d^{2} \cos\left(f x + e\right) + 2 i \, d^{2} \sin\left(f x + e\right) - 2 i \, d^{2}\right)} {\rm Li}_2\left(i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - {\left(2 i \, d^{2} \cos\left(f x + e\right) - 2 i \, d^{2} \sin\left(f x + e\right) + 2 i \, d^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(f x + e\right) + \sin\left(f x + e\right)\right) - 2 \, {\left(d^{2} e - c d f + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right) - {\left(d^{2} e - c d f\right)} \sin\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + 2 \, {\left(d^{2} f x + d^{2} e + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right) - {\left(d^{2} f x + d^{2} e\right)} \sin\left(f x + e\right)\right)} \log\left(i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) + 2 \, {\left(d^{2} f x + d^{2} e + {\left(d^{2} f x + d^{2} e\right)} \cos\left(f x + e\right) - {\left(d^{2} f x + d^{2} e\right)} \sin\left(f x + e\right)\right)} \log\left(-i \, \cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} e - c d f + {\left(d^{2} e - c d f\right)} \cos\left(f x + e\right) - {\left(d^{2} e - c d f\right)} \sin\left(f x + e\right)\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + i\right) + {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} \sin\left(f x + e\right)}{a f^{3} \cos\left(f x + e\right) - a f^{3} \sin\left(f x + e\right) + a f^{3}}"," ",0,"(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*cos(f*x + e) - (-2*I*d^2*cos(f*x + e) + 2*I*d^2*sin(f*x + e) - 2*I*d^2)*dilog(I*cos(f*x + e) + sin(f*x + e)) - (2*I*d^2*cos(f*x + e) - 2*I*d^2*sin(f*x + e) + 2*I*d^2)*dilog(-I*cos(f*x + e) + sin(f*x + e)) - 2*(d^2*e - c*d*f + (d^2*e - c*d*f)*cos(f*x + e) - (d^2*e - c*d*f)*sin(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + I) + 2*(d^2*f*x + d^2*e + (d^2*f*x + d^2*e)*cos(f*x + e) - (d^2*f*x + d^2*e)*sin(f*x + e))*log(I*cos(f*x + e) - sin(f*x + e) + 1) + 2*(d^2*f*x + d^2*e + (d^2*f*x + d^2*e)*cos(f*x + e) - (d^2*f*x + d^2*e)*sin(f*x + e))*log(-I*cos(f*x + e) - sin(f*x + e) + 1) - 2*(d^2*e - c*d*f + (d^2*e - c*d*f)*cos(f*x + e) - (d^2*e - c*d*f)*sin(f*x + e))*log(-cos(f*x + e) - I*sin(f*x + e) + I) + (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*sin(f*x + e))/(a*f^3*cos(f*x + e) - a*f^3*sin(f*x + e) + a*f^3)","B",0
119,1,101,0,1.039597," ","integrate((d*x+c)/(a-a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{d f x + c f + {\left(d f x + c f\right)} \cos\left(f x + e\right) + {\left(d \cos\left(f x + e\right) - d \sin\left(f x + e\right) + d\right)} \log\left(-\sin\left(f x + e\right) + 1\right) + {\left(d f x + c f\right)} \sin\left(f x + e\right)}{a f^{2} \cos\left(f x + e\right) - a f^{2} \sin\left(f x + e\right) + a f^{2}}"," ",0,"(d*f*x + c*f + (d*f*x + c*f)*cos(f*x + e) + (d*cos(f*x + e) - d*sin(f*x + e) + d)*log(-sin(f*x + e) + 1) + (d*f*x + c*f)*sin(f*x + e))/(a*f^2*cos(f*x + e) - a*f^2*sin(f*x + e) + a*f^2)","B",0
120,0,0,0,0.813820," ","integrate(1/(d*x+c)/(a-a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c - {\left(a d x + a c\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c - (a*d*x + a*c)*sin(f*x + e)), x)","F",0
121,0,0,0,0.866261," ","integrate(1/(d*x+c)^2/(a-a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} - {\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 - (a*d^2*x^2 + 2*a*c*d*x + a*c^2)*sin(f*x + e)), x)","F",0
122,-2,0,0,0.000000," ","integrate(x^3*(a+a*sin(d*x+c))^(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
123,-2,0,0,0.000000," ","integrate(x^2*(a+a*sin(d*x+c))^(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
124,-2,0,0,0.000000," ","integrate(x*(a+a*sin(d*x+c))^(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
125,-2,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/x,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
126,-2,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/x^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
127,-2,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/2)/x^3,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
128,-2,0,0,0.000000," ","integrate(x^3*(a+a*sin(f*x+e))^(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
129,-2,0,0,0.000000," ","integrate(x^2*(a+a*sin(f*x+e))^(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
130,-2,0,0,0.000000," ","integrate(x*(a+a*sin(f*x+e))^(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
131,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/x,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
132,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/x^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
133,-2,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(3/2)/x^3,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
134,0,0,0,0.902726," ","integrate(x^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x^3/sqrt(a*sin(d*x + c) + a), x)","F",0
135,0,0,0,0.631495," ","integrate(x^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x^2/sqrt(a*sin(d*x + c) + a), x)","F",0
136,0,0,0,0.862613," ","integrate(x/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{a \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x/sqrt(a*sin(d*x + c) + a), x)","F",0
137,0,0,0,0.847548," ","integrate(1/x/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sin\left(d x + c\right) + a}}{a x \sin\left(d x + c\right) + a x}, x\right)"," ",0,"integral(sqrt(a*sin(d*x + c) + a)/(a*x*sin(d*x + c) + a*x), x)","F",0
138,0,0,0,0.914191," ","integrate(1/x^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sin\left(d x + c\right) + a}}{a x^{2} \sin\left(d x + c\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(a*sin(d*x + c) + a)/(a*x^2*sin(d*x + c) + a*x^2), x)","F",0
139,0,0,0,0.869586," ","integrate(x^3/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} x^{3}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*x^3/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
140,0,0,0,0.917475," ","integrate(x^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} x^{2}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*x^2/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
141,0,0,0,0.768720," ","integrate(x/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} x}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*x/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
142,0,0,0,1.096648," ","integrate(1/x/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a}}{a^{2} x \cos\left(f x + e\right)^{2} - 2 \, a^{2} x \sin\left(f x + e\right) - 2 \, a^{2} x}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)/(a^2*x*cos(f*x + e)^2 - 2*a^2*x*sin(f*x + e) - 2*a^2*x), x)","F",0
143,0,0,0,0.836544," ","integrate(1/x^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a}}{a^{2} x^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} x^{2} \sin\left(f x + e\right) - 2 \, a^{2} x^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)/(a^2*x^2*cos(f*x + e)^2 - 2*a^2*x^2*sin(f*x + e) - 2*a^2*x^2), x)","F",0
144,-2,0,0,0.000000," ","integrate((a+a*sin(d*x+c))^(1/3)/x,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
145,0,0,0,0.935802," ","integrate((d*x+c)^m*(a+a*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(a \sin\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(a*sin(f*x + e) + a)^n, x)","F",0
146,1,378,0,0.962003," ","integrate((d*x+c)^m*(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} d m + a^{3} d\right)} e^{\left(-\frac{d m \log\left(\frac{3 i \, f}{d}\right) + 3 i \, d e - 3 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, d f x + 3 i \, c f}{d}\right) + {\left(-9 i \, a^{3} d m - 9 i \, a^{3} d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) - 45 \, {\left(a^{3} d m + a^{3} d\right)} e^{\left(-\frac{d m \log\left(\frac{i \, f}{d}\right) + i \, d e - i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, c f}{d}\right) - 45 \, {\left(a^{3} d m + a^{3} d\right)} e^{\left(-\frac{d m \log\left(-\frac{i \, f}{d}\right) - i \, d e + i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, c f}{d}\right) + {\left(9 i \, a^{3} d m + 9 i \, a^{3} d\right)} e^{\left(-\frac{d m \log\left(-\frac{2 i \, f}{d}\right) - 2 i \, d e + 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, d f x - 2 i \, c f}{d}\right) + {\left(a^{3} d m + a^{3} d\right)} e^{\left(-\frac{d m \log\left(-\frac{3 i \, f}{d}\right) - 3 i \, d e + 3 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, d f x - 3 i \, c f}{d}\right) + 60 \, {\left(a^{3} d f x + a^{3} c f\right)} {\left(d x + c\right)}^{m}}{24 \, {\left(d f m + d f\right)}}"," ",0,"1/24*((a^3*d*m + a^3*d)*e^(-(d*m*log(3*I*f/d) + 3*I*d*e - 3*I*c*f)/d)*gamma(m + 1, (3*I*d*f*x + 3*I*c*f)/d) + (-9*I*a^3*d*m - 9*I*a^3*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) - 45*(a^3*d*m + a^3*d)*e^(-(d*m*log(I*f/d) + I*d*e - I*c*f)/d)*gamma(m + 1, (I*d*f*x + I*c*f)/d) - 45*(a^3*d*m + a^3*d)*e^(-(d*m*log(-I*f/d) - I*d*e + I*c*f)/d)*gamma(m + 1, (-I*d*f*x - I*c*f)/d) + (9*I*a^3*d*m + 9*I*a^3*d)*e^(-(d*m*log(-2*I*f/d) - 2*I*d*e + 2*I*c*f)/d)*gamma(m + 1, (-2*I*d*f*x - 2*I*c*f)/d) + (a^3*d*m + a^3*d)*e^(-(d*m*log(-3*I*f/d) - 3*I*d*e + 3*I*c*f)/d)*gamma(m + 1, (-3*I*d*f*x - 3*I*c*f)/d) + 60*(a^3*d*f*x + a^3*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
147,1,266,0,1.114912," ","integrate((d*x+c)^m*(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, a^{2} d m - i \, a^{2} d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) - 8 \, {\left(a^{2} d m + a^{2} d\right)} e^{\left(-\frac{d m \log\left(\frac{i \, f}{d}\right) + i \, d e - i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, c f}{d}\right) - 8 \, {\left(a^{2} d m + a^{2} d\right)} e^{\left(-\frac{d m \log\left(-\frac{i \, f}{d}\right) - i \, d e + i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, c f}{d}\right) + {\left(i \, a^{2} d m + i \, a^{2} d\right)} e^{\left(-\frac{d m \log\left(-\frac{2 i \, f}{d}\right) - 2 i \, d e + 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, d f x - 2 i \, c f}{d}\right) + 12 \, {\left(a^{2} d f x + a^{2} c f\right)} {\left(d x + c\right)}^{m}}{8 \, {\left(d f m + d f\right)}}"," ",0,"1/8*((-I*a^2*d*m - I*a^2*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) - 8*(a^2*d*m + a^2*d)*e^(-(d*m*log(I*f/d) + I*d*e - I*c*f)/d)*gamma(m + 1, (I*d*f*x + I*c*f)/d) - 8*(a^2*d*m + a^2*d)*e^(-(d*m*log(-I*f/d) - I*d*e + I*c*f)/d)*gamma(m + 1, (-I*d*f*x - I*c*f)/d) + (I*a^2*d*m + I*a^2*d)*e^(-(d*m*log(-2*I*f/d) - 2*I*d*e + 2*I*c*f)/d)*gamma(m + 1, (-2*I*d*f*x - 2*I*c*f)/d) + 12*(a^2*d*f*x + a^2*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
148,1,136,0,1.063147," ","integrate((d*x+c)^m*(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a d m + a d\right)} e^{\left(-\frac{d m \log\left(\frac{i \, f}{d}\right) + i \, d e - i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, c f}{d}\right) + {\left(a d m + a d\right)} e^{\left(-\frac{d m \log\left(-\frac{i \, f}{d}\right) - i \, d e + i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, c f}{d}\right) - 2 \, {\left(a d f x + a c f\right)} {\left(d x + c\right)}^{m}}{2 \, {\left(d f m + d f\right)}}"," ",0,"-1/2*((a*d*m + a*d)*e^(-(d*m*log(I*f/d) + I*d*e - I*c*f)/d)*gamma(m + 1, (I*d*f*x + I*c*f)/d) + (a*d*m + a*d)*e^(-(d*m*log(-I*f/d) - I*d*e + I*c*f)/d)*gamma(m + 1, (-I*d*f*x - I*c*f)/d) - 2*(a*d*f*x + a*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
149,0,0,0,0.827487," ","integrate((d*x+c)^m/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(a*sin(f*x + e) + a), x)","F",0
150,0,0,0,0.851309," ","integrate((d*x+c)^m/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x + c\right)}^{m}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(d*x + c)^m/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
151,1,168,0,0.914237," ","integrate((d*x+c)^3*(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + b c^{3} f^{3} - 6 \, b c d^{2} f + 3 \, {\left(b c^{2} d f^{3} - 2 \, b d^{3} f\right)} x\right)} \cos\left(f x + e\right) + 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2} - 2 \, b d^{3}\right)} \sin\left(f x + e\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x - 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + b*c^3*f^3 - 6*b*c*d^2*f + 3*(b*c^2*d*f^3 - 2*b*d^3*f)*x)*cos(f*x + e) + 12*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2 - 2*b*d^3)*sin(f*x + e))/f^4","A",0
152,1,102,0,0.800712," ","integrate((d*x+c)^2*(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{2} f^{3} x^{3} + 3 \, a c d f^{3} x^{2} + 3 \, a c^{2} f^{3} x - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2} - 2 \, b d^{2}\right)} \cos\left(f x + e\right) + 6 \, {\left(b d^{2} f x + b c d f\right)} \sin\left(f x + e\right)}{3 \, f^{3}}"," ",0,"1/3*(a*d^2*f^3*x^3 + 3*a*c*d*f^3*x^2 + 3*a*c^2*f^3*x - 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2 - 2*b*d^2)*cos(f*x + e) + 6*(b*d^2*f*x + b*c*d*f)*sin(f*x + e))/f^3","A",0
153,1,51,0,0.713973," ","integrate((d*x+c)*(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x + 2 \, b d \sin\left(f x + e\right) - 2 \, {\left(b d f x + b c f\right)} \cos\left(f x + e\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x + 2*b*d*sin(f*x + e) - 2*(b*d*f*x + b*c*f)*cos(f*x + e))/f^2","A",0
154,1,93,0,0.939849," ","integrate((a+b*sin(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, b \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, a \log\left(d x + c\right) - {\left(b \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + b \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{2 \, d}"," ",0,"1/2*(2*b*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*a*log(d*x + c) - (b*cos_integral((d*f*x + c*f)/d) + b*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/d","A",0
155,1,135,0,0.876005," ","integrate((a+b*sin(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, b d \sin\left(f x + e\right) - 2 \, {\left(b d f x + b c f\right)} \sin\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, a d - {\left({\left(b d f x + b c f\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(b d f x + b c f\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*b*d*sin(f*x + e) - 2*(b*d*f*x + b*c*f)*sin(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*a*d - ((b*d*f*x + b*c*f)*cos_integral((d*f*x + c*f)/d) + (b*d*f*x + b*c*f)*cos_integral(-(d*f*x + c*f)/d))*cos(-(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
156,1,228,0,0.762614," ","integrate((a+b*sin(f*x+e))/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, b d^{2} \sin\left(f x + e\right) + 2 \, a d^{2} + 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + 2 \, {\left(b d^{2} f x + b c d f\right)} \cos\left(f x + e\right) - {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*b*d^2*sin(f*x + e) + 2*a*d^2 + 2*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 2*(b*d^2*f*x + b*c*d*f)*cos(f*x + e) - ((b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*cos_integral((d*f*x + c*f)/d) + (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
157,1,382,0,0.903120," ","integrate((d*x+c)^3*(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d^{3} f^{4} x^{4} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} c d^{2} f^{4} x^{3} + 3 \, {\left(2 \, {\left(2 \, a^{2} + b^{2}\right)} c^{2} d f^{4} + b^{2} d^{3} f^{2}\right)} x^{2} - 3 \, {\left(2 \, b^{2} d^{3} f^{2} x^{2} + 4 \, b^{2} c d^{2} f^{2} x + 2 \, b^{2} c^{2} d f^{2} - b^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} + b^{2}\right)} c^{3} f^{4} + 3 \, b^{2} c d^{2} f^{2}\right)} x - 16 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b c d^{2} f^{3} x^{2} + a b c^{3} f^{3} - 6 \, a b c d^{2} f + 3 \, {\left(a b c^{2} d f^{3} - 2 \, a b d^{3} f\right)} x\right)} \cos\left(f x + e\right) + 2 \, {\left(24 \, a b d^{3} f^{2} x^{2} + 48 \, a b c d^{2} f^{2} x + 24 \, a b c^{2} d f^{2} - 48 \, a b d^{3} - {\left(2 \, b^{2} d^{3} f^{3} x^{3} + 6 \, b^{2} c d^{2} f^{3} x^{2} + 2 \, b^{2} c^{3} f^{3} - 3 \, b^{2} c d^{2} f + 3 \, {\left(2 \, b^{2} c^{2} d f^{3} - b^{2} d^{3} f\right)} x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{8 \, f^{4}}"," ",0,"1/8*((2*a^2 + b^2)*d^3*f^4*x^4 + 4*(2*a^2 + b^2)*c*d^2*f^4*x^3 + 3*(2*(2*a^2 + b^2)*c^2*d*f^4 + b^2*d^3*f^2)*x^2 - 3*(2*b^2*d^3*f^2*x^2 + 4*b^2*c*d^2*f^2*x + 2*b^2*c^2*d*f^2 - b^2*d^3)*cos(f*x + e)^2 + 2*(2*(2*a^2 + b^2)*c^3*f^4 + 3*b^2*c*d^2*f^2)*x - 16*(a*b*d^3*f^3*x^3 + 3*a*b*c*d^2*f^3*x^2 + a*b*c^3*f^3 - 6*a*b*c*d^2*f + 3*(a*b*c^2*d*f^3 - 2*a*b*d^3*f)*x)*cos(f*x + e) + 2*(24*a*b*d^3*f^2*x^2 + 48*a*b*c*d^2*f^2*x + 24*a*b*c^2*d*f^2 - 48*a*b*d^3 - (2*b^2*d^3*f^3*x^3 + 6*b^2*c*d^2*f^3*x^2 + 2*b^2*c^3*f^3 - 3*b^2*c*d^2*f + 3*(2*b^2*c^2*d*f^3 - b^2*d^3*f)*x)*cos(f*x + e))*sin(f*x + e))/f^4","A",0
158,1,226,0,0.984876," ","integrate((d*x+c)^2*(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} f^{3} x^{3} + 6 \, {\left(2 \, a^{2} + b^{2}\right)} c d f^{3} x^{2} - 6 \, {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, {\left(2 \, a^{2} + b^{2}\right)} c^{2} f^{3} + b^{2} d^{2} f\right)} x - 24 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2} - 2 \, a b d^{2}\right)} \cos\left(f x + e\right) + 3 \, {\left(16 \, a b d^{2} f x + 16 \, a b c d f - {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 4 \, b^{2} c d f^{2} x + 2 \, b^{2} c^{2} f^{2} - b^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, f^{3}}"," ",0,"1/12*(2*(2*a^2 + b^2)*d^2*f^3*x^3 + 6*(2*a^2 + b^2)*c*d*f^3*x^2 - 6*(b^2*d^2*f*x + b^2*c*d*f)*cos(f*x + e)^2 + 3*(2*(2*a^2 + b^2)*c^2*f^3 + b^2*d^2*f)*x - 24*(a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2 - 2*a*b*d^2)*cos(f*x + e) + 3*(16*a*b*d^2*f*x + 16*a*b*c*d*f - (2*b^2*d^2*f^2*x^2 + 4*b^2*c*d*f^2*x + 2*b^2*c^2*f^2 - b^2*d^2)*cos(f*x + e))*sin(f*x + e))/f^3","A",0
159,1,109,0,0.882577," ","integrate((d*x+c)*(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d f^{2} x^{2} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} c f^{2} x - b^{2} d \cos\left(f x + e\right)^{2} - 8 \, {\left(a b d f x + a b c f\right)} \cos\left(f x + e\right) + 2 \, {\left(4 \, a b d - {\left(b^{2} d f x + b^{2} c f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, f^{2}}"," ",0,"1/4*((2*a^2 + b^2)*d*f^2*x^2 + 2*(2*a^2 + b^2)*c*f^2*x - b^2*d*cos(f*x + e)^2 - 8*(a*b*d*f*x + a*b*c*f)*cos(f*x + e) + 2*(4*a*b*d - (b^2*d*f*x + b^2*c*f)*cos(f*x + e))*sin(f*x + e))/f^2","A",0
160,1,189,0,0.745270," ","integrate((a+b*sin(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, b^{2} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 8 \, a b \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) + {\left(b^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + b^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(d x + c\right) + 4 \, {\left(a b \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + a b \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{4 \, d}"," ",0,"-1/4*(2*b^2*sin(-2*(d*e - c*f)/d)*sin_integral(2*(d*f*x + c*f)/d) - 8*a*b*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + (b^2*cos_integral(2*(d*f*x + c*f)/d) + b^2*cos_integral(-2*(d*f*x + c*f)/d))*cos(-2*(d*e - c*f)/d) - 2*(2*a^2 + b^2)*log(d*x + c) + 4*(a*b*cos_integral((d*f*x + c*f)/d) + a*b*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/d","A",0
161,1,281,0,0.934338," ","integrate((a+b*sin(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} d \cos\left(f x + e\right)^{2} - 4 \, a b d \sin\left(f x + e\right) + 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 4 \, {\left(a b d f x + a b c f\right)} \sin\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) - 2 \, {\left(a^{2} + b^{2}\right)} d + 2 \, {\left({\left(a b d f x + a b c f\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(a b d f x + a b c f\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \cos\left(-\frac{d e - c f}{d}\right) - {\left({\left(b^{2} d f x + b^{2} c f\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(b^{2} d f x + b^{2} c f\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/2*(2*b^2*d*cos(f*x + e)^2 - 4*a*b*d*sin(f*x + e) + 2*(b^2*d*f*x + b^2*c*f)*cos(-2*(d*e - c*f)/d)*sin_integral(2*(d*f*x + c*f)/d) + 4*(a*b*d*f*x + a*b*c*f)*sin(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) - 2*(a^2 + b^2)*d + 2*((a*b*d*f*x + a*b*c*f)*cos_integral((d*f*x + c*f)/d) + (a*b*d*f*x + a*b*c*f)*cos_integral(-(d*f*x + c*f)/d))*cos(-(d*e - c*f)/d) - ((b^2*d*f*x + b^2*c*f)*cos_integral(2*(d*f*x + c*f)/d) + (b^2*d*f*x + b^2*c*f)*cos_integral(-2*(d*f*x + c*f)/d))*sin(-2*(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
162,1,467,0,1.050017," ","integrate((a+b*sin(f*x+e))^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{b^{2} d^{2} \cos\left(f x + e\right)^{2} - {\left(a^{2} + b^{2}\right)} d^{2} + 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} \cos\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\right) - 2 \, {\left(a b d^{2} f x + a b c d f\right)} \cos\left(f x + e\right) + {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 2 \, {\left(a b d^{2} + {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) + {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{d f x + c f}{d}\right) + {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{d f x + c f}{d}\right)\right)} \sin\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*(b^2*d^2*cos(f*x + e)^2 - (a^2 + b^2)*d^2 + 2*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*sin(-2*(d*e - c*f)/d)*sin_integral(2*(d*f*x + c*f)/d) - 2*(a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*cos(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) - 2*(a*b*d^2*f*x + a*b*c*d*f)*cos(f*x + e) + ((b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*cos_integral(2*(d*f*x + c*f)/d) + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*cos_integral(-2*(d*f*x + c*f)/d))*cos(-2*(d*e - c*f)/d) - 2*(a*b*d^2 + (b^2*d^2*f*x + b^2*c*d*f)*cos(f*x + e))*sin(f*x + e) + ((a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*cos_integral((d*f*x + c*f)/d) + (a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*cos_integral(-(d*f*x + c*f)/d))*sin(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
163,1,2177,0,1.352247," ","integrate((d*x+c)^3/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{12 i \, b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b d^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-3 i \, b d^{3} f^{2} x^{2} - 6 i \, b c d^{2} f^{2} x - 3 i \, b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, b d^{3} f^{2} x^{2} + 6 i \, b c d^{2} f^{2} x + 3 i \, b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, b d^{3} f^{2} x^{2} + 6 i \, b c d^{2} f^{2} x + 3 i \, b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-3 i \, b d^{3} f^{2} x^{2} - 6 i \, b c d^{2} f^{2} x - 3 i \, b c^{2} d f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{4 \, {\left(a^{2} - b^{2}\right)} f^{4}}"," ",0,"-1/4*(12*I*b*d^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*d^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*d^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b*d^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-3*I*b*d^3*f^2*x^2 - 6*I*b*c*d^2*f^2*x - 3*I*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*b*d^3*f^2*x^2 + 6*I*b*c*d^2*f^2*x + 3*I*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*b*d^3*f^2*x^2 + 6*I*b*c*d^2*f^2*x + 3*I*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-3*I*b*d^3*f^2*x^2 - 6*I*b*c*d^2*f^2*x - 3*I*b*c^2*d*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 12*(b*d^3*f*x + b*c*d^2*f)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b*d^3*f*x + b*c*d^2*f)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b*d^3*f*x + b*c*d^2*f)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b*d^3*f*x + b*c*d^2*f)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b))/((a^2 - b^2)*f^4)","C",0
164,1,1543,0,1.359427," ","integrate((d*x+c)^2/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, b d^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - {\left(-2 i \, b d^{2} f x - 2 i \, b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(2 i \, b d^{2} f x + 2 i \, b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(2 i \, b d^{2} f x + 2 i \, b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-2 i \, b d^{2} f x - 2 i \, b c d f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{2 \, {\left(a^{2} - b^{2}\right)} f^{3}}"," ",0,"1/2*(2*b*d^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 2*b*d^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*b*d^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 2*b*d^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - (-2*I*b*d^2*f*x - 2*I*b*c*d*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (2*I*b*d^2*f*x + 2*I*b*c*d*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (2*I*b*d^2*f*x + 2*I*b*c*d*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-2*I*b*d^2*f*x - 2*I*b*c*d*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2 - b^2)*f^3)","C",0
165,1,1001,0,1.236858," ","integrate((d*x+c)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{-2 i \, b d \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b d \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b d \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b d \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d f x + b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d f x + b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b d e\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{4 \, {\left(a^{2} - b^{2}\right)} f^{2}}"," ",0,"-1/4*(-2*I*b*d*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*d*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*d*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b*d*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d*f*x + b*d*e)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*d*e)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d*f*x + b*d*e)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*d*e)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2 - b^2)*f^2)","B",0
166,0,0,0,0.737425," ","integrate(1/(d*x+c)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*sin(f*x + e)), x)","F",0
167,0,0,0,0.593743," ","integrate(1/(d*x+c)^2/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sin(f*x + e)), x)","F",0
168,1,5116,0,2.063007," ","integrate((d*x+c)^3/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(-6 i \, a b^{2} d^{3} \sin\left(f x + e\right) - 6 i \, a^{2} b d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(6 i \, a b^{2} d^{3} \sin\left(f x + e\right) + 6 i \, a^{2} b d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(6 i \, a b^{2} d^{3} \sin\left(f x + e\right) + 6 i \, a^{2} b d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-6 i \, a b^{2} d^{3} \sin\left(f x + e\right) - 6 i \, a^{2} b d^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d f^{3} x + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \cos\left(f x + e\right) + {\left(12 i \, {\left(a^{3} - a b^{2}\right)} d^{3} f x + 12 i \, {\left(a^{3} - a b^{2}\right)} c d^{2} f + {\left(12 i \, {\left(a^{2} b - b^{3}\right)} d^{3} f x + 12 i \, {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(f x + e\right) + 2 \, {\left(3 i \, a^{2} b d^{3} f^{2} x^{2} + 6 i \, a^{2} b c d^{2} f^{2} x + 3 i \, a^{2} b c^{2} d f^{2} + {\left(3 i \, a b^{2} d^{3} f^{2} x^{2} + 6 i \, a b^{2} c d^{2} f^{2} x + 3 i \, a b^{2} c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(12 i \, {\left(a^{3} - a b^{2}\right)} d^{3} f x + 12 i \, {\left(a^{3} - a b^{2}\right)} c d^{2} f + {\left(12 i \, {\left(a^{2} b - b^{3}\right)} d^{3} f x + 12 i \, {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(f x + e\right) + 2 \, {\left(-3 i \, a^{2} b d^{3} f^{2} x^{2} - 6 i \, a^{2} b c d^{2} f^{2} x - 3 i \, a^{2} b c^{2} d f^{2} + {\left(-3 i \, a b^{2} d^{3} f^{2} x^{2} - 6 i \, a b^{2} c d^{2} f^{2} x - 3 i \, a b^{2} c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-12 i \, {\left(a^{3} - a b^{2}\right)} d^{3} f x - 12 i \, {\left(a^{3} - a b^{2}\right)} c d^{2} f + {\left(-12 i \, {\left(a^{2} b - b^{3}\right)} d^{3} f x - 12 i \, {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(f x + e\right) + 2 \, {\left(-3 i \, a^{2} b d^{3} f^{2} x^{2} - 6 i \, a^{2} b c d^{2} f^{2} x - 3 i \, a^{2} b c^{2} d f^{2} + {\left(-3 i \, a b^{2} d^{3} f^{2} x^{2} - 6 i \, a b^{2} c d^{2} f^{2} x - 3 i \, a b^{2} c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-12 i \, {\left(a^{3} - a b^{2}\right)} d^{3} f x - 12 i \, {\left(a^{3} - a b^{2}\right)} c d^{2} f + {\left(-12 i \, {\left(a^{2} b - b^{3}\right)} d^{3} f x - 12 i \, {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \sin\left(f x + e\right) + 2 \, {\left(3 i \, a^{2} b d^{3} f^{2} x^{2} + 6 i \, a^{2} b c d^{2} f^{2} x + 3 i \, a^{2} b c^{2} d f^{2} + {\left(3 i \, a b^{2} d^{3} f^{2} x^{2} + 6 i \, a b^{2} c d^{2} f^{2} x + 3 i \, a b^{2} c^{2} d f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(3 \, {\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{3} - {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{3} + {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{3} - {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{3} + {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{4 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} \sin\left(f x + e\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{4}\right)}}"," ",0,"1/4*(2*(-6*I*a*b^2*d^3*sin(f*x + e) - 6*I*a^2*b*d^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(6*I*a*b^2*d^3*sin(f*x + e) + 6*I*a^2*b*d^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(6*I*a*b^2*d^3*sin(f*x + e) + 6*I*a^2*b*d^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-6*I*a*b^2*d^3*sin(f*x + e) - 6*I*a^2*b*d^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*c*d^2*f^3*x^2 + 3*(a^2*b - b^3)*c^2*d*f^3*x + (a^2*b - b^3)*c^3*f^3)*cos(f*x + e) + (12*I*(a^3 - a*b^2)*d^3*f*x + 12*I*(a^3 - a*b^2)*c*d^2*f + (12*I*(a^2*b - b^3)*d^3*f*x + 12*I*(a^2*b - b^3)*c*d^2*f)*sin(f*x + e) + 2*(3*I*a^2*b*d^3*f^2*x^2 + 6*I*a^2*b*c*d^2*f^2*x + 3*I*a^2*b*c^2*d*f^2 + (3*I*a*b^2*d^3*f^2*x^2 + 6*I*a*b^2*c*d^2*f^2*x + 3*I*a*b^2*c^2*d*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (12*I*(a^3 - a*b^2)*d^3*f*x + 12*I*(a^3 - a*b^2)*c*d^2*f + (12*I*(a^2*b - b^3)*d^3*f*x + 12*I*(a^2*b - b^3)*c*d^2*f)*sin(f*x + e) + 2*(-3*I*a^2*b*d^3*f^2*x^2 - 6*I*a^2*b*c*d^2*f^2*x - 3*I*a^2*b*c^2*d*f^2 + (-3*I*a*b^2*d^3*f^2*x^2 - 6*I*a*b^2*c*d^2*f^2*x - 3*I*a*b^2*c^2*d*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-12*I*(a^3 - a*b^2)*d^3*f*x - 12*I*(a^3 - a*b^2)*c*d^2*f + (-12*I*(a^2*b - b^3)*d^3*f*x - 12*I*(a^2*b - b^3)*c*d^2*f)*sin(f*x + e) + 2*(-3*I*a^2*b*d^3*f^2*x^2 - 6*I*a^2*b*c*d^2*f^2*x - 3*I*a^2*b*c^2*d*f^2 + (-3*I*a*b^2*d^3*f^2*x^2 - 6*I*a*b^2*c*d^2*f^2*x - 3*I*a*b^2*c^2*d*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-12*I*(a^3 - a*b^2)*d^3*f*x - 12*I*(a^3 - a*b^2)*c*d^2*f + (-12*I*(a^2*b - b^3)*d^3*f*x - 12*I*(a^2*b - b^3)*c*d^2*f)*sin(f*x + e) + 2*(3*I*a^2*b*d^3*f^2*x^2 + 6*I*a^2*b*c*d^2*f^2*x + 3*I*a^2*b*c^2*d*f^2 + (3*I*a*b^2*d^3*f^2*x^2 + 6*I*a*b^2*c*d^2*f^2*x + 3*I*a*b^2*c^2*d*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(3*(a^3 - a*b^2)*d^3*e^2 - 6*(a^3 - a*b^2)*c*d^2*e*f + 3*(a^3 - a*b^2)*c^2*d*f^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*sin(f*x + e) + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(3*(a^3 - a*b^2)*d^3*e^2 - 6*(a^3 - a*b^2)*c*d^2*e*f + 3*(a^3 - a*b^2)*c^2*d*f^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*sin(f*x + e) + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(3*(a^3 - a*b^2)*d^3*e^2 - 6*(a^3 - a*b^2)*c*d^2*e*f + 3*(a^3 - a*b^2)*c^2*d*f^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*sin(f*x + e) - (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(3*(a^3 - a*b^2)*d^3*e^2 - 6*(a^3 - a*b^2)*c*d^2*e*f + 3*(a^3 - a*b^2)*c^2*d*f^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*sin(f*x + e) - (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(3*(a^3 - a*b^2)*d^3*f^2*x^2 + 6*(a^3 - a*b^2)*c*d^2*f^2*x - 3*(a^3 - a*b^2)*d^3*e^2 + 6*(a^3 - a*b^2)*c*d^2*e*f + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*sin(f*x + e) + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(3*(a^3 - a*b^2)*d^3*f^2*x^2 + 6*(a^3 - a*b^2)*c*d^2*f^2*x - 3*(a^3 - a*b^2)*d^3*e^2 + 6*(a^3 - a*b^2)*c*d^2*e*f + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*sin(f*x + e) - (a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(3*(a^3 - a*b^2)*d^3*f^2*x^2 + 6*(a^3 - a*b^2)*c*d^2*f^2*x - 3*(a^3 - a*b^2)*d^3*e^2 + 6*(a^3 - a*b^2)*c*d^2*e*f + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*sin(f*x + e) + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(3*(a^3 - a*b^2)*d^3*f^2*x^2 + 6*(a^3 - a*b^2)*c*d^2*f^2*x - 3*(a^3 - a*b^2)*d^3*e^2 + 6*(a^3 - a*b^2)*c*d^2*e*f + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*sin(f*x + e) - (a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 12*((a^2*b - b^3)*d^3*sin(f*x + e) + (a^3 - a*b^2)*d^3 - (a^2*b*d^3*f*x + a^2*b*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*((a^2*b - b^3)*d^3*sin(f*x + e) + (a^3 - a*b^2)*d^3 + (a^2*b*d^3*f*x + a^2*b*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*((a^2*b - b^3)*d^3*sin(f*x + e) + (a^3 - a*b^2)*d^3 - (a^2*b*d^3*f*x + a^2*b*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*((a^2*b - b^3)*d^3*sin(f*x + e) + (a^3 - a*b^2)*d^3 + (a^2*b*d^3*f*x + a^2*b*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b))/((a^4*b - 2*a^2*b^3 + b^5)*f^4*sin(f*x + e) + (a^5 - 2*a^3*b^2 + a*b^4)*f^4)","C",0
169,1,3095,0,1.496473," ","integrate((d*x+c)^2/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{2} d^{2} \sin\left(f x + e\right) + a^{2} b d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a b^{2} d^{2} \sin\left(f x + e\right) + a^{2} b d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a b^{2} d^{2} \sin\left(f x + e\right) + a^{2} b d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a b^{2} d^{2} \sin\left(f x + e\right) + a^{2} b d^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(f x + e\right) + a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d f^{2} x + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cos\left(f x + e\right) + {\left(4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} \sin\left(f x + e\right) + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} + 2 \, {\left(2 i \, a^{2} b d^{2} f x + 2 i \, a^{2} b c d f + {\left(2 i \, a b^{2} d^{2} f x + 2 i \, a b^{2} c d f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} \sin\left(f x + e\right) + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} + 2 \, {\left(-2 i \, a^{2} b d^{2} f x - 2 i \, a^{2} b c d f + {\left(-2 i \, a b^{2} d^{2} f x - 2 i \, a b^{2} c d f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} \sin\left(f x + e\right) - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} + 2 \, {\left(-2 i \, a^{2} b d^{2} f x - 2 i \, a^{2} b c d f + {\left(-2 i \, a b^{2} d^{2} f x - 2 i \, a b^{2} c d f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} \sin\left(f x + e\right) - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} + 2 \, {\left(2 i \, a^{2} b d^{2} f x + 2 i \, a^{2} b c d f + {\left(2 i \, a b^{2} d^{2} f x + 2 i \, a b^{2} c d f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e - 2 \, {\left(a^{3} - a b^{2}\right)} c d f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e - 2 \, {\left(a^{3} - a b^{2}\right)} c d f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e - 2 \, {\left(a^{3} - a b^{2}\right)} c d f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e - 2 \, {\left(a^{3} - a b^{2}\right)} c d f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \sin\left(f x + e\right) + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d^{2} f x + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \sin\left(f x + e\right) - {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{4 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \sin\left(f x + e\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3}\right)}}"," ",0,"1/4*(4*(a*b^2*d^2*sin(f*x + e) + a^2*b*d^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(a*b^2*d^2*sin(f*x + e) + a^2*b*d^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(a*b^2*d^2*sin(f*x + e) + a^2*b*d^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(a*b^2*d^2*sin(f*x + e) + a^2*b*d^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(f*x + e) + a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*c*d*f^2*x + (a^2*b - b^3)*c^2*f^2)*cos(f*x + e) + (4*I*(a^2*b - b^3)*d^2*sin(f*x + e) + 4*I*(a^3 - a*b^2)*d^2 + 2*(2*I*a^2*b*d^2*f*x + 2*I*a^2*b*c*d*f + (2*I*a*b^2*d^2*f*x + 2*I*a*b^2*c*d*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (4*I*(a^2*b - b^3)*d^2*sin(f*x + e) + 4*I*(a^3 - a*b^2)*d^2 + 2*(-2*I*a^2*b*d^2*f*x - 2*I*a^2*b*c*d*f + (-2*I*a*b^2*d^2*f*x - 2*I*a*b^2*c*d*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-4*I*(a^2*b - b^3)*d^2*sin(f*x + e) - 4*I*(a^3 - a*b^2)*d^2 + 2*(-2*I*a^2*b*d^2*f*x - 2*I*a^2*b*c*d*f + (-2*I*a*b^2*d^2*f*x - 2*I*a*b^2*c*d*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-4*I*(a^2*b - b^3)*d^2*sin(f*x + e) - 4*I*(a^3 - a*b^2)*d^2 + 2*(2*I*a^2*b*d^2*f*x + 2*I*a^2*b*c*d*f + (2*I*a*b^2*d^2*f*x + 2*I*a*b^2*c*d*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(2*(a^3 - a*b^2)*d^2*e - 2*(a^3 - a*b^2)*c*d*f + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*sin(f*x + e) + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(2*(a^3 - a*b^2)*d^2*e - 2*(a^3 - a*b^2)*c*d*f + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*sin(f*x + e) + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(2*(a^3 - a*b^2)*d^2*e - 2*(a^3 - a*b^2)*c*d*f + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*sin(f*x + e) - (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(2*(a^3 - a*b^2)*d^2*e - 2*(a^3 - a*b^2)*c*d*f + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*sin(f*x + e) - (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(2*(a^3 - a*b^2)*d^2*f*x + 2*(a^3 - a*b^2)*d^2*e + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*sin(f*x + e) + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^3 - a*b^2)*d^2*f*x + 2*(a^3 - a*b^2)*d^2*e + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*sin(f*x + e) - (a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^3 - a*b^2)*d^2*f*x + 2*(a^3 - a*b^2)*d^2*e + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*sin(f*x + e) + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^3 - a*b^2)*d^2*f*x + 2*(a^3 - a*b^2)*d^2*e + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*sin(f*x + e) - (a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^4*b - 2*a^2*b^3 + b^5)*f^3*sin(f*x + e) + (a^5 - 2*a^3*b^2 + a*b^4)*f^3)","C",0
170,1,1512,0,1.512718," ","integrate((d*x+c)/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(i \, a b^{2} d \sin\left(f x + e\right) + i \, a^{2} b d\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, a b^{2} d \sin\left(f x + e\right) - i \, a^{2} b d\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, a b^{2} d \sin\left(f x + e\right) - i \, a^{2} b d\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, a b^{2} d \sin\left(f x + e\right) + i \, a^{2} b d\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) + i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) + {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(f x + e\right) - a \sin\left(f x + e\right) - {\left(b \cos\left(f x + e\right) - i \, b \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \cos\left(f x + e\right) - {\left({\left(a^{2} b - b^{3}\right)} d \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d + {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left({\left(a^{2} b - b^{3}\right)} d \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d + {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left({\left(a^{2} b - b^{3}\right)} d \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d - {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(f x + e\right) + 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left({\left(a^{2} b - b^{3}\right)} d \sin\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d - {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(f x + e\right) - 2 i \, b \sin\left(f x + e\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \sin\left(f x + e\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)}}"," ",0,"1/2*((I*a*b^2*d*sin(f*x + e) + I*a^2*b*d)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*a*b^2*d*sin(f*x + e) - I*a^2*b*d)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*a*b^2*d*sin(f*x + e) - I*a^2*b*d)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*a*b^2*d*sin(f*x + e) + I*a^2*b*d)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) + I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) + (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(f*x + e) - a*sin(f*x + e) - (b*cos(f*x + e) - I*b*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*cos(f*x + e) - ((a^2*b - b^3)*d*sin(f*x + e) + (a^3 - a*b^2)*d + (a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - ((a^2*b - b^3)*d*sin(f*x + e) + (a^3 - a*b^2)*d + (a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - ((a^2*b - b^3)*d*sin(f*x + e) + (a^3 - a*b^2)*d - (a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(f*x + e) + 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - ((a^2*b - b^3)*d*sin(f*x + e) + (a^3 - a*b^2)*d - (a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*sin(f*x + e))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(f*x + e) - 2*I*b*sin(f*x + e) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a))/((a^4*b - 2*a^2*b^3 + b^5)*f^2*sin(f*x + e) + (a^5 - 2*a^3*b^2 + a*b^4)*f^2)","B",0
171,0,0,0,0.966218," ","integrate(1/(d*x+c)/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} + b^{2}\right)} d x - {\left(b^{2} d x + b^{2} c\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} + b^{2}\right)} c + 2 \, {\left(a b d x + a b c\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/((a^2 + b^2)*d*x - (b^2*d*x + b^2*c)*cos(f*x + e)^2 + (a^2 + b^2)*c + 2*(a*b*d*x + a*b*c)*sin(f*x + e)), x)","F",0
172,0,0,0,0.738182," ","integrate(1/(d*x+c)^2/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{{\left(a^{2} + b^{2}\right)} d^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d x + {\left(a^{2} + b^{2}\right)} c^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(1/((a^2 + b^2)*d^2*x^2 + 2*(a^2 + b^2)*c*d*x + (a^2 + b^2)*c^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*sin(f*x + e)), x)","F",0
173,0,0,0,0.915255," ","integrate((d*x+c)^m*(a+b*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(b \sin\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*sin(f*x + e) + a)^n, x)","F",0
174,1,428,0,1.003119," ","integrate((d*x+c)^m*(a+b*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(b^{3} d m + b^{3} d\right)} e^{\left(-\frac{d m \log\left(\frac{3 i \, f}{d}\right) + 3 i \, d e - 3 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, d f x + 3 i \, c f}{d}\right) + {\left(-9 i \, a b^{2} d m - 9 i \, a b^{2} d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} e^{\left(-\frac{d m \log\left(\frac{i \, f}{d}\right) + i \, d e - i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, c f}{d}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} e^{\left(-\frac{d m \log\left(-\frac{i \, f}{d}\right) - i \, d e + i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, c f}{d}\right) + {\left(9 i \, a b^{2} d m + 9 i \, a b^{2} d\right)} e^{\left(-\frac{d m \log\left(-\frac{2 i \, f}{d}\right) - 2 i \, d e + 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, d f x - 2 i \, c f}{d}\right) + {\left(b^{3} d m + b^{3} d\right)} e^{\left(-\frac{d m \log\left(-\frac{3 i \, f}{d}\right) - 3 i \, d e + 3 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, d f x - 3 i \, c f}{d}\right) + 12 \, {\left({\left(2 \, a^{3} + 3 \, a b^{2}\right)} d f x + {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c f\right)} {\left(d x + c\right)}^{m}}{24 \, {\left(d f m + d f\right)}}"," ",0,"1/24*((b^3*d*m + b^3*d)*e^(-(d*m*log(3*I*f/d) + 3*I*d*e - 3*I*c*f)/d)*gamma(m + 1, (3*I*d*f*x + 3*I*c*f)/d) + (-9*I*a*b^2*d*m - 9*I*a*b^2*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) - 9*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*e^(-(d*m*log(I*f/d) + I*d*e - I*c*f)/d)*gamma(m + 1, (I*d*f*x + I*c*f)/d) - 9*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*e^(-(d*m*log(-I*f/d) - I*d*e + I*c*f)/d)*gamma(m + 1, (-I*d*f*x - I*c*f)/d) + (9*I*a*b^2*d*m + 9*I*a*b^2*d)*e^(-(d*m*log(-2*I*f/d) - 2*I*d*e + 2*I*c*f)/d)*gamma(m + 1, (-2*I*d*f*x - 2*I*c*f)/d) + (b^3*d*m + b^3*d)*e^(-(d*m*log(-3*I*f/d) - 3*I*d*e + 3*I*c*f)/d)*gamma(m + 1, (-3*I*d*f*x - 3*I*c*f)/d) + 12*((2*a^3 + 3*a*b^2)*d*f*x + (2*a^3 + 3*a*b^2)*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
175,1,274,0,0.936116," ","integrate((d*x+c)^m*(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, b^{2} d m - i \, b^{2} d\right)} e^{\left(-\frac{d m \log\left(\frac{2 i \, f}{d}\right) + 2 i \, d e - 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, c f}{d}\right) - 8 \, {\left(a b d m + a b d\right)} e^{\left(-\frac{d m \log\left(\frac{i \, f}{d}\right) + i \, d e - i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, c f}{d}\right) - 8 \, {\left(a b d m + a b d\right)} e^{\left(-\frac{d m \log\left(-\frac{i \, f}{d}\right) - i \, d e + i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, c f}{d}\right) + {\left(i \, b^{2} d m + i \, b^{2} d\right)} e^{\left(-\frac{d m \log\left(-\frac{2 i \, f}{d}\right) - 2 i \, d e + 2 i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-2 i \, d f x - 2 i \, c f}{d}\right) + 4 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d f x + {\left(2 \, a^{2} + b^{2}\right)} c f\right)} {\left(d x + c\right)}^{m}}{8 \, {\left(d f m + d f\right)}}"," ",0,"1/8*((-I*b^2*d*m - I*b^2*d)*e^(-(d*m*log(2*I*f/d) + 2*I*d*e - 2*I*c*f)/d)*gamma(m + 1, (2*I*d*f*x + 2*I*c*f)/d) - 8*(a*b*d*m + a*b*d)*e^(-(d*m*log(I*f/d) + I*d*e - I*c*f)/d)*gamma(m + 1, (I*d*f*x + I*c*f)/d) - 8*(a*b*d*m + a*b*d)*e^(-(d*m*log(-I*f/d) - I*d*e + I*c*f)/d)*gamma(m + 1, (-I*d*f*x - I*c*f)/d) + (I*b^2*d*m + I*b^2*d)*e^(-(d*m*log(-2*I*f/d) - 2*I*d*e + 2*I*c*f)/d)*gamma(m + 1, (-2*I*d*f*x - 2*I*c*f)/d) + 4*((2*a^2 + b^2)*d*f*x + (2*a^2 + b^2)*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
176,1,136,0,1.160655," ","integrate((d*x+c)^m*(a+b*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(b d m + b d\right)} e^{\left(-\frac{d m \log\left(\frac{i \, f}{d}\right) + i \, d e - i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, c f}{d}\right) + {\left(b d m + b d\right)} e^{\left(-\frac{d m \log\left(-\frac{i \, f}{d}\right) - i \, d e + i \, c f}{d}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, c f}{d}\right) - 2 \, {\left(a d f x + a c f\right)} {\left(d x + c\right)}^{m}}{2 \, {\left(d f m + d f\right)}}"," ",0,"-1/2*((b*d*m + b*d)*e^(-(d*m*log(I*f/d) + I*d*e - I*c*f)/d)*gamma(m + 1, (I*d*f*x + I*c*f)/d) + (b*d*m + b*d)*e^(-(d*m*log(-I*f/d) - I*d*e + I*c*f)/d)*gamma(m + 1, (-I*d*f*x - I*c*f)/d) - 2*(a*d*f*x + a*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
177,0,0,0,0.981388," ","integrate((d*x+c)^m/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{b \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(b*sin(f*x + e) + a), x)","F",0
178,0,0,0,0.895897," ","integrate((d*x+c)^m/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d x + c\right)}^{m}}{b^{2} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(d*x + c)^m/(b^2*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2), x)","F",0
179,1,1042,0,1.053356," ","integrate((f*x+e)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d^{4} f^{3} x^{4} + 4 \, d^{3} e^{3} + 4 \, {\left(d^{4} e f^{2} + d^{3} f^{3}\right)} x^{3} + 6 \, {\left(d^{4} e^{2} f + 2 \, d^{3} e f^{2}\right)} x^{2} + 4 \, {\left(d^{4} e^{3} + 3 \, d^{3} e^{2} f\right)} x + {\left(d^{4} f^{3} x^{4} + 4 \, d^{3} e^{3} + 4 \, {\left(d^{4} e f^{2} + d^{3} f^{3}\right)} x^{3} + 6 \, {\left(d^{4} e^{2} f + 2 \, d^{3} e f^{2}\right)} x^{2} + 4 \, {\left(d^{4} e^{3} + 3 \, d^{3} e^{2} f\right)} x\right)} \cos\left(d x + c\right) + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2} + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2} + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 24 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 24 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(d^{4} f^{3} x^{4} - 4 \, d^{3} e^{3} + 4 \, {\left(d^{4} e f^{2} - d^{3} f^{3}\right)} x^{3} + 6 \, {\left(d^{4} e^{2} f - 2 \, d^{3} e f^{2}\right)} x^{2} + 4 \, {\left(d^{4} e^{3} - 3 \, d^{3} e^{2} f\right)} x\right)} \sin\left(d x + c\right)}{4 \, {\left(a d^{4} \cos\left(d x + c\right) + a d^{4} \sin\left(d x + c\right) + a d^{4}\right)}}"," ",0,"1/4*(d^4*f^3*x^4 + 4*d^3*e^3 + 4*(d^4*e*f^2 + d^3*f^3)*x^3 + 6*(d^4*e^2*f + 2*d^3*e*f^2)*x^2 + 4*(d^4*e^3 + 3*d^3*e^2*f)*x + (d^4*f^3*x^4 + 4*d^3*e^3 + 4*(d^4*e*f^2 + d^3*f^3)*x^3 + 6*(d^4*e^2*f + 2*d^3*e*f^2)*x^2 + 4*(d^4*e^3 + 3*d^3*e^2*f)*x)*cos(d*x + c) + (24*I*d*f^3*x + 24*I*d*e*f^2 + (24*I*d*f^3*x + 24*I*d*e*f^2)*cos(d*x + c) + (24*I*d*f^3*x + 24*I*d*e*f^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-24*I*d*f^3*x - 24*I*d*e*f^2 + (-24*I*d*f^3*x - 24*I*d*e*f^2)*cos(d*x + c) + (-24*I*d*f^3*x - 24*I*d*e*f^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 24*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 24*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + (d^4*f^3*x^4 - 4*d^3*e^3 + 4*(d^4*e*f^2 - d^3*f^3)*x^3 + 6*(d^4*e^2*f - 2*d^3*e*f^2)*x^2 + 4*(d^4*e^3 - 3*d^3*e^2*f)*x)*sin(d*x + c))/(a*d^4*cos(d*x + c) + a*d^4*sin(d*x + c) + a*d^4)","C",0
180,1,581,0,0.868352," ","integrate((f*x+e)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d^{3} f^{2} x^{3} + 3 \, d^{2} e^{2} + 3 \, {\left(d^{3} e f + d^{2} f^{2}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} + 2 \, d^{2} e f\right)} x + {\left(d^{3} f^{2} x^{3} + 3 \, d^{2} e^{2} + 3 \, {\left(d^{3} e f + d^{2} f^{2}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} + 2 \, d^{2} e f\right)} x\right)} \cos\left(d x + c\right) + {\left(6 i \, f^{2} \cos\left(d x + c\right) + 6 i \, f^{2} \sin\left(d x + c\right) + 6 i \, f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-6 i \, f^{2} \cos\left(d x + c\right) - 6 i \, f^{2} \sin\left(d x + c\right) - 6 i \, f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 6 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 6 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} f^{2} x^{3} - 3 \, d^{2} e^{2} + 3 \, {\left(d^{3} e f - d^{2} f^{2}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} - 2 \, d^{2} e f\right)} x\right)} \sin\left(d x + c\right)}{3 \, {\left(a d^{3} \cos\left(d x + c\right) + a d^{3} \sin\left(d x + c\right) + a d^{3}\right)}}"," ",0,"1/3*(d^3*f^2*x^3 + 3*d^2*e^2 + 3*(d^3*e*f + d^2*f^2)*x^2 + 3*(d^3*e^2 + 2*d^2*e*f)*x + (d^3*f^2*x^3 + 3*d^2*e^2 + 3*(d^3*e*f + d^2*f^2)*x^2 + 3*(d^3*e^2 + 2*d^2*e*f)*x)*cos(d*x + c) + (6*I*f^2*cos(d*x + c) + 6*I*f^2*sin(d*x + c) + 6*I*f^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-6*I*f^2*cos(d*x + c) - 6*I*f^2*sin(d*x + c) - 6*I*f^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 6*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 6*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 6*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 6*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*f^2*x^3 - 3*d^2*e^2 + 3*(d^3*e*f - d^2*f^2)*x^2 + 3*(d^3*e^2 - 2*d^2*e*f)*x)*sin(d*x + c))/(a*d^3*cos(d*x + c) + a*d^3*sin(d*x + c) + a*d^3)","B",0
181,1,151,0,0.953862," ","integrate((f*x+e)*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d^{2} f x^{2} + 2 \, d e + 2 \, {\left(d^{2} e + d f\right)} x + {\left(d^{2} f x^{2} + 2 \, d e + 2 \, {\left(d^{2} e + d f\right)} x\right)} \cos\left(d x + c\right) - 2 \, {\left(f \cos\left(d x + c\right) + f \sin\left(d x + c\right) + f\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(d^{2} f x^{2} - 2 \, d e + 2 \, {\left(d^{2} e - d f\right)} x\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{2} \cos\left(d x + c\right) + a d^{2} \sin\left(d x + c\right) + a d^{2}\right)}}"," ",0,"1/2*(d^2*f*x^2 + 2*d*e + 2*(d^2*e + d*f)*x + (d^2*f*x^2 + 2*d*e + 2*(d^2*e + d*f)*x)*cos(d*x + c) - 2*(f*cos(d*x + c) + f*sin(d*x + c) + f)*log(sin(d*x + c) + 1) + (d^2*f*x^2 - 2*d*e + 2*(d^2*e - d*f)*x)*sin(d*x + c))/(a*d^2*cos(d*x + c) + a*d^2*sin(d*x + c) + a*d^2)","B",0
182,1,54,0,0.757312," ","integrate(sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d x + {\left(d x + 1\right)} \cos\left(d x + c\right) + {\left(d x - 1\right)} \sin\left(d x + c\right) + 1}{a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d}"," ",0,"(d*x + (d*x + 1)*cos(d*x + c) + (d*x - 1)*sin(d*x + c) + 1)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
183,0,0,0,1.030115," ","integrate(sin(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sin(d*x + c)/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
184,0,0,0,0.863055," ","integrate(sin(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sin(d*x + c)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
185,1,1313,0,1.161055," ","integrate((f*x+e)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{4} f^{3} x^{4} + 4 \, d^{3} e^{3} - 12 \, d^{2} e^{2} f + 4 \, {\left(d^{4} e f^{2} + d^{3} f^{3}\right)} x^{3} + 24 \, f^{3} + 6 \, {\left(d^{4} e^{2} f + 2 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + 4 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f - 6 \, d e f^{2} - 6 \, f^{3} + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(d^{4} e^{3} + 3 \, d^{3} e^{2} f - 6 \, d^{2} e f^{2}\right)} x + {\left(d^{4} f^{3} x^{4} + 8 \, d^{3} e^{3} - 24 \, d e f^{2} + 4 \, {\left(d^{4} e f^{2} + 2 \, d^{3} f^{3}\right)} x^{3} + 6 \, {\left(d^{4} e^{2} f + 4 \, d^{3} e f^{2}\right)} x^{2} + 4 \, {\left(d^{4} e^{3} + 6 \, d^{3} e^{2} f - 6 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) - {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2} + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(24 i \, d f^{3} x + 24 i \, d e f^{2} + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 24 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 24 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(d^{4} f^{3} x^{4} - 4 \, d^{3} e^{3} - 12 \, d^{2} e^{2} f + 4 \, {\left(d^{4} e f^{2} - d^{3} f^{3}\right)} x^{3} + 24 \, f^{3} + 6 \, {\left(d^{4} e^{2} f - 2 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + 4 \, {\left(d^{4} e^{3} - 3 \, d^{3} e^{2} f - 6 \, d^{2} e f^{2}\right)} x + 4 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 3 \, d^{2} e^{2} f - 6 \, d e f^{2} + 6 \, f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a d^{4} \cos\left(d x + c\right) + a d^{4} \sin\left(d x + c\right) + a d^{4}\right)}}"," ",0,"-1/4*(d^4*f^3*x^4 + 4*d^3*e^3 - 12*d^2*e^2*f + 4*(d^4*e*f^2 + d^3*f^3)*x^3 + 24*f^3 + 6*(d^4*e^2*f + 2*d^3*e*f^2 - 2*d^2*f^3)*x^2 + 4*(d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f - 6*d*e*f^2 - 6*f^3 + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^2 + 4*(d^4*e^3 + 3*d^3*e^2*f - 6*d^2*e*f^2)*x + (d^4*f^3*x^4 + 8*d^3*e^3 - 24*d*e*f^2 + 4*(d^4*e*f^2 + 2*d^3*f^3)*x^3 + 6*(d^4*e^2*f + 4*d^3*e*f^2)*x^2 + 4*(d^4*e^3 + 6*d^3*e^2*f - 6*d*f^3)*x)*cos(d*x + c) - (-24*I*d*f^3*x - 24*I*d*e*f^2 + (-24*I*d*f^3*x - 24*I*d*e*f^2)*cos(d*x + c) + (-24*I*d*f^3*x - 24*I*d*e*f^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) - (24*I*d*f^3*x + 24*I*d*e*f^2 + (24*I*d*f^3*x + 24*I*d*e*f^2)*cos(d*x + c) + (24*I*d*f^3*x + 24*I*d*e*f^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 24*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 24*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + (d^4*f^3*x^4 - 4*d^3*e^3 - 12*d^2*e^2*f + 4*(d^4*e*f^2 - d^3*f^3)*x^3 + 24*f^3 + 6*(d^4*e^2*f - 2*d^3*e*f^2 - 2*d^2*f^3)*x^2 + 4*(d^4*e^3 - 3*d^3*e^2*f - 6*d^2*e*f^2)*x + 4*(d^3*f^3*x^3 + d^3*e^3 - 3*d^2*e^2*f - 6*d*e*f^2 + 6*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c))*sin(d*x + c))/(a*d^4*cos(d*x + c) + a*d^4*sin(d*x + c) + a*d^4)","C",0
186,1,716,0,0.869172," ","integrate((f*x+e)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{3} f^{2} x^{3} + 3 \, d^{2} e^{2} - 6 \, d e f + 3 \, {\left(d^{3} e f + d^{2} f^{2}\right)} x^{2} + 3 \, {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f - 2 \, f^{2} + 2 \, {\left(d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(d^{3} e^{2} + 2 \, d^{2} e f - 2 \, d f^{2}\right)} x + {\left(d^{3} f^{2} x^{3} + 6 \, d^{2} e^{2} + 3 \, {\left(d^{3} e f + 2 \, d^{2} f^{2}\right)} x^{2} - 6 \, f^{2} + 3 \, {\left(d^{3} e^{2} + 4 \, d^{2} e f\right)} x\right)} \cos\left(d x + c\right) - {\left(-6 i \, f^{2} \cos\left(d x + c\right) - 6 i \, f^{2} \sin\left(d x + c\right) - 6 i \, f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(6 i \, f^{2} \cos\left(d x + c\right) + 6 i \, f^{2} \sin\left(d x + c\right) + 6 i \, f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 6 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 6 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} f^{2} x^{3} - 3 \, d^{2} e^{2} - 6 \, d e f + 3 \, {\left(d^{3} e f - d^{2} f^{2}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} - 2 \, d^{2} e f - 2 \, d f^{2}\right)} x + 3 \, {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} - 2 \, d e f - 2 \, f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(a d^{3} \cos\left(d x + c\right) + a d^{3} \sin\left(d x + c\right) + a d^{3}\right)}}"," ",0,"-1/3*(d^3*f^2*x^3 + 3*d^2*e^2 - 6*d*e*f + 3*(d^3*e*f + d^2*f^2)*x^2 + 3*(d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f - 2*f^2 + 2*(d^2*e*f + d*f^2)*x)*cos(d*x + c)^2 + 3*(d^3*e^2 + 2*d^2*e*f - 2*d*f^2)*x + (d^3*f^2*x^3 + 6*d^2*e^2 + 3*(d^3*e*f + 2*d^2*f^2)*x^2 - 6*f^2 + 3*(d^3*e^2 + 4*d^2*e*f)*x)*cos(d*x + c) - (-6*I*f^2*cos(d*x + c) - 6*I*f^2*sin(d*x + c) - 6*I*f^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) - (6*I*f^2*cos(d*x + c) + 6*I*f^2*sin(d*x + c) + 6*I*f^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 6*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 6*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 6*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 6*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*f^2*x^3 - 3*d^2*e^2 - 6*d*e*f + 3*(d^3*e*f - d^2*f^2)*x^2 + 3*(d^3*e^2 - 2*d^2*e*f - 2*d*f^2)*x + 3*(d^2*f^2*x^2 + d^2*e^2 - 2*d*e*f - 2*f^2 + 2*(d^2*e*f - d*f^2)*x)*cos(d*x + c))*sin(d*x + c))/(a*d^3*cos(d*x + c) + a*d^3*sin(d*x + c) + a*d^3)","B",0
187,1,196,0,0.974067," ","integrate((f*x+e)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{2} f x^{2} + 2 \, {\left(d f x + d e + f\right)} \cos\left(d x + c\right)^{2} + 2 \, d e + 2 \, {\left(d^{2} e + d f\right)} x + {\left(d^{2} f x^{2} + 4 \, d e + 2 \, {\left(d^{2} e + 2 \, d f\right)} x\right)} \cos\left(d x + c\right) - 2 \, {\left(f \cos\left(d x + c\right) + f \sin\left(d x + c\right) + f\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(d^{2} f x^{2} - 2 \, d e + 2 \, {\left(d^{2} e - d f\right)} x + 2 \, {\left(d f x + d e - f\right)} \cos\left(d x + c\right) - 2 \, f\right)} \sin\left(d x + c\right) - 2 \, f}{2 \, {\left(a d^{2} \cos\left(d x + c\right) + a d^{2} \sin\left(d x + c\right) + a d^{2}\right)}}"," ",0,"-1/2*(d^2*f*x^2 + 2*(d*f*x + d*e + f)*cos(d*x + c)^2 + 2*d*e + 2*(d^2*e + d*f)*x + (d^2*f*x^2 + 4*d*e + 2*(d^2*e + 2*d*f)*x)*cos(d*x + c) - 2*(f*cos(d*x + c) + f*sin(d*x + c) + f)*log(sin(d*x + c) + 1) + (d^2*f*x^2 - 2*d*e + 2*(d^2*e - d*f)*x + 2*(d*f*x + d*e - f)*cos(d*x + c) - 2*f)*sin(d*x + c) - 2*f)/(a*d^2*cos(d*x + c) + a*d^2*sin(d*x + c) + a*d^2)","B",0
188,1,69,0,0.982125," ","integrate(sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d x + {\left(d x + 2\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + {\left(d x + \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1}{a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d}"," ",0,"-(d*x + (d*x + 2)*cos(d*x + c) + cos(d*x + c)^2 + (d*x + cos(d*x + c) - 1)*sin(d*x + c) + 1)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
189,0,0,0,0.604218," ","integrate(sin(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(d x + c\right)^{2} - 1}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
190,0,0,0,1.008312," ","integrate(sin(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(d x + c\right)^{2} - 1}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
191,1,1563,0,1.328996," ","integrate((f*x+e)^3*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, d^{4} f^{3} x^{4} + 16 \, d^{3} e^{3} - 42 \, d^{2} e^{2} f + 8 \, {\left(3 \, d^{4} e f^{2} + 2 \, d^{3} f^{3}\right)} x^{3} + 2 \, {\left(4 \, d^{3} f^{3} x^{3} + 4 \, d^{3} e^{3} - 6 \, d^{2} e^{2} f - 6 \, d e f^{2} + 3 \, f^{3} + 6 \, {\left(2 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, d^{3} e^{2} f - 2 \, d^{2} e f^{2} - d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + 93 \, f^{3} + 6 \, {\left(6 \, d^{4} e^{2} f + 8 \, d^{3} e f^{2} - 7 \, d^{2} f^{3}\right)} x^{2} + 2 \, {\left(8 \, d^{3} f^{3} x^{3} + 8 \, d^{3} e^{3} + 18 \, d^{2} e^{2} f - 48 \, d e f^{2} - 45 \, f^{3} + 6 \, {\left(4 \, d^{3} e f^{2} + 3 \, d^{2} f^{3}\right)} x^{2} + 12 \, {\left(2 \, d^{3} e^{2} f + 3 \, d^{2} e f^{2} - 4 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(2 \, d^{4} e^{3} + 4 \, d^{3} e^{2} f - 7 \, d^{2} e f^{2}\right)} x + 3 \, {\left(2 \, d^{4} f^{3} x^{4} + 8 \, d^{3} e^{3} + 2 \, d^{2} e^{2} f - 28 \, d e f^{2} + 8 \, {\left(d^{4} e f^{2} + d^{3} f^{3}\right)} x^{3} - f^{3} + 2 \, {\left(6 \, d^{4} e^{2} f + 12 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 4 \, {\left(2 \, d^{4} e^{3} + 6 \, d^{3} e^{2} f + d^{2} e f^{2} - 7 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(96 i \, d f^{3} x + 96 i \, d e f^{2} + {\left(96 i \, d f^{3} x + 96 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(96 i \, d f^{3} x + 96 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-96 i \, d f^{3} x - 96 i \, d e f^{2} + {\left(-96 i \, d f^{3} x - 96 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(-96 i \, d f^{3} x - 96 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 48 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 48 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 48 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 48 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 96 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 96 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(6 \, d^{4} f^{3} x^{4} - 16 \, d^{3} e^{3} - 42 \, d^{2} e^{2} f + 8 \, {\left(3 \, d^{4} e f^{2} - 2 \, d^{3} f^{3}\right)} x^{3} + 93 \, f^{3} + 6 \, {\left(6 \, d^{4} e^{2} f - 8 \, d^{3} e f^{2} - 7 \, d^{2} f^{3}\right)} x^{2} - 2 \, {\left(4 \, d^{3} f^{3} x^{3} + 4 \, d^{3} e^{3} + 6 \, d^{2} e^{2} f - 6 \, d e f^{2} - 3 \, f^{3} + 6 \, {\left(2 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, d^{3} e^{2} f + 2 \, d^{2} e f^{2} - d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(2 \, d^{4} e^{3} - 4 \, d^{3} e^{2} f - 7 \, d^{2} e f^{2}\right)} x + 4 \, {\left(2 \, d^{3} f^{3} x^{3} + 2 \, d^{3} e^{3} - 12 \, d^{2} e^{2} f - 21 \, d e f^{2} + 24 \, f^{3} + 6 \, {\left(d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(2 \, d^{3} e^{2} f - 8 \, d^{2} e f^{2} - 7 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(a d^{4} \cos\left(d x + c\right) + a d^{4} \sin\left(d x + c\right) + a d^{4}\right)}}"," ",0,"1/16*(6*d^4*f^3*x^4 + 16*d^3*e^3 - 42*d^2*e^2*f + 8*(3*d^4*e*f^2 + 2*d^3*f^3)*x^3 + 2*(4*d^3*f^3*x^3 + 4*d^3*e^3 - 6*d^2*e^2*f - 6*d*e*f^2 + 3*f^3 + 6*(2*d^3*e*f^2 - d^2*f^3)*x^2 + 6*(2*d^3*e^2*f - 2*d^2*e*f^2 - d*f^3)*x)*cos(d*x + c)^3 + 93*f^3 + 6*(6*d^4*e^2*f + 8*d^3*e*f^2 - 7*d^2*f^3)*x^2 + 2*(8*d^3*f^3*x^3 + 8*d^3*e^3 + 18*d^2*e^2*f - 48*d*e*f^2 - 45*f^3 + 6*(4*d^3*e*f^2 + 3*d^2*f^3)*x^2 + 12*(2*d^3*e^2*f + 3*d^2*e*f^2 - 4*d*f^3)*x)*cos(d*x + c)^2 + 12*(2*d^4*e^3 + 4*d^3*e^2*f - 7*d^2*e*f^2)*x + 3*(2*d^4*f^3*x^4 + 8*d^3*e^3 + 2*d^2*e^2*f - 28*d*e*f^2 + 8*(d^4*e*f^2 + d^3*f^3)*x^3 - f^3 + 2*(6*d^4*e^2*f + 12*d^3*e*f^2 + d^2*f^3)*x^2 + 4*(2*d^4*e^3 + 6*d^3*e^2*f + d^2*e*f^2 - 7*d*f^3)*x)*cos(d*x + c) + (96*I*d*f^3*x + 96*I*d*e*f^2 + (96*I*d*f^3*x + 96*I*d*e*f^2)*cos(d*x + c) + (96*I*d*f^3*x + 96*I*d*e*f^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-96*I*d*f^3*x - 96*I*d*e*f^2 + (-96*I*d*f^3*x - 96*I*d*e*f^2)*cos(d*x + c) + (-96*I*d*f^3*x - 96*I*d*e*f^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 48*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 48*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 48*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 48*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 96*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 96*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + (6*d^4*f^3*x^4 - 16*d^3*e^3 - 42*d^2*e^2*f + 8*(3*d^4*e*f^2 - 2*d^3*f^3)*x^3 + 93*f^3 + 6*(6*d^4*e^2*f - 8*d^3*e*f^2 - 7*d^2*f^3)*x^2 - 2*(4*d^3*f^3*x^3 + 4*d^3*e^3 + 6*d^2*e^2*f - 6*d*e*f^2 - 3*f^3 + 6*(2*d^3*e*f^2 + d^2*f^3)*x^2 + 6*(2*d^3*e^2*f + 2*d^2*e*f^2 - d*f^3)*x)*cos(d*x + c)^2 + 12*(2*d^4*e^3 - 4*d^3*e^2*f - 7*d^2*e*f^2)*x + 4*(2*d^3*f^3*x^3 + 2*d^3*e^3 - 12*d^2*e^2*f - 21*d*e*f^2 + 24*f^3 + 6*(d^3*e*f^2 - 2*d^2*f^3)*x^2 + 3*(2*d^3*e^2*f - 8*d^2*e*f^2 - 7*d*f^3)*x)*cos(d*x + c))*sin(d*x + c))/(a*d^4*cos(d*x + c) + a*d^4*sin(d*x + c) + a*d^4)","C",0
192,1,844,0,1.306423," ","integrate((f*x+e)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{3} f^{2} x^{3} + 4 \, d^{2} e^{2} + {\left(2 \, d^{2} f^{2} x^{2} + 2 \, d^{2} e^{2} - 2 \, d e f - f^{2} + 2 \, {\left(2 \, d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{3} - 7 \, d e f + 2 \, {\left(3 \, d^{3} e f + 2 \, d^{2} f^{2}\right)} x^{2} + 2 \, {\left(2 \, d^{2} f^{2} x^{2} + 2 \, d^{2} e^{2} + 3 \, d e f - 4 \, f^{2} + {\left(4 \, d^{2} e f + 3 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, d^{3} e^{2} + 8 \, d^{2} e f - 7 \, d f^{2}\right)} x + {\left(2 \, d^{3} f^{2} x^{3} + 6 \, d^{2} e^{2} + d e f + 6 \, {\left(d^{3} e f + d^{2} f^{2}\right)} x^{2} - 7 \, f^{2} + {\left(6 \, d^{3} e^{2} + 12 \, d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right) + {\left(8 i \, f^{2} \cos\left(d x + c\right) + 8 i \, f^{2} \sin\left(d x + c\right) + 8 i \, f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-8 i \, f^{2} \cos\left(d x + c\right) - 8 i \, f^{2} \sin\left(d x + c\right) - 8 i \, f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 8 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 8 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 8 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 8 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(2 \, d^{3} f^{2} x^{3} - 4 \, d^{2} e^{2} - 7 \, d e f + 2 \, {\left(3 \, d^{3} e f - 2 \, d^{2} f^{2}\right)} x^{2} - {\left(2 \, d^{2} f^{2} x^{2} + 2 \, d^{2} e^{2} + 2 \, d e f - f^{2} + 2 \, {\left(2 \, d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(6 \, d^{3} e^{2} - 8 \, d^{2} e f - 7 \, d f^{2}\right)} x + {\left(2 \, d^{2} f^{2} x^{2} + 2 \, d^{2} e^{2} - 8 \, d e f - 7 \, f^{2} + 4 \, {\left(d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a d^{3} \cos\left(d x + c\right) + a d^{3} \sin\left(d x + c\right) + a d^{3}\right)}}"," ",0,"1/4*(2*d^3*f^2*x^3 + 4*d^2*e^2 + (2*d^2*f^2*x^2 + 2*d^2*e^2 - 2*d*e*f - f^2 + 2*(2*d^2*e*f - d*f^2)*x)*cos(d*x + c)^3 - 7*d*e*f + 2*(3*d^3*e*f + 2*d^2*f^2)*x^2 + 2*(2*d^2*f^2*x^2 + 2*d^2*e^2 + 3*d*e*f - 4*f^2 + (4*d^2*e*f + 3*d*f^2)*x)*cos(d*x + c)^2 + (6*d^3*e^2 + 8*d^2*e*f - 7*d*f^2)*x + (2*d^3*f^2*x^3 + 6*d^2*e^2 + d*e*f + 6*(d^3*e*f + d^2*f^2)*x^2 - 7*f^2 + (6*d^3*e^2 + 12*d^2*e*f + d*f^2)*x)*cos(d*x + c) + (8*I*f^2*cos(d*x + c) + 8*I*f^2*sin(d*x + c) + 8*I*f^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-8*I*f^2*cos(d*x + c) - 8*I*f^2*sin(d*x + c) - 8*I*f^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 8*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 8*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 8*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 8*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (2*d^3*f^2*x^3 - 4*d^2*e^2 - 7*d*e*f + 2*(3*d^3*e*f - 2*d^2*f^2)*x^2 - (2*d^2*f^2*x^2 + 2*d^2*e^2 + 2*d*e*f - f^2 + 2*(2*d^2*e*f + d*f^2)*x)*cos(d*x + c)^2 + (6*d^3*e^2 - 8*d^2*e*f - 7*d*f^2)*x + (2*d^2*f^2*x^2 + 2*d^2*e^2 - 8*d*e*f - 7*f^2 + 4*(d^2*e*f - 2*d*f^2)*x)*cos(d*x + c))*sin(d*x + c))/(a*d^3*cos(d*x + c) + a*d^3*sin(d*x + c) + a*d^3)","B",0
193,1,250,0,0.885765," ","integrate((f*x+e)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, d^{2} f x^{2} + 2 \, {\left(2 \, d f x + 2 \, d e - f\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(4 \, d f x + 4 \, d e + 3 \, f\right)} \cos\left(d x + c\right)^{2} + 8 \, d e + 4 \, {\left(3 \, d^{2} e + 2 \, d f\right)} x + {\left(6 \, d^{2} f x^{2} + 12 \, d e + 12 \, {\left(d^{2} e + d f\right)} x + f\right)} \cos\left(d x + c\right) - 8 \, {\left(f \cos\left(d x + c\right) + f \sin\left(d x + c\right) + f\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(6 \, d^{2} f x^{2} - 2 \, {\left(2 \, d f x + 2 \, d e + f\right)} \cos\left(d x + c\right)^{2} - 8 \, d e + 4 \, {\left(3 \, d^{2} e - 2 \, d f\right)} x + 4 \, {\left(d f x + d e - 2 \, f\right)} \cos\left(d x + c\right) - 7 \, f\right)} \sin\left(d x + c\right) - 7 \, f}{8 \, {\left(a d^{2} \cos\left(d x + c\right) + a d^{2} \sin\left(d x + c\right) + a d^{2}\right)}}"," ",0,"1/8*(6*d^2*f*x^2 + 2*(2*d*f*x + 2*d*e - f)*cos(d*x + c)^3 + 2*(4*d*f*x + 4*d*e + 3*f)*cos(d*x + c)^2 + 8*d*e + 4*(3*d^2*e + 2*d*f)*x + (6*d^2*f*x^2 + 12*d*e + 12*(d^2*e + d*f)*x + f)*cos(d*x + c) - 8*(f*cos(d*x + c) + f*sin(d*x + c) + f)*log(sin(d*x + c) + 1) + (6*d^2*f*x^2 - 2*(2*d*f*x + 2*d*e + f)*cos(d*x + c)^2 - 8*d*e + 4*(3*d^2*e - 2*d*f)*x + 4*(d*f*x + d*e - 2*f)*cos(d*x + c) - 7*f)*sin(d*x + c) - 7*f)/(a*d^2*cos(d*x + c) + a*d^2*sin(d*x + c) + a*d^2)","A",0
194,1,92,0,0.689390," ","integrate(sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{3} + 3 \, d x + 3 \, {\left(d x + 1\right)} \cos\left(d x + c\right) + 2 \, \cos\left(d x + c\right)^{2} + {\left(3 \, d x - \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 2}{2 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(cos(d*x + c)^3 + 3*d*x + 3*(d*x + 1)*cos(d*x + c) + 2*cos(d*x + c)^2 + (3*d*x - cos(d*x + c)^2 + cos(d*x + c) - 2)*sin(d*x + c) + 2)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
195,0,0,0,0.741140," ","integrate(sin(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right)}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*sin(d*x + c)/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
196,0,0,0,0.850690," ","integrate(sin(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right)}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*sin(d*x + c)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
197,1,2914,0,1.437150," ","integrate((f*x+e)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 6 \, d^{3} e^{2} f x + 2 \, d^{3} e^{3} + 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} \cos\left(d x + c\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} \cos\left(d x + c\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2} + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2} + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} \cos\left(d x + c\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} \cos\left(d x + c\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left(6 i \, f^{3} \cos\left(d x + c\right) + 6 i \, f^{3} \sin\left(d x + c\right) + 6 i \, f^{3}\right)} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-6 i \, f^{3} \cos\left(d x + c\right) - 6 i \, f^{3} \sin\left(d x + c\right) - 6 i \, f^{3}\right)} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(6 i \, f^{3} \cos\left(d x + c\right) + 6 i \, f^{3} \sin\left(d x + c\right) + 6 i \, f^{3}\right)} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-6 i \, f^{3} \cos\left(d x + c\right) - 6 i \, f^{3} \sin\left(d x + c\right) - 6 i \, f^{3}\right)} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 12 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 12 \, {\left(f^{3} \cos\left(d x + c\right) + f^{3} \sin\left(d x + c\right) + f^{3}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{4} \cos\left(d x + c\right) + a d^{4} \sin\left(d x + c\right) + a d^{4}\right)}}"," ",0,"1/2*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 6*d^3*e^2*f*x + 2*d^3*e^3 + 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*cos(d*x + c) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*sin(d*x + c))*dilog(cos(d*x + c) + I*sin(d*x + c)) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*cos(d*x + c) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*sin(d*x + c))*dilog(cos(d*x + c) - I*sin(d*x + c)) + (12*I*d*f^3*x + 12*I*d*e*f^2 + (12*I*d*f^3*x + 12*I*d*e*f^2)*cos(d*x + c) + (12*I*d*f^3*x + 12*I*d*e*f^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-12*I*d*f^3*x - 12*I*d*e*f^2 + (-12*I*d*f^3*x - 12*I*d*e*f^2)*cos(d*x + c) + (-12*I*d*f^3*x - 12*I*d*e*f^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*cos(d*x + c) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*sin(d*x + c))*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*cos(d*x + c) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*sin(d*x + c))*dilog(-cos(d*x + c) - I*sin(d*x + c)) - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*cos(d*x + c) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*cos(d*x + c) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*cos(d*x + c) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*cos(d*x + c) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + (6*I*f^3*cos(d*x + c) + 6*I*f^3*sin(d*x + c) + 6*I*f^3)*polylog(4, cos(d*x + c) + I*sin(d*x + c)) + (-6*I*f^3*cos(d*x + c) - 6*I*f^3*sin(d*x + c) - 6*I*f^3)*polylog(4, cos(d*x + c) - I*sin(d*x + c)) + (6*I*f^3*cos(d*x + c) + 6*I*f^3*sin(d*x + c) + 6*I*f^3)*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) + (-6*I*f^3*cos(d*x + c) - 6*I*f^3*sin(d*x + c) - 6*I*f^3)*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*cos(d*x + c) + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*cos(d*x + c) + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, cos(d*x + c) - I*sin(d*x + c)) - 12*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 12*(f^3*cos(d*x + c) + f^3*sin(d*x + c) + f^3)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) - 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*cos(d*x + c) + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) - 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*cos(d*x + c) + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*sin(d*x + c))/(a*d^4*cos(d*x + c) + a*d^4*sin(d*x + c) + a*d^4)","C",0
198,1,1636,0,1.155874," ","integrate((f*x+e)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} \cos\left(d x + c\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} \cos\left(d x + c\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(4 i \, f^{2} \cos\left(d x + c\right) + 4 i \, f^{2} \sin\left(d x + c\right) + 4 i \, f^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-4 i \, f^{2} \cos\left(d x + c\right) - 4 i \, f^{2} \sin\left(d x + c\right) - 4 i \, f^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} \cos\left(d x + c\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} \cos\left(d x + c\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 4 \, {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(f^{2} \cos\left(d x + c\right) + f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 2 \, {\left(f^{2} \cos\left(d x + c\right) + f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(f^{2} \cos\left(d x + c\right) + f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 2 \, {\left(f^{2} \cos\left(d x + c\right) + f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{3} \cos\left(d x + c\right) + a d^{3} \sin\left(d x + c\right) + a d^{3}\right)}}"," ",0,"1/2*(2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 + 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c) + (-2*I*d*f^2*x - 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f)*cos(d*x + c) + (-2*I*d*f^2*x - 2*I*d*e*f)*sin(d*x + c))*dilog(cos(d*x + c) + I*sin(d*x + c)) + (2*I*d*f^2*x + 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f)*cos(d*x + c) + (2*I*d*f^2*x + 2*I*d*e*f)*sin(d*x + c))*dilog(cos(d*x + c) - I*sin(d*x + c)) + (4*I*f^2*cos(d*x + c) + 4*I*f^2*sin(d*x + c) + 4*I*f^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-4*I*f^2*cos(d*x + c) - 4*I*f^2*sin(d*x + c) - 4*I*f^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (-2*I*d*f^2*x - 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f)*cos(d*x + c) + (-2*I*d*f^2*x - 2*I*d*e*f)*sin(d*x + c))*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (2*I*d*f^2*x + 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f)*cos(d*x + c) + (2*I*d*f^2*x + 2*I*d*e*f)*sin(d*x + c))*dilog(-cos(d*x + c) - I*sin(d*x + c)) - (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) - 4*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 4*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 4*(d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2 + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*cos(d*x + c) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2 + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*cos(d*x + c) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 4*(d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c) + (d*e*f - c*f^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + 2*(f^2*cos(d*x + c) + f^2*sin(d*x + c) + f^2)*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 2*(f^2*cos(d*x + c) + f^2*sin(d*x + c) + f^2)*polylog(3, cos(d*x + c) - I*sin(d*x + c)) - 2*(f^2*cos(d*x + c) + f^2*sin(d*x + c) + f^2)*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) - 2*(f^2*cos(d*x + c) + f^2*sin(d*x + c) + f^2)*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*sin(d*x + c))/(a*d^3*cos(d*x + c) + a*d^3*sin(d*x + c) + a*d^3)","C",0
199,1,609,0,1.255522," ","integrate((f*x+e)*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d f x + 2 \, d e + 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(-i \, f \cos\left(d x + c\right) - i \, f \sin\left(d x + c\right) - i \, f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(i \, f \cos\left(d x + c\right) + i \, f \sin\left(d x + c\right) + i \, f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(-i \, f \cos\left(d x + c\right) - i \, f \sin\left(d x + c\right) - i \, f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(i \, f \cos\left(d x + c\right) + i \, f \sin\left(d x + c\right) + i \, f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(d f x + d e + {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - {\left(d f x + d e + {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(d f x + d e\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left(d e - c f + {\left(d e - c f\right)} \cos\left(d x + c\right) + {\left(d e - c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(d e - c f + {\left(d e - c f\right)} \cos\left(d x + c\right) + {\left(d e - c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(d f x + c f + {\left(d f x + c f\right)} \cos\left(d x + c\right) + {\left(d f x + c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + {\left(d f x + c f + {\left(d f x + c f\right)} \cos\left(d x + c\right) + {\left(d f x + c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(f \cos\left(d x + c\right) + f \sin\left(d x + c\right) + f\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(d f x + d e\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{2} \cos\left(d x + c\right) + a d^{2} \sin\left(d x + c\right) + a d^{2}\right)}}"," ",0,"1/2*(2*d*f*x + 2*d*e + 2*(d*f*x + d*e)*cos(d*x + c) + (-I*f*cos(d*x + c) - I*f*sin(d*x + c) - I*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (I*f*cos(d*x + c) + I*f*sin(d*x + c) + I*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (-I*f*cos(d*x + c) - I*f*sin(d*x + c) - I*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (I*f*cos(d*x + c) + I*f*sin(d*x + c) + I*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) - (d*f*x + d*e + (d*f*x + d*e)*cos(d*x + c) + (d*f*x + d*e)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) - (d*f*x + d*e + (d*f*x + d*e)*cos(d*x + c) + (d*f*x + d*e)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) + (d*e - c*f + (d*e - c*f)*cos(d*x + c) + (d*e - c*f)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + (d*e - c*f + (d*e - c*f)*cos(d*x + c) + (d*e - c*f)*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + (d*f*x + c*f + (d*f*x + c*f)*cos(d*x + c) + (d*f*x + c*f)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + (d*f*x + c*f + (d*f*x + c*f)*cos(d*x + c) + (d*f*x + c*f)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 2*(f*cos(d*x + c) + f*sin(d*x + c) + f)*log(sin(d*x + c) + 1) - 2*(d*f*x + d*e)*sin(d*x + c))/(a*d^2*cos(d*x + c) + a*d^2*sin(d*x + c) + a*d^2)","B",0
200,1,97,0,1.364121," ","integrate(csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, \cos\left(d x + c\right) + 2 \, \sin\left(d x + c\right) - 2}{2 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"-1/2*((cos(d*x + c) + sin(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c) + sin(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) - 2*cos(d*x + c) + 2*sin(d*x + c) - 2)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","B",0
201,0,0,0,1.044431," ","integrate(csc(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(d x + c\right)}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(csc(d*x + c)/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
202,0,0,0,0.907842," ","integrate(csc(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(d x + c\right)}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(csc(d*x + c)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
203,1,4789,0,1.854579," ","integrate((f*x+e)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 6 \, d^{3} e^{2} f x + 2 \, d^{3} e^{3} - 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} - 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} - 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} - 6 i \, {\left(d^{2} e f^{2} - d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2} + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2} + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2} + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2} + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} - 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} + 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} + 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f + 6 i \, d e f^{2} + 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} - 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f - 6 i \, d e f^{2} - 6 i \, {\left(d^{2} e f^{2} + d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} - {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} - {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + {\left(d^{3} e^{3} - 3 \, {\left(c + 1\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} - {\left(c^{3} + 3 \, c^{2}\right)} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} + 2 \, c\right)} d e f^{2} + {\left(c^{3} + 3 \, c^{2}\right)} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left(6 i \, f^{3} \cos\left(d x + c\right)^{2} - 6 i \, f^{3} + {\left(-6 i \, f^{3} \cos\left(d x + c\right) - 6 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-6 i \, f^{3} \cos\left(d x + c\right)^{2} + 6 i \, f^{3} + {\left(6 i \, f^{3} \cos\left(d x + c\right) + 6 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(6 i \, f^{3} \cos\left(d x + c\right)^{2} - 6 i \, f^{3} + {\left(-6 i \, f^{3} \cos\left(d x + c\right) - 6 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-6 i \, f^{3} \cos\left(d x + c\right)^{2} + 6 i \, f^{3} + {\left(6 i \, f^{3} \cos\left(d x + c\right) + 6 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 6 \, {\left(d f^{3} x + d e f^{2} - f^{3} - {\left(d f^{3} x + d e f^{2} - f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{3} x + d e f^{2} - f^{3} + {\left(d f^{3} x + d e f^{2} - f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 6 \, {\left(d f^{3} x + d e f^{2} - f^{3} - {\left(d f^{3} x + d e f^{2} - f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{3} x + d e f^{2} - f^{3} + {\left(d f^{3} x + d e f^{2} - f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 12 \, {\left(f^{3} \cos\left(d x + c\right)^{2} - f^{3} - {\left(f^{3} \cos\left(d x + c\right) + f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 12 \, {\left(f^{3} \cos\left(d x + c\right)^{2} - f^{3} - {\left(f^{3} \cos\left(d x + c\right) + f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2} + f^{3} - {\left(d f^{3} x + d e f^{2} + f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{3} x + d e f^{2} + f^{3} + {\left(d f^{3} x + d e f^{2} + f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2} + f^{3} - {\left(d f^{3} x + d e f^{2} + f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{3} x + d e f^{2} + f^{3} + {\left(d f^{3} x + d e f^{2} + f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3} + 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{4} \cos\left(d x + c\right)^{2} - a d^{4} - {\left(a d^{4} \cos\left(d x + c\right) + a d^{4}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 6*d^3*e^2*f*x + 2*d^3*e^3 - 4*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c)^2 - 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c) + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f - 6*I*d*e*f^2 + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f + 6*I*d*e*f^2 - 6*I*(d^2*e*f^2 - d*f^3)*x)*cos(d*x + c)^2 + 6*I*(d^2*e*f^2 - d*f^3)*x + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f - 6*I*d*e*f^2 + 6*I*(d^2*e*f^2 - d*f^3)*x + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f - 6*I*d*e*f^2 + 6*I*(d^2*e*f^2 - d*f^3)*x)*cos(d*x + c))*sin(d*x + c))*dilog(cos(d*x + c) + I*sin(d*x + c)) + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f + 6*I*d*e*f^2 + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f - 6*I*d*e*f^2 + 6*I*(d^2*e*f^2 - d*f^3)*x)*cos(d*x + c)^2 - 6*I*(d^2*e*f^2 - d*f^3)*x + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f + 6*I*d*e*f^2 - 6*I*(d^2*e*f^2 - d*f^3)*x + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f + 6*I*d*e*f^2 - 6*I*(d^2*e*f^2 - d*f^3)*x)*cos(d*x + c))*sin(d*x + c))*dilog(cos(d*x + c) - I*sin(d*x + c)) + (-12*I*d*f^3*x - 12*I*d*e*f^2 + (12*I*d*f^3*x + 12*I*d*e*f^2)*cos(d*x + c)^2 + (-12*I*d*f^3*x - 12*I*d*e*f^2 + (-12*I*d*f^3*x - 12*I*d*e*f^2)*cos(d*x + c))*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + (12*I*d*f^3*x + 12*I*d*e*f^2 + (-12*I*d*f^3*x - 12*I*d*e*f^2)*cos(d*x + c)^2 + (12*I*d*f^3*x + 12*I*d*e*f^2 + (12*I*d*f^3*x + 12*I*d*e*f^2)*cos(d*x + c))*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f + 6*I*d*e*f^2 + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f - 6*I*d*e*f^2 - 6*I*(d^2*e*f^2 + d*f^3)*x)*cos(d*x + c)^2 + 6*I*(d^2*e*f^2 + d*f^3)*x + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f + 6*I*d*e*f^2 + 6*I*(d^2*e*f^2 + d*f^3)*x + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f + 6*I*d*e*f^2 + 6*I*(d^2*e*f^2 + d*f^3)*x)*cos(d*x + c))*sin(d*x + c))*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f - 6*I*d*e*f^2 + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f + 6*I*d*e*f^2 + 6*I*(d^2*e*f^2 + d*f^3)*x)*cos(d*x + c)^2 - 6*I*(d^2*e*f^2 + d*f^3)*x + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f - 6*I*d*e*f^2 - 6*I*(d^2*e*f^2 + d*f^3)*x + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f - 6*I*d*e*f^2 - 6*I*(d^2*e*f^2 + d*f^3)*x)*cos(d*x + c))*sin(d*x + c))*dilog(-cos(d*x + c) - I*sin(d*x + c)) + (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 - (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x)*cos(d*x + c)^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^2 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 - (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x)*cos(d*x + c)^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) + 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^2 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c))*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^2 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c))*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 - (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3)*cos(d*x + c)^2 + (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 + (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 - (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3)*cos(d*x + c)^2 + (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3 + (d^3*e^3 - 3*(c + 1)*d^2*e^2*f + 3*(c^2 + 2*c)*d*e*f^2 - (c^3 + 3*c^2)*f^3)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*cos(d*x + c)^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^2 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*cos(d*x + c)^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 + 2*c)*d*e*f^2 + (c^3 + 3*c^2)*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + (6*I*f^3*cos(d*x + c)^2 - 6*I*f^3 + (-6*I*f^3*cos(d*x + c) - 6*I*f^3)*sin(d*x + c))*polylog(4, cos(d*x + c) + I*sin(d*x + c)) + (-6*I*f^3*cos(d*x + c)^2 + 6*I*f^3 + (6*I*f^3*cos(d*x + c) + 6*I*f^3)*sin(d*x + c))*polylog(4, cos(d*x + c) - I*sin(d*x + c)) + (6*I*f^3*cos(d*x + c)^2 - 6*I*f^3 + (-6*I*f^3*cos(d*x + c) - 6*I*f^3)*sin(d*x + c))*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) + (-6*I*f^3*cos(d*x + c)^2 + 6*I*f^3 + (6*I*f^3*cos(d*x + c) + 6*I*f^3)*sin(d*x + c))*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) - 6*(d*f^3*x + d*e*f^2 - f^3 - (d*f^3*x + d*e*f^2 - f^3)*cos(d*x + c)^2 + (d*f^3*x + d*e*f^2 - f^3 + (d*f^3*x + d*e*f^2 - f^3)*cos(d*x + c))*sin(d*x + c))*polylog(3, cos(d*x + c) + I*sin(d*x + c)) - 6*(d*f^3*x + d*e*f^2 - f^3 - (d*f^3*x + d*e*f^2 - f^3)*cos(d*x + c)^2 + (d*f^3*x + d*e*f^2 - f^3 + (d*f^3*x + d*e*f^2 - f^3)*cos(d*x + c))*sin(d*x + c))*polylog(3, cos(d*x + c) - I*sin(d*x + c)) - 12*(f^3*cos(d*x + c)^2 - f^3 - (f^3*cos(d*x + c) + f^3)*sin(d*x + c))*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 12*(f^3*cos(d*x + c)^2 - f^3 - (f^3*cos(d*x + c) + f^3)*sin(d*x + c))*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2 + f^3 - (d*f^3*x + d*e*f^2 + f^3)*cos(d*x + c)^2 + (d*f^3*x + d*e*f^2 + f^3 + (d*f^3*x + d*e*f^2 + f^3)*cos(d*x + c))*sin(d*x + c))*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2 + f^3 - (d*f^3*x + d*e*f^2 + f^3)*cos(d*x + c)^2 + (d*f^3*x + d*e*f^2 + f^3 + (d*f^3*x + d*e*f^2 + f^3)*cos(d*x + c))*sin(d*x + c))*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3 + 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c))*sin(d*x + c))/(a*d^4*cos(d*x + c)^2 - a*d^4 - (a*d^4*cos(d*x + c) + a*d^4)*sin(d*x + c))","C",0
204,1,2533,0,1.153432," ","integrate((f*x+e)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} - 4 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f + 2 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 2 i \, f^{2} + {\left(2 i \, d f^{2} x + 2 i \, d e f - 2 i \, f^{2} + {\left(2 i \, d f^{2} x + 2 i \, d e f - 2 i \, f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f - 2 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 i \, f^{2} + {\left(-2 i \, d f^{2} x - 2 i \, d e f + 2 i \, f^{2} + {\left(-2 i \, d f^{2} x - 2 i \, d e f + 2 i \, f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(4 i \, f^{2} \cos\left(d x + c\right)^{2} - 4 i \, f^{2} + {\left(-4 i \, f^{2} \cos\left(d x + c\right) - 4 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-4 i \, f^{2} \cos\left(d x + c\right)^{2} + 4 i \, f^{2} + {\left(4 i \, f^{2} \cos\left(d x + c\right) + 4 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f - 2 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 i \, f^{2} + {\left(2 i \, d f^{2} x + 2 i \, d e f + 2 i \, f^{2} + {\left(2 i \, d f^{2} x + 2 i \, d e f + 2 i \, f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f + 2 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 2 i \, f^{2} + {\left(-2 i \, d f^{2} x - 2 i \, d e f - 2 i \, f^{2} + {\left(-2 i \, d f^{2} x - 2 i \, d e f - 2 i \, f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f - {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, {\left(d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d^{2} e f + d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, {\left(d^{2} e f + d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, {\left(d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(d e f - c f^{2} - {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f - {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, {\left(d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d^{2} e f + d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, {\left(d^{2} e f + d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, {\left(d^{2} e f + d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(d f^{2} x + c f^{2} - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 4 \, {\left(d f^{2} x + c f^{2} - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{2} x + c f^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2} - {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2} + {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2} - {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2} + {\left(d^{2} e^{2} - 2 \, {\left(c + 1\right)} d e f + {\left(c^{2} + 2 \, c\right)} f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} - {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(d e f - c f^{2} - {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d e f - c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} - {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x + {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} + 2 \, c\right)} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2} - {\left(f^{2} \cos\left(d x + c\right) + f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 2 \, {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2} - {\left(f^{2} \cos\left(d x + c\right) + f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2} - {\left(f^{2} \cos\left(d x + c\right) + f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 2 \, {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2} - {\left(f^{2} \cos\left(d x + c\right) + f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{3} \cos\left(d x + c\right)^{2} - a d^{3} - {\left(a d^{3} \cos\left(d x + c\right) + a d^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 - 4*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c)^2 - 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c) + (2*I*d*f^2*x + 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f + 2*I*f^2)*cos(d*x + c)^2 - 2*I*f^2 + (2*I*d*f^2*x + 2*I*d*e*f - 2*I*f^2 + (2*I*d*f^2*x + 2*I*d*e*f - 2*I*f^2)*cos(d*x + c))*sin(d*x + c))*dilog(cos(d*x + c) + I*sin(d*x + c)) + (-2*I*d*f^2*x - 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f - 2*I*f^2)*cos(d*x + c)^2 + 2*I*f^2 + (-2*I*d*f^2*x - 2*I*d*e*f + 2*I*f^2 + (-2*I*d*f^2*x - 2*I*d*e*f + 2*I*f^2)*cos(d*x + c))*sin(d*x + c))*dilog(cos(d*x + c) - I*sin(d*x + c)) + (4*I*f^2*cos(d*x + c)^2 - 4*I*f^2 + (-4*I*f^2*cos(d*x + c) - 4*I*f^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-4*I*f^2*cos(d*x + c)^2 + 4*I*f^2 + (4*I*f^2*cos(d*x + c) + 4*I*f^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (2*I*d*f^2*x + 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f - 2*I*f^2)*cos(d*x + c)^2 + 2*I*f^2 + (2*I*d*f^2*x + 2*I*d*e*f + 2*I*f^2 + (2*I*d*f^2*x + 2*I*d*e*f + 2*I*f^2)*cos(d*x + c))*sin(d*x + c))*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (-2*I*d*f^2*x - 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f + 2*I*f^2)*cos(d*x + c)^2 - 2*I*f^2 + (-2*I*d*f^2*x - 2*I*d*e*f - 2*I*f^2 + (-2*I*d*f^2*x - 2*I*d*e*f - 2*I*f^2)*cos(d*x + c))*sin(d*x + c))*dilog(-cos(d*x + c) - I*sin(d*x + c)) + (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f - (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*(d^2*e*f + d*f^2)*x)*cos(d*x + c)^2 + 2*(d^2*e*f + d*f^2)*x + (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*(d^2*e*f + d*f^2)*x + (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*(d^2*e*f + d*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 4*(d*e*f - c*f^2 - (d*e*f - c*f^2)*cos(d*x + c)^2 + (d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f - (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*(d^2*e*f + d*f^2)*x)*cos(d*x + c)^2 + 2*(d^2*e*f + d*f^2)*x + (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*(d^2*e*f + d*f^2)*x + (d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*(d^2*e*f + d*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) + 4*(d*f^2*x + c*f^2 - (d*f^2*x + c*f^2)*cos(d*x + c)^2 + (d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c))*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + 4*(d*f^2*x + c*f^2 - (d*f^2*x + c*f^2)*cos(d*x + c)^2 + (d*f^2*x + c*f^2 + (d*f^2*x + c*f^2)*cos(d*x + c))*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2 - (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2)*cos(d*x + c)^2 + (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2 + (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2 - (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2)*cos(d*x + c)^2 + (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2 + (d^2*e^2 - 2*(c + 1)*d*e*f + (c^2 + 2*c)*f^2)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 - (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 + 2*(d^2*e*f - d*f^2)*x)*cos(d*x + c)^2 + 2*(d^2*e*f - d*f^2)*x + (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 + 2*(d^2*e*f - d*f^2)*x + (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 + 2*(d^2*e*f - d*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 4*(d*e*f - c*f^2 - (d*e*f - c*f^2)*cos(d*x + c)^2 + (d*e*f - c*f^2 + (d*e*f - c*f^2)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) - (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 - (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 + 2*(d^2*e*f - d*f^2)*x)*cos(d*x + c)^2 + 2*(d^2*e*f - d*f^2)*x + (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 + 2*(d^2*e*f - d*f^2)*x + (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 + 2*c)*f^2 + 2*(d^2*e*f - d*f^2)*x)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + 2*(f^2*cos(d*x + c)^2 - f^2 - (f^2*cos(d*x + c) + f^2)*sin(d*x + c))*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 2*(f^2*cos(d*x + c)^2 - f^2 - (f^2*cos(d*x + c) + f^2)*sin(d*x + c))*polylog(3, cos(d*x + c) - I*sin(d*x + c)) - 2*(f^2*cos(d*x + c)^2 - f^2 - (f^2*cos(d*x + c) + f^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) - 2*(f^2*cos(d*x + c)^2 - f^2 - (f^2*cos(d*x + c) + f^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 + 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c))*sin(d*x + c))/(a*d^3*cos(d*x + c)^2 - a*d^3 - (a*d^3*cos(d*x + c) + a*d^3)*sin(d*x + c))","C",0
205,1,858,0,0.996407," ","integrate((f*x+e)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d f x - 4 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} + 2 \, d e - 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(-i \, f \cos\left(d x + c\right)^{2} + {\left(i \, f \cos\left(d x + c\right) + i \, f\right)} \sin\left(d x + c\right) + i \, f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(i \, f \cos\left(d x + c\right)^{2} + {\left(-i \, f \cos\left(d x + c\right) - i \, f\right)} \sin\left(d x + c\right) - i \, f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(-i \, f \cos\left(d x + c\right)^{2} + {\left(i \, f \cos\left(d x + c\right) + i \, f\right)} \sin\left(d x + c\right) + i \, f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(i \, f \cos\left(d x + c\right)^{2} + {\left(-i \, f \cos\left(d x + c\right) - i \, f\right)} \sin\left(d x + c\right) - i \, f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(d f x - {\left(d f x + d e + f\right)} \cos\left(d x + c\right)^{2} + d e + {\left(d f x + d e + {\left(d f x + d e + f\right)} \cos\left(d x + c\right) + f\right)} \sin\left(d x + c\right) + f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + {\left(d f x - {\left(d f x + d e + f\right)} \cos\left(d x + c\right)^{2} + d e + {\left(d f x + d e + {\left(d f x + d e + f\right)} \cos\left(d x + c\right) + f\right)} \sin\left(d x + c\right) + f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left({\left(d e - {\left(c + 1\right)} f\right)} \cos\left(d x + c\right)^{2} - d e + {\left(c + 1\right)} f - {\left(d e - {\left(c + 1\right)} f + {\left(d e - {\left(c + 1\right)} f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(d e - {\left(c + 1\right)} f\right)} \cos\left(d x + c\right)^{2} - d e + {\left(c + 1\right)} f - {\left(d e - {\left(c + 1\right)} f + {\left(d e - {\left(c + 1\right)} f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(d f x - {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} + c f + {\left(d f x + c f + {\left(d f x + c f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - {\left(d f x - {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} + c f + {\left(d f x + c f + {\left(d f x + c f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(f \cos\left(d x + c\right)^{2} - {\left(f \cos\left(d x + c\right) + f\right)} \sin\left(d x + c\right) - f\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(d f x + d e + 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a d^{2} \cos\left(d x + c\right)^{2} - a d^{2} - {\left(a d^{2} \cos\left(d x + c\right) + a d^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*d*f*x - 4*(d*f*x + d*e)*cos(d*x + c)^2 + 2*d*e - 2*(d*f*x + d*e)*cos(d*x + c) + (-I*f*cos(d*x + c)^2 + (I*f*cos(d*x + c) + I*f)*sin(d*x + c) + I*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (I*f*cos(d*x + c)^2 + (-I*f*cos(d*x + c) - I*f)*sin(d*x + c) - I*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (-I*f*cos(d*x + c)^2 + (I*f*cos(d*x + c) + I*f)*sin(d*x + c) + I*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (I*f*cos(d*x + c)^2 + (-I*f*cos(d*x + c) - I*f)*sin(d*x + c) - I*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + (d*f*x - (d*f*x + d*e + f)*cos(d*x + c)^2 + d*e + (d*f*x + d*e + (d*f*x + d*e + f)*cos(d*x + c) + f)*sin(d*x + c) + f)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + (d*f*x - (d*f*x + d*e + f)*cos(d*x + c)^2 + d*e + (d*f*x + d*e + (d*f*x + d*e + f)*cos(d*x + c) + f)*sin(d*x + c) + f)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + ((d*e - (c + 1)*f)*cos(d*x + c)^2 - d*e + (c + 1)*f - (d*e - (c + 1)*f + (d*e - (c + 1)*f)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + ((d*e - (c + 1)*f)*cos(d*x + c)^2 - d*e + (c + 1)*f - (d*e - (c + 1)*f + (d*e - (c + 1)*f)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - (d*f*x - (d*f*x + c*f)*cos(d*x + c)^2 + c*f + (d*f*x + c*f + (d*f*x + c*f)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - (d*f*x - (d*f*x + c*f)*cos(d*x + c)^2 + c*f + (d*f*x + c*f + (d*f*x + c*f)*cos(d*x + c))*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 2*(f*cos(d*x + c)^2 - (f*cos(d*x + c) + f)*sin(d*x + c) - f)*log(sin(d*x + c) + 1) - 2*(d*f*x + d*e + 2*(d*f*x + d*e)*cos(d*x + c))*sin(d*x + c))/(a*d^2*cos(d*x + c)^2 - a*d^2 - (a*d^2*cos(d*x + c) + a*d^2)*sin(d*x + c))","B",0
206,1,156,0,0.911908," ","integrate(csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right) - 2}{2 \, {\left(a d \cos\left(d x + c\right)^{2} - a d - {\left(a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2*(4*cos(d*x + c)^2 + (cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*(2*cos(d*x + c) + 1)*sin(d*x + c) + 2*cos(d*x + c) - 2)/(a*d*cos(d*x + c)^2 - a*d - (a*d*cos(d*x + c) + a*d)*sin(d*x + c))","B",0
207,0,0,0,0.916217," ","integrate(csc(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(d x + c\right)^{2}}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(csc(d*x + c)^2/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
208,0,0,0,1.042223," ","integrate(csc(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(d x + c\right)^{2}}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(csc(d*x + c)^2/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
209,1,7842,0,1.760506," ","integrate((f*x+e)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, d^{3} f^{3} x^{3} + 4 \, d^{3} e^{3} - 6 \, d^{2} e^{2} f - 8 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(2 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} - 6 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - d^{2} e^{2} f + {\left(3 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left(d^{3} e^{2} f - d^{2} e f^{2}\right)} x + 6 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right) - {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + 6 i \, f^{3} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 6 i \, f^{3} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} - 6 i \, f^{3} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 i \, f^{3} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 i \, {\left(3 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2} + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2} + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(24 i \, d f^{3} x + 24 i \, d e f^{2} + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2}\right)} \cos\left(d x + c\right) + {\left(24 i \, d f^{3} x + 24 i \, d e f^{2} + {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + 6 i \, f^{3} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + 6 i \, f^{3} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} - 6 i \, f^{3} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 i \, f^{3} - 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 i \, f^{3} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f + 12 i \, d e f^{2} + 6 i \, f^{3} + 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 i \, {\left(3 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 3 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 3 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 2 \, d^{2} e^{2} f + 2 \, d e f^{2} + {\left(3 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3} - {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 3 \, {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} - {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} - {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} - {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} - {\left(d^{3} e^{3} - {\left(3 \, c + 2\right)} d^{2} e^{2} f + {\left(3 \, c^{2} + 4 \, c + 2\right)} d e f^{2} - {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3} - {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 3 \, {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - {\left(3 \, c^{2} + 4 \, c\right)} d e f^{2} + {\left(c^{3} + 2 \, c^{2} + 2 \, c\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{3} e^{2} f - 4 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - {\left(18 i \, f^{3} \cos\left(d x + c\right)^{3} + 18 i \, f^{3} \cos\left(d x + c\right)^{2} - 18 i \, f^{3} \cos\left(d x + c\right) - 18 i \, f^{3} + {\left(18 i \, f^{3} \cos\left(d x + c\right)^{2} - 18 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(-18 i \, f^{3} \cos\left(d x + c\right)^{3} - 18 i \, f^{3} \cos\left(d x + c\right)^{2} + 18 i \, f^{3} \cos\left(d x + c\right) + 18 i \, f^{3} + {\left(-18 i \, f^{3} \cos\left(d x + c\right)^{2} + 18 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(18 i \, f^{3} \cos\left(d x + c\right)^{3} + 18 i \, f^{3} \cos\left(d x + c\right)^{2} - 18 i \, f^{3} \cos\left(d x + c\right) - 18 i \, f^{3} + {\left(18 i \, f^{3} \cos\left(d x + c\right)^{2} - 18 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(-18 i \, f^{3} \cos\left(d x + c\right)^{3} - 18 i \, f^{3} \cos\left(d x + c\right)^{2} + 18 i \, f^{3} \cos\left(d x + c\right) + 18 i \, f^{3} + {\left(-18 i \, f^{3} \cos\left(d x + c\right)^{2} + 18 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 6 \, {\left(3 \, d f^{3} x + 3 \, d e f^{2} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right)^{3} - 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right) + {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 \, {\left(3 \, d f^{3} x + 3 \, d e f^{2} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right)^{3} - 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right) + {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} - 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 24 \, {\left(f^{3} \cos\left(d x + c\right)^{3} + f^{3} \cos\left(d x + c\right)^{2} - f^{3} \cos\left(d x + c\right) - f^{3} + {\left(f^{3} \cos\left(d x + c\right)^{2} - f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 24 \, {\left(f^{3} \cos\left(d x + c\right)^{3} + f^{3} \cos\left(d x + c\right)^{2} - f^{3} \cos\left(d x + c\right) - f^{3} + {\left(f^{3} \cos\left(d x + c\right)^{2} - f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 6 \, {\left(3 \, d f^{3} x + 3 \, d e f^{2} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right) + {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 6 \, {\left(3 \, d f^{3} x + 3 \, d e f^{2} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right)^{3} + 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right) + {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3} - {\left(3 \, d f^{3} x + 3 \, d e f^{2} + 2 \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(2 \, d^{3} f^{3} x^{3} + 2 \, d^{3} e^{3} + 3 \, d^{2} e^{2} f + 3 \, {\left(2 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} - 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(d^{3} e^{2} f + d^{2} e f^{2}\right)} x - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 3 \, d^{2} e^{2} f + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a d^{4} \cos\left(d x + c\right)^{3} + a d^{4} \cos\left(d x + c\right)^{2} - a d^{4} \cos\left(d x + c\right) - a d^{4} + {\left(a d^{4} \cos\left(d x + c\right)^{2} - a d^{4}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/4*(4*d^3*f^3*x^3 + 4*d^3*e^3 - 6*d^2*e^2*f - 8*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c)^3 + 6*(2*d^3*e*f^2 - d^2*f^3)*x^2 - 6*(d^3*f^3*x^3 + d^3*e^3 - d^2*e^2*f + (3*d^3*e*f^2 - d^2*f^3)*x^2 + (3*d^3*e^2*f - 2*d^2*e*f^2)*x)*cos(d*x + c)^2 + 12*(d^3*e^2*f - d^2*e*f^2)*x + 6*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c) - (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*I*d*e*f^2 + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f + 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^3 + 6*I*f^3 + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f + 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^2 + 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c) + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*I*d*e*f^2 + 6*I*f^3 + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f + 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^2 + 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*sin(d*x + c))*dilog(cos(d*x + c) + I*sin(d*x + c)) - (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f + 12*I*d*e*f^2 + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^3 - 6*I*f^3 + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^2 - 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f + 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c) + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f + 12*I*d*e*f^2 - 6*I*f^3 + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*cos(d*x + c)^2 - 6*I*(3*d^2*e*f^2 - 2*d*f^3)*x)*sin(d*x + c))*dilog(cos(d*x + c) - I*sin(d*x + c)) - (-24*I*d*f^3*x - 24*I*d*e*f^2 + (24*I*d*f^3*x + 24*I*d*e*f^2)*cos(d*x + c)^3 + (24*I*d*f^3*x + 24*I*d*e*f^2)*cos(d*x + c)^2 + (-24*I*d*f^3*x - 24*I*d*e*f^2)*cos(d*x + c) + (-24*I*d*f^3*x - 24*I*d*e*f^2 + (24*I*d*f^3*x + 24*I*d*e*f^2)*cos(d*x + c)^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) - (24*I*d*f^3*x + 24*I*d*e*f^2 + (-24*I*d*f^3*x - 24*I*d*e*f^2)*cos(d*x + c)^3 + (-24*I*d*f^3*x - 24*I*d*e*f^2)*cos(d*x + c)^2 + (24*I*d*f^3*x + 24*I*d*e*f^2)*cos(d*x + c) + (24*I*d*f^3*x + 24*I*d*e*f^2 + (-24*I*d*f^3*x - 24*I*d*e*f^2)*cos(d*x + c)^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f + 12*I*d*e*f^2 + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^3 + 6*I*f^3 + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f + 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c) + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f + 12*I*d*e*f^2 + 6*I*f^3 + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*sin(d*x + c))*dilog(-cos(d*x + c) + I*sin(d*x + c)) - (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*I*d*e*f^2 + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f + 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^3 - 6*I*f^3 + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f + 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 - 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*I*d*e*f^2 - 6*I*f^3 - 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c) + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*I*d*e*f^2 - 6*I*f^3 + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f + 12*I*d*e*f^2 + 6*I*f^3 + 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 - 6*I*(3*d^2*e*f^2 + 2*d*f^3)*x)*sin(d*x + c))*dilog(-cos(d*x + c) - I*sin(d*x + c)) - 3*(d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 - (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^3 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x + (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c) + (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^2 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - 3*(d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 - (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^3 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x + (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c) + (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + d^3*e^3 + 2*d^2*e^2*f + 2*d*e*f^2 + (3*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f + 4*d^2*e*f^2 + 2*d*f^3)*x)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^2 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^2 + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3 - (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + 3*(d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3 - (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c)^3 - (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c)^2 + (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c) + (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3 - (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + 3*(d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3 - (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c)^3 - (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c)^2 + (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c) + (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3 - (d^3*e^3 - (3*c + 2)*d^2*e^2*f + (3*c^2 + 4*c + 2)*d*e*f^2 - (c^3 + 2*c^2 + 2*c)*f^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + 3*(d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c) + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^2 + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3 - (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + 3*(d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c) + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - (3*c^2 + 4*c)*d*e*f^2 + (c^3 + 2*c^2 + 2*c)*f^3 + (3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*cos(d*x + c)^2 + (3*d^3*e^2*f - 4*d^2*e*f^2 + 2*d*f^3)*x)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - (18*I*f^3*cos(d*x + c)^3 + 18*I*f^3*cos(d*x + c)^2 - 18*I*f^3*cos(d*x + c) - 18*I*f^3 + (18*I*f^3*cos(d*x + c)^2 - 18*I*f^3)*sin(d*x + c))*polylog(4, cos(d*x + c) + I*sin(d*x + c)) - (-18*I*f^3*cos(d*x + c)^3 - 18*I*f^3*cos(d*x + c)^2 + 18*I*f^3*cos(d*x + c) + 18*I*f^3 + (-18*I*f^3*cos(d*x + c)^2 + 18*I*f^3)*sin(d*x + c))*polylog(4, cos(d*x + c) - I*sin(d*x + c)) - (18*I*f^3*cos(d*x + c)^3 + 18*I*f^3*cos(d*x + c)^2 - 18*I*f^3*cos(d*x + c) - 18*I*f^3 + (18*I*f^3*cos(d*x + c)^2 - 18*I*f^3)*sin(d*x + c))*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) - (-18*I*f^3*cos(d*x + c)^3 - 18*I*f^3*cos(d*x + c)^2 + 18*I*f^3*cos(d*x + c) + 18*I*f^3 + (-18*I*f^3*cos(d*x + c)^2 + 18*I*f^3)*sin(d*x + c))*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) + 6*(3*d*f^3*x + 3*d*e*f^2 - (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c)^3 - 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c)^2 + (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c) + (3*d*f^3*x + 3*d*e*f^2 - 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 6*(3*d*f^3*x + 3*d*e*f^2 - (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c)^3 - 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c)^2 + (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c) + (3*d*f^3*x + 3*d*e*f^2 - 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 - 2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 24*(f^3*cos(d*x + c)^3 + f^3*cos(d*x + c)^2 - f^3*cos(d*x + c) - f^3 + (f^3*cos(d*x + c)^2 - f^3)*sin(d*x + c))*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 24*(f^3*cos(d*x + c)^3 + f^3*cos(d*x + c)^2 - f^3*cos(d*x + c) - f^3 + (f^3*cos(d*x + c)^2 - f^3)*sin(d*x + c))*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) - 6*(3*d*f^3*x + 3*d*e*f^2 - (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c)^3 + 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c)^2 + (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c) + (3*d*f^3*x + 3*d*e*f^2 + 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) - 6*(3*d*f^3*x + 3*d*e*f^2 - (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c)^3 + 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c)^2 + (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c) + (3*d*f^3*x + 3*d*e*f^2 + 2*f^3 - (3*d*f^3*x + 3*d*e*f^2 + 2*f^3)*cos(d*x + c)^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(2*d^3*f^3*x^3 + 2*d^3*e^3 + 3*d^2*e^2*f + 3*(2*d^3*e*f^2 + d^2*f^3)*x^2 - 4*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*cos(d*x + c)^2 + 6*(d^3*e^2*f + d^2*e*f^2)*x - (d^3*f^3*x^3 + d^3*e^3 - 3*d^2*e^2*f + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*cos(d*x + c))*sin(d*x + c))/(a*d^4*cos(d*x + c)^3 + a*d^4*cos(d*x + c)^2 - a*d^4*cos(d*x + c) - a*d^4 + (a*d^4*cos(d*x + c)^2 - a*d^4)*sin(d*x + c))","C",0
210,1,4026,0,1.763448," ","integrate((f*x+e)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e^{2} - 8 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right)^{3} - 4 \, d e f - 2 \, {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} - 2 \, d e f + 2 \, {\left(3 \, d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, d^{2} e f - d f^{2}\right)} x + 6 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right) - {\left(6 i \, d f^{2} x + {\left(-6 i \, d f^{2} x - 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{3} + 6 i \, d e f + {\left(-6 i \, d f^{2} x - 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 4 i \, f^{2} + {\left(6 i \, d f^{2} x + 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right) + {\left(6 i \, d f^{2} x + 6 i \, d e f + {\left(-6 i \, d f^{2} x - 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 4 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(-6 i \, d f^{2} x + {\left(6 i \, d f^{2} x + 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{3} - 6 i \, d e f + {\left(6 i \, d f^{2} x + 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 i \, f^{2} + {\left(-6 i \, d f^{2} x - 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right) + {\left(-6 i \, d f^{2} x - 6 i \, d e f + {\left(6 i \, d f^{2} x + 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(8 i \, f^{2} \cos\left(d x + c\right)^{3} + 8 i \, f^{2} \cos\left(d x + c\right)^{2} - 8 i \, f^{2} \cos\left(d x + c\right) - 8 i \, f^{2} + {\left(8 i \, f^{2} \cos\left(d x + c\right)^{2} - 8 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(-8 i \, f^{2} \cos\left(d x + c\right)^{3} - 8 i \, f^{2} \cos\left(d x + c\right)^{2} + 8 i \, f^{2} \cos\left(d x + c\right) + 8 i \, f^{2} + {\left(-8 i \, f^{2} \cos\left(d x + c\right)^{2} + 8 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(6 i \, d f^{2} x + {\left(-6 i \, d f^{2} x - 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{3} + 6 i \, d e f + {\left(-6 i \, d f^{2} x - 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 i \, f^{2} + {\left(6 i \, d f^{2} x + 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right) + {\left(6 i \, d f^{2} x + 6 i \, d e f + {\left(-6 i \, d f^{2} x - 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(-6 i \, d f^{2} x + {\left(6 i \, d f^{2} x + 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{3} - 6 i \, d e f + {\left(6 i \, d f^{2} x + 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 4 i \, f^{2} + {\left(-6 i \, d f^{2} x - 6 i \, d e f - 4 i \, f^{2}\right)} \cos\left(d x + c\right) + {\left(-6 i \, d f^{2} x - 6 i \, d e f + {\left(6 i \, d f^{2} x + 6 i \, d e f + 4 i \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 4 i \, f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{3} + 4 \, d e f - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right) + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 8 \, {\left({\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{3} - d e f + c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) - {\left(d e f - c f^{2} - {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{3} + 4 \, d e f - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right) + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 8 \, {\left(d f^{2} x - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{3} + c f^{2} - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2} - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 8 \, {\left(d f^{2} x - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{3} + c f^{2} - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) + {\left(d f^{2} x + c f^{2} - {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f - {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} - {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} - {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f - {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} - {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right) + {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2} - {\left(3 \, d^{2} e^{2} - 2 \, {\left(3 \, c + 2\right)} d e f + {\left(3 \, c^{2} + 4 \, c + 2\right)} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 8 \, {\left({\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{3} - d e f + c f^{2} + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) - {\left(d e f - c f^{2} - {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right) + {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} + 4 \, c\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(f^{2} \cos\left(d x + c\right)^{3} + f^{2} \cos\left(d x + c\right)^{2} - f^{2} \cos\left(d x + c\right) - f^{2} + {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 6 \, {\left(f^{2} \cos\left(d x + c\right)^{3} + f^{2} \cos\left(d x + c\right)^{2} - f^{2} \cos\left(d x + c\right) - f^{2} + {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 6 \, {\left(f^{2} \cos\left(d x + c\right)^{3} + f^{2} \cos\left(d x + c\right)^{2} - f^{2} \cos\left(d x + c\right) - f^{2} + {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 \, {\left(f^{2} \cos\left(d x + c\right)^{3} + f^{2} \cos\left(d x + c\right)^{2} - f^{2} \cos\left(d x + c\right) - f^{2} + {\left(f^{2} \cos\left(d x + c\right)^{2} - f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(2 \, d^{2} f^{2} x^{2} + 2 \, d^{2} e^{2} + 2 \, d e f - 4 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, d^{2} e f + d f^{2}\right)} x - {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} - 2 \, d e f + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a d^{3} \cos\left(d x + c\right)^{3} + a d^{3} \cos\left(d x + c\right)^{2} - a d^{3} \cos\left(d x + c\right) - a d^{3} + {\left(a d^{3} \cos\left(d x + c\right)^{2} - a d^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/4*(4*d^2*f^2*x^2 + 4*d^2*e^2 - 8*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c)^3 - 4*d*e*f - 2*(3*d^2*f^2*x^2 + 3*d^2*e^2 - 2*d*e*f + 2*(3*d^2*e*f - d*f^2)*x)*cos(d*x + c)^2 + 4*(2*d^2*e*f - d*f^2)*x + 6*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c) - (6*I*d*f^2*x + (-6*I*d*f^2*x - 6*I*d*e*f + 4*I*f^2)*cos(d*x + c)^3 + 6*I*d*e*f + (-6*I*d*f^2*x - 6*I*d*e*f + 4*I*f^2)*cos(d*x + c)^2 - 4*I*f^2 + (6*I*d*f^2*x + 6*I*d*e*f - 4*I*f^2)*cos(d*x + c) + (6*I*d*f^2*x + 6*I*d*e*f + (-6*I*d*f^2*x - 6*I*d*e*f + 4*I*f^2)*cos(d*x + c)^2 - 4*I*f^2)*sin(d*x + c))*dilog(cos(d*x + c) + I*sin(d*x + c)) - (-6*I*d*f^2*x + (6*I*d*f^2*x + 6*I*d*e*f - 4*I*f^2)*cos(d*x + c)^3 - 6*I*d*e*f + (6*I*d*f^2*x + 6*I*d*e*f - 4*I*f^2)*cos(d*x + c)^2 + 4*I*f^2 + (-6*I*d*f^2*x - 6*I*d*e*f + 4*I*f^2)*cos(d*x + c) + (-6*I*d*f^2*x - 6*I*d*e*f + (6*I*d*f^2*x + 6*I*d*e*f - 4*I*f^2)*cos(d*x + c)^2 + 4*I*f^2)*sin(d*x + c))*dilog(cos(d*x + c) - I*sin(d*x + c)) - (8*I*f^2*cos(d*x + c)^3 + 8*I*f^2*cos(d*x + c)^2 - 8*I*f^2*cos(d*x + c) - 8*I*f^2 + (8*I*f^2*cos(d*x + c)^2 - 8*I*f^2)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) - (-8*I*f^2*cos(d*x + c)^3 - 8*I*f^2*cos(d*x + c)^2 + 8*I*f^2*cos(d*x + c) + 8*I*f^2 + (-8*I*f^2*cos(d*x + c)^2 + 8*I*f^2)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - (6*I*d*f^2*x + (-6*I*d*f^2*x - 6*I*d*e*f - 4*I*f^2)*cos(d*x + c)^3 + 6*I*d*e*f + (-6*I*d*f^2*x - 6*I*d*e*f - 4*I*f^2)*cos(d*x + c)^2 + 4*I*f^2 + (6*I*d*f^2*x + 6*I*d*e*f + 4*I*f^2)*cos(d*x + c) + (6*I*d*f^2*x + 6*I*d*e*f + (-6*I*d*f^2*x - 6*I*d*e*f - 4*I*f^2)*cos(d*x + c)^2 + 4*I*f^2)*sin(d*x + c))*dilog(-cos(d*x + c) + I*sin(d*x + c)) - (-6*I*d*f^2*x + (6*I*d*f^2*x + 6*I*d*e*f + 4*I*f^2)*cos(d*x + c)^3 - 6*I*d*e*f + (6*I*d*f^2*x + 6*I*d*e*f + 4*I*f^2)*cos(d*x + c)^2 - 4*I*f^2 + (-6*I*d*f^2*x - 6*I*d*e*f - 4*I*f^2)*cos(d*x + c) + (-6*I*d*f^2*x - 6*I*d*e*f + (6*I*d*f^2*x + 6*I*d*e*f + 4*I*f^2)*cos(d*x + c)^2 - 4*I*f^2)*sin(d*x + c))*dilog(-cos(d*x + c) - I*sin(d*x + c)) - (3*d^2*f^2*x^2 + 3*d^2*e^2 - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c)^3 + 4*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c)^2 + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x + (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c) + (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c)^2 + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 8*((d*e*f - c*f^2)*cos(d*x + c)^3 - d*e*f + c*f^2 + (d*e*f - c*f^2)*cos(d*x + c)^2 - (d*e*f - c*f^2)*cos(d*x + c) - (d*e*f - c*f^2 - (d*e*f - c*f^2)*cos(d*x + c)^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) - (3*d^2*f^2*x^2 + 3*d^2*e^2 - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c)^3 + 4*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c)^2 + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x + (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c) + (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*cos(d*x + c)^2 + 2*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 8*(d*f^2*x - (d*f^2*x + c*f^2)*cos(d*x + c)^3 + c*f^2 - (d*f^2*x + c*f^2)*cos(d*x + c)^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2 - (d*f^2*x + c*f^2)*cos(d*x + c)^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 8*(d*f^2*x - (d*f^2*x + c*f^2)*cos(d*x + c)^3 + c*f^2 - (d*f^2*x + c*f^2)*cos(d*x + c)^2 + (d*f^2*x + c*f^2)*cos(d*x + c) + (d*f^2*x + c*f^2 - (d*f^2*x + c*f^2)*cos(d*x + c)^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (3*d^2*e^2 - 2*(3*c + 2)*d*e*f - (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c)^3 + (3*c^2 + 4*c + 2)*f^2 - (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c)^2 + (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c) + (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2 - (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + (3*d^2*e^2 - 2*(3*c + 2)*d*e*f - (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c)^3 + (3*c^2 + 4*c + 2)*f^2 - (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c)^2 + (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c) + (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2 - (3*d^2*e^2 - 2*(3*c + 2)*d*e*f + (3*c^2 + 4*c + 2)*f^2)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c)^3 - (3*c^2 + 4*c)*f^2 - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c)^2 + 2*(3*d^2*e*f - 2*d*f^2)*x + (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c) + (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c)^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 8*((d*e*f - c*f^2)*cos(d*x + c)^3 - d*e*f + c*f^2 + (d*e*f - c*f^2)*cos(d*x + c)^2 - (d*e*f - c*f^2)*cos(d*x + c) - (d*e*f - c*f^2 - (d*e*f - c*f^2)*cos(d*x + c)^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c)^3 - (3*c^2 + 4*c)*f^2 - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c)^2 + 2*(3*d^2*e*f - 2*d*f^2)*x + (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c) + (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 + 4*c)*f^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*cos(d*x + c)^2 + 2*(3*d^2*e*f - 2*d*f^2)*x)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 6*(f^2*cos(d*x + c)^3 + f^2*cos(d*x + c)^2 - f^2*cos(d*x + c) - f^2 + (f^2*cos(d*x + c)^2 - f^2)*sin(d*x + c))*polylog(3, cos(d*x + c) + I*sin(d*x + c)) - 6*(f^2*cos(d*x + c)^3 + f^2*cos(d*x + c)^2 - f^2*cos(d*x + c) - f^2 + (f^2*cos(d*x + c)^2 - f^2)*sin(d*x + c))*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 6*(f^2*cos(d*x + c)^3 + f^2*cos(d*x + c)^2 - f^2*cos(d*x + c) - f^2 + (f^2*cos(d*x + c)^2 - f^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 6*(f^2*cos(d*x + c)^3 + f^2*cos(d*x + c)^2 - f^2*cos(d*x + c) - f^2 + (f^2*cos(d*x + c)^2 - f^2)*sin(d*x + c))*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(2*d^2*f^2*x^2 + 2*d^2*e^2 + 2*d*e*f - 4*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*cos(d*x + c)^2 + 2*(2*d^2*e*f + d*f^2)*x - (d^2*f^2*x^2 + d^2*e^2 - 2*d*e*f + 2*(d^2*e*f - d*f^2)*x)*cos(d*x + c))*sin(d*x + c))/(a*d^3*cos(d*x + c)^3 + a*d^3*cos(d*x + c)^2 - a*d^3*cos(d*x + c) - a*d^3 + (a*d^3*cos(d*x + c)^2 - a*d^3)*sin(d*x + c))","C",0
211,1,1355,0,1.180931," ","integrate((f*x+e)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{3} - 4 \, d f x + 2 \, {\left(3 \, d f x + 3 \, d e - f\right)} \cos\left(d x + c\right)^{2} - 4 \, d e - 6 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) + {\left(-3 i \, f \cos\left(d x + c\right)^{3} - 3 i \, f \cos\left(d x + c\right)^{2} + 3 i \, f \cos\left(d x + c\right) + {\left(-3 i \, f \cos\left(d x + c\right)^{2} + 3 i \, f\right)} \sin\left(d x + c\right) + 3 i \, f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(3 i \, f \cos\left(d x + c\right)^{3} + 3 i \, f \cos\left(d x + c\right)^{2} - 3 i \, f \cos\left(d x + c\right) + {\left(3 i \, f \cos\left(d x + c\right)^{2} - 3 i \, f\right)} \sin\left(d x + c\right) - 3 i \, f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(-3 i \, f \cos\left(d x + c\right)^{3} - 3 i \, f \cos\left(d x + c\right)^{2} + 3 i \, f \cos\left(d x + c\right) + {\left(-3 i \, f \cos\left(d x + c\right)^{2} + 3 i \, f\right)} \sin\left(d x + c\right) + 3 i \, f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(3 i \, f \cos\left(d x + c\right)^{3} + 3 i \, f \cos\left(d x + c\right)^{2} - 3 i \, f \cos\left(d x + c\right) + {\left(3 i \, f \cos\left(d x + c\right)^{2} - 3 i \, f\right)} \sin\left(d x + c\right) - 3 i \, f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left({\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right)^{3} - 3 \, d f x + {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right)^{2} - 3 \, d e - {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right) - {\left(3 \, d f x - {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right)^{2} + 3 \, d e + 2 \, f\right)} \sin\left(d x + c\right) - 2 \, f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - {\left({\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right)^{3} - 3 \, d f x + {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right)^{2} - 3 \, d e - {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right) - {\left(3 \, d f x - {\left(3 \, d f x + 3 \, d e + 2 \, f\right)} \cos\left(d x + c\right)^{2} + 3 \, d e + 2 \, f\right)} \sin\left(d x + c\right) - 2 \, f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right)^{2} - 3 \, d e + {\left(3 \, c + 2\right)} f - {\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right) + {\left({\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right)^{2} - 3 \, d e + {\left(3 \, c + 2\right)} f\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right)^{2} - 3 \, d e + {\left(3 \, c + 2\right)} f - {\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right) + {\left({\left(3 \, d e - {\left(3 \, c + 2\right)} f\right)} \cos\left(d x + c\right)^{2} - 3 \, d e + {\left(3 \, c + 2\right)} f\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(d f x + c f\right)} \cos\left(d x + c\right)^{3} - d f x + {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} - c f - {\left(d f x + c f\right)} \cos\left(d x + c\right) - {\left(d f x - {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} + c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(d f x + c f\right)} \cos\left(d x + c\right)^{3} - d f x + {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} - c f - {\left(d f x + c f\right)} \cos\left(d x + c\right) - {\left(d f x - {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} + c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(f \cos\left(d x + c\right)^{3} + f \cos\left(d x + c\right)^{2} - f \cos\left(d x + c\right) + {\left(f \cos\left(d x + c\right)^{2} - f\right)} \sin\left(d x + c\right) - f\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, d f x - 4 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} + 2 \, d e - {\left(d f x + d e - f\right)} \cos\left(d x + c\right) + f\right)} \sin\left(d x + c\right) + 2 \, f}{4 \, {\left(a d^{2} \cos\left(d x + c\right)^{3} + a d^{2} \cos\left(d x + c\right)^{2} - a d^{2} \cos\left(d x + c\right) - a d^{2} + {\left(a d^{2} \cos\left(d x + c\right)^{2} - a d^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(8*(d*f*x + d*e)*cos(d*x + c)^3 - 4*d*f*x + 2*(3*d*f*x + 3*d*e - f)*cos(d*x + c)^2 - 4*d*e - 6*(d*f*x + d*e)*cos(d*x + c) + (-3*I*f*cos(d*x + c)^3 - 3*I*f*cos(d*x + c)^2 + 3*I*f*cos(d*x + c) + (-3*I*f*cos(d*x + c)^2 + 3*I*f)*sin(d*x + c) + 3*I*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (3*I*f*cos(d*x + c)^3 + 3*I*f*cos(d*x + c)^2 - 3*I*f*cos(d*x + c) + (3*I*f*cos(d*x + c)^2 - 3*I*f)*sin(d*x + c) - 3*I*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (-3*I*f*cos(d*x + c)^3 - 3*I*f*cos(d*x + c)^2 + 3*I*f*cos(d*x + c) + (-3*I*f*cos(d*x + c)^2 + 3*I*f)*sin(d*x + c) + 3*I*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (3*I*f*cos(d*x + c)^3 + 3*I*f*cos(d*x + c)^2 - 3*I*f*cos(d*x + c) + (3*I*f*cos(d*x + c)^2 - 3*I*f)*sin(d*x + c) - 3*I*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) - ((3*d*f*x + 3*d*e + 2*f)*cos(d*x + c)^3 - 3*d*f*x + (3*d*f*x + 3*d*e + 2*f)*cos(d*x + c)^2 - 3*d*e - (3*d*f*x + 3*d*e + 2*f)*cos(d*x + c) - (3*d*f*x - (3*d*f*x + 3*d*e + 2*f)*cos(d*x + c)^2 + 3*d*e + 2*f)*sin(d*x + c) - 2*f)*log(cos(d*x + c) + I*sin(d*x + c) + 1) - ((3*d*f*x + 3*d*e + 2*f)*cos(d*x + c)^3 - 3*d*f*x + (3*d*f*x + 3*d*e + 2*f)*cos(d*x + c)^2 - 3*d*e - (3*d*f*x + 3*d*e + 2*f)*cos(d*x + c) - (3*d*f*x - (3*d*f*x + 3*d*e + 2*f)*cos(d*x + c)^2 + 3*d*e + 2*f)*sin(d*x + c) - 2*f)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + ((3*d*e - (3*c + 2)*f)*cos(d*x + c)^3 + (3*d*e - (3*c + 2)*f)*cos(d*x + c)^2 - 3*d*e + (3*c + 2)*f - (3*d*e - (3*c + 2)*f)*cos(d*x + c) + ((3*d*e - (3*c + 2)*f)*cos(d*x + c)^2 - 3*d*e + (3*c + 2)*f)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + ((3*d*e - (3*c + 2)*f)*cos(d*x + c)^3 + (3*d*e - (3*c + 2)*f)*cos(d*x + c)^2 - 3*d*e + (3*c + 2)*f - (3*d*e - (3*c + 2)*f)*cos(d*x + c) + ((3*d*e - (3*c + 2)*f)*cos(d*x + c)^2 - 3*d*e + (3*c + 2)*f)*sin(d*x + c))*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + 3*((d*f*x + c*f)*cos(d*x + c)^3 - d*f*x + (d*f*x + c*f)*cos(d*x + c)^2 - c*f - (d*f*x + c*f)*cos(d*x + c) - (d*f*x - (d*f*x + c*f)*cos(d*x + c)^2 + c*f)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 3*((d*f*x + c*f)*cos(d*x + c)^3 - d*f*x + (d*f*x + c*f)*cos(d*x + c)^2 - c*f - (d*f*x + c*f)*cos(d*x + c) - (d*f*x - (d*f*x + c*f)*cos(d*x + c)^2 + c*f)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 4*(f*cos(d*x + c)^3 + f*cos(d*x + c)^2 - f*cos(d*x + c) + (f*cos(d*x + c)^2 - f)*sin(d*x + c) - f)*log(sin(d*x + c) + 1) + 2*(2*d*f*x - 4*(d*f*x + d*e)*cos(d*x + c)^2 + 2*d*e - (d*f*x + d*e - f)*cos(d*x + c) + f)*sin(d*x + c) + 2*f)/(a*d^2*cos(d*x + c)^3 + a*d^2*cos(d*x + c)^2 - a*d^2*cos(d*x + c) - a*d^2 + (a*d^2*cos(d*x + c)^2 - a*d^2)*sin(d*x + c))","B",0
212,1,232,0,0.550496," ","integrate(csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(4 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right) - 4}{4 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d + {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(8*cos(d*x + c)^3 + 6*cos(d*x + c)^2 - 3*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) + 3*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) - 2*(4*cos(d*x + c)^2 + cos(d*x + c) - 2)*sin(d*x + c) - 6*cos(d*x + c) - 4)/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d + (a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","B",0
213,0,0,0,1.107098," ","integrate(csc(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(d x + c\right)^{3}}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(csc(d*x + c)^3/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
214,0,0,0,1.093141," ","integrate(csc(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\csc\left(d x + c\right)^{3}}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(csc(d*x + c)^3/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
215,0,0,0,1.027982," ","integrate((f*x+e)^m*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(f x + e\right)}^{m}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(f*x + e)^m/(a*sin(d*x + c) + a), x)","F",0
216,0,0,0,0.915861," ","integrate((f*x+e)^m*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \sin\left(d x + c\right)}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*sin(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
217,0,0,0,0.877797," ","integrate((f*x+e)^m/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m/(a*sin(d*x + c) + a), x)","F",0
218,0,0,0,0.698950," ","integrate((f*x+e)^m*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*csc(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
219,0,0,0,0.642072," ","integrate((f*x+e)^m*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)^{2}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*csc(d*x + c)^2/(a*sin(d*x + c) + a), x)","F",0
220,1,2322,0,1.365234," ","integrate((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} - b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{2} - b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{2} - b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{2} - b^{2}\right)} d^{4} e^{3} x + 12 i \, a b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, a b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, a b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, a b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(3 i \, a b d^{2} f^{3} x^{2} + 6 i \, a b d^{2} e f^{2} x + 3 i \, a b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-3 i \, a b d^{2} f^{3} x^{2} - 6 i \, a b d^{2} e f^{2} x - 3 i \, a b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-3 i \, a b d^{2} f^{3} x^{2} - 6 i \, a b d^{2} e f^{2} x - 3 i \, a b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(3 i \, a b d^{2} f^{3} x^{2} + 6 i \, a b d^{2} e f^{2} x + 3 i \, a b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{4 \, {\left(a^{2} b - b^{3}\right)} d^{4}}"," ",0,"1/4*((a^2 - b^2)*d^4*f^3*x^4 + 4*(a^2 - b^2)*d^4*e*f^2*x^3 + 6*(a^2 - b^2)*d^4*e^2*f*x^2 + 4*(a^2 - b^2)*d^4*e^3*x + 12*I*a*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*a*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*a*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*a*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 2*(3*I*a*b*d^2*f^3*x^2 + 6*I*a*b*d^2*e*f^2*x + 3*I*a*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-3*I*a*b*d^2*f^3*x^2 - 6*I*a*b*d^2*e*f^2*x - 3*I*a*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-3*I*a*b*d^2*f^3*x^2 - 6*I*a*b*d^2*e*f^2*x - 3*I*a*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(3*I*a*b*d^2*f^3*x^2 + 6*I*a*b*d^2*e*f^2*x + 3*I*a*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 12*(a*b*d*f^3*x + a*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a*b*d*f^3*x + a*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(a*b*d*f^3*x + a*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a*b*d*f^3*x + a*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b))/((a^2*b - b^3)*d^4)","C",0
221,1,1646,0,1.292763," ","integrate((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - b^{2}\right)} d^{3} f^{2} x^{3} + 6 \, {\left(a^{2} - b^{2}\right)} d^{3} e f x^{2} + 6 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} x - 6 \, a b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, a b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, a b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, a b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - {\left(6 i \, a b d f^{2} x + 6 i \, a b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-6 i \, a b d f^{2} x - 6 i \, a b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-6 i \, a b d f^{2} x - 6 i \, a b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(6 i \, a b d f^{2} x + 6 i \, a b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 3 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 3 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{6 \, {\left(a^{2} b - b^{3}\right)} d^{3}}"," ",0,"1/6*(2*(a^2 - b^2)*d^3*f^2*x^3 + 6*(a^2 - b^2)*d^3*e*f*x^2 + 6*(a^2 - b^2)*d^3*e^2*x - 6*a*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*a*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*a*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*a*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - (6*I*a*b*d*f^2*x + 6*I*a*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-6*I*a*b*d*f^2*x - 6*I*a*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-6*I*a*b*d*f^2*x - 6*I*a*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (6*I*a*b*d*f^2*x + 6*I*a*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 3*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 3*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 3*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2*b - b^3)*d^3)","C",0
222,1,1057,0,1.644554," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - b^{2}\right)} d^{2} f x^{2} + 4 \, {\left(a^{2} - b^{2}\right)} d^{2} e x - 2 i \, a b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, a b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, a b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, a b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a b d e - a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(a b d e - a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a b d e - a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(a b d e - a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a b d f x + a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b d f x + a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a b d f x + a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b d f x + a b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{4 \, {\left(a^{2} b - b^{3}\right)} d^{2}}"," ",0,"1/4*(2*(a^2 - b^2)*d^2*f*x^2 + 4*(a^2 - b^2)*d^2*e*x - 2*I*a*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*a*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*a*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*a*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(a*b*d*e - a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(a*b*d*e - a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a*b*d*e - a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(a*b*d*e - a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a*b*d*f*x + a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a*b*d*f*x + a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a*b*d*f*x + a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a*b*d*f*x + a*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2*b - b^3)*d^2)","B",0
223,1,237,0,1.236166," ","integrate(sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} - b^{2}\right)} d x - \sqrt{-a^{2} + b^{2}} a \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}, \frac{{\left(a^{2} - b^{2}\right)} d x + \sqrt{a^{2} - b^{2}} a \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{{\left(a^{2} b - b^{3}\right)} d}\right]"," ",0,"[1/2*(2*(a^2 - b^2)*d*x - sqrt(-a^2 + b^2)*a*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/((a^2*b - b^3)*d), ((a^2 - b^2)*d*x + sqrt(a^2 - b^2)*a*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/((a^2*b - b^3)*d)]","A",0
224,1,2671,0,2.053358," ","integrate((f*x+e)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{3} - a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} - a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} - a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} d^{4} e^{3} x + 12 i \, a^{2} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, a^{2} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, a^{2} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, a^{2} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-3 i \, a^{2} b d^{2} f^{3} x^{2} - 6 i \, a^{2} b d^{2} e f^{2} x - 3 i \, a^{2} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, a^{2} b d^{2} f^{3} x^{2} + 6 i \, a^{2} b d^{2} e f^{2} x + 3 i \, a^{2} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, a^{2} b d^{2} f^{3} x^{2} + 6 i \, a^{2} b d^{2} e f^{2} x + 3 i \, a^{2} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-3 i \, a^{2} b d^{2} f^{3} x^{2} - 6 i \, a^{2} b d^{2} e f^{2} x - 3 i \, a^{2} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b - b^{3}\right)} d e f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x + {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{2} b - b^{3}\right)} f^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{4}}"," ",0,"-1/4*((a^3 - a*b^2)*d^4*f^3*x^4 + 4*(a^3 - a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 - a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 - a*b^2)*d^4*e^3*x + 12*I*a^2*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*a^2*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*a^2*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*a^2*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-3*I*a^2*b*d^2*f^3*x^2 - 6*I*a^2*b*d^2*e*f^2*x - 3*I*a^2*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*a^2*b*d^2*f^3*x^2 + 6*I*a^2*b*d^2*e*f^2*x + 3*I*a^2*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*a^2*b*d^2*f^3*x^2 + 6*I*a^2*b*d^2*e*f^2*x + 3*I*a^2*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-3*I*a^2*b*d^2*f^3*x^2 - 6*I*a^2*b*d^2*e*f^2*x - 3*I*a^2*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 12*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + (a^2*b - b^3)*d^3*e^3 - 6*(a^2*b - b^3)*d*e*f^2 + 3*((a^2*b - b^3)*d^3*e^2*f - 2*(a^2*b - b^3)*d*f^3)*x)*cos(d*x + c) - 12*((a^2*b - b^3)*d^2*f^3*x^2 + 2*(a^2*b - b^3)*d^2*e*f^2*x + (a^2*b - b^3)*d^2*e^2*f - 2*(a^2*b - b^3)*f^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d^4)","C",0
225,1,1851,0,1.474974," ","integrate((f*x+e)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{3} + 6 \, {\left(a^{3} - a b^{2}\right)} d^{3} e f x^{2} + 6 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} x - 6 \, a^{2} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, a^{2} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, a^{2} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, a^{2} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + {\left(-6 i \, a^{2} b d f^{2} x - 6 i \, a^{2} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(6 i \, a^{2} b d f^{2} x + 6 i \, a^{2} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(6 i \, a^{2} b d f^{2} x + 6 i \, a^{2} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-6 i \, a^{2} b d f^{2} x - 6 i \, a^{2} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cos\left(d x + c\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{2} x + {\left(a^{2} b - b^{3}\right)} d e f\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{3}}"," ",0,"-1/6*(2*(a^3 - a*b^2)*d^3*f^2*x^3 + 6*(a^3 - a*b^2)*d^3*e*f*x^2 + 6*(a^3 - a*b^2)*d^3*e^2*x - 6*a^2*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*a^2*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*a^2*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*a^2*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + (-6*I*a^2*b*d*f^2*x - 6*I*a^2*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (6*I*a^2*b*d*f^2*x + 6*I*a^2*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (6*I*a^2*b*d*f^2*x + 6*I*a^2*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-6*I*a^2*b*d*f^2*x - 6*I*a^2*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + (a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*f^2)*cos(d*x + c) - 12*((a^2*b - b^3)*d*f^2*x + (a^2*b - b^3)*d*e*f)*sin(d*x + c))/((a^2*b^2 - b^4)*d^3)","C",0
226,1,1159,0,1.737889," ","integrate((f*x+e)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} - a b^{2}\right)} d^{2} f x^{2} - 2 i \, a^{2} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, a^{2} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, a^{2} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, a^{2} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(a^{3} - a b^{2}\right)} d^{2} e x - 4 \, {\left(a^{2} b - b^{3}\right)} f \sin\left(d x + c\right) - 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e\right)} \cos\left(d x + c\right)}{4 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2}}"," ",0,"-1/4*(2*(a^3 - a*b^2)*d^2*f*x^2 - 2*I*a^2*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*a^2*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*a^2*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*a^2*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 4*(a^3 - a*b^2)*d^2*e*x - 4*(a^2*b - b^3)*f*sin(d*x + c) - 2*(a^2*b*d*e - a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(a^2*b*d*e - a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a^2*b*d*e - a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(a^2*b*d*e - a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(a^2*b*d*f*x + a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a^2*b*d*f*x + a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a^2*b*d*f*x + a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a^2*b*d*f*x + a^2*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e)*cos(d*x + c))/((a^2*b^2 - b^4)*d^2)","B",0
227,1,283,0,0.930576," ","integrate(sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} a^{2} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{3} - a b^{2}\right)} d x + 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}, -\frac{\sqrt{a^{2} - b^{2}} a^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(a^{3} - a b^{2}\right)} d x + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*a^2*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(a^3 - a*b^2)*d*x + 2*(a^2*b - b^3)*cos(d*x + c))/((a^2*b^2 - b^4)*d), -(sqrt(a^2 - b^2)*a^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (a^3 - a*b^2)*d*x + (a^2*b - b^3)*cos(d*x + c))/((a^2*b^2 - b^4)*d)]","A",0
228,1,3008,0,2.233480," ","integrate((f*x+e)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 24 i \, a^{3} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 i \, a^{3} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 i \, a^{3} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 i \, a^{3} b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f + {\left(a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} - 3 \, {\left(2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} f^{3} x^{2} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f - {\left(a^{2} b^{2} - b^{4}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(6 i \, a^{3} b d^{2} f^{3} x^{2} + 12 i \, a^{3} b d^{2} e f^{2} x + 6 i \, a^{3} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-6 i \, a^{3} b d^{2} f^{3} x^{2} - 12 i \, a^{3} b d^{2} e f^{2} x - 6 i \, a^{3} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-6 i \, a^{3} b d^{2} f^{3} x^{2} - 12 i \, a^{3} b d^{2} e f^{2} x - 6 i \, a^{3} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(6 i \, a^{3} b d^{2} f^{3} x^{2} + 12 i \, a^{3} b d^{2} e f^{2} x + 6 i \, a^{3} b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 24 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x + 8 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b - a b^{3}\right)} d^{3} e f^{2} x^{2} + {\left(a^{3} b - a b^{3}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b - a b^{3}\right)} d e f^{2} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} b - a b^{3}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right) - 2 \, {\left(12 \, {\left(a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 24 \, {\left(a^{3} b - a b^{3}\right)} f^{3} + {\left(2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{3} f^{3} x^{3} + 6 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{3} e f^{2} x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b^{2} - b^{4}\right)} d e f^{2} + 3 \, {\left(2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} f - {\left(a^{2} b^{2} - b^{4}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{4}}"," ",0,"1/8*((2*a^4 - a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(2*a^4 - a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 24*I*a^3*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*I*a^3*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*I*a^3*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*I*a^3*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 3*(2*(2*a^4 - a^2*b^2 - b^4)*d^4*e^2*f + (a^2*b^2 - b^4)*d^2*f^3)*x^2 - 3*(2*(a^2*b^2 - b^4)*d^2*f^3*x^2 + 4*(a^2*b^2 - b^4)*d^2*e*f^2*x + 2*(a^2*b^2 - b^4)*d^2*e^2*f - (a^2*b^2 - b^4)*f^3)*cos(d*x + c)^2 - 2*(6*I*a^3*b*d^2*f^3*x^2 + 12*I*a^3*b*d^2*e*f^2*x + 6*I*a^3*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-6*I*a^3*b*d^2*f^3*x^2 - 12*I*a^3*b*d^2*e*f^2*x - 6*I*a^3*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-6*I*a^3*b*d^2*f^3*x^2 - 12*I*a^3*b*d^2*e*f^2*x - 6*I*a^3*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(6*I*a^3*b*d^2*f^3*x^2 + 12*I*a^3*b*d^2*e*f^2*x + 6*I*a^3*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 24*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(2*(2*a^4 - a^2*b^2 - b^4)*d^4*e^3 + 3*(a^2*b^2 - b^4)*d^2*e*f^2)*x + 8*((a^3*b - a*b^3)*d^3*f^3*x^3 + 3*(a^3*b - a*b^3)*d^3*e*f^2*x^2 + (a^3*b - a*b^3)*d^3*e^3 - 6*(a^3*b - a*b^3)*d*e*f^2 + 3*((a^3*b - a*b^3)*d^3*e^2*f - 2*(a^3*b - a*b^3)*d*f^3)*x)*cos(d*x + c) - 2*(12*(a^3*b - a*b^3)*d^2*f^3*x^2 + 24*(a^3*b - a*b^3)*d^2*e*f^2*x + 12*(a^3*b - a*b^3)*d^2*e^2*f - 24*(a^3*b - a*b^3)*f^3 + (2*(a^2*b^2 - b^4)*d^3*f^3*x^3 + 6*(a^2*b^2 - b^4)*d^3*e*f^2*x^2 + 2*(a^2*b^2 - b^4)*d^3*e^3 - 3*(a^2*b^2 - b^4)*d*e*f^2 + 3*(2*(a^2*b^2 - b^4)*d^3*e^2*f - (a^2*b^2 - b^4)*d*f^3)*x)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d^4)","C",0
229,1,2050,0,2.020271," ","integrate((f*x+e)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 6 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} - 12 \, a^{3} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, a^{3} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, a^{3} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, a^{3} b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} - b^{4}\right)} d e f\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(6 i \, a^{3} b d f^{2} x + 6 i \, a^{3} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-6 i \, a^{3} b d f^{2} x - 6 i \, a^{3} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-6 i \, a^{3} b d f^{2} x - 6 i \, a^{3} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(6 i \, a^{3} b d f^{2} x + 6 i \, a^{3} b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} + {\left(a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x + 12 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f x + {\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} f^{2}\right)} \cos\left(d x + c\right) - 3 \, {\left(8 \, {\left(a^{3} b - a b^{3}\right)} d f^{2} x + 8 \, {\left(a^{3} b - a b^{3}\right)} d e f + {\left(2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} f^{2} x^{2} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} - {\left(a^{2} b^{2} - b^{4}\right)} f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{3}}"," ",0,"1/12*(2*(2*a^4 - a^2*b^2 - b^4)*d^3*f^2*x^3 + 6*(2*a^4 - a^2*b^2 - b^4)*d^3*e*f*x^2 - 12*a^3*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*a^3*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*a^3*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*a^3*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*((a^2*b^2 - b^4)*d*f^2*x + (a^2*b^2 - b^4)*d*e*f)*cos(d*x + c)^2 - 2*(6*I*a^3*b*d*f^2*x + 6*I*a^3*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-6*I*a^3*b*d*f^2*x - 6*I*a^3*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-6*I*a^3*b*d*f^2*x - 6*I*a^3*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(6*I*a^3*b*d*f^2*x + 6*I*a^3*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*(2*(2*a^4 - a^2*b^2 - b^4)*d^3*e^2 + (a^2*b^2 - b^4)*d*f^2)*x + 12*((a^3*b - a*b^3)*d^2*f^2*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f*x + (a^3*b - a*b^3)*d^2*e^2 - 2*(a^3*b - a*b^3)*f^2)*cos(d*x + c) - 3*(8*(a^3*b - a*b^3)*d*f^2*x + 8*(a^3*b - a*b^3)*d*e*f + (2*(a^2*b^2 - b^4)*d^2*f^2*x^2 + 4*(a^2*b^2 - b^4)*d^2*e*f*x + 2*(a^2*b^2 - b^4)*d^2*e^2 - (a^2*b^2 - b^4)*f^2)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d^3)","C",0
230,1,1247,0,1.265827," ","integrate((f*x+e)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 i \, a^{3} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, a^{3} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, a^{3} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, a^{3} b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} - 2 \, {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d^{2} e x + {\left(a^{2} b^{2} - b^{4}\right)} f \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} d e\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} f + {\left({\left(a^{2} b^{2} - b^{4}\right)} d f x + {\left(a^{2} b^{2} - b^{4}\right)} d e\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} b^{3} - b^{5}\right)} d^{2}}"," ",0,"-1/4*(2*I*a^3*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*a^3*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*a^3*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*a^3*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (2*a^4 - a^2*b^2 - b^4)*d^2*f*x^2 - 2*(2*a^4 - a^2*b^2 - b^4)*d^2*e*x + (a^2*b^2 - b^4)*f*cos(d*x + c)^2 + 2*(a^3*b*d*e - a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(a^3*b*d*e - a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(a^3*b*d*e - a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(a^3*b*d*e - a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(a^3*b*d*f*x + a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a^3*b*d*f*x + a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(a^3*b*d*f*x + a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a^3*b*d*f*x + a^3*b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*d*e)*cos(d*x + c) + 2*(2*(a^3*b - a*b^3)*f + ((a^2*b^2 - b^4)*d*f*x + (a^2*b^2 - b^4)*d*e)*cos(d*x + c))*sin(d*x + c))/((a^2*b^3 - b^5)*d^2)","B",0
231,1,359,0,1.118082," ","integrate(sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} a^{3} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d x + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}, \frac{2 \, \sqrt{a^{2} - b^{2}} a^{3} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(2 \, a^{4} - a^{2} b^{2} - b^{4}\right)} d x - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} - b^{5}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*a^3*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - (2*a^4 - a^2*b^2 - b^4)*d*x + (a^2*b^2 - b^4)*cos(d*x + c)*sin(d*x + c) - 2*(a^3*b - a*b^3)*cos(d*x + c))/((a^2*b^3 - b^5)*d), 1/2*(2*sqrt(a^2 - b^2)*a^3*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (2*a^4 - a^2*b^2 - b^4)*d*x - (a^2*b^2 - b^4)*cos(d*x + c)*sin(d*x + c) + 2*(a^3*b - a*b^3)*cos(d*x + c))/((a^2*b^3 - b^5)*d)]","A",0
232,1,3588,0,2.245780," ","integrate((f*x+e)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{-12 i \, b^{2} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b^{2} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b^{2} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b^{2} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 12 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left(3 i \, b^{2} d^{2} f^{3} x^{2} + 6 i \, b^{2} d^{2} e f^{2} x + 3 i \, b^{2} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-3 i \, b^{2} d^{2} f^{3} x^{2} - 6 i \, b^{2} d^{2} e f^{2} x - 3 i \, b^{2} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-3 i \, b^{2} d^{2} f^{3} x^{2} - 6 i \, b^{2} d^{2} e f^{2} x - 3 i \, b^{2} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, b^{2} d^{2} f^{3} x^{2} + 6 i \, b^{2} d^{2} e f^{2} x + 3 i \, b^{2} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + {\left(6 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-6 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(6 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-6 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} - b^{2}\right)} d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} - b^{2}\right)} d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 12 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 12 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 12 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d^{4}}"," ",0,"-1/4*(-12*I*b^2*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b^2*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b^2*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b^2*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*(a^2 - b^2)*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c)) + 12*I*(a^2 - b^2)*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c)) - 12*I*(a^2 - b^2)*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) + 12*I*(a^2 - b^2)*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) + 2*(3*I*b^2*d^2*f^3*x^2 + 6*I*b^2*d^2*e*f^2*x + 3*I*b^2*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-3*I*b^2*d^2*f^3*x^2 - 6*I*b^2*d^2*e*f^2*x - 3*I*b^2*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-3*I*b^2*d^2*f^3*x^2 - 6*I*b^2*d^2*e*f^2*x - 3*I*b^2*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*b^2*d^2*f^3*x^2 + 6*I*b^2*d^2*e*f^2*x + 3*I*b^2*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 12*(b^2*d*f^3*x + b^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b^2*d*f^3*x + b^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b^2*d*f^3*x + b^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b^2*d*f^3*x + b^2*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + (6*I*(a^2 - b^2)*d^2*f^3*x^2 + 12*I*(a^2 - b^2)*d^2*e*f^2*x + 6*I*(a^2 - b^2)*d^2*e^2*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (-6*I*(a^2 - b^2)*d^2*f^3*x^2 - 12*I*(a^2 - b^2)*d^2*e*f^2*x - 6*I*(a^2 - b^2)*d^2*e^2*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (6*I*(a^2 - b^2)*d^2*f^3*x^2 + 12*I*(a^2 - b^2)*d^2*e*f^2*x + 6*I*(a^2 - b^2)*d^2*e^2*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (-6*I*(a^2 - b^2)*d^2*f^3*x^2 - 12*I*(a^2 - b^2)*d^2*e*f^2*x - 6*I*(a^2 - b^2)*d^2*e^2*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + 2*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + (a^2 - b^2)*d^3*e^3)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 2*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + (a^2 - b^2)*d^3*e^3)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 2*((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - 2*((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - 2*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 2*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 12*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, cos(d*x + c) + I*sin(d*x + c)) - 12*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 12*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 12*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -cos(d*x + c) - I*sin(d*x + c)))/((a^3 - a*b^2)*d^4)","C",0
233,1,2414,0,1.820388," ","integrate((f*x+e)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, b^{2} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, b^{2} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, b^{2} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, b^{2} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left(2 i \, b^{2} d f^{2} x + 2 i \, b^{2} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-2 i \, b^{2} d f^{2} x - 2 i \, b^{2} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-2 i \, b^{2} d f^{2} x - 2 i \, b^{2} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(2 i \, b^{2} d f^{2} x + 2 i \, b^{2} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + {\left(a^{2} - b^{2}\right)} d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + {\left(a^{2} - b^{2}\right)} d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d^{3}}"," ",0,"-1/4*(4*b^2*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*b^2*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*b^2*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*b^2*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(a^2 - b^2)*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c)) - 4*(a^2 - b^2)*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 4*(a^2 - b^2)*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 4*(a^2 - b^2)*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) + 2*(2*I*b^2*d*f^2*x + 2*I*b^2*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-2*I*b^2*d*f^2*x - 2*I*b^2*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-2*I*b^2*d*f^2*x - 2*I*b^2*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(2*I*b^2*d*f^2*x + 2*I*b^2*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (4*I*(a^2 - b^2)*d*f^2*x + 4*I*(a^2 - b^2)*d*e*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (-4*I*(a^2 - b^2)*d*f^2*x - 4*I*(a^2 - b^2)*d*e*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (4*I*(a^2 - b^2)*d*f^2*x + 4*I*(a^2 - b^2)*d*e*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (-4*I*(a^2 - b^2)*d*f^2*x - 4*I*(a^2 - b^2)*d*e*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + (a^2 - b^2)*d^2*e^2)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + (a^2 - b^2)*d^2*e^2)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 2*((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - 2*((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-cos(d*x + c) - I*sin(d*x + c) + 1))/((a^3 - a*b^2)*d^3)","C",0
234,1,1436,0,1.601881," ","integrate((f*x+e)*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 i \, b^{2} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b^{2} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b^{2} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b^{2} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left(b^{2} d e - b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b^{2} d e - b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{2} d e - b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b^{2} d e - b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} d e\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} d e\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right)}{4 \, {\left(a^{3} - a b^{2}\right)} d^{2}}"," ",0,"-1/4*(2*I*b^2*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b^2*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b^2*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b^2*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*(a^2 - b^2)*f*dilog(cos(d*x + c) + I*sin(d*x + c)) - 2*I*(a^2 - b^2)*f*dilog(cos(d*x + c) - I*sin(d*x + c)) + 2*I*(a^2 - b^2)*f*dilog(-cos(d*x + c) + I*sin(d*x + c)) - 2*I*(a^2 - b^2)*f*dilog(-cos(d*x + c) - I*sin(d*x + c)) + 2*(b^2*d*e - b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b^2*d*e - b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^2*d*e - b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b^2*d*e - b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^2*d*f*x + b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^2*d*f*x + b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^2*d*f*x + b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^2*d*f*x + b^2*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*d*e)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*d*e)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 2*((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - 2*((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1))/((a^3 - a*b^2)*d^2)","B",0
235,1,297,0,1.426960," ","integrate(csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} b \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + {\left(a^{2} - b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{2} - b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}, \frac{2 \, \sqrt{a^{2} - b^{2}} b \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{2} - b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{2} - b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*b*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + (a^2 - b^2)*log(1/2*cos(d*x + c) + 1/2) - (a^2 - b^2)*log(-1/2*cos(d*x + c) + 1/2))/((a^3 - a*b^2)*d), 1/2*(2*sqrt(a^2 - b^2)*b*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^2 - b^2)*log(1/2*cos(d*x + c) + 1/2) + (a^2 - b^2)*log(-1/2*cos(d*x + c) + 1/2))/((a^3 - a*b^2)*d)]","A",0
236,1,4564,0,2.506360," ","integrate((f*x+e)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, {\left(-3 i \, b^{3} d^{2} f^{3} x^{2} - 6 i \, b^{3} d^{2} e f^{2} x - 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(3 i \, b^{3} d^{2} f^{3} x^{2} + 6 i \, b^{3} d^{2} e f^{2} x + 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(3 i \, b^{3} d^{2} f^{3} x^{2} + 6 i \, b^{3} d^{2} e f^{2} x + 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(-3 i \, b^{3} d^{2} f^{3} x^{2} - 6 i \, b^{3} d^{2} e f^{2} x - 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{3} - a b^{2}\right)} d e f^{2} - 12 i \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} - a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{3} - a b^{2}\right)} d e f^{2} + 12 i \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} - a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{3} - a b^{2}\right)} d e f^{2} - 12 i \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} - a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{3} - a b^{2}\right)} d e f^{2} + 12 i \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} - a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} - a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} - a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b - b^{3}\right)} c^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b - b^{3}\right)} c^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b - b^{3}\right)} c^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} - a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b - b^{3}\right)} c^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} - a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2} - {\left(a^{3} - a b^{2}\right)} f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2} - {\left(a^{3} - a b^{2}\right)} f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2} + {\left(a^{3} - a b^{2}\right)} f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2} + {\left(a^{3} - a b^{2}\right)} f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} f x + {\left(a^{3} - a b^{2}\right)} d^{3} e^{3}\right)} \cos\left(d x + c\right)}{4 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{4} \sin\left(d x + c\right)}"," ",0,"-1/4*(12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*I*(a^2*b - b^3)*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 12*I*(a^2*b - b^3)*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 12*I*(a^2*b - b^3)*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 12*I*(a^2*b - b^3)*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*(-3*I*b^3*d^2*f^3*x^2 - 6*I*b^3*d^2*e*f^2*x - 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(3*I*b^3*d^2*f^3*x^2 + 6*I*b^3*d^2*e*f^2*x + 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(3*I*b^3*d^2*f^3*x^2 + 6*I*b^3*d^2*e*f^2*x + 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(-3*I*b^3*d^2*f^3*x^2 - 6*I*b^3*d^2*e*f^2*x - 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + (-6*I*(a^2*b - b^3)*d^2*f^3*x^2 - 6*I*(a^2*b - b^3)*d^2*e^2*f + 12*I*(a^3 - a*b^2)*d*e*f^2 - 12*I*((a^2*b - b^3)*d^2*e*f^2 - (a^3 - a*b^2)*d*f^3)*x)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + (6*I*(a^2*b - b^3)*d^2*f^3*x^2 + 6*I*(a^2*b - b^3)*d^2*e^2*f - 12*I*(a^3 - a*b^2)*d*e*f^2 + 12*I*((a^2*b - b^3)*d^2*e*f^2 - (a^3 - a*b^2)*d*f^3)*x)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + (-6*I*(a^2*b - b^3)*d^2*f^3*x^2 - 6*I*(a^2*b - b^3)*d^2*e^2*f - 12*I*(a^3 - a*b^2)*d*e*f^2 - 12*I*((a^2*b - b^3)*d^2*e*f^2 + (a^3 - a*b^2)*d*f^3)*x)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + (6*I*(a^2*b - b^3)*d^2*f^3*x^2 + 6*I*(a^2*b - b^3)*d^2*e^2*f + 12*I*(a^3 - a*b^2)*d*e*f^2 + 12*I*((a^2*b - b^3)*d^2*e*f^2 + (a^3 - a*b^2)*d*f^3)*x)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 2*((a^2*b - b^3)*d^3*f^3*x^3 + (a^2*b - b^3)*d^3*e^3 + 3*(a^3 - a*b^2)*d^2*e^2*f + 3*((a^2*b - b^3)*d^3*e*f^2 + (a^3 - a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b - b^3)*d^3*e^2*f + 2*(a^3 - a*b^2)*d^2*e*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) - 2*((a^2*b - b^3)*d^3*f^3*x^3 + (a^2*b - b^3)*d^3*e^3 + 3*(a^3 - a*b^2)*d^2*e^2*f + 3*((a^2*b - b^3)*d^3*e*f^2 + (a^3 - a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b - b^3)*d^3*e^2*f + 2*(a^3 - a*b^2)*d^2*e*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*e^3 - 3*(a^3 - a*b^2 + (a^2*b - b^3)*c)*d^2*e^2*f + 3*((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*d*e*f^2 - ((a^2*b - b^3)*c^3 + 3*(a^3 - a*b^2)*c^2)*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*e^3 - 3*(a^3 - a*b^2 + (a^2*b - b^3)*c)*d^2*e^2*f + 3*((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*d*e*f^2 - ((a^2*b - b^3)*c^3 + 3*(a^3 - a*b^2)*c^2)*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*d*e*f^2 + ((a^2*b - b^3)*c^3 + 3*(a^3 - a*b^2)*c^2)*f^3 + 3*((a^2*b - b^3)*d^3*e*f^2 - (a^3 - a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b - b^3)*d^3*e^2*f - 2*(a^3 - a*b^2)*d^2*e*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*d*e*f^2 + ((a^2*b - b^3)*c^3 + 3*(a^3 - a*b^2)*c^2)*f^3 + 3*((a^2*b - b^3)*d^3*e*f^2 - (a^3 - a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b - b^3)*d^3*e^2*f - 2*(a^3 - a*b^2)*d^2*e*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2 - (a^3 - a*b^2)*f^3)*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2 - (a^3 - a*b^2)*f^3)*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2 + (a^3 - a*b^2)*f^3)*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2 + (a^3 - a*b^2)*f^3)*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 4*((a^3 - a*b^2)*d^3*f^3*x^3 + 3*(a^3 - a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 - a*b^2)*d^3*e^2*f*x + (a^3 - a*b^2)*d^3*e^3)*cos(d*x + c))/((a^4 - a^2*b^2)*d^4*sin(d*x + c))","C",0
237,1,2978,0,2.342110," ","integrate((f*x+e)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 4 \, {\left(a^{2} b - b^{3}\right)} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, {\left(a^{2} b - b^{3}\right)} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 4 \, {\left(a^{2} b - b^{3}\right)} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 4 \, {\left(a^{2} b - b^{3}\right)} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 \, {\left(-2 i \, b^{3} d f^{2} x - 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 \, {\left(2 i \, b^{3} d f^{2} x + 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 \, {\left(2 i \, b^{3} d f^{2} x + 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 \, {\left(-2 i \, b^{3} d f^{2} x - 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - {\left(-4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{2} b - b^{3}\right)} d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{2} b - b^{3}\right)} d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{2} b - b^{3}\right)} d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{2} b - b^{3}\right)} d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f + {\left(a^{3} - a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f + {\left(a^{3} - a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f - {\left(a^{3} - a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left({\left(a^{2} b - b^{3}\right)} c^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e f - {\left(a^{3} - a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + {\left(a^{3} - a b^{2}\right)} d^{2} e^{2}\right)} \cos\left(d x + c\right)}{4 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{3} \sin\left(d x + c\right)}"," ",0,"1/4*(4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 4*(a^2*b - b^3)*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 4*(a^2*b - b^3)*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 4*(a^2*b - b^3)*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 4*(a^2*b - b^3)*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 2*(-2*I*b^3*d*f^2*x - 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*(2*I*b^3*d*f^2*x + 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*(2*I*b^3*d*f^2*x + 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*(-2*I*b^3*d*f^2*x - 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - (-4*I*(a^2*b - b^3)*d*f^2*x - 4*I*(a^2*b - b^3)*d*e*f + 4*I*(a^3 - a*b^2)*f^2)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (4*I*(a^2*b - b^3)*d*f^2*x + 4*I*(a^2*b - b^3)*d*e*f - 4*I*(a^3 - a*b^2)*f^2)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - (-4*I*(a^2*b - b^3)*d*f^2*x - 4*I*(a^2*b - b^3)*d*e*f - 4*I*(a^3 - a*b^2)*f^2)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (4*I*(a^2*b - b^3)*d*f^2*x + 4*I*(a^2*b - b^3)*d*e*f + 4*I*(a^3 - a*b^2)*f^2)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*((a^2*b - b^3)*d^2*f^2*x^2 + (a^2*b - b^3)*d^2*e^2 + 2*(a^3 - a*b^2)*d*e*f + 2*((a^2*b - b^3)*d^2*e*f + (a^3 - a*b^2)*d*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*((a^2*b - b^3)*d^2*f^2*x^2 + (a^2*b - b^3)*d^2*e^2 + 2*(a^3 - a*b^2)*d*e*f + 2*((a^2*b - b^3)*d^2*e*f + (a^3 - a*b^2)*d*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 2*((a^2*b - b^3)*d^2*e^2 - 2*(a^3 - a*b^2 + (a^2*b - b^3)*c)*d*e*f + ((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) - 2*((a^2*b - b^3)*d^2*e^2 - 2*(a^3 - a*b^2 + (a^2*b - b^3)*c)*d*e*f + ((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) - 2*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*c*d*e*f - ((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*f^2 + 2*((a^2*b - b^3)*d^2*e*f - (a^3 - a*b^2)*d*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) - 2*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*c*d*e*f - ((a^2*b - b^3)*c^2 + 2*(a^3 - a*b^2)*c)*f^2 + 2*((a^2*b - b^3)*d^2*e*f - (a^3 - a*b^2)*d*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 4*((a^3 - a*b^2)*d^2*f^2*x^2 + 2*(a^3 - a*b^2)*d^2*e*f*x + (a^3 - a*b^2)*d^2*e^2)*cos(d*x + c))/((a^4 - a^2*b^2)*d^3*sin(d*x + c))","C",0
238,1,1692,0,1.879169," ","integrate((f*x+e)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{-2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 i \, {\left(a^{2} b - b^{3}\right)} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 i \, {\left(a^{2} b - b^{3}\right)} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 i \, {\left(a^{2} b - b^{3}\right)} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 i \, {\left(a^{2} b - b^{3}\right)} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e + {\left(a^{3} - a b^{2}\right)} f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e + {\left(a^{3} - a b^{2}\right)} f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d f x + {\left(a^{3} - a b^{2}\right)} d e\right)} \cos\left(d x + c\right)}{4 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} \sin\left(d x + c\right)}"," ",0,"-1/4*(-2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*I*(a^2*b - b^3)*f*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*I*(a^2*b - b^3)*f*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 2*I*(a^2*b - b^3)*f*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*I*(a^2*b - b^3)*f*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e + (a^3 - a*b^2)*f)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) - 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e + (a^3 - a*b^2)*f)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 2*((a^2*b - b^3)*d*e - (a^3 - a*b^2 + (a^2*b - b^3)*c)*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*((a^2*b - b^3)*d*e - (a^3 - a*b^2 + (a^2*b - b^3)*c)*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 4*((a^3 - a*b^2)*d*f*x + (a^3 - a*b^2)*d*e)*cos(d*x + c))/((a^4 - a^2*b^2)*d^2*sin(d*x + c))","B",0
239,1,400,0,1.749077," ","integrate(csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} b^{2} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - {\left(a^{2} b - b^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(a^{2} b - b^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(d x + c\right)}, -\frac{2 \, \sqrt{a^{2} - b^{2}} b^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - {\left(a^{2} b - b^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(a^{2} b - b^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(d x + c\right)}\right]"," ",0,"[-1/2*(sqrt(-a^2 + b^2)*b^2*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - (a^2*b - b^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + (a^2*b - b^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*(a^3 - a*b^2)*cos(d*x + c))/((a^4 - a^2*b^2)*d*sin(d*x + c)), -1/2*(2*sqrt(a^2 - b^2)*b^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - (a^2*b - b^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + (a^2*b - b^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*(a^3 - a*b^2)*cos(d*x + c))/((a^4 - a^2*b^2)*d*sin(d*x + c))]","B",0
240,0,0,0,1.382394," ","integrate((f*x+e)^m*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right)^{2} - 1\right)} {\left(f x + e\right)}^{m}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(cos(d*x + c)^2 - 1)*(f*x + e)^m/(b*sin(d*x + c) + a), x)","F",0
241,0,0,0,1.526837," ","integrate((f*x+e)^m*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \sin\left(d x + c\right)}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*sin(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
242,0,0,0,1.463426," ","integrate((f*x+e)^m/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m/(b*sin(d*x + c) + a), x)","F",0
243,0,0,0,1.120179," ","integrate((f*x+e)^m*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*csc(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
244,0,0,0,1.758607," ","integrate((f*x+e)^m*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \csc\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*csc(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
245,1,1506,0,1.953580," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(-i \, b^{4} f \sin\left(d x + c\right) - i \, a b^{3} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, b^{4} f \sin\left(d x + c\right) + i \, a b^{3} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, b^{4} f \sin\left(d x + c\right) + i \, a b^{3} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, b^{4} f \sin\left(d x + c\right) - i \, a b^{3} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a b^{3} d f x + a b^{3} c f + {\left(b^{4} d f x + b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a b^{3} d f x + a b^{3} c f + {\left(b^{4} d f x + b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a b^{3} d f x + a b^{3} c f + {\left(b^{4} d f x + b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a b^{3} d f x + a b^{3} c f + {\left(b^{4} d f x + b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f x + {\left(a^{3} b - a b^{3}\right)} d e\right)} \cos\left(d x + c\right) + {\left({\left(a^{3} b - a b^{3}\right)} f \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f - {\left(a b^{3} d e - a b^{3} c f + {\left(b^{4} d e - b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{3} b - a b^{3}\right)} f \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f - {\left(a b^{3} d e - a b^{3} c f + {\left(b^{4} d e - b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left({\left(a^{3} b - a b^{3}\right)} f \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f + {\left(a b^{3} d e - a b^{3} c f + {\left(b^{4} d e - b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{3} b - a b^{3}\right)} f \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f + {\left(a b^{3} d e - a b^{3} c f + {\left(b^{4} d e - b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right)}{2 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d^{2} \sin\left(d x + c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2}\right)}}"," ",0,"1/2*((-I*b^4*f*sin(d*x + c) - I*a*b^3*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*b^4*f*sin(d*x + c) + I*a*b^3*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*b^4*f*sin(d*x + c) + I*a*b^3*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*b^4*f*sin(d*x + c) - I*a*b^3*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (a*b^3*d*f*x + a*b^3*c*f + (b^4*d*f*x + b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a*b^3*d*f*x + a*b^3*c*f + (b^4*d*f*x + b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a*b^3*d*f*x + a*b^3*c*f + (b^4*d*f*x + b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a*b^3*d*f*x + a*b^3*c*f + (b^4*d*f*x + b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*((a^3*b - a*b^3)*d*f*x + (a^3*b - a*b^3)*d*e)*cos(d*x + c) + ((a^3*b - a*b^3)*f*sin(d*x + c) + (a^4 - a^2*b^2)*f - (a*b^3*d*e - a*b^3*c*f + (b^4*d*e - b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^3*b - a*b^3)*f*sin(d*x + c) + (a^4 - a^2*b^2)*f - (a*b^3*d*e - a*b^3*c*f + (b^4*d*e - b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + ((a^3*b - a*b^3)*f*sin(d*x + c) + (a^4 - a^2*b^2)*f + (a*b^3*d*e - a*b^3*c*f + (b^4*d*e - b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^3*b - a*b^3)*f*sin(d*x + c) + (a^4 - a^2*b^2)*f + (a*b^3*d*e - a*b^3*c*f + (b^4*d*e - b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d^2*sin(d*x + c) + (a^5*b - 2*a^3*b^3 + a*b^5)*d^2)","B",0
246,1,3126,0,2.084101," ","integrate((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(b^{4} f^{2} \sin\left(d x + c\right) + a b^{3} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(b^{4} f^{2} \sin\left(d x + c\right) + a b^{3} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(b^{4} f^{2} \sin\left(d x + c\right) + a b^{3} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(b^{4} f^{2} \sin\left(d x + c\right) + a b^{3} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f x + {\left(a^{3} b - a b^{3}\right)} d^{2} e^{2}\right)} \cos\left(d x + c\right) - {\left(-4 i \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) - 4 i \, {\left(a^{4} - a^{2} b^{2}\right)} f^{2} + 2 \, {\left(-2 i \, a b^{3} d f^{2} x - 2 i \, a b^{3} d e f + {\left(-2 i \, b^{4} d f^{2} x - 2 i \, b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-4 i \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) - 4 i \, {\left(a^{4} - a^{2} b^{2}\right)} f^{2} + 2 \, {\left(2 i \, a b^{3} d f^{2} x + 2 i \, a b^{3} d e f + {\left(2 i \, b^{4} d f^{2} x + 2 i \, b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(4 i \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) + 4 i \, {\left(a^{4} - a^{2} b^{2}\right)} f^{2} + 2 \, {\left(2 i \, a b^{3} d f^{2} x + 2 i \, a b^{3} d e f + {\left(2 i \, b^{4} d f^{2} x + 2 i \, b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(4 i \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) + 4 i \, {\left(a^{4} - a^{2} b^{2}\right)} f^{2} + 2 \, {\left(-2 i \, a b^{3} d f^{2} x - 2 i \, a b^{3} d e f + {\left(-2 i \, b^{4} d f^{2} x - 2 i \, b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f - {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{2} e^{2} - 2 \, a b^{3} c d e f + a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f - {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{2} e^{2} - 2 \, a b^{3} c d e f + a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f - {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{2} e^{2} - 2 \, a b^{3} c d e f + a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f - {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{2} e^{2} - 2 \, a b^{3} c d e f + a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{2} x + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{2} x + {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{2} f^{2} x^{2} + 2 \, a b^{3} d^{2} e f x + 2 \, a b^{3} c d e f - a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{2} x + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{2} x + {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{2} f^{2} x^{2} + 2 \, a b^{3} d^{2} e f x + 2 \, a b^{3} c d e f - a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{2} x + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{2} x + {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{2} f^{2} x^{2} + 2 \, a b^{3} d^{2} e f x + 2 \, a b^{3} c d e f - a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{2} x + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{2} x + {\left(a^{3} b - a b^{3}\right)} c f^{2}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{2} f^{2} x^{2} + 2 \, a b^{3} d^{2} e f x + 2 \, a b^{3} c d e f - a b^{3} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{4 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d^{3} \sin\left(d x + c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{3}\right)}}"," ",0,"-1/4*(4*(b^4*f^2*sin(d*x + c) + a*b^3*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(b^4*f^2*sin(d*x + c) + a*b^3*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(b^4*f^2*sin(d*x + c) + a*b^3*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(b^4*f^2*sin(d*x + c) + a*b^3*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*((a^3*b - a*b^3)*d^2*f^2*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f*x + (a^3*b - a*b^3)*d^2*e^2)*cos(d*x + c) - (-4*I*(a^3*b - a*b^3)*f^2*sin(d*x + c) - 4*I*(a^4 - a^2*b^2)*f^2 + 2*(-2*I*a*b^3*d*f^2*x - 2*I*a*b^3*d*e*f + (-2*I*b^4*d*f^2*x - 2*I*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-4*I*(a^3*b - a*b^3)*f^2*sin(d*x + c) - 4*I*(a^4 - a^2*b^2)*f^2 + 2*(2*I*a*b^3*d*f^2*x + 2*I*a*b^3*d*e*f + (2*I*b^4*d*f^2*x + 2*I*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (4*I*(a^3*b - a*b^3)*f^2*sin(d*x + c) + 4*I*(a^4 - a^2*b^2)*f^2 + 2*(2*I*a*b^3*d*f^2*x + 2*I*a*b^3*d*e*f + (2*I*b^4*d*f^2*x + 2*I*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (4*I*(a^3*b - a*b^3)*f^2*sin(d*x + c) + 4*I*(a^4 - a^2*b^2)*f^2 + 2*(-2*I*a*b^3*d*f^2*x - 2*I*a*b^3*d*e*f + (-2*I*b^4*d*f^2*x - 2*I*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(2*(a^4 - a^2*b^2)*d*e*f - 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*e*f - (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) - (a*b^3*d^2*e^2 - 2*a*b^3*c*d*e*f + a*b^3*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(2*(a^4 - a^2*b^2)*d*e*f - 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*e*f - (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) - (a*b^3*d^2*e^2 - 2*a*b^3*c*d*e*f + a*b^3*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(2*(a^4 - a^2*b^2)*d*e*f - 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*e*f - (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) + (a*b^3*d^2*e^2 - 2*a*b^3*c*d*e*f + a*b^3*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(2*(a^4 - a^2*b^2)*d*e*f - 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*e*f - (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) + (a*b^3*d^2*e^2 - 2*a*b^3*c*d*e*f + a*b^3*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(2*(a^4 - a^2*b^2)*d*f^2*x + 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*f^2*x + (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) + (a*b^3*d^2*f^2*x^2 + 2*a*b^3*d^2*e*f*x + 2*a*b^3*c*d*e*f - a*b^3*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^4 - a^2*b^2)*d*f^2*x + 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*f^2*x + (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) - (a*b^3*d^2*f^2*x^2 + 2*a*b^3*d^2*e*f*x + 2*a*b^3*c*d*e*f - a*b^3*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^4 - a^2*b^2)*d*f^2*x + 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*f^2*x + (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) + (a*b^3*d^2*f^2*x^2 + 2*a*b^3*d^2*e*f*x + 2*a*b^3*c*d*e*f - a*b^3*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^4 - a^2*b^2)*d*f^2*x + 2*(a^4 - a^2*b^2)*c*f^2 + 2*((a^3*b - a*b^3)*d*f^2*x + (a^3*b - a*b^3)*c*f^2)*sin(d*x + c) - (a*b^3*d^2*f^2*x^2 + 2*a*b^3*d^2*e*f*x + 2*a*b^3*c*d*e*f - a*b^3*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d^3*sin(d*x + c) + (a^5*b - 2*a^3*b^3 + a*b^5)*d^3)","C",0
247,1,5180,0,2.948892," ","integrate((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(6 i \, b^{4} f^{3} \sin\left(d x + c\right) + 6 i \, a b^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-6 i \, b^{4} f^{3} \sin\left(d x + c\right) - 6 i \, a b^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-6 i \, b^{4} f^{3} \sin\left(d x + c\right) - 6 i \, a b^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(6 i \, b^{4} f^{3} \sin\left(d x + c\right) + 6 i \, a b^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b - a b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b - a b^{3}\right)} d^{3} e^{2} f x + {\left(a^{3} b - a b^{3}\right)} d^{3} e^{3}\right)} \cos\left(d x + c\right) + {\left(-12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d e f^{2} + {\left(-12 i \, {\left(a^{3} b - a b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} b - a b^{3}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(-3 i \, a b^{3} d^{2} f^{3} x^{2} - 6 i \, a b^{3} d^{2} e f^{2} x - 3 i \, a b^{3} d^{2} e^{2} f + {\left(-3 i \, b^{4} d^{2} f^{3} x^{2} - 6 i \, b^{4} d^{2} e f^{2} x - 3 i \, b^{4} d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d e f^{2} + {\left(-12 i \, {\left(a^{3} b - a b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} b - a b^{3}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(3 i \, a b^{3} d^{2} f^{3} x^{2} + 6 i \, a b^{3} d^{2} e f^{2} x + 3 i \, a b^{3} d^{2} e^{2} f + {\left(3 i \, b^{4} d^{2} f^{3} x^{2} + 6 i \, b^{4} d^{2} e f^{2} x + 3 i \, b^{4} d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d e f^{2} + {\left(12 i \, {\left(a^{3} b - a b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} b - a b^{3}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(3 i \, a b^{3} d^{2} f^{3} x^{2} + 6 i \, a b^{3} d^{2} e f^{2} x + 3 i \, a b^{3} d^{2} e^{2} f + {\left(3 i \, b^{4} d^{2} f^{3} x^{2} + 6 i \, b^{4} d^{2} e f^{2} x + 3 i \, b^{4} d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{4} - a^{2} b^{2}\right)} d e f^{2} + {\left(12 i \, {\left(a^{3} b - a b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} b - a b^{3}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(-3 i \, a b^{3} d^{2} f^{3} x^{2} - 6 i \, a b^{3} d^{2} e f^{2} x - 3 i \, a b^{3} d^{2} e^{2} f + {\left(-3 i \, b^{4} d^{2} f^{3} x^{2} - 6 i \, b^{4} d^{2} e f^{2} x - 3 i \, b^{4} d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{3} e^{3} - 3 \, a b^{3} c d^{2} e^{2} f + 3 \, a b^{3} c^{2} d e f^{2} - a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{3} e^{3} - 3 \, a b^{3} c d^{2} e^{2} f + 3 \, a b^{3} c^{2} d e f^{2} - a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{3} e^{3} - 3 \, a b^{3} c d^{2} e^{2} f + 3 \, a b^{3} c^{2} d e f^{2} - a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{3} e^{3} - 3 \, a b^{3} c d^{2} e^{2} f + 3 \, a b^{3} c^{2} d e f^{2} - a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e f^{2} x + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} - 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{3} f^{3} x^{3} + 3 \, a b^{3} d^{3} e f^{2} x^{2} + 3 \, a b^{3} d^{3} e^{2} f x + 3 \, a b^{3} c d^{2} e^{2} f - 3 \, a b^{3} c^{2} d e f^{2} + a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e f^{2} x + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} - 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{3} f^{3} x^{3} + 3 \, a b^{3} d^{3} e f^{2} x^{2} + 3 \, a b^{3} d^{3} e^{2} f x + 3 \, a b^{3} c d^{2} e^{2} f - 3 \, a b^{3} c^{2} d e f^{2} + a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e f^{2} x + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} - 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left(a b^{3} d^{3} f^{3} x^{3} + 3 \, a b^{3} d^{3} e f^{2} x^{2} + 3 \, a b^{3} d^{3} e^{2} f x + 3 \, a b^{3} c d^{2} e^{2} f - 3 \, a b^{3} c^{2} d e f^{2} + a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} d^{2} e f^{2} x + 6 \, {\left(a^{4} - a^{2} b^{2}\right)} c d e f^{2} - 3 \, {\left(a^{4} - a^{2} b^{2}\right)} c^{2} f^{3} + 3 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left(a b^{3} d^{3} f^{3} x^{3} + 3 \, a b^{3} d^{3} e f^{2} x^{2} + 3 \, a b^{3} d^{3} e^{2} f x + 3 \, a b^{3} c d^{2} e^{2} f - 3 \, a b^{3} c^{2} d e f^{2} + a b^{3} c^{3} f^{3} + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left({\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f^{3} - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f^{3} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f^{3} - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) + {\left(a^{4} - a^{2} b^{2}\right)} f^{3} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{4 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d^{4} \sin\left(d x + c\right) + {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{4}\right)}}"," ",0,"1/4*(2*(6*I*b^4*f^3*sin(d*x + c) + 6*I*a*b^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-6*I*b^4*f^3*sin(d*x + c) - 6*I*a*b^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-6*I*b^4*f^3*sin(d*x + c) - 6*I*a*b^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(6*I*b^4*f^3*sin(d*x + c) + 6*I*a*b^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*((a^3*b - a*b^3)*d^3*f^3*x^3 + 3*(a^3*b - a*b^3)*d^3*e*f^2*x^2 + 3*(a^3*b - a*b^3)*d^3*e^2*f*x + (a^3*b - a*b^3)*d^3*e^3)*cos(d*x + c) + (-12*I*(a^4 - a^2*b^2)*d*f^3*x - 12*I*(a^4 - a^2*b^2)*d*e*f^2 + (-12*I*(a^3*b - a*b^3)*d*f^3*x - 12*I*(a^3*b - a*b^3)*d*e*f^2)*sin(d*x + c) + 2*(-3*I*a*b^3*d^2*f^3*x^2 - 6*I*a*b^3*d^2*e*f^2*x - 3*I*a*b^3*d^2*e^2*f + (-3*I*b^4*d^2*f^3*x^2 - 6*I*b^4*d^2*e*f^2*x - 3*I*b^4*d^2*e^2*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-12*I*(a^4 - a^2*b^2)*d*f^3*x - 12*I*(a^4 - a^2*b^2)*d*e*f^2 + (-12*I*(a^3*b - a*b^3)*d*f^3*x - 12*I*(a^3*b - a*b^3)*d*e*f^2)*sin(d*x + c) + 2*(3*I*a*b^3*d^2*f^3*x^2 + 6*I*a*b^3*d^2*e*f^2*x + 3*I*a*b^3*d^2*e^2*f + (3*I*b^4*d^2*f^3*x^2 + 6*I*b^4*d^2*e*f^2*x + 3*I*b^4*d^2*e^2*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (12*I*(a^4 - a^2*b^2)*d*f^3*x + 12*I*(a^4 - a^2*b^2)*d*e*f^2 + (12*I*(a^3*b - a*b^3)*d*f^3*x + 12*I*(a^3*b - a*b^3)*d*e*f^2)*sin(d*x + c) + 2*(3*I*a*b^3*d^2*f^3*x^2 + 6*I*a*b^3*d^2*e*f^2*x + 3*I*a*b^3*d^2*e^2*f + (3*I*b^4*d^2*f^3*x^2 + 6*I*b^4*d^2*e*f^2*x + 3*I*b^4*d^2*e^2*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (12*I*(a^4 - a^2*b^2)*d*f^3*x + 12*I*(a^4 - a^2*b^2)*d*e*f^2 + (12*I*(a^3*b - a*b^3)*d*f^3*x + 12*I*(a^3*b - a*b^3)*d*e*f^2)*sin(d*x + c) + 2*(-3*I*a*b^3*d^2*f^3*x^2 - 6*I*a*b^3*d^2*e*f^2*x - 3*I*a*b^3*d^2*e^2*f + (-3*I*b^4*d^2*f^3*x^2 - 6*I*b^4*d^2*e*f^2*x - 3*I*b^4*d^2*e^2*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*(a^4 - a^2*b^2)*d^2*e^2*f - 6*(a^4 - a^2*b^2)*c*d*e*f^2 + 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*e^2*f - 2*(a^3*b - a*b^3)*c*d*e*f^2 + (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) - (a*b^3*d^3*e^3 - 3*a*b^3*c*d^2*e^2*f + 3*a*b^3*c^2*d*e*f^2 - a*b^3*c^3*f^3 + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(3*(a^4 - a^2*b^2)*d^2*e^2*f - 6*(a^4 - a^2*b^2)*c*d*e*f^2 + 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*e^2*f - 2*(a^3*b - a*b^3)*c*d*e*f^2 + (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) - (a*b^3*d^3*e^3 - 3*a*b^3*c*d^2*e^2*f + 3*a*b^3*c^2*d*e*f^2 - a*b^3*c^3*f^3 + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(3*(a^4 - a^2*b^2)*d^2*e^2*f - 6*(a^4 - a^2*b^2)*c*d*e*f^2 + 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*e^2*f - 2*(a^3*b - a*b^3)*c*d*e*f^2 + (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) + (a*b^3*d^3*e^3 - 3*a*b^3*c*d^2*e^2*f + 3*a*b^3*c^2*d*e*f^2 - a*b^3*c^3*f^3 + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(3*(a^4 - a^2*b^2)*d^2*e^2*f - 6*(a^4 - a^2*b^2)*c*d*e*f^2 + 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*e^2*f - 2*(a^3*b - a*b^3)*c*d*e*f^2 + (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) + (a*b^3*d^3*e^3 - 3*a*b^3*c*d^2*e^2*f + 3*a*b^3*c^2*d*e*f^2 - a*b^3*c^3*f^3 + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(3*(a^4 - a^2*b^2)*d^2*f^3*x^2 + 6*(a^4 - a^2*b^2)*d^2*e*f^2*x + 6*(a^4 - a^2*b^2)*c*d*e*f^2 - 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f^2*x + 2*(a^3*b - a*b^3)*c*d*e*f^2 - (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) + (a*b^3*d^3*f^3*x^3 + 3*a*b^3*d^3*e*f^2*x^2 + 3*a*b^3*d^3*e^2*f*x + 3*a*b^3*c*d^2*e^2*f - 3*a*b^3*c^2*d*e*f^2 + a*b^3*c^3*f^3 + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(3*(a^4 - a^2*b^2)*d^2*f^3*x^2 + 6*(a^4 - a^2*b^2)*d^2*e*f^2*x + 6*(a^4 - a^2*b^2)*c*d*e*f^2 - 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f^2*x + 2*(a^3*b - a*b^3)*c*d*e*f^2 - (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) - (a*b^3*d^3*f^3*x^3 + 3*a*b^3*d^3*e*f^2*x^2 + 3*a*b^3*d^3*e^2*f*x + 3*a*b^3*c*d^2*e^2*f - 3*a*b^3*c^2*d*e*f^2 + a*b^3*c^3*f^3 + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(3*(a^4 - a^2*b^2)*d^2*f^3*x^2 + 6*(a^4 - a^2*b^2)*d^2*e*f^2*x + 6*(a^4 - a^2*b^2)*c*d*e*f^2 - 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f^2*x + 2*(a^3*b - a*b^3)*c*d*e*f^2 - (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) + (a*b^3*d^3*f^3*x^3 + 3*a*b^3*d^3*e*f^2*x^2 + 3*a*b^3*d^3*e^2*f*x + 3*a*b^3*c*d^2*e^2*f - 3*a*b^3*c^2*d*e*f^2 + a*b^3*c^3*f^3 + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(3*(a^4 - a^2*b^2)*d^2*f^3*x^2 + 6*(a^4 - a^2*b^2)*d^2*e*f^2*x + 6*(a^4 - a^2*b^2)*c*d*e*f^2 - 3*(a^4 - a^2*b^2)*c^2*f^3 + 3*((a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f^2*x + 2*(a^3*b - a*b^3)*c*d*e*f^2 - (a^3*b - a*b^3)*c^2*f^3)*sin(d*x + c) - (a*b^3*d^3*f^3*x^3 + 3*a*b^3*d^3*e*f^2*x^2 + 3*a*b^3*d^3*e^2*f*x + 3*a*b^3*c*d^2*e^2*f - 3*a*b^3*c^2*d*e*f^2 + a*b^3*c^3*f^3 + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 12*((a^3*b - a*b^3)*f^3*sin(d*x + c) + (a^4 - a^2*b^2)*f^3 - (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (b^4*d*f^3*x + b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*((a^3*b - a*b^3)*f^3*sin(d*x + c) + (a^4 - a^2*b^2)*f^3 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (b^4*d*f^3*x + b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*((a^3*b - a*b^3)*f^3*sin(d*x + c) + (a^4 - a^2*b^2)*f^3 - (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (b^4*d*f^3*x + b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*((a^3*b - a*b^3)*f^3*sin(d*x + c) + (a^4 - a^2*b^2)*f^3 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (b^4*d*f^3*x + b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d^4*sin(d*x + c) + (a^5*b - 2*a^3*b^3 + a*b^5)*d^4)","C",0
248,1,2421,0,2.426715," ","integrate((f*x+e)*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(-3 i \, a b^{5} f \cos\left(d x + c\right)^{2} + 6 i \, a^{2} b^{4} f \sin\left(d x + c\right) + 3 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, a b^{5} f \cos\left(d x + c\right)^{2} - 6 i \, a^{2} b^{4} f \sin\left(d x + c\right) - 3 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, a b^{5} f \cos\left(d x + c\right)^{2} - 6 i \, a^{2} b^{4} f \sin\left(d x + c\right) - 3 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-3 i \, a b^{5} f \cos\left(d x + c\right)^{2} + 6 i \, a^{2} b^{4} f \sin\left(d x + c\right) + 3 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d f x + a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f x + a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d f x + a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f x + a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d f x + a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f x + a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d f x + a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f x + a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f + 2 \, {\left({\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d f x + {\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d e\right)} \cos\left(d x + c\right) + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d e - {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d e - a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d e - a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d e - {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d e - a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d e - a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d e - {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d e - a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d e - a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d e - {\left(a^{3} b^{3} + a b^{5}\right)} c f - {\left(a b^{5} d e - a b^{5} c f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d e - a^{2} b^{4} c f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} f + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d^{2} \sin\left(d x + c\right) - {\left(a^{8} b - 2 \, a^{6} b^{3} + 2 \, a^{2} b^{7} - b^{9}\right)} d^{2}\right)}}"," ",0,"1/4*((-3*I*a*b^5*f*cos(d*x + c)^2 + 6*I*a^2*b^4*f*sin(d*x + c) + 3*I*(a^3*b^3 + a*b^5)*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*a*b^5*f*cos(d*x + c)^2 - 6*I*a^2*b^4*f*sin(d*x + c) - 3*I*(a^3*b^3 + a*b^5)*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*a*b^5*f*cos(d*x + c)^2 - 6*I*a^2*b^4*f*sin(d*x + c) - 3*I*(a^3*b^3 + a*b^5)*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-3*I*a*b^5*f*cos(d*x + c)^2 + 6*I*a^2*b^4*f*sin(d*x + c) + 3*I*(a^3*b^3 + a*b^5)*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 3*((a^3*b^3 + a*b^5)*d*f*x + (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*f*x + a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f*x + a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*((a^3*b^3 + a*b^5)*d*f*x + (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*f*x + a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f*x + a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*((a^3*b^3 + a*b^5)*d*f*x + (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*f*x + a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f*x + a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*((a^3*b^3 + a*b^5)*d*f*x + (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*f*x + a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f*x + a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*f + 2*((2*a^5*b - a^3*b^3 - a*b^5)*d*f*x + (2*a^5*b - a^3*b^3 - a*b^5)*d*e)*cos(d*x + c) + ((a^4*b^2 + a^2*b^4 - 2*b^6)*f*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f + 3*((a^3*b^3 + a*b^5)*d*e - (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*e - a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*e - a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^4*b^2 + a^2*b^4 - 2*b^6)*f*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f + 3*((a^3*b^3 + a*b^5)*d*e - (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*e - a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*e - a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + ((a^4*b^2 + a^2*b^4 - 2*b^6)*f*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f - 3*((a^3*b^3 + a*b^5)*d*e - (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*e - a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*e - a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^4*b^2 + a^2*b^4 - 2*b^6)*f*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f - 3*((a^3*b^3 + a*b^5)*d*e - (a^3*b^3 + a*b^5)*c*f - (a*b^5*d*e - a*b^5*c*f)*cos(d*x + c)^2 + 2*(a^2*b^4*d*e - a^2*b^4*c*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^5*b - 2*a^3*b^3 + a*b^5)*f + ((a^4*b^2 + a^2*b^4 - 2*b^6)*d*f*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*d*e)*cos(d*x + c))*sin(d*x + c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d^2*cos(d*x + c)^2 - 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d^2*sin(d*x + c) - (a^8*b - 2*a^6*b^3 + 2*a^2*b^7 - b^9)*d^2)","B",0
249,1,5747,0,3.561006," ","integrate((f*x+e)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f^{2} x + 8 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e f - 12 \, {\left(a b^{5} f^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{4} f^{2} \sin\left(d x + c\right) - {\left(a^{3} b^{3} + a b^{5}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a b^{5} f^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{4} f^{2} \sin\left(d x + c\right) - {\left(a^{3} b^{3} + a b^{5}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b^{5} f^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{4} f^{2} \sin\left(d x + c\right) - {\left(a^{3} b^{3} + a b^{5}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a b^{5} f^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{4} f^{2} \sin\left(d x + c\right) - {\left(a^{3} b^{3} + a b^{5}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{2} e f x + {\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{2} e^{2}\right)} \cos\left(d x + c\right) + {\left(-4 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} \cos\left(d x + c\right)^{2} + 8 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{2} \sin\left(d x + c\right) + 4 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} + 2 \, {\left(6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d f^{2} x + 6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d e f + {\left(-6 i \, a b^{5} d f^{2} x - 6 i \, a b^{5} d e f\right)} \cos\left(d x + c\right)^{2} + {\left(12 i \, a^{2} b^{4} d f^{2} x + 12 i \, a^{2} b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-4 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} \cos\left(d x + c\right)^{2} + 8 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{2} \sin\left(d x + c\right) + 4 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} + 2 \, {\left(-6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d f^{2} x - 6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d e f + {\left(6 i \, a b^{5} d f^{2} x + 6 i \, a b^{5} d e f\right)} \cos\left(d x + c\right)^{2} + {\left(-12 i \, a^{2} b^{4} d f^{2} x - 12 i \, a^{2} b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(4 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} \cos\left(d x + c\right)^{2} - 8 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{2} \sin\left(d x + c\right) - 4 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} + 2 \, {\left(-6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d f^{2} x - 6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d e f + {\left(6 i \, a b^{5} d f^{2} x + 6 i \, a b^{5} d e f\right)} \cos\left(d x + c\right)^{2} + {\left(-12 i \, a^{2} b^{4} d f^{2} x - 12 i \, a^{2} b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(4 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} \cos\left(d x + c\right)^{2} - 8 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{2} \sin\left(d x + c\right) - 4 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{2} + 2 \, {\left(6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d f^{2} x + 6 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d e f + {\left(-6 i \, a b^{5} d f^{2} x - 6 i \, a b^{5} d e f\right)} \cos\left(d x + c\right)^{2} + {\left(12 i \, a^{2} b^{4} d f^{2} x + 12 i \, a^{2} b^{4} d e f\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) - {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} - 6 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} f^{2} - {\left(3 \, a b^{5} d^{2} e^{2} - 6 \, a b^{5} c d e f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{4} d^{2} e^{2} - 6 \, a^{2} b^{4} c d e f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) - {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} - 6 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} f^{2} - {\left(3 \, a b^{5} d^{2} e^{2} - 6 \, a b^{5} c d e f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{4} d^{2} e^{2} - 6 \, a^{2} b^{4} c d e f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) + {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} - 6 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} f^{2} - {\left(3 \, a b^{5} d^{2} e^{2} - 6 \, a b^{5} c d e f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{4} d^{2} e^{2} - 6 \, a^{2} b^{4} c d e f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) + {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} - 6 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} f^{2} - {\left(3 \, a b^{5} d^{2} e^{2} - 6 \, a b^{5} c d e f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{4} d^{2} e^{2} - 6 \, a^{2} b^{4} c d e f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{2} x + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f x + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} f^{2} - {\left(a b^{5} d^{2} f^{2} x^{2} + 2 \, a b^{5} d^{2} e f x + 2 \, a b^{5} c d e f - a b^{5} c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{4} d^{2} e f x + 2 \, a^{2} b^{4} c d e f - a^{2} b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{2} x + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f x + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} f^{2} - {\left(a b^{5} d^{2} f^{2} x^{2} + 2 \, a b^{5} d^{2} e f x + 2 \, a b^{5} c d e f - a b^{5} c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{4} d^{2} e f x + 2 \, a^{2} b^{4} c d e f - a^{2} b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{2} x + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f x + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} f^{2} - {\left(a b^{5} d^{2} f^{2} x^{2} + 2 \, a b^{5} d^{2} e f x + 2 \, a b^{5} c d e f - a b^{5} c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{4} d^{2} e f x + 2 \, a^{2} b^{4} c d e f - a^{2} b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2} - 2 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{2} x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{2} x + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c f^{2}\right)} \sin\left(d x + c\right) - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f x + 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d e f - {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} f^{2} - {\left(a b^{5} d^{2} f^{2} x^{2} + 2 \, a b^{5} d^{2} e f x + 2 \, a b^{5} c d e f - a b^{5} c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{4} d^{2} e f x + 2 \, a^{2} b^{4} c d e f - a^{2} b^{4} c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d f^{2} x + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d e f + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d^{3} \sin\left(d x + c\right) - {\left(a^{8} b - 2 \, a^{6} b^{3} + 2 \, a^{2} b^{7} - b^{9}\right)} d^{3}\right)}}"," ",0,"1/8*(8*(a^6 - 2*a^4*b^2 + a^2*b^4)*d*f^2*x + 8*(a^6 - 2*a^4*b^2 + a^2*b^4)*d*e*f - 12*(a*b^5*f^2*cos(d*x + c)^2 - 2*a^2*b^4*f^2*sin(d*x + c) - (a^3*b^3 + a*b^5)*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a*b^5*f^2*cos(d*x + c)^2 - 2*a^2*b^4*f^2*sin(d*x + c) - (a^3*b^3 + a*b^5)*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(a*b^5*f^2*cos(d*x + c)^2 - 2*a^2*b^4*f^2*sin(d*x + c) - (a^3*b^3 + a*b^5)*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a*b^5*f^2*cos(d*x + c)^2 - 2*a^2*b^4*f^2*sin(d*x + c) - (a^3*b^3 + a*b^5)*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*((2*a^5*b - a^3*b^3 - a*b^5)*d^2*f^2*x^2 + 2*(2*a^5*b - a^3*b^3 - a*b^5)*d^2*e*f*x + (2*a^5*b - a^3*b^3 - a*b^5)*d^2*e^2)*cos(d*x + c) + (-4*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*f^2*cos(d*x + c)^2 + 8*I*(a^5*b + a^3*b^3 - 2*a*b^5)*f^2*sin(d*x + c) + 4*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^2 + 2*(6*I*(a^3*b^3 + a*b^5)*d*f^2*x + 6*I*(a^3*b^3 + a*b^5)*d*e*f + (-6*I*a*b^5*d*f^2*x - 6*I*a*b^5*d*e*f)*cos(d*x + c)^2 + (12*I*a^2*b^4*d*f^2*x + 12*I*a^2*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-4*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*f^2*cos(d*x + c)^2 + 8*I*(a^5*b + a^3*b^3 - 2*a*b^5)*f^2*sin(d*x + c) + 4*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^2 + 2*(-6*I*(a^3*b^3 + a*b^5)*d*f^2*x - 6*I*(a^3*b^3 + a*b^5)*d*e*f + (6*I*a*b^5*d*f^2*x + 6*I*a*b^5*d*e*f)*cos(d*x + c)^2 + (-12*I*a^2*b^4*d*f^2*x - 12*I*a^2*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (4*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*f^2*cos(d*x + c)^2 - 8*I*(a^5*b + a^3*b^3 - 2*a*b^5)*f^2*sin(d*x + c) - 4*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^2 + 2*(-6*I*(a^3*b^3 + a*b^5)*d*f^2*x - 6*I*(a^3*b^3 + a*b^5)*d*e*f + (6*I*a*b^5*d*f^2*x + 6*I*a*b^5*d*e*f)*cos(d*x + c)^2 + (-12*I*a^2*b^4*d*f^2*x - 12*I*a^2*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (4*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*f^2*cos(d*x + c)^2 - 8*I*(a^5*b + a^3*b^3 - 2*a*b^5)*f^2*sin(d*x + c) - 4*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^2 + 2*(6*I*(a^3*b^3 + a*b^5)*d*f^2*x + 6*I*(a^3*b^3 + a*b^5)*d*e*f + (-6*I*a*b^5*d*f^2*x - 6*I*a*b^5*d*e*f)*cos(d*x + c)^2 + (12*I*a^2*b^4*d*f^2*x + 12*I*a^2*b^4*d*e*f)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f - (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f - (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) - (3*(a^3*b^3 + a*b^5)*d^2*e^2 - 6*(a^3*b^3 + a*b^5)*c*d*e*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*f^2 - (3*a*b^5*d^2*e^2 - 6*a*b^5*c*d*e*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*f^2)*cos(d*x + c)^2 + 2*(3*a^2*b^4*d^2*e^2 - 6*a^2*b^4*c*d*e*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f - (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f - (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) - (3*(a^3*b^3 + a*b^5)*d^2*e^2 - 6*(a^3*b^3 + a*b^5)*c*d*e*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*f^2 - (3*a*b^5*d^2*e^2 - 6*a*b^5*c*d*e*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*f^2)*cos(d*x + c)^2 + 2*(3*a^2*b^4*d^2*e^2 - 6*a^2*b^4*c*d*e*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f - (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f - (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) + (3*(a^3*b^3 + a*b^5)*d^2*e^2 - 6*(a^3*b^3 + a*b^5)*c*d*e*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*f^2 - (3*a*b^5*d^2*e^2 - 6*a*b^5*c*d*e*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*f^2)*cos(d*x + c)^2 + 2*(3*a^2*b^4*d^2*e^2 - 6*a^2*b^4*c*d*e*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f - (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f - (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) + (3*(a^3*b^3 + a*b^5)*d^2*e^2 - 6*(a^3*b^3 + a*b^5)*c*d*e*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*f^2 - (3*a*b^5*d^2*e^2 - 6*a*b^5*c*d*e*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*f^2)*cos(d*x + c)^2 + 2*(3*a^2*b^4*d^2*e^2 - 6*a^2*b^4*c*d*e*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^2*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*f^2*x + (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) + 3*((a^3*b^3 + a*b^5)*d^2*f^2*x^2 + 2*(a^3*b^3 + a*b^5)*d^2*e*f*x + 2*(a^3*b^3 + a*b^5)*c*d*e*f - (a^3*b^3 + a*b^5)*c^2*f^2 - (a*b^5*d^2*f^2*x^2 + 2*a*b^5*d^2*e*f*x + 2*a*b^5*c*d*e*f - a*b^5*c^2*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d^2*f^2*x^2 + 2*a^2*b^4*d^2*e*f*x + 2*a^2*b^4*c*d*e*f - a^2*b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^2*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*f^2*x + (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) - 3*((a^3*b^3 + a*b^5)*d^2*f^2*x^2 + 2*(a^3*b^3 + a*b^5)*d^2*e*f*x + 2*(a^3*b^3 + a*b^5)*c*d*e*f - (a^3*b^3 + a*b^5)*c^2*f^2 - (a*b^5*d^2*f^2*x^2 + 2*a*b^5*d^2*e*f*x + 2*a*b^5*c*d*e*f - a*b^5*c^2*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d^2*f^2*x^2 + 2*a^2*b^4*d^2*e*f*x + 2*a^2*b^4*c*d*e*f - a^2*b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^2*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*f^2*x + (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) + 3*((a^3*b^3 + a*b^5)*d^2*f^2*x^2 + 2*(a^3*b^3 + a*b^5)*d^2*e*f*x + 2*(a^3*b^3 + a*b^5)*c*d*e*f - (a^3*b^3 + a*b^5)*c^2*f^2 - (a*b^5*d^2*f^2*x^2 + 2*a*b^5*d^2*e*f*x + 2*a*b^5*c*d*e*f - a*b^5*c^2*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d^2*f^2*x^2 + 2*a^2*b^4*d^2*e*f*x + 2*a^2*b^4*c*d*e*f - a^2*b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f^2 - 2*((a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^2*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*c*f^2)*cos(d*x + c)^2 + 4*((a^5*b + a^3*b^3 - 2*a*b^5)*d*f^2*x + (a^5*b + a^3*b^3 - 2*a*b^5)*c*f^2)*sin(d*x + c) - 3*((a^3*b^3 + a*b^5)*d^2*f^2*x^2 + 2*(a^3*b^3 + a*b^5)*d^2*e*f*x + 2*(a^3*b^3 + a*b^5)*c*d*e*f - (a^3*b^3 + a*b^5)*c^2*f^2 - (a*b^5*d^2*f^2*x^2 + 2*a*b^5*d^2*e*f*x + 2*a*b^5*c*d*e*f - a*b^5*c^2*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d^2*f^2*x^2 + 2*a^2*b^4*d^2*e*f*x + 2*a^2*b^4*c*d*e*f - a^2*b^4*c^2*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*(2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*f^2*x + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*d*e*f + ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*f^2*x^2 + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e*f*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e^2)*cos(d*x + c))*sin(d*x + c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d^3*cos(d*x + c)^2 - 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d^3*sin(d*x + c) - (a^8*b - 2*a^6*b^3 + 2*a^2*b^7 - b^9)*d^3)","C",0
250,1,10602,0,5.317014," ","integrate((f*x+e)^3*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} e^{2} f + 2 \, {\left(18 i \, a b^{5} f^{3} \cos\left(d x + c\right)^{2} - 36 i \, a^{2} b^{4} f^{3} \sin\left(d x + c\right) - 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-18 i \, a b^{5} f^{3} \cos\left(d x + c\right)^{2} + 36 i \, a^{2} b^{4} f^{3} \sin\left(d x + c\right) + 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-18 i \, a b^{5} f^{3} \cos\left(d x + c\right)^{2} + 36 i \, a^{2} b^{4} f^{3} \sin\left(d x + c\right) + 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(18 i \, a b^{5} f^{3} \cos\left(d x + c\right)^{2} - 36 i \, a^{2} b^{4} f^{3} \sin\left(d x + c\right) - 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{3} e^{2} f x + {\left(2 \, a^{5} b - a^{3} b^{3} - a b^{5}\right)} d^{3} e^{3}\right)} \cos\left(d x + c\right) + {\left(12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x + 12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2} + {\left(-12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x - 12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{3} x + 24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{3} x^{2} + 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f^{2} x + 9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{5} b - a b^{5}\right)} f^{3} + {\left(-9 i \, a b^{5} d^{2} f^{3} x^{2} - 18 i \, a b^{5} d^{2} e f^{2} x - 9 i \, a b^{5} d^{2} e^{2} f + 6 i \, {\left(a^{3} b^{3} - a b^{5}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(18 i \, a^{2} b^{4} d^{2} f^{3} x^{2} + 36 i \, a^{2} b^{4} d^{2} e f^{2} x + 18 i \, a^{2} b^{4} d^{2} e^{2} f - 12 i \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x + 12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2} + {\left(-12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x - 12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{3} x + 24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(-9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{3} x^{2} - 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f^{2} x - 9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{5} b - a b^{5}\right)} f^{3} + {\left(9 i \, a b^{5} d^{2} f^{3} x^{2} + 18 i \, a b^{5} d^{2} e f^{2} x + 9 i \, a b^{5} d^{2} e^{2} f - 6 i \, {\left(a^{3} b^{3} - a b^{5}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(-18 i \, a^{2} b^{4} d^{2} f^{3} x^{2} - 36 i \, a^{2} b^{4} d^{2} e f^{2} x - 18 i \, a^{2} b^{4} d^{2} e^{2} f + 12 i \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x - 12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2} + {\left(12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x + 12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{3} x - 24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(-9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{3} x^{2} - 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f^{2} x - 9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{5} b - a b^{5}\right)} f^{3} + {\left(9 i \, a b^{5} d^{2} f^{3} x^{2} + 18 i \, a b^{5} d^{2} e f^{2} x + 9 i \, a b^{5} d^{2} e^{2} f - 6 i \, {\left(a^{3} b^{3} - a b^{5}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(-18 i \, a^{2} b^{4} d^{2} f^{3} x^{2} - 36 i \, a^{2} b^{4} d^{2} e f^{2} x - 18 i \, a^{2} b^{4} d^{2} e^{2} f + 12 i \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x - 12 i \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2} + {\left(12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d f^{3} x + 12 i \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d f^{3} x - 24 i \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d e f^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} f^{3} x^{2} + 18 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e f^{2} x + 9 i \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{5} b - a b^{5}\right)} f^{3} + {\left(-9 i \, a b^{5} d^{2} f^{3} x^{2} - 18 i \, a b^{5} d^{2} e f^{2} x - 9 i \, a b^{5} d^{2} e^{2} f + 6 i \, {\left(a^{3} b^{3} - a b^{5}\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(18 i \, a^{2} b^{4} d^{2} f^{3} x^{2} + 36 i \, a^{2} b^{4} d^{2} e f^{2} x + 18 i \, a^{2} b^{4} d^{2} e^{2} f - 12 i \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e^{2} f - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} d e f^{2} - {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} e^{3} - 3 \, a b^{5} c d^{2} e^{2} f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} d e f^{2} - {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{3} e^{3} - 3 \, a^{2} b^{4} c d^{2} e^{2} f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} d e f^{2} - {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e^{2} f - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} d e f^{2} - {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} e^{3} - 3 \, a b^{5} c d^{2} e^{2} f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} d e f^{2} - {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{3} e^{3} - 3 \, a^{2} b^{4} c d^{2} e^{2} f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} d e f^{2} - {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e^{2} f - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} d e f^{2} - {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} e^{3} - 3 \, a b^{5} c d^{2} e^{2} f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} d e f^{2} - {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{3} e^{3} - 3 \, a^{2} b^{4} c d^{2} e^{2} f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} d e f^{2} - {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e^{2} f - 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e^{2} f - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} + {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - {\left(2 \, a^{5} b - 2 \, a b^{5} - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2}\right)} d e f^{2} - {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} e^{3} - 3 \, a b^{5} c d^{2} e^{2} f + {\left(3 \, a b^{5} c^{2} - 2 \, a^{3} b^{3} + 2 \, a b^{5}\right)} d e f^{2} - {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d^{3} e^{3} - 3 \, a^{2} b^{4} c d^{2} e^{2} f + {\left(3 \, a^{2} b^{4} c^{2} - 2 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} d e f^{2} - {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} d e f^{2} + {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} f^{3} x^{3} + 3 \, a b^{5} d^{3} e f^{2} x^{2} + 3 \, a b^{5} c d^{2} e^{2} f - 3 \, a b^{5} c^{2} d e f^{2} + {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3} + {\left(3 \, a b^{5} d^{3} e^{2} f - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{2} f - 2 \, {\left(a^{5} b - a b^{5}\right)} d f^{3}\right)} x + 2 \, {\left(a^{2} b^{4} d^{3} f^{3} x^{3} + 3 \, a^{2} b^{4} d^{3} e f^{2} x^{2} + 3 \, a^{2} b^{4} c d^{2} e^{2} f - 3 \, a^{2} b^{4} c^{2} d e f^{2} + {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3} + {\left(3 \, a^{2} b^{4} d^{3} e^{2} f - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} d e f^{2} + {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} f^{3} x^{3} + 3 \, a b^{5} d^{3} e f^{2} x^{2} + 3 \, a b^{5} c d^{2} e^{2} f - 3 \, a b^{5} c^{2} d e f^{2} + {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3} + {\left(3 \, a b^{5} d^{3} e^{2} f - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{2} f - 2 \, {\left(a^{5} b - a b^{5}\right)} d f^{3}\right)} x + 2 \, {\left(a^{2} b^{4} d^{3} f^{3} x^{3} + 3 \, a^{2} b^{4} d^{3} e f^{2} x^{2} + 3 \, a^{2} b^{4} c d^{2} e^{2} f - 3 \, a^{2} b^{4} c^{2} d e f^{2} + {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3} + {\left(3 \, a^{2} b^{4} d^{3} e^{2} f - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} d e f^{2} + {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} f^{3} x^{3} + 3 \, a b^{5} d^{3} e f^{2} x^{2} + 3 \, a b^{5} c d^{2} e^{2} f - 3 \, a b^{5} c^{2} d e f^{2} + {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3} + {\left(3 \, a b^{5} d^{3} e^{2} f - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{2} f - 2 \, {\left(a^{5} b - a b^{5}\right)} d f^{3}\right)} x + 2 \, {\left(a^{2} b^{4} d^{3} f^{3} x^{3} + 3 \, a^{2} b^{4} d^{3} e f^{2} x^{2} + 3 \, a^{2} b^{4} c d^{2} e^{2} f - 3 \, a^{2} b^{4} c^{2} d e f^{2} + {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3} + {\left(3 \, a^{2} b^{4} d^{3} e^{2} f - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3} - {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c d e f^{2} - {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c d e f^{2} - {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} c^{2} f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b^{3} + a b^{5}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b^{3} + a b^{5}\right)} c^{2} d e f^{2} + {\left({\left(a^{3} b^{3} + a b^{5}\right)} c^{3} - 2 \, {\left(a^{5} b - a b^{5}\right)} c\right)} f^{3} - {\left(a b^{5} d^{3} f^{3} x^{3} + 3 \, a b^{5} d^{3} e f^{2} x^{2} + 3 \, a b^{5} c d^{2} e^{2} f - 3 \, a b^{5} c^{2} d e f^{2} + {\left(a b^{5} c^{3} - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} c\right)} f^{3} + {\left(3 \, a b^{5} d^{3} e^{2} f - 2 \, {\left(a^{3} b^{3} - a b^{5}\right)} d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, {\left(a^{3} b^{3} + a b^{5}\right)} d^{3} e^{2} f - 2 \, {\left(a^{5} b - a b^{5}\right)} d f^{3}\right)} x + 2 \, {\left(a^{2} b^{4} d^{3} f^{3} x^{3} + 3 \, a^{2} b^{4} d^{3} e f^{2} x^{2} + 3 \, a^{2} b^{4} c d^{2} e^{2} f - 3 \, a^{2} b^{4} c^{2} d e f^{2} + {\left(a^{2} b^{4} c^{3} - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} c\right)} f^{3} + {\left(3 \, a^{2} b^{4} d^{3} e^{2} f - 2 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{3} \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f^{3} x + {\left(a^{3} b^{3} + a b^{5}\right)} d e f^{2} - {\left(a b^{5} d f^{3} x + a b^{5} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f^{3} x + a^{2} b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{3} \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f^{3} x + {\left(a^{3} b^{3} + a b^{5}\right)} d e f^{2} - {\left(a b^{5} d f^{3} x + a b^{5} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f^{3} x + a^{2} b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{3} \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} + 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f^{3} x + {\left(a^{3} b^{3} + a b^{5}\right)} d e f^{2} - {\left(a b^{5} d f^{3} x + a b^{5} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f^{3} x + a^{2} b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + a^{3} b^{3} - 2 \, a b^{5}\right)} f^{3} \sin\left(d x + c\right) - {\left(a^{6} + 2 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f^{3} - 3 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f^{3} x + {\left(a^{3} b^{3} + a b^{5}\right)} d e f^{2} - {\left(a b^{5} d f^{3} x + a b^{5} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{4} d f^{3} x + a^{2} b^{4} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} e f^{2} x + 3 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d^{2} e^{2} f + {\left({\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{3} e^{2} f x + {\left(a^{4} b^{2} + a^{2} b^{4} - 2 \, b^{6}\right)} d^{3} e^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d^{4} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d^{4} \sin\left(d x + c\right) - {\left(a^{8} b - 2 \, a^{6} b^{3} + 2 \, a^{2} b^{7} - b^{9}\right)} d^{4}\right)}}"," ",0,"1/8*(12*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^2*f^3*x^2 + 24*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^2*e*f^2*x + 12*(a^6 - 2*a^4*b^2 + a^2*b^4)*d^2*e^2*f + 2*(18*I*a*b^5*f^3*cos(d*x + c)^2 - 36*I*a^2*b^4*f^3*sin(d*x + c) - 18*I*(a^3*b^3 + a*b^5)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-18*I*a*b^5*f^3*cos(d*x + c)^2 + 36*I*a^2*b^4*f^3*sin(d*x + c) + 18*I*(a^3*b^3 + a*b^5)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-18*I*a*b^5*f^3*cos(d*x + c)^2 + 36*I*a^2*b^4*f^3*sin(d*x + c) + 18*I*(a^3*b^3 + a*b^5)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(18*I*a*b^5*f^3*cos(d*x + c)^2 - 36*I*a^2*b^4*f^3*sin(d*x + c) - 18*I*(a^3*b^3 + a*b^5)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*((2*a^5*b - a^3*b^3 - a*b^5)*d^3*f^3*x^3 + 3*(2*a^5*b - a^3*b^3 - a*b^5)*d^3*e*f^2*x^2 + 3*(2*a^5*b - a^3*b^3 - a*b^5)*d^3*e^2*f*x + (2*a^5*b - a^3*b^3 - a*b^5)*d^3*e^3)*cos(d*x + c) + (12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^3*x + 12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f^2 + (-12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^3*x - 12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f^2)*cos(d*x + c)^2 + (24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*f^3*x + 24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f^2)*sin(d*x + c) + 2*(9*I*(a^3*b^3 + a*b^5)*d^2*f^3*x^2 + 18*I*(a^3*b^3 + a*b^5)*d^2*e*f^2*x + 9*I*(a^3*b^3 + a*b^5)*d^2*e^2*f - 6*I*(a^5*b - a*b^5)*f^3 + (-9*I*a*b^5*d^2*f^3*x^2 - 18*I*a*b^5*d^2*e*f^2*x - 9*I*a*b^5*d^2*e^2*f + 6*I*(a^3*b^3 - a*b^5)*f^3)*cos(d*x + c)^2 + (18*I*a^2*b^4*d^2*f^3*x^2 + 36*I*a^2*b^4*d^2*e*f^2*x + 18*I*a^2*b^4*d^2*e^2*f - 12*I*(a^4*b^2 - a^2*b^4)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^3*x + 12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f^2 + (-12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^3*x - 12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f^2)*cos(d*x + c)^2 + (24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*f^3*x + 24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f^2)*sin(d*x + c) + 2*(-9*I*(a^3*b^3 + a*b^5)*d^2*f^3*x^2 - 18*I*(a^3*b^3 + a*b^5)*d^2*e*f^2*x - 9*I*(a^3*b^3 + a*b^5)*d^2*e^2*f + 6*I*(a^5*b - a*b^5)*f^3 + (9*I*a*b^5*d^2*f^3*x^2 + 18*I*a*b^5*d^2*e*f^2*x + 9*I*a*b^5*d^2*e^2*f - 6*I*(a^3*b^3 - a*b^5)*f^3)*cos(d*x + c)^2 + (-18*I*a^2*b^4*d^2*f^3*x^2 - 36*I*a^2*b^4*d^2*e*f^2*x - 18*I*a^2*b^4*d^2*e^2*f + 12*I*(a^4*b^2 - a^2*b^4)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^3*x - 12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f^2 + (12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^3*x + 12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f^2)*cos(d*x + c)^2 + (-24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*f^3*x - 24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f^2)*sin(d*x + c) + 2*(-9*I*(a^3*b^3 + a*b^5)*d^2*f^3*x^2 - 18*I*(a^3*b^3 + a*b^5)*d^2*e*f^2*x - 9*I*(a^3*b^3 + a*b^5)*d^2*e^2*f + 6*I*(a^5*b - a*b^5)*f^3 + (9*I*a*b^5*d^2*f^3*x^2 + 18*I*a*b^5*d^2*e*f^2*x + 9*I*a*b^5*d^2*e^2*f - 6*I*(a^3*b^3 - a*b^5)*f^3)*cos(d*x + c)^2 + (-18*I*a^2*b^4*d^2*f^3*x^2 - 36*I*a^2*b^4*d^2*e*f^2*x - 18*I*a^2*b^4*d^2*e^2*f + 12*I*(a^4*b^2 - a^2*b^4)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f^3*x - 12*I*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e*f^2 + (12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*f^3*x + 12*I*(a^4*b^2 + a^2*b^4 - 2*b^6)*d*e*f^2)*cos(d*x + c)^2 + (-24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*f^3*x - 24*I*(a^5*b + a^3*b^3 - 2*a*b^5)*d*e*f^2)*sin(d*x + c) + 2*(9*I*(a^3*b^3 + a*b^5)*d^2*f^3*x^2 + 18*I*(a^3*b^3 + a*b^5)*d^2*e*f^2*x + 9*I*(a^3*b^3 + a*b^5)*d^2*e^2*f - 6*I*(a^5*b - a*b^5)*f^3 + (-9*I*a*b^5*d^2*f^3*x^2 - 18*I*a*b^5*d^2*e*f^2*x - 9*I*a*b^5*d^2*e^2*f + 6*I*(a^3*b^3 - a*b^5)*f^3)*cos(d*x + c)^2 + (18*I*a^2*b^4*d^2*f^3*x^2 + 36*I*a^2*b^4*d^2*e*f^2*x + 18*I*a^2*b^4*d^2*e^2*f - 12*I*(a^4*b^2 - a^2*b^4)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e^2*f - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 + (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) - ((a^3*b^3 + a*b^5)*d^3*e^3 - 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*d*e*f^2 - ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*e^3 - 3*a*b^5*c*d^2*e^2*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*d*e*f^2 - (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3)*cos(d*x + c)^2 + 2*(a^2*b^4*d^3*e^3 - 3*a^2*b^4*c*d^2*e^2*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*d*e*f^2 - (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e^2*f - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 + (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) - ((a^3*b^3 + a*b^5)*d^3*e^3 - 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*d*e*f^2 - ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*e^3 - 3*a*b^5*c*d^2*e^2*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*d*e*f^2 - (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3)*cos(d*x + c)^2 + 2*(a^2*b^4*d^3*e^3 - 3*a^2*b^4*c*d^2*e^2*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*d*e*f^2 - (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e^2*f - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 + (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) + ((a^3*b^3 + a*b^5)*d^3*e^3 - 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*d*e*f^2 - ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*e^3 - 3*a*b^5*c*d^2*e^2*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*d*e*f^2 - (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3)*cos(d*x + c)^2 + 2*(a^2*b^4*d^3*e^3 - 3*a^2*b^4*c*d^2*e^2*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*d*e*f^2 - (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e^2*f - 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 + (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e^2*f - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 + (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) + ((a^3*b^3 + a*b^5)*d^3*e^3 - 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - (2*a^5*b - 2*a*b^5 - 3*(a^3*b^3 + a*b^5)*c^2)*d*e*f^2 - ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*e^3 - 3*a*b^5*c*d^2*e^2*f + (3*a*b^5*c^2 - 2*a^3*b^3 + 2*a*b^5)*d*e*f^2 - (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3)*cos(d*x + c)^2 + 2*(a^2*b^4*d^3*e^3 - 3*a^2*b^4*c*d^2*e^2*f + (3*a^2*b^4*c^2 - 2*a^4*b^2 + 2*a^2*b^4)*d*e*f^2 - (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*f^3*x^2 + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e*f^2*x + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 - (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) + ((a^3*b^3 + a*b^5)*d^3*f^3*x^3 + 3*(a^3*b^3 + a*b^5)*d^3*e*f^2*x^2 + 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - 3*(a^3*b^3 + a*b^5)*c^2*d*e*f^2 + ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*f^3*x^3 + 3*a*b^5*d^3*e*f^2*x^2 + 3*a*b^5*c*d^2*e^2*f - 3*a*b^5*c^2*d*e*f^2 + (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3 + (3*a*b^5*d^3*e^2*f - 2*(a^3*b^3 - a*b^5)*d*f^3)*x)*cos(d*x + c)^2 + (3*(a^3*b^3 + a*b^5)*d^3*e^2*f - 2*(a^5*b - a*b^5)*d*f^3)*x + 2*(a^2*b^4*d^3*f^3*x^3 + 3*a^2*b^4*d^3*e*f^2*x^2 + 3*a^2*b^4*c*d^2*e^2*f - 3*a^2*b^4*c^2*d*e*f^2 + (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3 + (3*a^2*b^4*d^3*e^2*f - 2*(a^4*b^2 - a^2*b^4)*d*f^3)*x)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*f^3*x^2 + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e*f^2*x + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 - (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) - ((a^3*b^3 + a*b^5)*d^3*f^3*x^3 + 3*(a^3*b^3 + a*b^5)*d^3*e*f^2*x^2 + 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - 3*(a^3*b^3 + a*b^5)*c^2*d*e*f^2 + ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*f^3*x^3 + 3*a*b^5*d^3*e*f^2*x^2 + 3*a*b^5*c*d^2*e^2*f - 3*a*b^5*c^2*d*e*f^2 + (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3 + (3*a*b^5*d^3*e^2*f - 2*(a^3*b^3 - a*b^5)*d*f^3)*x)*cos(d*x + c)^2 + (3*(a^3*b^3 + a*b^5)*d^3*e^2*f - 2*(a^5*b - a*b^5)*d*f^3)*x + 2*(a^2*b^4*d^3*f^3*x^3 + 3*a^2*b^4*d^3*e*f^2*x^2 + 3*a^2*b^4*c*d^2*e^2*f - 3*a^2*b^4*c^2*d*e*f^2 + (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3 + (3*a^2*b^4*d^3*e^2*f - 2*(a^4*b^2 - a^2*b^4)*d*f^3)*x)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*f^3*x^2 + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e*f^2*x + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 - (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) + ((a^3*b^3 + a*b^5)*d^3*f^3*x^3 + 3*(a^3*b^3 + a*b^5)*d^3*e*f^2*x^2 + 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - 3*(a^3*b^3 + a*b^5)*c^2*d*e*f^2 + ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*f^3*x^3 + 3*a*b^5*d^3*e*f^2*x^2 + 3*a*b^5*c*d^2*e^2*f - 3*a*b^5*c^2*d*e*f^2 + (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3 + (3*a*b^5*d^3*e^2*f - 2*(a^3*b^3 - a*b^5)*d*f^3)*x)*cos(d*x + c)^2 + (3*(a^3*b^3 + a*b^5)*d^3*e^2*f - 2*(a^5*b - a*b^5)*d*f^3)*x + 2*(a^2*b^4*d^3*f^3*x^3 + 3*a^2*b^4*d^3*e*f^2*x^2 + 3*a^2*b^4*c*d^2*e^2*f - 3*a^2*b^4*c^2*d*e*f^2 + (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3 + (3*a^2*b^4*d^3*e^2*f - 2*(a^4*b^2 - a^2*b^4)*d*f^3)*x)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*((a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*c^2*f^3 - ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*f^3*x^2 + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^2*e*f^2*x + 2*(a^4*b^2 + a^2*b^4 - 2*b^6)*c*d*e*f^2 - (a^4*b^2 + a^2*b^4 - 2*b^6)*c^2*f^3)*cos(d*x + c)^2 + 2*((a^5*b + a^3*b^3 - 2*a*b^5)*d^2*f^3*x^2 + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*d^2*e*f^2*x + 2*(a^5*b + a^3*b^3 - 2*a*b^5)*c*d*e*f^2 - (a^5*b + a^3*b^3 - 2*a*b^5)*c^2*f^3)*sin(d*x + c) - ((a^3*b^3 + a*b^5)*d^3*f^3*x^3 + 3*(a^3*b^3 + a*b^5)*d^3*e*f^2*x^2 + 3*(a^3*b^3 + a*b^5)*c*d^2*e^2*f - 3*(a^3*b^3 + a*b^5)*c^2*d*e*f^2 + ((a^3*b^3 + a*b^5)*c^3 - 2*(a^5*b - a*b^5)*c)*f^3 - (a*b^5*d^3*f^3*x^3 + 3*a*b^5*d^3*e*f^2*x^2 + 3*a*b^5*c*d^2*e^2*f - 3*a*b^5*c^2*d*e*f^2 + (a*b^5*c^3 - 2*(a^3*b^3 - a*b^5)*c)*f^3 + (3*a*b^5*d^3*e^2*f - 2*(a^3*b^3 - a*b^5)*d*f^3)*x)*cos(d*x + c)^2 + (3*(a^3*b^3 + a*b^5)*d^3*e^2*f - 2*(a^5*b - a*b^5)*d*f^3)*x + 2*(a^2*b^4*d^3*f^3*x^3 + 3*a^2*b^4*d^3*e*f^2*x^2 + 3*a^2*b^4*c*d^2*e^2*f - 3*a^2*b^4*c^2*d*e*f^2 + (a^2*b^4*c^3 - 2*(a^4*b^2 - a^2*b^4)*c)*f^3 + (3*a^2*b^4*d^3*e^2*f - 2*(a^4*b^2 - a^2*b^4)*d*f^3)*x)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 12*((a^4*b^2 + a^2*b^4 - 2*b^6)*f^3*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f^3*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^3 + 3*((a^3*b^3 + a*b^5)*d*f^3*x + (a^3*b^3 + a*b^5)*d*e*f^2 - (a*b^5*d*f^3*x + a*b^5*d*e*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f^3*x + a^2*b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*((a^4*b^2 + a^2*b^4 - 2*b^6)*f^3*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f^3*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^3 - 3*((a^3*b^3 + a*b^5)*d*f^3*x + (a^3*b^3 + a*b^5)*d*e*f^2 - (a*b^5*d*f^3*x + a*b^5*d*e*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f^3*x + a^2*b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*((a^4*b^2 + a^2*b^4 - 2*b^6)*f^3*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f^3*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^3 + 3*((a^3*b^3 + a*b^5)*d*f^3*x + (a^3*b^3 + a*b^5)*d*e*f^2 - (a*b^5*d*f^3*x + a*b^5*d*e*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f^3*x + a^2*b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*((a^4*b^2 + a^2*b^4 - 2*b^6)*f^3*cos(d*x + c)^2 - 2*(a^5*b + a^3*b^3 - 2*a*b^5)*f^3*sin(d*x + c) - (a^6 + 2*a^4*b^2 - a^2*b^4 - 2*b^6)*f^3 - 3*((a^3*b^3 + a*b^5)*d*f^3*x + (a^3*b^3 + a*b^5)*d*e*f^2 - (a*b^5*d*f^3*x + a*b^5*d*e*f^2)*cos(d*x + c)^2 + 2*(a^2*b^4*d*f^3*x + a^2*b^4*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(3*(a^5*b - 2*a^3*b^3 + a*b^5)*d^2*f^3*x^2 + 6*(a^5*b - 2*a^3*b^3 + a*b^5)*d^2*e*f^2*x + 3*(a^5*b - 2*a^3*b^3 + a*b^5)*d^2*e^2*f + ((a^4*b^2 + a^2*b^4 - 2*b^6)*d^3*f^3*x^3 + 3*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^3*e*f^2*x^2 + 3*(a^4*b^2 + a^2*b^4 - 2*b^6)*d^3*e^2*f*x + (a^4*b^2 + a^2*b^4 - 2*b^6)*d^3*e^3)*cos(d*x + c))*sin(d*x + c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d^4*cos(d*x + c)^2 - 2*(a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d^4*sin(d*x + c) - (a^8*b - 2*a^6*b^3 + 2*a^2*b^7 - b^9)*d^4)","C",0
251,1,490,0,1.448970," ","integrate((f*x+e)^3*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 i \, f^{3} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 6 i \, f^{3} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right)}{a d^{4}}"," ",0,"(6*I*f^3*polylog(4, I*cos(d*x + c) - sin(d*x + c)) - 6*I*f^3*polylog(4, -I*cos(d*x + c) - sin(d*x + c)) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(-cos(d*x + c) + I*sin(d*x + c) + I) + 6*(d*f^3*x + d*e*f^2)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)))/(a*d^4)","C",0
252,1,302,0,1.503714," ","integrate((f*x+e)^2*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, f^{2} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 2 \, f^{2} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right)}{a d^{3}}"," ",0,"(2*f^2*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 2*f^2*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + (-2*I*d*f^2*x - 2*I*d*e*f)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (2*I*d*f^2*x + 2*I*d*e*f)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(-cos(d*x + c) + I*sin(d*x + c) + I))/(a*d^3)","C",0
253,1,156,0,1.007406," ","integrate((f*x+e)*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{-i \, f {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + i \, f {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(d e - c f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d f x + c f\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d f x + c f\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d e - c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right)}{a d^{2}}"," ",0,"(-I*f*dilog(I*cos(d*x + c) - sin(d*x + c)) + I*f*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (d*e - c*f)*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d*f*x + c*f)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + (d*f*x + c*f)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d*e - c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + I))/(a*d^2)","B",0
254,1,16,0,1.327859," ","integrate(cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a d}"," ",0,"log(sin(d*x + c) + 1)/(a*d)","A",0
255,0,0,0,1.165307," ","integrate(cos(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(cos(d*x + c)/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
256,0,0,0,1.381342," ","integrate(cos(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(cos(d*x + c)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
257,1,157,0,1.497241," ","integrate((f*x+e)^3*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d^{4} f^{3} x^{4} + 4 \, d^{4} e f^{2} x^{3} + 6 \, d^{4} e^{2} f x^{2} + 4 \, d^{4} e^{3} x + 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + d^{3} e^{3} - 6 \, d e f^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f - 2 \, f^{3}\right)} \sin\left(d x + c\right)}{4 \, a d^{4}}"," ",0,"1/4*(d^4*f^3*x^4 + 4*d^4*e*f^2*x^3 + 6*d^4*e^2*f*x^2 + 4*d^4*e^3*x + 4*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + d^3*e^3 - 6*d*e*f^2 + 3*(d^3*e^2*f - 2*d*f^3)*x)*cos(d*x + c) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f - 2*f^3)*sin(d*x + c))/(a*d^4)","A",0
258,1,96,0,1.177902," ","integrate((f*x+e)^2*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} - 2 \, f^{2}\right)} \cos\left(d x + c\right) - 6 \, {\left(d f^{2} x + d e f\right)} \sin\left(d x + c\right)}{3 \, a d^{3}}"," ",0,"1/3*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 3*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 - 2*f^2)*cos(d*x + c) - 6*(d*f^2*x + d*e*f)*sin(d*x + c))/(a*d^3)","A",0
259,1,49,0,1.200645," ","integrate((f*x+e)*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d^{2} f x^{2} + 2 \, d^{2} e x + 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right) - 2 \, f \sin\left(d x + c\right)}{2 \, a d^{2}}"," ",0,"1/2*(d^2*f*x^2 + 2*d^2*e*x + 2*(d*f*x + d*e)*cos(d*x + c) - 2*f*sin(d*x + c))/(a*d^2)","A",0
260,1,17,0,1.279848," ","integrate(cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{d x + \cos\left(d x + c\right)}{a d}"," ",0,"(d*x + cos(d*x + c))/(a*d)","A",0
261,1,89,0,1.287195," ","integrate(cos(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(\operatorname{Ci}\left(\frac{d f x + d e}{f}\right) + \operatorname{Ci}\left(-\frac{d f x + d e}{f}\right)\right)} \sin\left(-\frac{d e - c f}{f}\right) + 2 \, \cos\left(-\frac{d e - c f}{f}\right) \operatorname{Si}\left(\frac{d f x + d e}{f}\right) - 2 \, \log\left(f x + e\right)}{2 \, a f}"," ",0,"-1/2*((cos_integral((d*f*x + d*e)/f) + cos_integral(-(d*f*x + d*e)/f))*sin(-(d*e - c*f)/f) + 2*cos(-(d*e - c*f)/f)*sin_integral((d*f*x + d*e)/f) - 2*log(f*x + e))/(a*f)","A",0
262,1,129,0,1.263049," ","integrate(cos(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(d f x + d e\right)} \sin\left(-\frac{d e - c f}{f}\right) \operatorname{Si}\left(\frac{d f x + d e}{f}\right) - {\left({\left(d f x + d e\right)} \operatorname{Ci}\left(\frac{d f x + d e}{f}\right) + {\left(d f x + d e\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{f}\right)\right)} \cos\left(-\frac{d e - c f}{f}\right) + 2 \, f \sin\left(d x + c\right) - 2 \, f}{2 \, {\left(a f^{3} x + a e f^{2}\right)}}"," ",0,"1/2*(2*(d*f*x + d*e)*sin(-(d*e - c*f)/f)*sin_integral((d*f*x + d*e)/f) - ((d*f*x + d*e)*cos_integral((d*f*x + d*e)/f) + (d*f*x + d*e)*cos_integral(-(d*f*x + d*e)/f))*cos(-(d*e - c*f)/f) + 2*f*sin(d*x + c) - 2*f)/(a*f^3*x + a*e*f^2)","A",0
263,1,270,0,1.468176," ","integrate((f*x+e)^3*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} - 2 \, {\left(2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 2 \, d^{3} e^{3} - 3 \, d e f^{2} + 3 \, {\left(2 \, d^{3} e^{2} f - d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, d^{3} e^{2} f - d f^{3}\right)} x - 24 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f - 2 \, f^{3}\right)} \cos\left(d x + c\right) - {\left(8 \, d^{3} f^{3} x^{3} + 24 \, d^{3} e f^{2} x^{2} + 8 \, d^{3} e^{3} - 48 \, d e f^{2} + 24 \, {\left(d^{3} e^{2} f - 2 \, d f^{3}\right)} x - 3 \, {\left(2 \, d^{2} f^{3} x^{2} + 4 \, d^{2} e f^{2} x + 2 \, d^{2} e^{2} f - f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, a d^{4}}"," ",0,"-1/8*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 - 2*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 2*d^3*e^3 - 3*d*e*f^2 + 3*(2*d^3*e^2*f - d*f^3)*x)*cos(d*x + c)^2 + 3*(2*d^3*e^2*f - d*f^3)*x - 24*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f - 2*f^3)*cos(d*x + c) - (8*d^3*f^3*x^3 + 24*d^3*e*f^2*x^2 + 8*d^3*e^3 - 48*d*e*f^2 + 24*(d^3*e^2*f - 2*d*f^3)*x - 3*(2*d^2*f^3*x^2 + 4*d^2*e*f^2*x + 2*d^2*e^2*f - f^3)*cos(d*x + c))*sin(d*x + c))/(a*d^4)","A",0
264,1,149,0,1.390335," ","integrate((f*x+e)^2*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{2} f^{2} x^{2} + 2 \, d^{2} e f x - {\left(2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} - f^{2}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) - 2 \, {\left(2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} - 4 \, f^{2} - {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, a d^{3}}"," ",0,"-1/4*(d^2*f^2*x^2 + 2*d^2*e*f*x - (2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 - f^2)*cos(d*x + c)^2 - 8*(d*f^2*x + d*e*f)*cos(d*x + c) - 2*(2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 - 4*f^2 - (d*f^2*x + d*e*f)*cos(d*x + c))*sin(d*x + c))/(a*d^3)","A",0
265,1,67,0,1.238187," ","integrate((f*x+e)*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d f x - 2 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} - 4 \, f \cos\left(d x + c\right) - {\left(4 \, d f x + 4 \, d e - f \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, a d^{2}}"," ",0,"-1/4*(d*f*x - 2*(d*f*x + d*e)*cos(d*x + c)^2 - 4*f*cos(d*x + c) - (4*d*f*x + 4*d*e - f*cos(d*x + c))*sin(d*x + c))/(a*d^2)","A",0
266,1,25,0,1.343823," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"1/2*(cos(d*x + c)^2 + 2*sin(d*x + c))/(a*d)","A",0
267,1,157,0,1.521696," ","integrate(cos(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(\operatorname{Ci}\left(\frac{d f x + d e}{f}\right) + \operatorname{Ci}\left(-\frac{d f x + d e}{f}\right)\right)} \cos\left(-\frac{d e - c f}{f}\right) - {\left(\operatorname{Ci}\left(\frac{2 \, {\left(d f x + d e\right)}}{f}\right) + \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + d e\right)}}{f}\right)\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right) - 2 \, \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + d e\right)}}{f}\right) - 4 \, \sin\left(-\frac{d e - c f}{f}\right) \operatorname{Si}\left(\frac{d f x + d e}{f}\right)}{4 \, a f}"," ",0,"1/4*(2*(cos_integral((d*f*x + d*e)/f) + cos_integral(-(d*f*x + d*e)/f))*cos(-(d*e - c*f)/f) - (cos_integral(2*(d*f*x + d*e)/f) + cos_integral(-2*(d*f*x + d*e)/f))*sin(-2*(d*e - c*f)/f) - 2*cos(-2*(d*e - c*f)/f)*sin_integral(2*(d*f*x + d*e)/f) - 4*sin(-(d*e - c*f)/f)*sin_integral((d*f*x + d*e)/f))/(a*f)","A",0
268,1,242,0,1.036940," ","integrate(cos(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, f \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, {\left(d f x + d e\right)} \sin\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + d e\right)}}{f}\right) - 2 \, {\left(d f x + d e\right)} \cos\left(-\frac{d e - c f}{f}\right) \operatorname{Si}\left(\frac{d f x + d e}{f}\right) - 2 \, f \cos\left(d x + c\right) - {\left({\left(d f x + d e\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + d e\right)}}{f}\right) + {\left(d f x + d e\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + d e\right)}}{f}\right)\right)} \cos\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right) - {\left({\left(d f x + d e\right)} \operatorname{Ci}\left(\frac{d f x + d e}{f}\right) + {\left(d f x + d e\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{f}\right)\right)} \sin\left(-\frac{d e - c f}{f}\right)}{2 \, {\left(a f^{3} x + a e f^{2}\right)}}"," ",0,"1/2*(2*f*cos(d*x + c)*sin(d*x + c) + 2*(d*f*x + d*e)*sin(-2*(d*e - c*f)/f)*sin_integral(2*(d*f*x + d*e)/f) - 2*(d*f*x + d*e)*cos(-(d*e - c*f)/f)*sin_integral((d*f*x + d*e)/f) - 2*f*cos(d*x + c) - ((d*f*x + d*e)*cos_integral(2*(d*f*x + d*e)/f) + (d*f*x + d*e)*cos_integral(-2*(d*f*x + d*e)/f))*cos(-2*(d*e - c*f)/f) - ((d*f*x + d*e)*cos_integral((d*f*x + d*e)/f) + (d*f*x + d*e)*cos_integral(-(d*f*x + d*e)/f))*sin(-(d*e - c*f)/f))/(a*f^3*x + a*e*f^2)","A",0
269,1,1884,0,2.157473," ","integrate((f*x+e)^3*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 6 \, d^{3} e^{2} f x + 2 \, d^{3} e^{3} + 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} \cos\left(d x + c\right) - {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f - 12 i \, f^{3} + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f - 12 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f + 12 i \, f^{3} + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f + 12 i \, f^{3}\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 12 \, c\right)} f^{3} + 3 \, {\left(d^{3} e^{2} f + 4 \, d f^{3}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 12 \, c\right)} f^{3} + 3 \, {\left(d^{3} e^{2} f + 4 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 12 \, c\right)} f^{3} + 3 \, {\left(d^{3} e^{2} f + 4 \, d f^{3}\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 12 \, c\right)} f^{3} + 3 \, {\left(d^{3} e^{2} f + 4 \, d f^{3}\right)} x\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, {\left(c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 12 \, c\right)} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left(6 i \, f^{3} \sin\left(d x + c\right) + 6 i \, f^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(6 i \, f^{3} \sin\left(d x + c\right) + 6 i \, f^{3}\right)} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(-6 i \, f^{3} \sin\left(d x + c\right) - 6 i \, f^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(-6 i \, f^{3} \sin\left(d x + c\right) - 6 i \, f^{3}\right)} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 6 \, {\left(d f^{3} x + d e f^{2} + {\left(d f^{3} x + d e f^{2}\right)} \sin\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right)}{4 \, {\left(a d^{4} \sin\left(d x + c\right) + a d^{4}\right)}}"," ",0,"-1/4*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 6*d^3*e^2*f*x + 2*d^3*e^3 + 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*cos(d*x + c) - (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*sin(d*x + c))*dilog(I*cos(d*x + c) + sin(d*x + c)) - (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f - 12*I*f^3 + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f - 12*I*f^3)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) - (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*sin(d*x + c))*dilog(-I*cos(d*x + c) + sin(d*x + c)) - (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f + 12*I*f^3 + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f + 12*I*f^3)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - (d^3*e^3 - 3*c*d^2*e^2*f + 3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + I) - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 12*c)*f^3 + 3*(d^3*e^2*f + 4*d*f^3)*x + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 12*c)*f^3 + 3*(d^3*e^2*f + 4*d*f^3)*x)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*sin(d*x + c))*log(I*cos(d*x + c) - sin(d*x + c) + 1) - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 12*c)*f^3 + 3*(d^3*e^2*f + 4*d*f^3)*x + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 12*c)*f^3 + 3*(d^3*e^2*f + 4*d*f^3)*x)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*sin(d*x + c))*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - (d^3*e^3 - 3*c*d^2*e^2*f + 3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*(c^2 + 4)*d*e*f^2 - (c^3 + 12*c)*f^3)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + I) - (6*I*f^3*sin(d*x + c) + 6*I*f^3)*polylog(4, I*cos(d*x + c) + sin(d*x + c)) - (6*I*f^3*sin(d*x + c) + 6*I*f^3)*polylog(4, I*cos(d*x + c) - sin(d*x + c)) - (-6*I*f^3*sin(d*x + c) - 6*I*f^3)*polylog(4, -I*cos(d*x + c) + sin(d*x + c)) - (-6*I*f^3*sin(d*x + c) - 6*I*f^3)*polylog(4, -I*cos(d*x + c) - sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, I*cos(d*x + c) + sin(d*x + c)) - 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) - 6*(d*f^3*x + d*e*f^2 + (d*f^3*x + d*e*f^2)*sin(d*x + c))*polylog(3, -I*cos(d*x + c) - sin(d*x + c)))/(a*d^4*sin(d*x + c) + a*d^4)","C",0
270,1,1064,0,1.327152," ","integrate((f*x+e)^2*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} + 4 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) - {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} \sin\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 4\right)} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 4\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left(d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 4\right)} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} + 4\right)} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 2 \, {\left(f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 2 \, {\left(f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 2 \, {\left(f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 2 \, {\left(f^{2} \sin\left(d x + c\right) + f^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right)}{4 \, {\left(a d^{3} \sin\left(d x + c\right) + a d^{3}\right)}}"," ",0,"-1/4*(2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 + 4*(d*f^2*x + d*e*f)*cos(d*x + c) - (-2*I*d*f^2*x - 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f)*sin(d*x + c))*dilog(I*cos(d*x + c) + sin(d*x + c)) - (-2*I*d*f^2*x - 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f)*sin(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) - (2*I*d*f^2*x + 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f)*sin(d*x + c))*dilog(-I*cos(d*x + c) + sin(d*x + c)) - (2*I*d*f^2*x + 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f)*sin(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) - (d^2*e^2 - 2*c*d*e*f + (c^2 + 4)*f^2 + (d^2*e^2 - 2*c*d*e*f + (c^2 + 4)*f^2)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2 + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + I) - (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*sin(d*x + c))*log(I*cos(d*x + c) - sin(d*x + c) + 1) - (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*sin(d*x + c))*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - (d^2*e^2 - 2*c*d*e*f + (c^2 + 4)*f^2 + (d^2*e^2 - 2*c*d*e*f + (c^2 + 4)*f^2)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2 + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + I) + 2*(f^2*sin(d*x + c) + f^2)*polylog(3, I*cos(d*x + c) + sin(d*x + c)) - 2*(f^2*sin(d*x + c) + f^2)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 2*(f^2*sin(d*x + c) + f^2)*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) - 2*(f^2*sin(d*x + c) + f^2)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)))/(a*d^3*sin(d*x + c) + a*d^3)","C",0
271,1,508,0,1.498303," ","integrate((f*x+e)*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d f x + 2 \, d e + 2 \, f \cos\left(d x + c\right) - {\left(-i \, f \sin\left(d x + c\right) - i \, f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(-i \, f \sin\left(d x + c\right) - i \, f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(i \, f \sin\left(d x + c\right) + i \, f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(i \, f \sin\left(d x + c\right) + i \, f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(d e - c f + {\left(d e - c f\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d e - c f + {\left(d e - c f\right)} \sin\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left(d f x + c f + {\left(d f x + c f\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d f x + c f + {\left(d f x + c f\right)} \sin\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left(d f x + c f + {\left(d f x + c f\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left(d f x + c f + {\left(d f x + c f\right)} \sin\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left(d e - c f + {\left(d e - c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left(d e - c f + {\left(d e - c f\right)} \sin\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right)}{4 \, {\left(a d^{2} \sin\left(d x + c\right) + a d^{2}\right)}}"," ",0,"-1/4*(2*d*f*x + 2*d*e + 2*f*cos(d*x + c) - (-I*f*sin(d*x + c) - I*f)*dilog(I*cos(d*x + c) + sin(d*x + c)) - (-I*f*sin(d*x + c) - I*f)*dilog(I*cos(d*x + c) - sin(d*x + c)) - (I*f*sin(d*x + c) + I*f)*dilog(-I*cos(d*x + c) + sin(d*x + c)) - (I*f*sin(d*x + c) + I*f)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - (d*e - c*f + (d*e - c*f)*sin(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + (d*e - c*f + (d*e - c*f)*sin(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + I) - (d*f*x + c*f + (d*f*x + c*f)*sin(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + (d*f*x + c*f + (d*f*x + c*f)*sin(d*x + c))*log(I*cos(d*x + c) - sin(d*x + c) + 1) - (d*f*x + c*f + (d*f*x + c*f)*sin(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + (d*f*x + c*f + (d*f*x + c*f)*sin(d*x + c))*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - (d*e - c*f + (d*e - c*f)*sin(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + (d*e - c*f + (d*e - c*f)*sin(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + I))/(a*d^2*sin(d*x + c) + a*d^2)","B",0
272,1,58,0,1.171706," ","integrate(sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(\sin\left(d x + c\right) + 1\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2}{4 \, {\left(a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/4*((sin(d*x + c) + 1)*log(sin(d*x + c) + 1) - (sin(d*x + c) + 1)*log(-sin(d*x + c) + 1) - 2)/(a*d*sin(d*x + c) + a*d)","A",0
273,0,0,0,1.169318," ","integrate(sec(d*x+c)/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sec(d*x + c)/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
274,0,0,0,1.437524," ","integrate(sec(d*x+c)/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sec(d*x + c)/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
275,1,1527,0,1.861454," ","integrate((f*x+e)^3*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d^{3} f^{3} x^{3} + 12 \, d^{3} e f^{2} x^{2} + 12 \, d^{3} e^{2} f x + 4 \, d^{3} e^{3} - 4 \, {\left(2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 2 \, d^{3} e^{3} + 3 \, d e f^{2} + 3 \, {\left(2 \, d^{3} e^{2} f + d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} \cos\left(d x + c\right) + {\left({\left(18 i \, d f^{3} x + 18 i \, d e f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(18 i \, d f^{3} x + 18 i \, d e f^{2}\right)} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left({\left(-30 i \, d f^{3} x - 30 i \, d e f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(-30 i \, d f^{3} x - 30 i \, d e f^{2}\right)} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left({\left(-18 i \, d f^{3} x - 18 i \, d e f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2}\right)} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left({\left(30 i \, d f^{3} x + 30 i \, d e f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(30 i \, d f^{3} x + 30 i \, d e f^{2}\right)} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 3 \, {\left({\left(5 \, d^{2} e^{2} f - 10 \, c d e f^{2} + {\left(5 \, c^{2} + 4\right)} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(5 \, d^{2} e^{2} f - 10 \, c d e f^{2} + {\left(5 \, c^{2} + 4\right)} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 9 \, {\left({\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 15 \, {\left({\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 9 \, {\left({\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + 15 \, {\left({\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 9 \, {\left({\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(5 \, d^{2} e^{2} f - 10 \, c d e f^{2} + {\left(5 \, c^{2} + 4\right)} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(5 \, d^{2} e^{2} f - 10 \, c d e f^{2} + {\left(5 \, c^{2} + 4\right)} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 9 \, {\left({\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 18 \, {\left(f^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + f^{3} \cos\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 30 \, {\left(f^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + f^{3} \cos\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 18 \, {\left(f^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + f^{3} \cos\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 30 \, {\left(f^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + f^{3} \cos\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 8 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(a d^{4} \cos\left(d x + c\right) \sin\left(d x + c\right) + a d^{4} \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(4*d^3*f^3*x^3 + 12*d^3*e*f^2*x^2 + 12*d^3*e^2*f*x + 4*d^3*e^3 - 4*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 2*d^3*e^3 + 3*d*e*f^2 + 3*(2*d^3*e^2*f + d*f^3)*x)*cos(d*x + c)^2 - 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*cos(d*x + c) + ((18*I*d*f^3*x + 18*I*d*e*f^2)*cos(d*x + c)*sin(d*x + c) + (18*I*d*f^3*x + 18*I*d*e*f^2)*cos(d*x + c))*dilog(I*cos(d*x + c) + sin(d*x + c)) + ((-30*I*d*f^3*x - 30*I*d*e*f^2)*cos(d*x + c)*sin(d*x + c) + (-30*I*d*f^3*x - 30*I*d*e*f^2)*cos(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + ((-18*I*d*f^3*x - 18*I*d*e*f^2)*cos(d*x + c)*sin(d*x + c) + (-18*I*d*f^3*x - 18*I*d*e*f^2)*cos(d*x + c))*dilog(-I*cos(d*x + c) + sin(d*x + c)) + ((30*I*d*f^3*x + 30*I*d*e*f^2)*cos(d*x + c)*sin(d*x + c) + (30*I*d*f^3*x + 30*I*d*e*f^2)*cos(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) + 3*((5*d^2*e^2*f - 10*c*d*e*f^2 + (5*c^2 + 4)*f^3)*cos(d*x + c)*sin(d*x + c) + (5*d^2*e^2*f - 10*c*d*e*f^2 + (5*c^2 + 4)*f^3)*cos(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + 9*((d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)*sin(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + I) + 15*((d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)*sin(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + 9*((d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)*sin(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c))*log(I*cos(d*x + c) - sin(d*x + c) + 1) + 15*((d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)*sin(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + 9*((d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c)*sin(d*x + c) + (d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*cos(d*x + c))*log(-I*cos(d*x + c) - sin(d*x + c) + 1) + 3*((5*d^2*e^2*f - 10*c*d*e*f^2 + (5*c^2 + 4)*f^3)*cos(d*x + c)*sin(d*x + c) + (5*d^2*e^2*f - 10*c*d*e*f^2 + (5*c^2 + 4)*f^3)*cos(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + 9*((d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c)*sin(d*x + c) + (d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*cos(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + I) + 18*(f^3*cos(d*x + c)*sin(d*x + c) + f^3*cos(d*x + c))*polylog(3, I*cos(d*x + c) + sin(d*x + c)) + 30*(f^3*cos(d*x + c)*sin(d*x + c) + f^3*cos(d*x + c))*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 18*(f^3*cos(d*x + c)*sin(d*x + c) + f^3*cos(d*x + c))*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) + 30*(f^3*cos(d*x + c)*sin(d*x + c) + f^3*cos(d*x + c))*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + 8*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*sin(d*x + c))/(a*d^4*cos(d*x + c)*sin(d*x + c) + a*d^4*cos(d*x + c))","C",0
276,1,855,0,1.840434," ","integrate((f*x+e)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} - 2 \, {\left(2 \, d^{2} f^{2} x^{2} + 4 \, d^{2} e f x + 2 \, d^{2} e^{2} + f^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) + {\left(3 i \, f^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 i \, f^{2} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(-5 i \, f^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 5 i \, f^{2} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-3 i \, f^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 3 i \, f^{2} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(5 i \, f^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 5 i \, f^{2} \cos\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 5 \, {\left({\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 3 \, {\left({\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 5 \, {\left({\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + 5 \, {\left({\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d f^{2} x + c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + 5 \, {\left({\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 3 \, {\left({\left(d e f - c f^{2}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(d e f - c f^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 4 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a d^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + a d^{3} \cos\left(d x + c\right)\right)}}"," ",0,"1/6*(2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 - 2*(2*d^2*f^2*x^2 + 4*d^2*e*f*x + 2*d^2*e^2 + f^2)*cos(d*x + c)^2 - 2*(d*f^2*x + d*e*f)*cos(d*x + c) + (3*I*f^2*cos(d*x + c)*sin(d*x + c) + 3*I*f^2*cos(d*x + c))*dilog(I*cos(d*x + c) + sin(d*x + c)) + (-5*I*f^2*cos(d*x + c)*sin(d*x + c) - 5*I*f^2*cos(d*x + c))*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-3*I*f^2*cos(d*x + c)*sin(d*x + c) - 3*I*f^2*cos(d*x + c))*dilog(-I*cos(d*x + c) + sin(d*x + c)) + (5*I*f^2*cos(d*x + c)*sin(d*x + c) + 5*I*f^2*cos(d*x + c))*dilog(-I*cos(d*x + c) - sin(d*x + c)) + 5*((d*e*f - c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*e*f - c*f^2)*cos(d*x + c))*log(cos(d*x + c) + I*sin(d*x + c) + I) + 3*((d*e*f - c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*e*f - c*f^2)*cos(d*x + c))*log(cos(d*x + c) - I*sin(d*x + c) + I) + 5*((d*f^2*x + c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*f^2*x + c*f^2)*cos(d*x + c))*log(I*cos(d*x + c) + sin(d*x + c) + 1) + 3*((d*f^2*x + c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*f^2*x + c*f^2)*cos(d*x + c))*log(I*cos(d*x + c) - sin(d*x + c) + 1) + 5*((d*f^2*x + c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*f^2*x + c*f^2)*cos(d*x + c))*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + 3*((d*f^2*x + c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*f^2*x + c*f^2)*cos(d*x + c))*log(-I*cos(d*x + c) - sin(d*x + c) + 1) + 5*((d*e*f - c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*e*f - c*f^2)*cos(d*x + c))*log(-cos(d*x + c) + I*sin(d*x + c) + I) + 3*((d*e*f - c*f^2)*cos(d*x + c)*sin(d*x + c) + (d*e*f - c*f^2)*cos(d*x + c))*log(-cos(d*x + c) - I*sin(d*x + c) + I) + 4*(d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*sin(d*x + c))/(a*d^3*cos(d*x + c)*sin(d*x + c) + a*d^3*cos(d*x + c))","B",0
277,1,156,0,1.329404," ","integrate((f*x+e)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d f x - 8 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} + 4 \, d e - 2 \, f \cos\left(d x + c\right) + 5 \, {\left(f \cos\left(d x + c\right) \sin\left(d x + c\right) + f \cos\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(f \cos\left(d x + c\right) \sin\left(d x + c\right) + f \cos\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, {\left(d f x + d e\right)} \sin\left(d x + c\right)}{12 \, {\left(a d^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + a d^{2} \cos\left(d x + c\right)\right)}}"," ",0,"1/12*(4*d*f*x - 8*(d*f*x + d*e)*cos(d*x + c)^2 + 4*d*e - 2*f*cos(d*x + c) + 5*(f*cos(d*x + c)*sin(d*x + c) + f*cos(d*x + c))*log(sin(d*x + c) + 1) + 3*(f*cos(d*x + c)*sin(d*x + c) + f*cos(d*x + c))*log(-sin(d*x + c) + 1) + 8*(d*f*x + d*e)*sin(d*x + c))/(a*d^2*cos(d*x + c)*sin(d*x + c) + a*d^2*cos(d*x + c))","A",0
278,1,49,0,1.255234," ","integrate(sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 1}{3 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(2*cos(d*x + c)^2 - 2*sin(d*x + c) - 1)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
279,0,0,0,1.113400," ","integrate(sec(d*x+c)^2/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sec(d*x + c)^2/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
280,0,0,0,1.303699," ","integrate(sec(d*x+c)^2/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{2}}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sec(d*x + c)^2/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
281,1,2566,0,2.501430," ","integrate((f*x+e)^3*sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 6 \, d^{3} e^{2} f x + 2 \, d^{3} e^{3} - 4 \, {\left(2 \, d^{2} f^{3} x^{2} + 4 \, d^{2} e f^{2} x + 2 \, d^{2} e^{2} f + f^{3}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{3} + 2 \, d e f^{2} + {\left(9 \, d^{3} e^{2} f + 2 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - 14 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} \cos\left(d x + c\right) + {\left({\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f - 12 i \, f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f - 12 i \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left({\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f - 28 i \, f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f - 28 i \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left({\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f + 12 i \, f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f + 12 i \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left({\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f + 28 i \, f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f + 28 i \, f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left({\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 3 \, {\left({\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + {\left({\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f + 28 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f + 28 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f + 4 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f + 4 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f + 28 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} + 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f + 28 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f + 4 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} + 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f + 4 \, d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} + 28\right)} d e f^{2} - {\left(3 \, c^{3} + 28 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 3 \, {\left({\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} + 4\right)} d e f^{2} - {\left(c^{3} + 4 \, c\right)} f^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + {\left(18 i \, f^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 18 i \, f^{3} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(18 i \, f^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 18 i \, f^{3} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-18 i \, f^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 18 i \, f^{3} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(-18 i \, f^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 18 i \, f^{3} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 18 \, {\left({\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 18 \, {\left({\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 18 \, {\left({\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 18 \, {\left({\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f^{3} x + d e f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, d^{3} e^{2} f x + 3 \, d^{3} e^{3} - 5 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(a d^{4} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d^{4} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 6*d^3*e^2*f*x + 2*d^3*e^3 - 4*(2*d^2*f^3*x^2 + 4*d^2*e*f^2*x + 2*d^2*e^2*f + f^3)*cos(d*x + c)^3 - 2*(3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 3*d^3*e^3 + 2*d*e*f^2 + (9*d^3*e^2*f + 2*d*f^3)*x)*cos(d*x + c)^2 - 14*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*cos(d*x + c) + ((-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f - 12*I*f^3)*cos(d*x + c)^2*sin(d*x + c) + (-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f - 12*I*f^3)*cos(d*x + c)^2)*dilog(I*cos(d*x + c) + sin(d*x + c)) + ((-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f - 28*I*f^3)*cos(d*x + c)^2*sin(d*x + c) + (-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f - 28*I*f^3)*cos(d*x + c)^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) + ((9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f + 12*I*f^3)*cos(d*x + c)^2*sin(d*x + c) + (9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f + 12*I*f^3)*cos(d*x + c)^2)*dilog(-I*cos(d*x + c) + sin(d*x + c)) + ((9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f + 28*I*f^3)*cos(d*x + c)^2*sin(d*x + c) + (9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f + 28*I*f^3)*cos(d*x + c)^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + ((3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(d*x + c)^2*sin(d*x + c) + (3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(d*x + c)^2)*log(cos(d*x + c) + I*sin(d*x + c) + I) - 3*((d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(d*x + c)^2*sin(d*x + c) + (d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(d*x + c)^2)*log(cos(d*x + c) - I*sin(d*x + c) + I) + ((3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 + 28*c)*f^3 + (9*d^3*e^2*f + 28*d*f^3)*x)*cos(d*x + c)^2*sin(d*x + c) + (3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 + 28*c)*f^3 + (9*d^3*e^2*f + 28*d*f^3)*x)*cos(d*x + c)^2)*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 3*((d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 4*c)*f^3 + (3*d^3*e^2*f + 4*d*f^3)*x)*cos(d*x + c)^2*sin(d*x + c) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 4*c)*f^3 + (3*d^3*e^2*f + 4*d*f^3)*x)*cos(d*x + c)^2)*log(I*cos(d*x + c) - sin(d*x + c) + 1) + ((3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 + 28*c)*f^3 + (9*d^3*e^2*f + 28*d*f^3)*x)*cos(d*x + c)^2*sin(d*x + c) + (3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 + 28*c)*f^3 + (9*d^3*e^2*f + 28*d*f^3)*x)*cos(d*x + c)^2)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 3*((d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 4*c)*f^3 + (3*d^3*e^2*f + 4*d*f^3)*x)*cos(d*x + c)^2*sin(d*x + c) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 + 4*c)*f^3 + (3*d^3*e^2*f + 4*d*f^3)*x)*cos(d*x + c)^2)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) + ((3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(d*x + c)^2*sin(d*x + c) + (3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 + 28)*d*e*f^2 - (3*c^3 + 28*c)*f^3)*cos(d*x + c)^2)*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 3*((d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(d*x + c)^2*sin(d*x + c) + (d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 + 4)*d*e*f^2 - (c^3 + 4*c)*f^3)*cos(d*x + c)^2)*log(-cos(d*x + c) - I*sin(d*x + c) + I) + (18*I*f^3*cos(d*x + c)^2*sin(d*x + c) + 18*I*f^3*cos(d*x + c)^2)*polylog(4, I*cos(d*x + c) + sin(d*x + c)) + (18*I*f^3*cos(d*x + c)^2*sin(d*x + c) + 18*I*f^3*cos(d*x + c)^2)*polylog(4, I*cos(d*x + c) - sin(d*x + c)) + (-18*I*f^3*cos(d*x + c)^2*sin(d*x + c) - 18*I*f^3*cos(d*x + c)^2)*polylog(4, -I*cos(d*x + c) + sin(d*x + c)) + (-18*I*f^3*cos(d*x + c)^2*sin(d*x + c) - 18*I*f^3*cos(d*x + c)^2)*polylog(4, -I*cos(d*x + c) - sin(d*x + c)) - 18*((d*f^3*x + d*e*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d*f^3*x + d*e*f^2)*cos(d*x + c)^2)*polylog(3, I*cos(d*x + c) + sin(d*x + c)) + 18*((d*f^3*x + d*e*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d*f^3*x + d*e*f^2)*cos(d*x + c)^2)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 18*((d*f^3*x + d*e*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d*f^3*x + d*e*f^2)*cos(d*x + c)^2)*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) + 18*((d*f^3*x + d*e*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d*f^3*x + d*e*f^2)*cos(d*x + c)^2)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + 2*(3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*d^3*e^2*f*x + 3*d^3*e^3 - 5*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*cos(d*x + c))*sin(d*x + c))/(a*d^4*cos(d*x + c)^2*sin(d*x + c) + a*d^4*cos(d*x + c)^2)","C",0
282,1,1513,0,1.939567," ","integrate((f*x+e)^2*sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, d^{2} f^{2} x^{2} + 12 \, d^{2} e f x + 6 \, d^{2} e^{2} - 16 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(9 \, d^{2} f^{2} x^{2} + 18 \, d^{2} e f x + 9 \, d^{2} e^{2} + 2 \, f^{2}\right)} \cos\left(d x + c\right)^{2} - 28 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right) + {\left({\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left({\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left({\left(18 i \, d f^{2} x + 18 i \, d e f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(18 i \, d f^{2} x + 18 i \, d e f\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left({\left(18 i \, d f^{2} x + 18 i \, d e f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(18 i \, d f^{2} x + 18 i \, d e f\right)} \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left({\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} + 28\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} + 28\right)} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 3 \, {\left({\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} + 4\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} + 4\right)} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 9 \, {\left({\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + 9 \, {\left({\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) + {\left({\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} + 28\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} + 28\right)} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 3 \, {\left({\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} + 4\right)} f^{2}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} + 4\right)} f^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 18 \, {\left(f^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + f^{2} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 18 \, {\left(f^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + f^{2} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 18 \, {\left(f^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + f^{2} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 18 \, {\left(f^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + f^{2} \cos\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 2 \, {\left(9 \, d^{2} f^{2} x^{2} + 18 \, d^{2} e f x + 9 \, d^{2} e^{2} - 10 \, {\left(d f^{2} x + d e f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a d^{3} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d^{3} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(6*d^2*f^2*x^2 + 12*d^2*e*f*x + 6*d^2*e^2 - 16*(d*f^2*x + d*e*f)*cos(d*x + c)^3 - 2*(9*d^2*f^2*x^2 + 18*d^2*e*f*x + 9*d^2*e^2 + 2*f^2)*cos(d*x + c)^2 - 28*(d*f^2*x + d*e*f)*cos(d*x + c) + ((-18*I*d*f^2*x - 18*I*d*e*f)*cos(d*x + c)^2*sin(d*x + c) + (-18*I*d*f^2*x - 18*I*d*e*f)*cos(d*x + c)^2)*dilog(I*cos(d*x + c) + sin(d*x + c)) + ((-18*I*d*f^2*x - 18*I*d*e*f)*cos(d*x + c)^2*sin(d*x + c) + (-18*I*d*f^2*x - 18*I*d*e*f)*cos(d*x + c)^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) + ((18*I*d*f^2*x + 18*I*d*e*f)*cos(d*x + c)^2*sin(d*x + c) + (18*I*d*f^2*x + 18*I*d*e*f)*cos(d*x + c)^2)*dilog(-I*cos(d*x + c) + sin(d*x + c)) + ((18*I*d*f^2*x + 18*I*d*e*f)*cos(d*x + c)^2*sin(d*x + c) + (18*I*d*f^2*x + 18*I*d*e*f)*cos(d*x + c)^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + ((9*d^2*e^2 - 18*c*d*e*f + (9*c^2 + 28)*f^2)*cos(d*x + c)^2*sin(d*x + c) + (9*d^2*e^2 - 18*c*d*e*f + (9*c^2 + 28)*f^2)*cos(d*x + c)^2)*log(cos(d*x + c) + I*sin(d*x + c) + I) - 3*((3*d^2*e^2 - 6*c*d*e*f + (3*c^2 + 4)*f^2)*cos(d*x + c)^2*sin(d*x + c) + (3*d^2*e^2 - 6*c*d*e*f + (3*c^2 + 4)*f^2)*cos(d*x + c)^2)*log(cos(d*x + c) - I*sin(d*x + c) + I) + 9*((d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2)*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 9*((d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2)*log(I*cos(d*x + c) - sin(d*x + c) + 1) + 9*((d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 9*((d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2*sin(d*x + c) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*cos(d*x + c)^2)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) + ((9*d^2*e^2 - 18*c*d*e*f + (9*c^2 + 28)*f^2)*cos(d*x + c)^2*sin(d*x + c) + (9*d^2*e^2 - 18*c*d*e*f + (9*c^2 + 28)*f^2)*cos(d*x + c)^2)*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 3*((3*d^2*e^2 - 6*c*d*e*f + (3*c^2 + 4)*f^2)*cos(d*x + c)^2*sin(d*x + c) + (3*d^2*e^2 - 6*c*d*e*f + (3*c^2 + 4)*f^2)*cos(d*x + c)^2)*log(-cos(d*x + c) - I*sin(d*x + c) + I) - 18*(f^2*cos(d*x + c)^2*sin(d*x + c) + f^2*cos(d*x + c)^2)*polylog(3, I*cos(d*x + c) + sin(d*x + c)) + 18*(f^2*cos(d*x + c)^2*sin(d*x + c) + f^2*cos(d*x + c)^2)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 18*(f^2*cos(d*x + c)^2*sin(d*x + c) + f^2*cos(d*x + c)^2)*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) + 18*(f^2*cos(d*x + c)^2*sin(d*x + c) + f^2*cos(d*x + c)^2)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + 2*(9*d^2*f^2*x^2 + 18*d^2*e*f*x + 9*d^2*e^2 - 10*(d*f^2*x + d*e*f)*cos(d*x + c))*sin(d*x + c))/(a*d^3*cos(d*x + c)^2*sin(d*x + c) + a*d^3*cos(d*x + c)^2)","C",0
283,1,792,0,1.574189," ","integrate((f*x+e)*sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, f \cos\left(d x + c\right)^{3} - 6 \, d f x + 18 \, {\left(d f x + d e\right)} \cos\left(d x + c\right)^{2} - 6 \, d e + 14 \, f \cos\left(d x + c\right) - {\left(-9 i \, f \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 9 i \, f \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(-9 i \, f \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 9 i \, f \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(9 i \, f \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 9 i \, f \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(9 i \, f \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + 9 i \, f \cos\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 9 \, {\left({\left(d e - c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d e - c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 9 \, {\left({\left(d e - c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d e - c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 9 \, {\left({\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 9 \, {\left({\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + 9 \, {\left({\left(d f x + c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d f x + c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - 9 \, {\left({\left(d e - c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d e - c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + 9 \, {\left({\left(d e - c f\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(d e - c f\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 2 \, {\left(9 \, d f x + 9 \, d e - 5 \, f \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a d^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d^{2} \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/48*(8*f*cos(d*x + c)^3 - 6*d*f*x + 18*(d*f*x + d*e)*cos(d*x + c)^2 - 6*d*e + 14*f*cos(d*x + c) - (-9*I*f*cos(d*x + c)^2*sin(d*x + c) - 9*I*f*cos(d*x + c)^2)*dilog(I*cos(d*x + c) + sin(d*x + c)) - (-9*I*f*cos(d*x + c)^2*sin(d*x + c) - 9*I*f*cos(d*x + c)^2)*dilog(I*cos(d*x + c) - sin(d*x + c)) - (9*I*f*cos(d*x + c)^2*sin(d*x + c) + 9*I*f*cos(d*x + c)^2)*dilog(-I*cos(d*x + c) + sin(d*x + c)) - (9*I*f*cos(d*x + c)^2*sin(d*x + c) + 9*I*f*cos(d*x + c)^2)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 9*((d*e - c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*e - c*f)*cos(d*x + c)^2)*log(cos(d*x + c) + I*sin(d*x + c) + I) + 9*((d*e - c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*e - c*f)*cos(d*x + c)^2)*log(cos(d*x + c) - I*sin(d*x + c) + I) - 9*((d*f*x + c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*f*x + c*f)*cos(d*x + c)^2)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + 9*((d*f*x + c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*f*x + c*f)*cos(d*x + c)^2)*log(I*cos(d*x + c) - sin(d*x + c) + 1) - 9*((d*f*x + c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*f*x + c*f)*cos(d*x + c)^2)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + 9*((d*f*x + c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*f*x + c*f)*cos(d*x + c)^2)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - 9*((d*e - c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*e - c*f)*cos(d*x + c)^2)*log(-cos(d*x + c) + I*sin(d*x + c) + I) + 9*((d*e - c*f)*cos(d*x + c)^2*sin(d*x + c) + (d*e - c*f)*cos(d*x + c)^2)*log(-cos(d*x + c) - I*sin(d*x + c) + I) - 2*(9*d*f*x + 9*d*e - 5*f*cos(d*x + c))*sin(d*x + c))/(a*d^2*cos(d*x + c)^2*sin(d*x + c) + a*d^2*cos(d*x + c)^2)","B",0
284,1,125,0,1.536623," ","integrate(sec(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(\cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 6 \, \sin\left(d x + c\right) - 2}{16 \, {\left(a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(6*cos(d*x + c)^2 - 3*(cos(d*x + c)^2*sin(d*x + c) + cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*(cos(d*x + c)^2*sin(d*x + c) + cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 6*sin(d*x + c) - 2)/(a*d*cos(d*x + c)^2*sin(d*x + c) + a*d*cos(d*x + c)^2)","A",0
285,0,0,0,1.539195," ","integrate(sec(d*x+c)^3/(f*x+e)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{3}}{a f x + a e + {\left(a f x + a e\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sec(d*x + c)^3/(a*f*x + a*e + (a*f*x + a*e)*sin(d*x + c)), x)","F",0
286,0,0,0,1.284847," ","integrate(sec(d*x+c)^3/(f*x+e)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(d x + c\right)^{3}}{a f^{2} x^{2} + 2 \, a e f x + a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sec(d*x + c)^3/(a*f^2*x^2 + 2*a*e*f*x + a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*sin(d*x + c)), x)","F",0
287,1,334,0,1.253409," ","integrate((f*x+e)^m*cos(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(f m + f\right)} e^{\left(-\frac{f m \log\left(\frac{3 i \, d}{f}\right) - 3 i \, d e + 3 i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{3 i \, d f x + 3 i \, d e}{f}\right) + {\left(3 i \, f m + 3 i \, f\right)} e^{\left(-\frac{f m \log\left(\frac{2 i \, d}{f}\right) - 2 i \, d e + 2 i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, d e}{f}\right) + 3 \, {\left(f m + f\right)} e^{\left(-\frac{f m \log\left(\frac{i \, d}{f}\right) - i \, d e + i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, d e}{f}\right) + 3 \, {\left(f m + f\right)} e^{\left(-\frac{f m \log\left(-\frac{i \, d}{f}\right) + i \, d e - i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, d e}{f}\right) + {\left(-3 i \, f m - 3 i \, f\right)} e^{\left(-\frac{f m \log\left(-\frac{2 i \, d}{f}\right) + 2 i \, d e - 2 i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{-2 i \, d f x - 2 i \, d e}{f}\right) + {\left(f m + f\right)} e^{\left(-\frac{f m \log\left(-\frac{3 i \, d}{f}\right) + 3 i \, d e - 3 i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{-3 i \, d f x - 3 i \, d e}{f}\right) + 12 \, {\left(d f x + d e\right)} {\left(f x + e\right)}^{m}}{24 \, {\left(a d f m + a d f\right)}}"," ",0,"1/24*((f*m + f)*e^(-(f*m*log(3*I*d/f) - 3*I*d*e + 3*I*c*f)/f)*gamma(m + 1, (3*I*d*f*x + 3*I*d*e)/f) + (3*I*f*m + 3*I*f)*e^(-(f*m*log(2*I*d/f) - 2*I*d*e + 2*I*c*f)/f)*gamma(m + 1, (2*I*d*f*x + 2*I*d*e)/f) + 3*(f*m + f)*e^(-(f*m*log(I*d/f) - I*d*e + I*c*f)/f)*gamma(m + 1, (I*d*f*x + I*d*e)/f) + 3*(f*m + f)*e^(-(f*m*log(-I*d/f) + I*d*e - I*c*f)/f)*gamma(m + 1, (-I*d*f*x - I*d*e)/f) + (-3*I*f*m - 3*I*f)*e^(-(f*m*log(-2*I*d/f) + 2*I*d*e - 2*I*c*f)/f)*gamma(m + 1, (-2*I*d*f*x - 2*I*d*e)/f) + (f*m + f)*e^(-(f*m*log(-3*I*d/f) + 3*I*d*e - 3*I*c*f)/f)*gamma(m + 1, (-3*I*d*f*x - 3*I*d*e)/f) + 12*(d*f*x + d*e)*(f*x + e)^m)/(a*d*f*m + a*d*f)","A",0
288,1,187,0,1.391278," ","integrate((f*x+e)^m*cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{e^{\left(-\frac{f m \log\left(\frac{2 i \, d}{f}\right) - 2 i \, d e + 2 i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{2 i \, d f x + 2 i \, d e}{f}\right) + 4 i \, e^{\left(-\frac{f m \log\left(\frac{i \, d}{f}\right) - i \, d e + i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, d e}{f}\right) - 4 i \, e^{\left(-\frac{f m \log\left(-\frac{i \, d}{f}\right) + i \, d e - i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, d e}{f}\right) + e^{\left(-\frac{f m \log\left(-\frac{2 i \, d}{f}\right) + 2 i \, d e - 2 i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{-2 i \, d f x - 2 i \, d e}{f}\right)}{8 \, a d}"," ",0,"1/8*(e^(-(f*m*log(2*I*d/f) - 2*I*d*e + 2*I*c*f)/f)*gamma(m + 1, (2*I*d*f*x + 2*I*d*e)/f) + 4*I*e^(-(f*m*log(I*d/f) - I*d*e + I*c*f)/f)*gamma(m + 1, (I*d*f*x + I*d*e)/f) - 4*I*e^(-(f*m*log(-I*d/f) + I*d*e - I*c*f)/f)*gamma(m + 1, (-I*d*f*x - I*d*e)/f) + e^(-(f*m*log(-2*I*d/f) + 2*I*d*e - 2*I*c*f)/f)*gamma(m + 1, (-2*I*d*f*x - 2*I*d*e)/f))/(a*d)","A",0
289,1,130,0,1.130912," ","integrate((f*x+e)^m*cos(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(f m + f\right)} e^{\left(-\frac{f m \log\left(\frac{i \, d}{f}\right) - i \, d e + i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{i \, d f x + i \, d e}{f}\right) + {\left(f m + f\right)} e^{\left(-\frac{f m \log\left(-\frac{i \, d}{f}\right) + i \, d e - i \, c f}{f}\right)} \Gamma\left(m + 1, \frac{-i \, d f x - i \, d e}{f}\right) + 2 \, {\left(d f x + d e\right)} {\left(f x + e\right)}^{m}}{2 \, {\left(a d f m + a d f\right)}}"," ",0,"1/2*((f*m + f)*e^(-(f*m*log(I*d/f) - I*d*e + I*c*f)/f)*gamma(m + 1, (I*d*f*x + I*d*e)/f) + (f*m + f)*e^(-(f*m*log(-I*d/f) + I*d*e - I*c*f)/f)*gamma(m + 1, (-I*d*f*x - I*d*e)/f) + 2*(d*f*x + d*e)*(f*x + e)^m)/(a*d*f*m + a*d*f)","A",0
290,0,0,0,1.245007," ","integrate((f*x+e)^m*cos(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*cos(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
291,0,0,0,1.389003," ","integrate((f*x+e)^m/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m/(a*sin(d*x + c) + a), x)","F",0
292,0,0,0,1.116302," ","integrate((f*x+e)^m*sec(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \sec\left(d x + c\right)}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*sec(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
293,0,0,0,1.239214," ","integrate((f*x+e)^m*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \sec\left(d x + c\right)^{2}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*sec(d*x + c)^2/(a*sin(d*x + c) + a), x)","F",0
294,1,1773,0,1.310769," ","integrate((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{-6 i \, f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 i \, f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 i \, f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 i \, f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{2 \, b d^{4}}"," ",0,"1/2*(-6*I*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*I*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*I*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*I*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(d*f^3*x + d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(d*f^3*x + d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(d*f^3*x + d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(d*f^3*x + d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b))/(b*d^4)","C",0
295,1,1231,0,1.754937," ","integrate((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{2 \, b d^{3}}"," ",0,"1/2*(2*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + (-2*I*d*f^2*x - 2*I*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-2*I*d*f^2*x - 2*I*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*d*f^2*x + 2*I*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*d*f^2*x + 2*I*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/(b*d^3)","C",0
296,1,773,0,1.703001," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{-i \, f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - i \, f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + i \, f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + i \, f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(d e - c f\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(d e - c f\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(d e - c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(d e - c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(d f x + c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d f x + c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d f x + c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(d f x + c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{2 \, b d^{2}}"," ",0,"1/2*(-I*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - I*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + I*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + I*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (d*e - c*f)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (d*e - c*f)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (d*e - c*f)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (d*e - c*f)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (d*f*x + c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d*f*x + c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d*f*x + c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (d*f*x + c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/(b*d^2)","B",0
297,1,18,0,1.460772," ","integrate(cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(b \sin\left(d x + c\right) + a\right)}{b d}"," ",0,"log(b*sin(d*x + c) + a)/(b*d)","A",0
298,1,2331,0,2.192318," ","integrate((f*x+e)^3*cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x + 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(-3 i \, b d^{2} f^{3} x^{2} - 6 i \, b d^{2} e f^{2} x - 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, b d^{2} f^{3} x^{2} + 6 i \, b d^{2} e f^{2} x + 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(3 i \, b d^{2} f^{3} x^{2} + 6 i \, b d^{2} e f^{2} x + 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-3 i \, b d^{2} f^{3} x^{2} - 6 i \, b d^{2} e f^{2} x - 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + b d^{3} e^{3} - 6 \, b d e f^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d f^{3}\right)} x\right)} \cos\left(d x + c\right) - 12 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f - 2 \, b f^{3}\right)} \sin\left(d x + c\right)}{4 \, b^{2} d^{4}}"," ",0,"1/4*(a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x + 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(-3*I*b*d^2*f^3*x^2 - 6*I*b*d^2*e*f^2*x - 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*b*d^2*f^3*x^2 + 6*I*b*d^2*e*f^2*x + 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(3*I*b*d^2*f^3*x^2 + 6*I*b*d^2*e*f^2*x + 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-3*I*b*d^2*f^3*x^2 - 6*I*b*d^2*e*f^2*x - 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + b*d^3*e^3 - 6*b*d*e*f^2 + 3*(b*d^3*e^2*f - 2*b*d*f^3)*x)*cos(d*x + c) - 12*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f - 2*b*f^3)*sin(d*x + c))/(b^2*d^4)","C",0
299,1,1632,0,1.877188," ","integrate((f*x+e)^2*cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{3} f^{2} x^{3} + 6 \, a d^{3} e f x^{2} + 6 \, a d^{3} e^{2} x - 6 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + {\left(-6 i \, b d f^{2} x - 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(6 i \, b d f^{2} x + 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(6 i \, b d f^{2} x + 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-6 i \, b d f^{2} x - 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + b d^{2} e^{2} - 2 \, b f^{2}\right)} \cos\left(d x + c\right) - 12 \, {\left(b d f^{2} x + b d e f\right)} \sin\left(d x + c\right)}{6 \, b^{2} d^{3}}"," ",0,"1/6*(2*a*d^3*f^2*x^3 + 6*a*d^3*e*f*x^2 + 6*a*d^3*e^2*x - 6*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + (-6*I*b*d*f^2*x - 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (6*I*b*d*f^2*x + 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (6*I*b*d*f^2*x + 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-6*I*b*d*f^2*x - 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + b*d^2*e^2 - 2*b*f^2)*cos(d*x + c) - 12*(b*d*f^2*x + b*d*e*f)*sin(d*x + c))/(b^2*d^3)","C",0
300,1,1039,0,1.717457," ","integrate((f*x+e)*cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d^{2} f x^{2} + 4 \, a d^{2} e x - 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, b f \sin\left(d x + c\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(b d f x + b d e\right)} \cos\left(d x + c\right)}{4 \, b^{2} d^{2}}"," ",0,"1/4*(2*a*d^2*f*x^2 + 4*a*d^2*e*x - 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 4*b*f*sin(d*x + c) - 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*(b*d*f*x + b*d*e)*cos(d*x + c))/(b^2*d^2)","B",0
301,1,214,0,0.922587," ","integrate(cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{2 \, a d x + 2 \, b \cos\left(d x + c\right) + \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, b^{2} d}, \frac{a d x + b \cos\left(d x + c\right) + \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{b^{2} d}\right]"," ",0,"[1/2*(2*a*d*x + 2*b*cos(d*x + c) + sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(b^2*d), (a*d*x + b*cos(d*x + c) + sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(b^2*d)]","A",0
302,1,2684,0,1.849178," ","integrate((f*x+e)^3*cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} d^{3} f^{3} x^{3} + 6 \, b^{2} d^{3} e f^{2} x^{2} - 24 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(2 \, b^{2} d^{3} f^{3} x^{3} + 6 \, b^{2} d^{3} e f^{2} x^{2} + 2 \, b^{2} d^{3} e^{3} - 3 \, b^{2} d e f^{2} + 3 \, {\left(2 \, b^{2} d^{3} e^{2} f - b^{2} d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, b^{2} d^{3} e^{2} f - b^{2} d f^{3}\right)} x - 24 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f - 2 \, a b f^{3}\right)} \cos\left(d x + c\right) - {\left(12 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(12 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-12 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-12 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - {\left(8 \, a b d^{3} f^{3} x^{3} + 24 \, a b d^{3} e f^{2} x^{2} + 8 \, a b d^{3} e^{3} - 48 \, a b d e f^{2} + 24 \, {\left(a b d^{3} e^{2} f - 2 \, a b d f^{3}\right)} x - 3 \, {\left(2 \, b^{2} d^{2} f^{3} x^{2} + 4 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} d^{2} e^{2} f - b^{2} f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, b^{3} d^{4}}"," ",0,"-1/8*(2*b^2*d^3*f^3*x^3 + 6*b^2*d^3*e*f^2*x^2 - 24*I*(a^2 - b^2)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*I*(a^2 - b^2)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*I*(a^2 - b^2)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*I*(a^2 - b^2)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 2*(2*b^2*d^3*f^3*x^3 + 6*b^2*d^3*e*f^2*x^2 + 2*b^2*d^3*e^3 - 3*b^2*d*e*f^2 + 3*(2*b^2*d^3*e^2*f - b^2*d*f^3)*x)*cos(d*x + c)^2 + 3*(2*b^2*d^3*e^2*f - b^2*d*f^3)*x - 24*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f - 2*a*b*f^3)*cos(d*x + c) - (12*I*(a^2 - b^2)*d^2*f^3*x^2 + 24*I*(a^2 - b^2)*d^2*e*f^2*x + 12*I*(a^2 - b^2)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (12*I*(a^2 - b^2)*d^2*f^3*x^2 + 24*I*(a^2 - b^2)*d^2*e*f^2*x + 12*I*(a^2 - b^2)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-12*I*(a^2 - b^2)*d^2*f^3*x^2 - 24*I*(a^2 - b^2)*d^2*e*f^2*x - 12*I*(a^2 - b^2)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-12*I*(a^2 - b^2)*d^2*f^3*x^2 - 24*I*(a^2 - b^2)*d^2*e*f^2*x - 12*I*(a^2 - b^2)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 4*((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 4*((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 4*((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 4*((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 4*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 24*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - (8*a*b*d^3*f^3*x^3 + 24*a*b*d^3*e*f^2*x^2 + 8*a*b*d^3*e^3 - 48*a*b*d*e*f^2 + 24*(a*b*d^3*e^2*f - 2*a*b*d*f^3)*x - 3*(2*b^2*d^2*f^3*x^2 + 4*b^2*d^2*e*f^2*x + 2*b^2*d^2*e^2*f - b^2*f^3)*cos(d*x + c))*sin(d*x + c))/(b^3*d^4)","C",0
303,1,1779,0,2.014205," ","integrate((f*x+e)^2*cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 4 \, b^{2} d^{2} e f x + 2 \, b^{2} d^{2} e^{2} - b^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} - 8 \, {\left(a b d f^{2} x + a b d e f\right)} \cos\left(d x + c\right) - {\left(4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-4 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, a b d^{2} f^{2} x^{2} + 4 \, a b d^{2} e f x + 2 \, a b d^{2} e^{2} - 4 \, a b f^{2} - {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, b^{3} d^{3}}"," ",0,"-1/4*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 4*(a^2 - b^2)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(a^2 - b^2)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(a^2 - b^2)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(a^2 - b^2)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - (2*b^2*d^2*f^2*x^2 + 4*b^2*d^2*e*f*x + 2*b^2*d^2*e^2 - b^2*f^2)*cos(d*x + c)^2 - 8*(a*b*d*f^2*x + a*b*d*e*f)*cos(d*x + c) - (4*I*(a^2 - b^2)*d*f^2*x + 4*I*(a^2 - b^2)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (4*I*(a^2 - b^2)*d*f^2*x + 4*I*(a^2 - b^2)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-4*I*(a^2 - b^2)*d*f^2*x - 4*I*(a^2 - b^2)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-4*I*(a^2 - b^2)*d*f^2*x - 4*I*(a^2 - b^2)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*a*b*d^2*f^2*x^2 + 4*a*b*d^2*e*f*x + 2*a*b*d^2*e^2 - 4*a*b*f^2 - (b^2*d*f^2*x + b^2*d*e*f)*cos(d*x + c))*sin(d*x + c))/(b^3*d^3)","C",0
304,1,1037,0,2.351644," ","integrate((f*x+e)*cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} d f x - 4 \, a b f \cos\left(d x + c\right) - 2 \, {\left(b^{2} d f x + b^{2} d e\right)} \cos\left(d x + c\right)^{2} - 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(4 \, a b d f x + 4 \, a b d e - b^{2} f \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, b^{3} d^{2}}"," ",0,"-1/4*(b^2*d*f*x - 4*a*b*f*cos(d*x + c) - 2*(b^2*d*f*x + b^2*d*e)*cos(d*x + c)^2 - 2*I*(a^2 - b^2)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*(a^2 - b^2)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*(a^2 - b^2)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*(a^2 - b^2)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (4*a*b*d*f*x + 4*a*b*d*e - b^2*f*cos(d*x + c))*sin(d*x + c))/(b^3*d^2)","B",0
305,1,53,0,1.502488," ","integrate(cos(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b^{2} \cos\left(d x + c\right)^{2} + 2 \, a b \sin\left(d x + c\right) - 2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{2 \, b^{3} d}"," ",0,"1/2*(b^2*cos(d*x + c)^2 + 2*a*b*sin(d*x + c) - 2*(a^2 - b^2)*log(b*sin(d*x + c) + a))/(b^3*d)","A",0
306,1,3061,0,2.215436," ","integrate((f*x+e)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{-6 i \, b f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 i \, b f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 i \, b f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 i \, b f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 i \, {\left(a - b\right)} f^{3} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 6 i \, {\left(a + b\right)} f^{3} {\rm polylog}\left(4, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 6 i \, {\left(a - b\right)} f^{3} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 6 i \, {\left(a + b\right)} f^{3} {\rm polylog}\left(4, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-3 i \, b d^{2} f^{3} x^{2} - 6 i \, b d^{2} e f^{2} x - 3 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-3 i \, b d^{2} f^{3} x^{2} - 6 i \, b d^{2} e f^{2} x - 3 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, b d^{2} f^{3} x^{2} + 6 i \, b d^{2} e f^{2} x + 3 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, b d^{2} f^{3} x^{2} + 6 i \, b d^{2} e f^{2} x + 3 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, {\left(a - b\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a - b\right)} d^{2} e f^{2} x + 3 i \, {\left(a - b\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(3 i \, {\left(a + b\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a + b\right)} d^{2} e f^{2} x + 3 i \, {\left(a + b\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-3 i \, {\left(a - b\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a - b\right)} d^{2} e f^{2} x - 3 i \, {\left(a - b\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(-3 i \, {\left(a + b\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a + b\right)} d^{2} e f^{2} x - 3 i \, {\left(a + b\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a + b\right)} d^{3} e^{3} - 3 \, {\left(a + b\right)} c d^{2} e^{2} f + 3 \, {\left(a + b\right)} c^{2} d e f^{2} - {\left(a + b\right)} c^{3} f^{3}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left({\left(a - b\right)} d^{3} e^{3} - 3 \, {\left(a - b\right)} c d^{2} e^{2} f + 3 \, {\left(a - b\right)} c^{2} d e f^{2} - {\left(a - b\right)} c^{3} f^{3}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left({\left(a + b\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a + b\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a + b\right)} d^{3} e^{2} f x + 3 \, {\left(a + b\right)} c d^{2} e^{2} f - 3 \, {\left(a + b\right)} c^{2} d e f^{2} + {\left(a + b\right)} c^{3} f^{3}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left({\left(a - b\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a - b\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a - b\right)} d^{3} e^{2} f x + 3 \, {\left(a - b\right)} c d^{2} e^{2} f - 3 \, {\left(a - b\right)} c^{2} d e f^{2} + {\left(a - b\right)} c^{3} f^{3}\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left({\left(a + b\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a + b\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a + b\right)} d^{3} e^{2} f x + 3 \, {\left(a + b\right)} c d^{2} e^{2} f - 3 \, {\left(a + b\right)} c^{2} d e f^{2} + {\left(a + b\right)} c^{3} f^{3}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left({\left(a - b\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a - b\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a - b\right)} d^{3} e^{2} f x + 3 \, {\left(a - b\right)} c d^{2} e^{2} f - 3 \, {\left(a - b\right)} c^{2} d e f^{2} + {\left(a - b\right)} c^{3} f^{3}\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left({\left(a + b\right)} d^{3} e^{3} - 3 \, {\left(a + b\right)} c d^{2} e^{2} f + 3 \, {\left(a + b\right)} c^{2} d e f^{2} - {\left(a + b\right)} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left({\left(a - b\right)} d^{3} e^{3} - 3 \, {\left(a - b\right)} c d^{2} e^{2} f + 3 \, {\left(a - b\right)} c^{2} d e f^{2} - {\left(a - b\right)} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) + 6 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a - b\right)} d f^{3} x + {\left(a - b\right)} d e f^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 6 \, {\left({\left(a + b\right)} d f^{3} x + {\left(a + b\right)} d e f^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 6 \, {\left({\left(a - b\right)} d f^{3} x + {\left(a - b\right)} d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 6 \, {\left({\left(a + b\right)} d f^{3} x + {\left(a + b\right)} d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right)}{2 \, {\left(a^{2} - b^{2}\right)} d^{4}}"," ",0,"-1/2*(-6*I*b*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*I*b*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*I*b*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*I*b*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*I*(a - b)*f^3*polylog(4, I*cos(d*x + c) + sin(d*x + c)) - 6*I*(a + b)*f^3*polylog(4, I*cos(d*x + c) - sin(d*x + c)) + 6*I*(a - b)*f^3*polylog(4, -I*cos(d*x + c) + sin(d*x + c)) + 6*I*(a + b)*f^3*polylog(4, -I*cos(d*x + c) - sin(d*x + c)) + (-3*I*b*d^2*f^3*x^2 - 6*I*b*d^2*e*f^2*x - 3*I*b*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-3*I*b*d^2*f^3*x^2 - 6*I*b*d^2*e*f^2*x - 3*I*b*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*b*d^2*f^3*x^2 + 6*I*b*d^2*e*f^2*x + 3*I*b*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*b*d^2*f^3*x^2 + 6*I*b*d^2*e*f^2*x + 3*I*b*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*(a - b)*d^2*f^3*x^2 + 6*I*(a - b)*d^2*e*f^2*x + 3*I*(a - b)*d^2*e^2*f)*dilog(I*cos(d*x + c) + sin(d*x + c)) + (3*I*(a + b)*d^2*f^3*x^2 + 6*I*(a + b)*d^2*e*f^2*x + 3*I*(a + b)*d^2*e^2*f)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-3*I*(a - b)*d^2*f^3*x^2 - 6*I*(a - b)*d^2*e*f^2*x - 3*I*(a - b)*d^2*e^2*f)*dilog(-I*cos(d*x + c) + sin(d*x + c)) + (-3*I*(a + b)*d^2*f^3*x^2 - 6*I*(a + b)*d^2*e*f^2*x - 3*I*(a + b)*d^2*e^2*f)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a + b)*d^3*e^3 - 3*(a + b)*c*d^2*e^2*f + 3*(a + b)*c^2*d*e*f^2 - (a + b)*c^3*f^3)*log(cos(d*x + c) + I*sin(d*x + c) + I) + ((a - b)*d^3*e^3 - 3*(a - b)*c*d^2*e^2*f + 3*(a - b)*c^2*d*e*f^2 - (a - b)*c^3*f^3)*log(cos(d*x + c) - I*sin(d*x + c) + I) - ((a + b)*d^3*f^3*x^3 + 3*(a + b)*d^3*e*f^2*x^2 + 3*(a + b)*d^3*e^2*f*x + 3*(a + b)*c*d^2*e^2*f - 3*(a + b)*c^2*d*e*f^2 + (a + b)*c^3*f^3)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + ((a - b)*d^3*f^3*x^3 + 3*(a - b)*d^3*e*f^2*x^2 + 3*(a - b)*d^3*e^2*f*x + 3*(a - b)*c*d^2*e^2*f - 3*(a - b)*c^2*d*e*f^2 + (a - b)*c^3*f^3)*log(I*cos(d*x + c) - sin(d*x + c) + 1) - ((a + b)*d^3*f^3*x^3 + 3*(a + b)*d^3*e*f^2*x^2 + 3*(a + b)*d^3*e^2*f*x + 3*(a + b)*c*d^2*e^2*f - 3*(a + b)*c^2*d*e*f^2 + (a + b)*c^3*f^3)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + ((a - b)*d^3*f^3*x^3 + 3*(a - b)*d^3*e*f^2*x^2 + 3*(a - b)*d^3*e^2*f*x + 3*(a - b)*c*d^2*e^2*f - 3*(a - b)*c^2*d*e*f^2 + (a - b)*c^3*f^3)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - ((a + b)*d^3*e^3 - 3*(a + b)*c*d^2*e^2*f + 3*(a + b)*c^2*d*e*f^2 - (a + b)*c^3*f^3)*log(-cos(d*x + c) + I*sin(d*x + c) + I) + ((a - b)*d^3*e^3 - 3*(a - b)*c*d^2*e^2*f + 3*(a - b)*c^2*d*e*f^2 - (a - b)*c^3*f^3)*log(-cos(d*x + c) - I*sin(d*x + c) + I) + 6*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*((a - b)*d*f^3*x + (a - b)*d*e*f^2)*polylog(3, I*cos(d*x + c) + sin(d*x + c)) - 6*((a + b)*d*f^3*x + (a + b)*d*e*f^2)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 6*((a - b)*d*f^3*x + (a - b)*d*e*f^2)*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) - 6*((a + b)*d*f^3*x + (a + b)*d*e*f^2)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)))/((a^2 - b^2)*d^4)","C",0
307,1,2027,0,1.897889," ","integrate((f*x+e)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, b f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, b f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, b f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a - b\right)} f^{2} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 2 \, {\left(a + b\right)} f^{2} {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 2 \, {\left(a - b\right)} f^{2} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 2 \, {\left(a + b\right)} f^{2} {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-2 i \, b d f^{2} x - 2 i \, b d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-2 i \, b d f^{2} x - 2 i \, b d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, b d f^{2} x + 2 i \, b d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, b d f^{2} x + 2 i \, b d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, {\left(a - b\right)} d f^{2} x + 2 i \, {\left(a - b\right)} d e f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(2 i \, {\left(a + b\right)} d f^{2} x + 2 i \, {\left(a + b\right)} d e f\right)} {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(-2 i \, {\left(a - b\right)} d f^{2} x - 2 i \, {\left(a - b\right)} d e f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + {\left(-2 i \, {\left(a + b\right)} d f^{2} x - 2 i \, {\left(a + b\right)} d e f\right)} {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a + b\right)} d^{2} e^{2} - 2 \, {\left(a + b\right)} c d e f + {\left(a + b\right)} c^{2} f^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left({\left(a - b\right)} d^{2} e^{2} - 2 \, {\left(a - b\right)} c d e f + {\left(a - b\right)} c^{2} f^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left({\left(a + b\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a + b\right)} d^{2} e f x + 2 \, {\left(a + b\right)} c d e f - {\left(a + b\right)} c^{2} f^{2}\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left({\left(a - b\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a - b\right)} d^{2} e f x + 2 \, {\left(a - b\right)} c d e f - {\left(a - b\right)} c^{2} f^{2}\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left({\left(a + b\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a + b\right)} d^{2} e f x + 2 \, {\left(a + b\right)} c d e f - {\left(a + b\right)} c^{2} f^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left({\left(a - b\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a - b\right)} d^{2} e f x + 2 \, {\left(a - b\right)} c d e f - {\left(a - b\right)} c^{2} f^{2}\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left({\left(a + b\right)} d^{2} e^{2} - 2 \, {\left(a + b\right)} c d e f + {\left(a + b\right)} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left({\left(a - b\right)} d^{2} e^{2} - 2 \, {\left(a - b\right)} c d e f + {\left(a - b\right)} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right)}{2 \, {\left(a^{2} - b^{2}\right)} d^{3}}"," ",0,"-1/2*(2*b*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*b*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*b*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*b*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(a - b)*f^2*polylog(3, I*cos(d*x + c) + sin(d*x + c)) - 2*(a + b)*f^2*polylog(3, I*cos(d*x + c) - sin(d*x + c)) + 2*(a - b)*f^2*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) - 2*(a + b)*f^2*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) + (-2*I*b*d*f^2*x - 2*I*b*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-2*I*b*d*f^2*x - 2*I*b*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*b*d*f^2*x + 2*I*b*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*b*d*f^2*x + 2*I*b*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*(a - b)*d*f^2*x + 2*I*(a - b)*d*e*f)*dilog(I*cos(d*x + c) + sin(d*x + c)) + (2*I*(a + b)*d*f^2*x + 2*I*(a + b)*d*e*f)*dilog(I*cos(d*x + c) - sin(d*x + c)) + (-2*I*(a - b)*d*f^2*x - 2*I*(a - b)*d*e*f)*dilog(-I*cos(d*x + c) + sin(d*x + c)) + (-2*I*(a + b)*d*f^2*x - 2*I*(a + b)*d*e*f)*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a + b)*d^2*e^2 - 2*(a + b)*c*d*e*f + (a + b)*c^2*f^2)*log(cos(d*x + c) + I*sin(d*x + c) + I) + ((a - b)*d^2*e^2 - 2*(a - b)*c*d*e*f + (a - b)*c^2*f^2)*log(cos(d*x + c) - I*sin(d*x + c) + I) - ((a + b)*d^2*f^2*x^2 + 2*(a + b)*d^2*e*f*x + 2*(a + b)*c*d*e*f - (a + b)*c^2*f^2)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + ((a - b)*d^2*f^2*x^2 + 2*(a - b)*d^2*e*f*x + 2*(a - b)*c*d*e*f - (a - b)*c^2*f^2)*log(I*cos(d*x + c) - sin(d*x + c) + 1) - ((a + b)*d^2*f^2*x^2 + 2*(a + b)*d^2*e*f*x + 2*(a + b)*c*d*e*f - (a + b)*c^2*f^2)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + ((a - b)*d^2*f^2*x^2 + 2*(a - b)*d^2*e*f*x + 2*(a - b)*c*d*e*f - (a - b)*c^2*f^2)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - ((a + b)*d^2*e^2 - 2*(a + b)*c*d*e*f + (a + b)*c^2*f^2)*log(-cos(d*x + c) + I*sin(d*x + c) + I) + ((a - b)*d^2*e^2 - 2*(a - b)*c*d*e*f + (a - b)*c^2*f^2)*log(-cos(d*x + c) - I*sin(d*x + c) + I))/((a^2 - b^2)*d^3)","C",0
308,1,1181,0,1.790006," ","integrate((f*x+e)*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{-i \, b f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - i \, b f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + i \, b f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + i \, b f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + i \, {\left(a - b\right)} f {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + i \, {\left(a + b\right)} f {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - i \, {\left(a - b\right)} f {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - i \, {\left(a + b\right)} f {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + {\left(b d e - b c f\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d e - b c f\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(b d e - b c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(b d e - b c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(b d f x + b c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d f x + b c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d f x + b c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d f x + b c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a + b\right)} d e - {\left(a + b\right)} c f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left({\left(a - b\right)} d e - {\left(a - b\right)} c f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - {\left({\left(a + b\right)} d f x + {\left(a + b\right)} c f\right)} \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left({\left(a - b\right)} d f x + {\left(a - b\right)} c f\right)} \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left({\left(a + b\right)} d f x + {\left(a + b\right)} c f\right)} \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) + {\left({\left(a - b\right)} d f x + {\left(a - b\right)} c f\right)} \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - {\left({\left(a + b\right)} d e - {\left(a + b\right)} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) + {\left({\left(a - b\right)} d e - {\left(a - b\right)} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right)}{2 \, {\left(a^{2} - b^{2}\right)} d^{2}}"," ",0,"-1/2*(-I*b*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - I*b*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + I*b*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + I*b*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + I*(a - b)*f*dilog(I*cos(d*x + c) + sin(d*x + c)) + I*(a + b)*f*dilog(I*cos(d*x + c) - sin(d*x + c)) - I*(a - b)*f*dilog(-I*cos(d*x + c) + sin(d*x + c)) - I*(a + b)*f*dilog(-I*cos(d*x + c) - sin(d*x + c)) + (b*d*e - b*c*f)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d*e - b*c*f)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (b*d*e - b*c*f)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (b*d*e - b*c*f)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (b*d*f*x + b*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d*f*x + b*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d*f*x + b*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b*d*f*x + b*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a + b)*d*e - (a + b)*c*f)*log(cos(d*x + c) + I*sin(d*x + c) + I) + ((a - b)*d*e - (a - b)*c*f)*log(cos(d*x + c) - I*sin(d*x + c) + I) - ((a + b)*d*f*x + (a + b)*c*f)*log(I*cos(d*x + c) + sin(d*x + c) + 1) + ((a - b)*d*f*x + (a - b)*c*f)*log(I*cos(d*x + c) - sin(d*x + c) + 1) - ((a + b)*d*f*x + (a + b)*c*f)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) + ((a - b)*d*f*x + (a - b)*c*f)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - ((a + b)*d*e - (a + b)*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + I) + ((a - b)*d*e - (a - b)*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + I))/((a^2 - b^2)*d^2)","B",0
309,1,62,0,1.095183," ","integrate(sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \log\left(b \sin\left(d x + c\right) + a\right) - {\left(a + b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a - b\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"-1/2*(2*b*log(b*sin(d*x + c) + a) - (a + b)*log(sin(d*x + c) + 1) + (a - b)*log(-sin(d*x + c) + 1))/((a^2 - b^2)*d)","A",0
310,1,4120,0,3.051355," ","integrate((f*x+e)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 12 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} - 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b^{3} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 4 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 12 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} f^{3} \cos\left(d x + c\right) {\rm polylog}\left(3, i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 12 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} f^{3} \cos\left(d x + c\right) {\rm polylog}\left(3, i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 12 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} f^{3} \cos\left(d x + c\right) {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 12 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} f^{3} \cos\left(d x + c\right) {\rm polylog}\left(3, -i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 2 \, {\left(-3 i \, b^{3} d^{2} f^{3} x^{2} - 6 i \, b^{3} d^{2} e f^{2} x - 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(3 i \, b^{3} d^{2} f^{3} x^{2} + 6 i \, b^{3} d^{2} e f^{2} x + 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(3 i \, b^{3} d^{2} f^{3} x^{2} + 6 i \, b^{3} d^{2} e f^{2} x + 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-3 i \, b^{3} d^{2} f^{3} x^{2} - 6 i \, b^{3} d^{2} e f^{2} x - 3 i \, b^{3} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - {\left(12 i \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d e f^{2}\right)} \cos\left(d x + c\right) {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(-12 i \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d e f^{2}\right)} \cos\left(d x + c\right) {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - {\left(-12 i \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d e f^{2}\right)} \cos\left(d x + c\right) {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - {\left(12 i \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d e f^{2}\right)} \cos\left(d x + c\right) {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 6 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c d e f^{2} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 6 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c d e f^{2} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 6 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c d e f^{2} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c d e f^{2} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c d e f^{2} - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c d e f^{2} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c d e f^{2} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 6 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c d e f^{2} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c^{2} f^{3}\right)} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} f x + {\left(a^{3} - a b^{2}\right)} d^{3} e^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cos\left(d x + c\right)}"," ",0,"-1/4*(4*(a^2*b - b^3)*d^3*f^3*x^3 + 12*(a^2*b - b^3)*d^3*e*f^2*x^2 - 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b^3*f^3*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a^2*b - b^3)*d^3*e^2*f*x + 4*(a^2*b - b^3)*d^3*e^3 - 12*(a^3 - a^2*b - a*b^2 + b^3)*f^3*cos(d*x + c)*polylog(3, I*cos(d*x + c) + sin(d*x + c)) - 12*(a^3 + a^2*b - a*b^2 - b^3)*f^3*cos(d*x + c)*polylog(3, I*cos(d*x + c) - sin(d*x + c)) - 12*(a^3 - a^2*b - a*b^2 + b^3)*f^3*cos(d*x + c)*polylog(3, -I*cos(d*x + c) + sin(d*x + c)) - 12*(a^3 + a^2*b - a*b^2 - b^3)*f^3*cos(d*x + c)*polylog(3, -I*cos(d*x + c) - sin(d*x + c)) - 2*(-3*I*b^3*d^2*f^3*x^2 - 6*I*b^3*d^2*e*f^2*x - 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(3*I*b^3*d^2*f^3*x^2 + 6*I*b^3*d^2*e*f^2*x + 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(3*I*b^3*d^2*f^3*x^2 + 6*I*b^3*d^2*e*f^2*x + 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-3*I*b^3*d^2*f^3*x^2 - 6*I*b^3*d^2*e*f^2*x - 3*I*b^3*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b^3*d*f^3*x + b^3*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - (12*I*(a^3 - a^2*b - a*b^2 + b^3)*d*f^3*x + 12*I*(a^3 - a^2*b - a*b^2 + b^3)*d*e*f^2)*cos(d*x + c)*dilog(I*cos(d*x + c) + sin(d*x + c)) - (-12*I*(a^3 + a^2*b - a*b^2 - b^3)*d*f^3*x - 12*I*(a^3 + a^2*b - a*b^2 - b^3)*d*e*f^2)*cos(d*x + c)*dilog(I*cos(d*x + c) - sin(d*x + c)) - (-12*I*(a^3 - a^2*b - a*b^2 + b^3)*d*f^3*x - 12*I*(a^3 - a^2*b - a*b^2 + b^3)*d*e*f^2)*cos(d*x + c)*dilog(-I*cos(d*x + c) + sin(d*x + c)) - (12*I*(a^3 + a^2*b - a*b^2 - b^3)*d*f^3*x + 12*I*(a^3 + a^2*b - a*b^2 - b^3)*d*e*f^2)*cos(d*x + c)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 6*((a^3 + a^2*b - a*b^2 - b^3)*d^2*e^2*f - 2*(a^3 + a^2*b - a*b^2 - b^3)*c*d*e*f^2 + (a^3 + a^2*b - a*b^2 - b^3)*c^2*f^3)*cos(d*x + c)*log(cos(d*x + c) + I*sin(d*x + c) + I) - 6*((a^3 - a^2*b - a*b^2 + b^3)*d^2*e^2*f - 2*(a^3 - a^2*b - a*b^2 + b^3)*c*d*e*f^2 + (a^3 - a^2*b - a*b^2 + b^3)*c^2*f^3)*cos(d*x + c)*log(cos(d*x + c) - I*sin(d*x + c) + I) - 6*((a^3 + a^2*b - a*b^2 - b^3)*d^2*f^3*x^2 + 2*(a^3 + a^2*b - a*b^2 - b^3)*d^2*e*f^2*x + 2*(a^3 + a^2*b - a*b^2 - b^3)*c*d*e*f^2 - (a^3 + a^2*b - a*b^2 - b^3)*c^2*f^3)*cos(d*x + c)*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 6*((a^3 - a^2*b - a*b^2 + b^3)*d^2*f^3*x^2 + 2*(a^3 - a^2*b - a*b^2 + b^3)*d^2*e*f^2*x + 2*(a^3 - a^2*b - a*b^2 + b^3)*c*d*e*f^2 - (a^3 - a^2*b - a*b^2 + b^3)*c^2*f^3)*cos(d*x + c)*log(I*cos(d*x + c) - sin(d*x + c) + 1) - 6*((a^3 + a^2*b - a*b^2 - b^3)*d^2*f^3*x^2 + 2*(a^3 + a^2*b - a*b^2 - b^3)*d^2*e*f^2*x + 2*(a^3 + a^2*b - a*b^2 - b^3)*c*d*e*f^2 - (a^3 + a^2*b - a*b^2 - b^3)*c^2*f^3)*cos(d*x + c)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 6*((a^3 - a^2*b - a*b^2 + b^3)*d^2*f^3*x^2 + 2*(a^3 - a^2*b - a*b^2 + b^3)*d^2*e*f^2*x + 2*(a^3 - a^2*b - a*b^2 + b^3)*c*d*e*f^2 - (a^3 - a^2*b - a*b^2 + b^3)*c^2*f^3)*cos(d*x + c)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - 6*((a^3 + a^2*b - a*b^2 - b^3)*d^2*e^2*f - 2*(a^3 + a^2*b - a*b^2 - b^3)*c*d*e*f^2 + (a^3 + a^2*b - a*b^2 - b^3)*c^2*f^3)*cos(d*x + c)*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 6*((a^3 - a^2*b - a*b^2 + b^3)*d^2*e^2*f - 2*(a^3 - a^2*b - a*b^2 + b^3)*c*d*e*f^2 + (a^3 - a^2*b - a*b^2 + b^3)*c^2*f^3)*cos(d*x + c)*log(-cos(d*x + c) - I*sin(d*x + c) + I) - 4*((a^3 - a*b^2)*d^3*f^3*x^3 + 3*(a^3 - a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 - a*b^2)*d^3*e^2*f*x + (a^3 - a*b^2)*d^3*e^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d^4*cos(d*x + c))","C",0
311,1,2663,0,2.005965," ","integrate((f*x+e)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, b^{3} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 8 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 4 \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 4 i \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} f^{2} \cos\left(d x + c\right) {\rm Li}_2\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) + 4 i \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} f^{2} \cos\left(d x + c\right) {\rm Li}_2\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) + 4 i \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} f^{2} \cos\left(d x + c\right) {\rm Li}_2\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right)\right) - 4 i \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} f^{2} \cos\left(d x + c\right) {\rm Li}_2\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right)\right) - 2 \, {\left(-2 i \, b^{3} d f^{2} x - 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(2 i \, b^{3} d f^{2} x + 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(2 i \, b^{3} d f^{2} x + 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-2 i \, b^{3} d f^{2} x - 2 i \, b^{3} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d e f - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 4 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d e f - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 4 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d f^{2} x + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d f^{2} x + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d f^{2} x + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(-i \, \cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d f^{2} x + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(-i \, \cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d e f - {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + i\right) - 4 \, {\left({\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} d e f - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} c f^{2}\right)} \cos\left(d x + c\right) \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + i\right) - 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + {\left(a^{3} - a b^{2}\right)} d^{2} e^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cos\left(d x + c\right)}"," ",0,"-1/4*(4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*b^3*f^2*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(a^2*b - b^3)*d^2*f^2*x^2 + 8*(a^2*b - b^3)*d^2*e*f*x + 4*(a^2*b - b^3)*d^2*e^2 - 4*I*(a^3 - a^2*b - a*b^2 + b^3)*f^2*cos(d*x + c)*dilog(I*cos(d*x + c) + sin(d*x + c)) + 4*I*(a^3 + a^2*b - a*b^2 - b^3)*f^2*cos(d*x + c)*dilog(I*cos(d*x + c) - sin(d*x + c)) + 4*I*(a^3 - a^2*b - a*b^2 + b^3)*f^2*cos(d*x + c)*dilog(-I*cos(d*x + c) + sin(d*x + c)) - 4*I*(a^3 + a^2*b - a*b^2 - b^3)*f^2*cos(d*x + c)*dilog(-I*cos(d*x + c) - sin(d*x + c)) - 2*(-2*I*b^3*d*f^2*x - 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(2*I*b^3*d*f^2*x + 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(2*I*b^3*d*f^2*x + 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-2*I*b^3*d*f^2*x - 2*I*b^3*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*((a^3 + a^2*b - a*b^2 - b^3)*d*e*f - (a^3 + a^2*b - a*b^2 - b^3)*c*f^2)*cos(d*x + c)*log(cos(d*x + c) + I*sin(d*x + c) + I) - 4*((a^3 - a^2*b - a*b^2 + b^3)*d*e*f - (a^3 - a^2*b - a*b^2 + b^3)*c*f^2)*cos(d*x + c)*log(cos(d*x + c) - I*sin(d*x + c) + I) - 4*((a^3 + a^2*b - a*b^2 - b^3)*d*f^2*x + (a^3 + a^2*b - a*b^2 - b^3)*c*f^2)*cos(d*x + c)*log(I*cos(d*x + c) + sin(d*x + c) + 1) - 4*((a^3 - a^2*b - a*b^2 + b^3)*d*f^2*x + (a^3 - a^2*b - a*b^2 + b^3)*c*f^2)*cos(d*x + c)*log(I*cos(d*x + c) - sin(d*x + c) + 1) - 4*((a^3 + a^2*b - a*b^2 - b^3)*d*f^2*x + (a^3 + a^2*b - a*b^2 - b^3)*c*f^2)*cos(d*x + c)*log(-I*cos(d*x + c) + sin(d*x + c) + 1) - 4*((a^3 - a^2*b - a*b^2 + b^3)*d*f^2*x + (a^3 - a^2*b - a*b^2 + b^3)*c*f^2)*cos(d*x + c)*log(-I*cos(d*x + c) - sin(d*x + c) + 1) - 4*((a^3 + a^2*b - a*b^2 - b^3)*d*e*f - (a^3 + a^2*b - a*b^2 - b^3)*c*f^2)*cos(d*x + c)*log(-cos(d*x + c) + I*sin(d*x + c) + I) - 4*((a^3 - a^2*b - a*b^2 + b^3)*d*e*f - (a^3 - a^2*b - a*b^2 + b^3)*c*f^2)*cos(d*x + c)*log(-cos(d*x + c) - I*sin(d*x + c) + I) - 4*((a^3 - a*b^2)*d^2*f^2*x^2 + 2*(a^3 - a*b^2)*d^2*e*f*x + (a^3 - a*b^2)*d^2*e^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d^3*cos(d*x + c))","C",0
312,1,1271,0,2.118594," ","integrate((f*x+e)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b^{3} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(a^{2} b - b^{3}\right)} d f x + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} f \cos\left(d x + c\right) \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} f \cos\left(d x + c\right) \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \cos\left(d x + c\right) \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(a^{2} b - b^{3}\right)} d e + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d f x + {\left(a^{3} - a b^{2}\right)} d e\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cos\left(d x + c\right)}"," ",0,"1/4*(-2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b^3*f*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 4*(a^2*b - b^3)*d*f*x + 2*(a^3 + a^2*b - a*b^2 - b^3)*f*cos(d*x + c)*log(sin(d*x + c) + 1) + 2*(a^3 - a^2*b - a*b^2 + b^3)*f*cos(d*x + c)*log(-sin(d*x + c) + 1) - 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b^3*d*e - b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b^3*d*f*x + b^3*c*f)*sqrt(-(a^2 - b^2)/b^2)*cos(d*x + c)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*(a^2*b - b^3)*d*e + 4*((a^3 - a*b^2)*d*f*x + (a^3 - a*b^2)*d*e)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d^2*cos(d*x + c))","B",0
313,1,305,0,1.440781," ","integrate(sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} b^{2} \cos\left(d x + c\right) \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}, \frac{\sqrt{a^{2} - b^{2}} b^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - a^{2} b + b^{3} + {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*b^2*cos(d*x + c)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^2*b + 2*b^3 + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)), (sqrt(a^2 - b^2)*b^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - a^2*b + b^3 + (a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c))]","A",0
314,0,0,0,1.441835," ","integrate((f*x+e)^m*cos(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*cos(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
315,0,0,0,1.229164," ","integrate((f*x+e)^m*cos(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \cos\left(d x + c\right)}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*cos(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
316,0,0,0,1.038088," ","integrate((f*x+e)^m/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m/(b*sin(d*x + c) + a), x)","F",0
317,0,0,0,1.336272," ","integrate((f*x+e)^m*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \sec\left(d x + c\right)}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*sec(d*x + c)/(b*sin(d*x + c) + a), x)","F",0
318,0,0,0,1.216952," ","integrate((f*x+e)^m*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(f x + e\right)}^{m} \sec\left(d x + c\right)^{2}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((f*x + e)^m*sec(d*x + c)^2/(b*sin(d*x + c) + a), x)","F",0
319,1,339,0,1.527983," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{2} - b^{2}\right)} d f x + 2 \, {\left(a^{2} - b^{2}\right)} d e + {\left(b f \sin\left(d x + c\right) + a f\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} \sin\left(d x + c\right) + {\left(a^{3} b - a b^{3}\right)} d^{2}\right)}}, -\frac{{\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} d e + {\left(b f \sin\left(d x + c\right) + a f\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d^{2} \sin\left(d x + c\right) + {\left(a^{3} b - a b^{3}\right)} d^{2}}\right]"," ",0,"[-1/2*(2*(a^2 - b^2)*d*f*x + 2*(a^2 - b^2)*d*e + (b*f*sin(d*x + c) + a*f)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/((a^2*b^2 - b^4)*d^2*sin(d*x + c) + (a^3*b - a*b^3)*d^2), -((a^2 - b^2)*d*f*x + (a^2 - b^2)*d*e + (b*f*sin(d*x + c) + a*f)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/((a^2*b^2 - b^4)*d^2*sin(d*x + c) + (a^3*b - a*b^3)*d^2)]","A",0
320,1,1393,0,1.973394," ","integrate((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + {\left(a^{2} - b^{2}\right)} d^{2} e^{2} + {\left(-i \, b^{2} f^{2} \sin\left(d x + c\right) - i \, a b f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, b^{2} f^{2} \sin\left(d x + c\right) + i \, a b f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, b^{2} f^{2} \sin\left(d x + c\right) + i \, a b f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, b^{2} f^{2} \sin\left(d x + c\right) - i \, a b f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{{\left(a^{2} b^{2} - b^{4}\right)} d^{3} \sin\left(d x + c\right) + {\left(a^{3} b - a b^{3}\right)} d^{3}}"," ",0,"-((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + (a^2 - b^2)*d^2*e^2 + (-I*b^2*f^2*sin(d*x + c) - I*a*b*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*b^2*f^2*sin(d*x + c) + I*a*b*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*b^2*f^2*sin(d*x + c) + I*a*b*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*b^2*f^2*sin(d*x + c) - I*a*b*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - (a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + (a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + (a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2*b^2 - b^4)*d^3*sin(d*x + c) + (a^3*b - a*b^3)*d^3)","B",0
321,1,2280,0,2.057420," ","integrate((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 6 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 6 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 2 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{3} + {\left(-6 i \, a b d f^{3} x - 6 i \, a b d e f^{2} + {\left(-6 i \, b^{2} d f^{3} x - 6 i \, b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(6 i \, a b d f^{3} x + 6 i \, a b d e f^{2} + {\left(6 i \, b^{2} d f^{3} x + 6 i \, b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(6 i \, a b d f^{3} x + 6 i \, a b d e f^{2} + {\left(6 i \, b^{2} d f^{3} x + 6 i \, b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-6 i \, a b d f^{3} x - 6 i \, a b d e f^{2} + {\left(-6 i \, b^{2} d f^{3} x - 6 i \, b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 3 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 3 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 3 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b^{2} f^{3} \sin\left(d x + c\right) + a b f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} f^{3} \sin\left(d x + c\right) + a b f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{2} f^{3} \sin\left(d x + c\right) + a b f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} f^{3} \sin\left(d x + c\right) + a b f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{4} \sin\left(d x + c\right) + {\left(a^{3} b - a b^{3}\right)} d^{4}\right)}}"," ",0,"-1/2*(2*(a^2 - b^2)*d^3*f^3*x^3 + 6*(a^2 - b^2)*d^3*e*f^2*x^2 + 6*(a^2 - b^2)*d^3*e^2*f*x + 2*(a^2 - b^2)*d^3*e^3 + (-6*I*a*b*d*f^3*x - 6*I*a*b*d*e*f^2 + (-6*I*b^2*d*f^3*x - 6*I*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (6*I*a*b*d*f^3*x + 6*I*a*b*d*e*f^2 + (6*I*b^2*d*f^3*x + 6*I*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (6*I*a*b*d*f^3*x + 6*I*a*b*d*e*f^2 + (6*I*b^2*d*f^3*x + 6*I*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-6*I*a*b*d*f^3*x - 6*I*a*b*d*e*f^2 + (-6*I*b^2*d*f^3*x - 6*I*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 3*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 3*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 3*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 3*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 3*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*(b^2*f^3*sin(d*x + c) + a*b*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(b^2*f^3*sin(d*x + c) + a*b*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*(b^2*f^3*sin(d*x + c) + a*b*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(b^2*f^3*sin(d*x + c) + a*b*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b))/((a^2*b^2 - b^4)*d^4*sin(d*x + c) + (a^3*b - a*b^3)*d^4)","C",0
322,1,625,0,1.445855," ","integrate((f*x+e)*cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f x - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} f \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e - 2 \, {\left(a^{3} b - a b^{3}\right)} f \cos\left(d x + c\right) + {\left(a b^{2} f \cos\left(d x + c\right)^{2} - 2 \, a^{2} b f \sin\left(d x + c\right) - {\left(a^{3} + a b^{2}\right)} f\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{4 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \sin\left(d x + c\right) - {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{2}\right)}}, \frac{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f x - {\left(a^{2} b^{2} - b^{4}\right)} f \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{3} b - a b^{3}\right)} f \cos\left(d x + c\right) - {\left(a b^{2} f \cos\left(d x + c\right)^{2} - 2 \, a^{2} b f \sin\left(d x + c\right) - {\left(a^{3} + a b^{2}\right)} f\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{2 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \sin\left(d x + c\right) - {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{2}\right)}}\right]"," ",0,"[1/4*(2*(a^4 - 2*a^2*b^2 + b^4)*d*f*x - 2*(a^2*b^2 - b^4)*f*cos(d*x + c)*sin(d*x + c) + 2*(a^4 - 2*a^2*b^2 + b^4)*d*e - 2*(a^3*b - a*b^3)*f*cos(d*x + c) + (a*b^2*f*cos(d*x + c)^2 - 2*a^2*b*f*sin(d*x + c) - (a^3 + a*b^2)*f)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d^2*cos(d*x + c)^2 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d^2*sin(d*x + c) - (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^2), 1/2*((a^4 - 2*a^2*b^2 + b^4)*d*f*x - (a^2*b^2 - b^4)*f*cos(d*x + c)*sin(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*e - (a^3*b - a*b^3)*f*cos(d*x + c) - (a*b^2*f*cos(d*x + c)^2 - 2*a^2*b*f*sin(d*x + c) - (a^3 + a*b^2)*f)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d^2*cos(d*x + c)^2 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d^2*sin(d*x + c) - (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^2)]","B",0
323,1,2375,0,2.377792," ","integrate((f*x+e)^2*cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} - b^{4}\right)} d e f\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(-i \, a b^{3} f^{2} \cos\left(d x + c\right)^{2} + 2 i \, a^{2} b^{2} f^{2} \sin\left(d x + c\right) + i \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(i \, a b^{3} f^{2} \cos\left(d x + c\right)^{2} - 2 i \, a^{2} b^{2} f^{2} \sin\left(d x + c\right) - i \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(i \, a b^{3} f^{2} \cos\left(d x + c\right)^{2} - 2 i \, a^{2} b^{2} f^{2} \sin\left(d x + c\right) - i \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-i \, a b^{3} f^{2} \cos\left(d x + c\right)^{2} + 2 i \, a^{2} b^{2} f^{2} \sin\left(d x + c\right) + i \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x + {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x + {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x + {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x + {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{2} x + {\left(a^{3} b - a b^{3}\right)} d e f\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} b^{2} - b^{4}\right)} f^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) - {\left(a^{4} - b^{4}\right)} f^{2} + {\left({\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left({\left(a^{2} b^{2} - b^{4}\right)} f^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) - {\left(a^{4} - b^{4}\right)} f^{2} + {\left({\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left({\left(a^{2} b^{2} - b^{4}\right)} f^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) - {\left(a^{4} - b^{4}\right)} f^{2} - {\left({\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left({\left(a^{2} b^{2} - b^{4}\right)} f^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b - a b^{3}\right)} f^{2} \sin\left(d x + c\right) - {\left(a^{4} - b^{4}\right)} f^{2} - {\left({\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right)}{2 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \sin\left(d x + c\right) - {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{3}\right)}}"," ",0,"1/2*((a^4 - 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f*x + (a^4 - 2*a^2*b^2 + b^4)*d^2*e^2 - 2*((a^2*b^2 - b^4)*d*f^2*x + (a^2*b^2 - b^4)*d*e*f)*cos(d*x + c)*sin(d*x + c) - (-I*a*b^3*f^2*cos(d*x + c)^2 + 2*I*a^2*b^2*f^2*sin(d*x + c) + I*(a^3*b + a*b^3)*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (I*a*b^3*f^2*cos(d*x + c)^2 - 2*I*a^2*b^2*f^2*sin(d*x + c) - I*(a^3*b + a*b^3)*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (I*a*b^3*f^2*cos(d*x + c)^2 - 2*I*a^2*b^2*f^2*sin(d*x + c) - I*(a^3*b + a*b^3)*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-I*a*b^3*f^2*cos(d*x + c)^2 + 2*I*a^2*b^2*f^2*sin(d*x + c) + I*(a^3*b + a*b^3)*f^2)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + ((a^3*b + a*b^3)*d*f^2*x + (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a^3*b + a*b^3)*d*f^2*x + (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^3*b + a*b^3)*d*f^2*x + (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a^3*b + a*b^3)*d*f^2*x + (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*((a^3*b - a*b^3)*d*f^2*x + (a^3*b - a*b^3)*d*e*f)*cos(d*x + c) - ((a^2*b^2 - b^4)*f^2*cos(d*x + c)^2 - 2*(a^3*b - a*b^3)*f^2*sin(d*x + c) - (a^4 - b^4)*f^2 + ((a^3*b + a*b^3)*d*e*f - (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - ((a^2*b^2 - b^4)*f^2*cos(d*x + c)^2 - 2*(a^3*b - a*b^3)*f^2*sin(d*x + c) - (a^4 - b^4)*f^2 + ((a^3*b + a*b^3)*d*e*f - (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - ((a^2*b^2 - b^4)*f^2*cos(d*x + c)^2 - 2*(a^3*b - a*b^3)*f^2*sin(d*x + c) - (a^4 - b^4)*f^2 - ((a^3*b + a*b^3)*d*e*f - (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - ((a^2*b^2 - b^4)*f^2*cos(d*x + c)^2 - 2*(a^3*b - a*b^3)*f^2*sin(d*x + c) - (a^4 - b^4)*f^2 - ((a^3*b + a*b^3)*d*e*f - (a^3*b + a*b^3)*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cos(d*x + c)^2 + 2*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d^3*cos(d*x + c)^2 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d^3*sin(d*x + c) - (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^3)","B",0
324,1,4917,0,2.654668," ","integrate((f*x+e)^3*cos(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 12 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2} x + {\left(a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 12 \, {\left(a b^{3} f^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{2} f^{3} \sin\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b^{3} f^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{2} f^{3} \sin\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a b^{3} f^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{2} f^{3} \sin\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b^{3} f^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{2} b^{2} f^{3} \sin\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left({\left(a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + {\left(a^{3} b - a b^{3}\right)} d^{2} e^{2} f\right)} \cos\left(d x + c\right) - {\left(-12 i \, {\left(a^{2} b^{2} - b^{4}\right)} f^{3} \cos\left(d x + c\right)^{2} + 24 i \, {\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) + 12 i \, {\left(a^{4} - b^{4}\right)} f^{3} + 2 \, {\left(6 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 6 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + {\left(-6 i \, a b^{3} d f^{3} x - 6 i \, a b^{3} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(12 i \, a^{2} b^{2} d f^{3} x + 12 i \, a^{2} b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-12 i \, {\left(a^{2} b^{2} - b^{4}\right)} f^{3} \cos\left(d x + c\right)^{2} + 24 i \, {\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) + 12 i \, {\left(a^{4} - b^{4}\right)} f^{3} + 2 \, {\left(-6 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x - 6 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + {\left(6 i \, a b^{3} d f^{3} x + 6 i \, a b^{3} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(-12 i \, a^{2} b^{2} d f^{3} x - 12 i \, a^{2} b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(12 i \, {\left(a^{2} b^{2} - b^{4}\right)} f^{3} \cos\left(d x + c\right)^{2} - 24 i \, {\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) - 12 i \, {\left(a^{4} - b^{4}\right)} f^{3} + 2 \, {\left(-6 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x - 6 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + {\left(6 i \, a b^{3} d f^{3} x + 6 i \, a b^{3} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(-12 i \, a^{2} b^{2} d f^{3} x - 12 i \, a^{2} b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(12 i \, {\left(a^{2} b^{2} - b^{4}\right)} f^{3} \cos\left(d x + c\right)^{2} - 24 i \, {\left(a^{3} b - a b^{3}\right)} f^{3} \sin\left(d x + c\right) - 12 i \, {\left(a^{4} - b^{4}\right)} f^{3} + 2 \, {\left(6 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 6 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + {\left(-6 i \, a b^{3} d f^{3} x - 6 i \, a b^{3} d e f^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(12 i \, a^{2} b^{2} d f^{3} x + 12 i \, a^{2} b^{2} d e f^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d e f^{2} - 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d e f^{2} - 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d e f^{2} - 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d e f^{2} - 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d e f^{2} - {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d f^{3} x + 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{3} x + {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d f^{3} x + 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{3} x + {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d f^{3} x + 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{3} x + {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) + {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(2 \, {\left(a^{4} - b^{4}\right)} d f^{3} x + 2 \, {\left(a^{4} - b^{4}\right)} c f^{3} - 2 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b - a b^{3}\right)} d f^{3} x + {\left(a^{3} b - a b^{3}\right)} c f^{3}\right)} \sin\left(d x + c\right) - {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{8 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \sin\left(d x + c\right) - {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7}\right)} d^{4}\right)}}"," ",0,"1/8*(4*(a^4 - 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 12*(a^4 - 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 12*(a^4 - 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 4*(a^4 - 2*a^2*b^2 + b^4)*d^3*e^3 - 12*((a^2*b^2 - b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 - b^4)*d^2*e*f^2*x + (a^2*b^2 - b^4)*d^2*e^2*f)*cos(d*x + c)*sin(d*x + c) + 12*(a*b^3*f^3*cos(d*x + c)^2 - 2*a^2*b^2*f^3*sin(d*x + c) - (a^3*b + a*b^3)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(a*b^3*f^3*cos(d*x + c)^2 - 2*a^2*b^2*f^3*sin(d*x + c) - (a^3*b + a*b^3)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a*b^3*f^3*cos(d*x + c)^2 - 2*a^2*b^2*f^3*sin(d*x + c) - (a^3*b + a*b^3)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(a*b^3*f^3*cos(d*x + c)^2 - 2*a^2*b^2*f^3*sin(d*x + c) - (a^3*b + a*b^3)*f^3)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*((a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(a^3*b - a*b^3)*d^2*e*f^2*x + (a^3*b - a*b^3)*d^2*e^2*f)*cos(d*x + c) - (-12*I*(a^2*b^2 - b^4)*f^3*cos(d*x + c)^2 + 24*I*(a^3*b - a*b^3)*f^3*sin(d*x + c) + 12*I*(a^4 - b^4)*f^3 + 2*(6*I*(a^3*b + a*b^3)*d*f^3*x + 6*I*(a^3*b + a*b^3)*d*e*f^2 + (-6*I*a*b^3*d*f^3*x - 6*I*a*b^3*d*e*f^2)*cos(d*x + c)^2 + (12*I*a^2*b^2*d*f^3*x + 12*I*a^2*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (-12*I*(a^2*b^2 - b^4)*f^3*cos(d*x + c)^2 + 24*I*(a^3*b - a*b^3)*f^3*sin(d*x + c) + 12*I*(a^4 - b^4)*f^3 + 2*(-6*I*(a^3*b + a*b^3)*d*f^3*x - 6*I*(a^3*b + a*b^3)*d*e*f^2 + (6*I*a*b^3*d*f^3*x + 6*I*a*b^3*d*e*f^2)*cos(d*x + c)^2 + (-12*I*a^2*b^2*d*f^3*x - 12*I*a^2*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (12*I*(a^2*b^2 - b^4)*f^3*cos(d*x + c)^2 - 24*I*(a^3*b - a*b^3)*f^3*sin(d*x + c) - 12*I*(a^4 - b^4)*f^3 + 2*(-6*I*(a^3*b + a*b^3)*d*f^3*x - 6*I*(a^3*b + a*b^3)*d*e*f^2 + (6*I*a*b^3*d*f^3*x + 6*I*a*b^3*d*e*f^2)*cos(d*x + c)^2 + (-12*I*a^2*b^2*d*f^3*x - 12*I*a^2*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (12*I*(a^2*b^2 - b^4)*f^3*cos(d*x + c)^2 - 24*I*(a^3*b - a*b^3)*f^3*sin(d*x + c) - 12*I*(a^4 - b^4)*f^3 + 2*(6*I*(a^3*b + a*b^3)*d*f^3*x + 6*I*(a^3*b + a*b^3)*d*e*f^2 + (-6*I*a*b^3*d*f^3*x - 6*I*a*b^3*d*e*f^2)*cos(d*x + c)^2 + (12*I*a^2*b^2*d*f^3*x + 12*I*a^2*b^2*d*e*f^2)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 6*(2*(a^4 - b^4)*d*e*f^2 - 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*e*f^2 - (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*e*f^2 - (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) - ((a^3*b + a*b^3)*d^2*e^2*f - 2*(a^3*b + a*b^3)*c*d*e*f^2 + (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 6*(2*(a^4 - b^4)*d*e*f^2 - 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*e*f^2 - (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*e*f^2 - (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) - ((a^3*b + a*b^3)*d^2*e^2*f - 2*(a^3*b + a*b^3)*c*d*e*f^2 + (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*(2*(a^4 - b^4)*d*e*f^2 - 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*e*f^2 - (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*e*f^2 - (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) + ((a^3*b + a*b^3)*d^2*e^2*f - 2*(a^3*b + a*b^3)*c*d*e*f^2 + (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 6*(2*(a^4 - b^4)*d*e*f^2 - 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*e*f^2 - (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*e*f^2 - (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) + ((a^3*b + a*b^3)*d^2*e^2*f - 2*(a^3*b + a*b^3)*c*d*e*f^2 + (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*(2*(a^4 - b^4)*d*f^3*x + 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*f^3*x + (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*f^3*x + (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) + ((a^3*b + a*b^3)*d^2*f^3*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f^2*x + 2*(a^3*b + a*b^3)*c*d*e*f^2 - (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(2*(a^4 - b^4)*d*f^3*x + 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*f^3*x + (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*f^3*x + (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) - ((a^3*b + a*b^3)*d^2*f^3*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f^2*x + 2*(a^3*b + a*b^3)*c*d*e*f^2 - (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(2*(a^4 - b^4)*d*f^3*x + 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*f^3*x + (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*f^3*x + (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) + ((a^3*b + a*b^3)*d^2*f^3*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f^2*x + 2*(a^3*b + a*b^3)*c*d*e*f^2 - (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(2*(a^4 - b^4)*d*f^3*x + 2*(a^4 - b^4)*c*f^3 - 2*((a^2*b^2 - b^4)*d*f^3*x + (a^2*b^2 - b^4)*c*f^3)*cos(d*x + c)^2 + 4*((a^3*b - a*b^3)*d*f^3*x + (a^3*b - a*b^3)*c*f^3)*sin(d*x + c) - ((a^3*b + a*b^3)*d^2*f^3*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f^2*x + 2*(a^3*b + a*b^3)*c*d*e*f^2 - (a^3*b + a*b^3)*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cos(d*x + c)^2 + 2*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d^4*cos(d*x + c)^2 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d^4*sin(d*x + c) - (a^6*b - a^4*b^3 - a^2*b^5 + b^7)*d^4)","C",0
325,1,3089,0,2.323557," ","integrate((f*x+e)^3*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x + 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 i \, b f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 i \, b f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 i \, b f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 12 i \, b f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 i \, b f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(3 i \, b d^{2} f^{3} x^{2} + 6 i \, b d^{2} e f^{2} x + 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-3 i \, b d^{2} f^{3} x^{2} - 6 i \, b d^{2} e f^{2} x - 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-3 i \, b d^{2} f^{3} x^{2} - 6 i \, b d^{2} e f^{2} x - 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(3 i \, b d^{2} f^{3} x^{2} + 6 i \, b d^{2} e f^{2} x + 3 i \, b d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - {\left(-6 i \, b d^{2} f^{3} x^{2} - 12 i \, b d^{2} e f^{2} x - 6 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(6 i \, b d^{2} f^{3} x^{2} + 12 i \, b d^{2} e f^{2} x + 6 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(-6 i \, b d^{2} f^{3} x^{2} - 12 i \, b d^{2} e f^{2} x - 6 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(6 i \, b d^{2} f^{3} x^{2} + 12 i \, b d^{2} e f^{2} x + 6 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + b d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + b d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right)}{4 \, a b d^{4}}"," ",0,"-1/4*(a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x + 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*I*b*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*I*b*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c)) + 12*I*b*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c)) - 12*I*b*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) + 12*I*b*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) - 2*(3*I*b*d^2*f^3*x^2 + 6*I*b*d^2*e*f^2*x + 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-3*I*b*d^2*f^3*x^2 - 6*I*b*d^2*e*f^2*x - 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-3*I*b*d^2*f^3*x^2 - 6*I*b*d^2*e*f^2*x - 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(3*I*b*d^2*f^3*x^2 + 6*I*b*d^2*e*f^2*x + 3*I*b*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(b*d*f^3*x + b*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - (-6*I*b*d^2*f^3*x^2 - 12*I*b*d^2*e*f^2*x - 6*I*b*d^2*e^2*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) - (6*I*b*d^2*f^3*x^2 + 12*I*b*d^2*e*f^2*x + 6*I*b*d^2*e^2*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) - (-6*I*b*d^2*f^3*x^2 - 12*I*b*d^2*e*f^2*x - 6*I*b*d^2*e^2*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) - (6*I*b*d^2*f^3*x^2 + 12*I*b*d^2*e*f^2*x + 6*I*b*d^2*e^2*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + b*d^3*e^3)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + b*d^3*e^3)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - 2*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 12*(b*d*f^3*x + b*d*e*f^2)*polylog(3, cos(d*x + c) + I*sin(d*x + c)) - 12*(b*d*f^3*x + b*d*e*f^2)*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 12*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 12*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -cos(d*x + c) - I*sin(d*x + c)))/(a*b*d^4)","C",0
326,1,2109,0,1.454153," ","integrate((f*x+e)^2*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a d^{3} f^{2} x^{3} + 12 \, a d^{3} e f x^{2} + 12 \, a d^{3} e^{2} x - 12 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, b f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, b f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 12 \, b f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 12 \, b f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 \, b f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(6 i \, b d f^{2} x + 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-6 i \, b d f^{2} x - 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(-6 i \, b d f^{2} x - 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(6 i \, b d f^{2} x + 6 i \, b d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(-12 i \, b d f^{2} x - 12 i \, b d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(12 i \, b d f^{2} x + 12 i \, b d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - {\left(-12 i \, b d f^{2} x - 12 i \, b d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - {\left(12 i \, b d f^{2} x + 12 i \, b d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + b d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + b d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right)}{12 \, a b d^{3}}"," ",0,"-1/12*(4*a*d^3*f^2*x^3 + 12*a*d^3*e*f*x^2 + 12*a*d^3*e^2*x - 12*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*b*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*b*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c)) - 12*b*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 12*b*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 12*b*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(6*I*b*d*f^2*x + 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-6*I*b*d*f^2*x - 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(-6*I*b*d*f^2*x - 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*(6*I*b*d*f^2*x + 6*I*b*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (-12*I*b*d*f^2*x - 12*I*b*d*e*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) - (12*I*b*d*f^2*x + 12*I*b*d*e*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) - (-12*I*b*d*f^2*x - 12*I*b*d*e*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) - (12*I*b*d*f^2*x + 12*I*b*d*e*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + b*d^2*e^2)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + b*d^2*e^2)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - 6*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 6*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-cos(d*x + c) - I*sin(d*x + c) + 1))/(a*b*d^3)","C",0
327,1,1280,0,2.248106," ","integrate((f*x+e)*cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d^{2} f x^{2} + 4 \, a d^{2} e x - 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 2 i \, b f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 i \, b f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 2 i \, b f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(b d f x + b d e\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(b d e - b c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(b d e - b c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(b d f x + b c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(b d f x + b c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right)}{4 \, a b d^{2}}"," ",0,"-1/4*(2*a*d^2*f*x^2 + 4*a*d^2*e*x - 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*f*dilog(cos(d*x + c) + I*sin(d*x + c)) - 2*I*b*f*dilog(cos(d*x + c) - I*sin(d*x + c)) + 2*I*b*f*dilog(-cos(d*x + c) + I*sin(d*x + c)) - 2*I*b*f*dilog(-cos(d*x + c) - I*sin(d*x + c)) - 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(b*d*e - b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d*f*x + b*d*e)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + 2*(b*d*f*x + b*d*e)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - 2*(b*d*e - b*c*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - 2*(b*d*e - b*c*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - 2*(b*d*f*x + b*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - 2*(b*d*f*x + b*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1))/(a*b*d^2)","B",0
328,1,262,0,1.223513," ","integrate(cos(d*x+c)*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, a d x + b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, a b d}, -\frac{2 \, a d x + b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{2 \, a b d}\right]"," ",0,"[-1/2*(2*a*d*x + b*log(1/2*cos(d*x + c) + 1/2) - b*log(-1/2*cos(d*x + c) + 1/2) - sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(a*b*d), -1/2*(2*a*d*x + b*log(1/2*cos(d*x + c) + 1/2) - b*log(-1/2*cos(d*x + c) + 1/2) + 2*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(a*b*d)]","A",0
329,1,3441,0,2.919318," ","integrate((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 i \, b^{2} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 6 i \, b^{2} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 6 i \, b^{2} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 i \, b^{2} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f - 2 \, a b f^{3}\right)} \cos\left(d x + c\right) + {\left(-3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-3 i \, b^{2} d^{2} f^{3} x^{2} - 6 i \, b^{2} d^{2} e f^{2} x - 3 i \, b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(3 i \, b^{2} d^{2} f^{3} x^{2} + 6 i \, b^{2} d^{2} e f^{2} x + 3 i \, b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(3 i \, b^{2} d^{2} f^{3} x^{2} + 6 i \, b^{2} d^{2} e f^{2} x + 3 i \, b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-3 i \, b^{2} d^{2} f^{3} x^{2} - 6 i \, b^{2} d^{2} e f^{2} x - 3 i \, b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + b^{2} d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + b^{2} d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + a b d^{3} e^{3} - 6 \, a b d e f^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d f^{3}\right)} x\right)} \sin\left(d x + c\right)}{2 \, a b^{2} d^{4}}"," ",0,"1/2*(6*I*b^2*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c)) - 6*I*b^2*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c)) - 6*I*b^2*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) + 6*I*b^2*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) - 6*I*(a^2 - b^2)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*I*(a^2 - b^2)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*I*(a^2 - b^2)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*I*(a^2 - b^2)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f - 2*a*b*f^3)*cos(d*x + c) + (-3*I*(a^2 - b^2)*d^2*f^3*x^2 - 6*I*(a^2 - b^2)*d^2*e*f^2*x - 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-3*I*(a^2 - b^2)*d^2*f^3*x^2 - 6*I*(a^2 - b^2)*d^2*e*f^2*x - 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*(a^2 - b^2)*d^2*f^3*x^2 + 6*I*(a^2 - b^2)*d^2*e*f^2*x + 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (3*I*(a^2 - b^2)*d^2*f^3*x^2 + 6*I*(a^2 - b^2)*d^2*e*f^2*x + 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-3*I*b^2*d^2*f^3*x^2 - 6*I*b^2*d^2*e*f^2*x - 3*I*b^2*d^2*e^2*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (3*I*b^2*d^2*f^3*x^2 + 6*I*b^2*d^2*e*f^2*x + 3*I*b^2*d^2*e^2*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (3*I*b^2*d^2*f^3*x^2 + 6*I*b^2*d^2*e*f^2*x + 3*I*b^2*d^2*e^2*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (-3*I*b^2*d^2*f^3*x^2 - 6*I*b^2*d^2*e*f^2*x - 3*I*b^2*d^2*e^2*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + b^2*d^3*e^3)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + b^2*d^3*e^3)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 6*(b^2*d*f^3*x + b^2*d*e*f^2)*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 6*(b^2*d*f^3*x + b^2*d*e*f^2)*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 6*(b^2*d*f^3*x + b^2*d*e*f^2)*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 6*(b^2*d*f^3*x + b^2*d*e*f^2)*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + a*b*d^3*e^3 - 6*a*b*d*e*f^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d*f^3)*x)*sin(d*x + c))/(a*b^2*d^4)","C",0
330,1,2252,0,2.301317," ","integrate((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{2} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a b d f^{2} x + a b d e f\right)} \cos\left(d x + c\right) + {\left(-2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-2 i \, b^{2} d f^{2} x - 2 i \, b^{2} d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(2 i \, b^{2} d f^{2} x + 2 i \, b^{2} d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(2 i \, b^{2} d f^{2} x + 2 i \, b^{2} d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(-2 i \, b^{2} d f^{2} x - 2 i \, b^{2} d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + b^{2} d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + b^{2} d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2} - 2 \, a b f^{2}\right)} \sin\left(d x + c\right)}{2 \, a b^{2} d^{3}}"," ",0,"1/2*(2*b^2*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 2*b^2*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c)) + 2*b^2*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) + 2*b^2*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) + 2*(a^2 - b^2)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(a^2 - b^2)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(a^2 - b^2)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(a^2 - b^2)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(a*b*d*f^2*x + a*b*d*e*f)*cos(d*x + c) + (-2*I*(a^2 - b^2)*d*f^2*x - 2*I*(a^2 - b^2)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-2*I*(a^2 - b^2)*d*f^2*x - 2*I*(a^2 - b^2)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*(a^2 - b^2)*d*f^2*x + 2*I*(a^2 - b^2)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (2*I*(a^2 - b^2)*d*f^2*x + 2*I*(a^2 - b^2)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-2*I*b^2*d*f^2*x - 2*I*b^2*d*e*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (2*I*b^2*d*f^2*x + 2*I*b^2*d*e*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (2*I*b^2*d*f^2*x + 2*I*b^2*d*e*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (-2*I*b^2*d*f^2*x - 2*I*b^2*d*e*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + b^2*d^2*e^2)*log(cos(d*x + c) + I*sin(d*x + c) + 1) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + b^2*d^2*e^2)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2 - 2*a*b*f^2)*sin(d*x + c))/(a*b^2*d^3)","C",0
331,1,1293,0,2.358900," ","integrate((f*x+e)*cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b f \cos\left(d x + c\right) + i \, b^{2} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - i \, b^{2} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - i \, b^{2} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + i \, b^{2} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d f x + b^{2} d e\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - {\left(b^{2} d f x + b^{2} d e\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - {\left(b^{2} d e - b^{2} c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(b^{2} d e - b^{2} c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) - {\left(b^{2} d f x + b^{2} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - {\left(b^{2} d f x + b^{2} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(a b d f x + a b d e\right)} \sin\left(d x + c\right)}{2 \, a b^{2} d^{2}}"," ",0,"-1/2*(2*a*b*f*cos(d*x + c) + I*b^2*f*dilog(cos(d*x + c) + I*sin(d*x + c)) - I*b^2*f*dilog(cos(d*x + c) - I*sin(d*x + c)) - I*b^2*f*dilog(-cos(d*x + c) + I*sin(d*x + c)) + I*b^2*f*dilog(-cos(d*x + c) - I*sin(d*x + c)) + I*(a^2 - b^2)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + I*(a^2 - b^2)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - I*(a^2 - b^2)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - I*(a^2 - b^2)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (b^2*d*f*x + b^2*d*e)*log(cos(d*x + c) + I*sin(d*x + c) + 1) - (b^2*d*f*x + b^2*d*e)*log(cos(d*x + c) - I*sin(d*x + c) + 1) - (b^2*d*e - b^2*c*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) - (b^2*d*e - b^2*c*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) - (b^2*d*f*x + b^2*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) - (b^2*d*f*x + b^2*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + 2*(a*b*d*f*x + a*b*d*e)*sin(d*x + c))/(a*b^2*d^2)","B",0
332,1,55,0,1.502586," ","integrate(cos(d*x+c)^2*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b^{2} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - a b \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a b^{2} d}"," ",0,"(b^2*log(-1/2*sin(d*x + c)) - a*b*sin(d*x + c) + (a^2 - b^2)*log(b*sin(d*x + c) + a))/(a*b^2*d)","A",0
333,1,4201,0,3.495608," ","integrate((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{4} e f^{2} x^{3} + 24 i \, b^{3} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 24 i \, b^{3} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 24 i \, b^{3} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 24 i \, b^{3} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + 24 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{4} e^{2} f + a b^{2} d^{2} f^{3}\right)} x^{2} - 3 \, {\left(2 \, a b^{2} d^{2} f^{3} x^{2} + 4 \, a b^{2} d^{2} e f^{2} x + 2 \, a b^{2} d^{2} e^{2} f - a b^{2} f^{3}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 24 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{4} e^{3} + 3 \, a b^{2} d^{2} e f^{2}\right)} x + 8 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + a^{2} b d^{3} e^{3} - 6 \, a^{2} b d e f^{2} + 3 \, {\left(a^{2} b d^{3} e^{2} f - 2 \, a^{2} b d f^{3}\right)} x\right)} \cos\left(d x + c\right) + {\left(-12 i \, b^{3} d^{2} f^{3} x^{2} - 24 i \, b^{3} d^{2} e f^{2} x - 12 i \, b^{3} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(12 i \, b^{3} d^{2} f^{3} x^{2} + 24 i \, b^{3} d^{2} e f^{2} x + 12 i \, b^{3} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(-12 i \, b^{3} d^{2} f^{3} x^{2} - 24 i \, b^{3} d^{2} e f^{2} x - 12 i \, b^{3} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(12 i \, b^{3} d^{2} f^{3} x^{2} + 24 i \, b^{3} d^{2} e f^{2} x + 12 i \, b^{3} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 4 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + b^{3} d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 4 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + b^{3} d^{3} e^{3}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 4 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 24 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 24 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 24 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 24 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 \, {\left(12 \, a^{2} b d^{2} f^{3} x^{2} + 24 \, a^{2} b d^{2} e f^{2} x + 12 \, a^{2} b d^{2} e^{2} f - 24 \, a^{2} b f^{3} + {\left(2 \, a b^{2} d^{3} f^{3} x^{3} + 6 \, a b^{2} d^{3} e f^{2} x^{2} + 2 \, a b^{2} d^{3} e^{3} - 3 \, a b^{2} d e f^{2} + 3 \, {\left(2 \, a b^{2} d^{3} e^{2} f - a b^{2} d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, a b^{3} d^{4}}"," ",0,"1/8*((2*a^3 - 3*a*b^2)*d^4*f^3*x^4 + 4*(2*a^3 - 3*a*b^2)*d^4*e*f^2*x^3 + 24*I*b^3*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c)) - 24*I*b^3*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c)) + 24*I*b^3*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c)) - 24*I*b^3*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c)) + 24*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 3*(2*(2*a^3 - 3*a*b^2)*d^4*e^2*f + a*b^2*d^2*f^3)*x^2 - 3*(2*a*b^2*d^2*f^3*x^2 + 4*a*b^2*d^2*e*f^2*x + 2*a*b^2*d^2*e^2*f - a*b^2*f^3)*cos(d*x + c)^2 + 2*(-6*I*(a^2*b - b^3)*d^2*f^3*x^2 - 12*I*(a^2*b - b^3)*d^2*e*f^2*x - 6*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(6*I*(a^2*b - b^3)*d^2*f^3*x^2 + 12*I*(a^2*b - b^3)*d^2*e*f^2*x + 6*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(6*I*(a^2*b - b^3)*d^2*f^3*x^2 + 12*I*(a^2*b - b^3)*d^2*e*f^2*x + 6*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-6*I*(a^2*b - b^3)*d^2*f^3*x^2 - 12*I*(a^2*b - b^3)*d^2*e*f^2*x - 6*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 4*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 4*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 4*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 4*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 4*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 24*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 24*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 24*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 2*(2*(2*a^3 - 3*a*b^2)*d^4*e^3 + 3*a*b^2*d^2*e*f^2)*x + 8*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + a^2*b*d^3*e^3 - 6*a^2*b*d*e*f^2 + 3*(a^2*b*d^3*e^2*f - 2*a^2*b*d*f^3)*x)*cos(d*x + c) + (-12*I*b^3*d^2*f^3*x^2 - 24*I*b^3*d^2*e*f^2*x - 12*I*b^3*d^2*e^2*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (12*I*b^3*d^2*f^3*x^2 + 24*I*b^3*d^2*e*f^2*x + 12*I*b^3*d^2*e^2*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (-12*I*b^3*d^2*f^3*x^2 - 24*I*b^3*d^2*e*f^2*x - 12*I*b^3*d^2*e^2*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (12*I*b^3*d^2*f^3*x^2 + 24*I*b^3*d^2*e*f^2*x + 12*I*b^3*d^2*e^2*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) - 4*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + b^3*d^3*e^3)*log(cos(d*x + c) + I*sin(d*x + c) + 1) - 4*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + b^3*d^3*e^3)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + 4*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + 4*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + 4*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 4*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) + 24*(b^3*d*f^3*x + b^3*d*e*f^2)*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 24*(b^3*d*f^3*x + b^3*d*e*f^2)*polylog(3, cos(d*x + c) - I*sin(d*x + c)) - 24*(b^3*d*f^3*x + b^3*d*e*f^2)*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) - 24*(b^3*d*f^3*x + b^3*d*e*f^2)*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 2*(12*a^2*b*d^2*f^3*x^2 + 24*a^2*b*d^2*e*f^2*x + 12*a^2*b*d^2*e^2*f - 24*a^2*b*f^3 + (2*a*b^2*d^3*f^3*x^3 + 6*a*b^2*d^3*e*f^2*x^2 + 2*a*b^2*d^3*e^3 - 3*a*b^2*d*e*f^2 + 3*(2*a*b^2*d^3*e^2*f - a*b^2*d*f^3)*x)*cos(d*x + c))*sin(d*x + c))/(a*b^3*d^4)","C",0
334,1,2783,0,2.934030," ","integrate((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{3} f^{2} x^{3} + 6 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{3} e f x^{2} + 12 \, b^{3} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 12 \, b^{3} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 12 \, b^{3} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) - 12 \, b^{3} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{3} e^{2} + a b^{2} d f^{2}\right)} x + 12 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + a^{2} b d^{2} e^{2} - 2 \, a^{2} b f^{2}\right)} \cos\left(d x + c\right) + {\left(-12 i \, b^{3} d f^{2} x - 12 i \, b^{3} d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(12 i \, b^{3} d f^{2} x + 12 i \, b^{3} d e f\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) + {\left(-12 i \, b^{3} d f^{2} x - 12 i \, b^{3} d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + {\left(12 i \, b^{3} d f^{2} x + 12 i \, b^{3} d e f\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + b^{3} d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + b^{3} d^{2} e^{2}\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 6 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, a^{2} b d f^{2} x + 8 \, a^{2} b d e f + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 2 \, a b^{2} d^{2} e^{2} - a b^{2} f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, a b^{3} d^{3}}"," ",0,"1/12*(2*(2*a^3 - 3*a*b^2)*d^3*f^2*x^3 + 6*(2*a^3 - 3*a*b^2)*d^3*e*f*x^2 + 12*b^3*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c)) + 12*b^3*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c)) - 12*b^3*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c)) - 12*b^3*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c)) - 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 6*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cos(d*x + c)^2 + 2*(-6*I*(a^2*b - b^3)*d*f^2*x - 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(6*I*(a^2*b - b^3)*d*f^2*x + 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(6*I*(a^2*b - b^3)*d*f^2*x + 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(-6*I*(a^2*b - b^3)*d*f^2*x - 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 3*(2*(2*a^3 - 3*a*b^2)*d^3*e^2 + a*b^2*d*f^2)*x + 12*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + a^2*b*d^2*e^2 - 2*a^2*b*f^2)*cos(d*x + c) + (-12*I*b^3*d*f^2*x - 12*I*b^3*d*e*f)*dilog(cos(d*x + c) + I*sin(d*x + c)) + (12*I*b^3*d*f^2*x + 12*I*b^3*d*e*f)*dilog(cos(d*x + c) - I*sin(d*x + c)) + (-12*I*b^3*d*f^2*x - 12*I*b^3*d*e*f)*dilog(-cos(d*x + c) + I*sin(d*x + c)) + (12*I*b^3*d*f^2*x + 12*I*b^3*d*e*f)*dilog(-cos(d*x + c) - I*sin(d*x + c)) - 6*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + b^3*d^2*e^2)*log(cos(d*x + c) + I*sin(d*x + c) + 1) - 6*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + b^3*d^2*e^2)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + 6*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + 6*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + 6*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 6*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 3*(8*a^2*b*d*f^2*x + 8*a^2*b*d*e*f + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 2*a*b^2*d^2*e^2 - a*b^2*f^2)*cos(d*x + c))*sin(d*x + c))/(a*b^3*d^3)","C",0
335,1,1611,0,2.544196," ","integrate((f*x+e)*cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{2} f x^{2} - a b^{2} f \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d^{2} e x - 2 i \, b^{3} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 2 i \, b^{3} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 i \, b^{3} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) + 2 i \, b^{3} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) - 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(a^{2} b d f x + a^{2} b d e\right)} \cos\left(d x + c\right) - 2 \, {\left(b^{3} d f x + b^{3} d e\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(b^{3} d f x + b^{3} d e\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{2} b f + {\left(a b^{2} d f x + a b^{2} d e\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, a b^{3} d^{2}}"," ",0,"1/4*((2*a^3 - 3*a*b^2)*d^2*f*x^2 - a*b^2*f*cos(d*x + c)^2 + 2*(2*a^3 - 3*a*b^2)*d^2*e*x - 2*I*b^3*f*dilog(cos(d*x + c) + I*sin(d*x + c)) + 2*I*b^3*f*dilog(cos(d*x + c) - I*sin(d*x + c)) - 2*I*b^3*f*dilog(-cos(d*x + c) + I*sin(d*x + c)) + 2*I*b^3*f*dilog(-cos(d*x + c) - I*sin(d*x + c)) - 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 4*(a^2*b*d*f*x + a^2*b*d*e)*cos(d*x + c) - 2*(b^3*d*f*x + b^3*d*e)*log(cos(d*x + c) + I*sin(d*x + c) + 1) - 2*(b^3*d*f*x + b^3*d*e)*log(cos(d*x + c) - I*sin(d*x + c) + 1) + 2*(b^3*d*e - b^3*c*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2) + 2*(b^3*d*e - b^3*c*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2) + 2*(b^3*d*f*x + b^3*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1) + 2*(b^3*d*f*x + b^3*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1) - 2*(2*a^2*b*f + (a*b^2*d*f*x + a*b^2*d*e)*cos(d*x + c))*sin(d*x + c))/(a*b^3*d^2)","B",0
336,1,350,0,1.939855," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} b \cos\left(d x + c\right) + b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x - {\left(-a^{2} + b^{2}\right)}^{\frac{3}{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, a b^{3} d}, -\frac{a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} b \cos\left(d x + c\right) + b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x - 2 \, {\left(a^{2} - b^{2}\right)}^{\frac{3}{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{2 \, a b^{3} d}\right]"," ",0,"[-1/2*(a*b^2*cos(d*x + c)*sin(d*x + c) - 2*a^2*b*cos(d*x + c) + b^3*log(1/2*cos(d*x + c) + 1/2) - b^3*log(-1/2*cos(d*x + c) + 1/2) - (2*a^3 - 3*a*b^2)*d*x - (-a^2 + b^2)^(3/2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(a*b^3*d), -1/2*(a*b^2*cos(d*x + c)*sin(d*x + c) - 2*a^2*b*cos(d*x + c) + b^3*log(1/2*cos(d*x + c) + 1/2) - b^3*log(-1/2*cos(d*x + c) + 1/2) - (2*a^3 - 3*a*b^2)*d*x - 2*(a^2 - b^2)^(3/2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(a*b^3*d)]","A",0
337,1,3903,0,2.805778," ","integrate((f*x+e)^3*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b d^{3} f^{3} x^{3} + 6 \, a b d^{3} e f^{2} x^{2} + 6 \, a b d^{3} e^{2} f x + 2 \, a b d^{3} e^{3} + 6 i \, b^{2} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 6 i \, b^{2} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 6 i \, b^{2} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 6 i \, b^{2} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 6 i \, {\left(a^{2} - b^{2}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - {\left(3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x + 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(-3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(-3 i \, {\left(a^{2} - b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} - b^{2}\right)} d^{2} e f^{2} x - 3 i \, {\left(a^{2} - b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(3 i \, b^{2} d^{2} f^{3} x^{2} + 3 i \, b^{2} d^{2} e^{2} f - 6 i \, a b d e f^{2} + 6 i \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-3 i \, b^{2} d^{2} f^{3} x^{2} - 3 i \, b^{2} d^{2} e^{2} f + 6 i \, a b d e f^{2} - 6 i \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-3 i \, b^{2} d^{2} f^{3} x^{2} - 3 i \, b^{2} d^{2} e^{2} f - 6 i \, a b d e f^{2} - 6 i \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(3 i \, b^{2} d^{2} f^{3} x^{2} + 3 i \, b^{2} d^{2} e^{2} f + 6 i \, a b d e f^{2} + 6 i \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} - b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} - b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} - b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} - b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} - b^{2}\right)} d f^{3} x + {\left(a^{2} - b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right)}{2 \, a^{2} b d^{4} \sin\left(d x + c\right)}"," ",0,"-1/2*(2*a*b*d^3*f^3*x^3 + 6*a*b*d^3*e*f^2*x^2 + 6*a*b*d^3*e^2*f*x + 2*a*b*d^3*e^3 + 6*I*b^2*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 6*I*b^2*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 6*I*b^2*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 6*I*b^2*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 6*I*(a^2 - b^2)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 6*I*(a^2 - b^2)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 6*I*(a^2 - b^2)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 6*I*(a^2 - b^2)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - (3*I*(a^2 - b^2)*d^2*f^3*x^2 + 6*I*(a^2 - b^2)*d^2*e*f^2*x + 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (3*I*(a^2 - b^2)*d^2*f^3*x^2 + 6*I*(a^2 - b^2)*d^2*e*f^2*x + 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (-3*I*(a^2 - b^2)*d^2*f^3*x^2 - 6*I*(a^2 - b^2)*d^2*e*f^2*x - 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (-3*I*(a^2 - b^2)*d^2*f^3*x^2 - 6*I*(a^2 - b^2)*d^2*e*f^2*x - 3*I*(a^2 - b^2)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (3*I*b^2*d^2*f^3*x^2 + 3*I*b^2*d^2*e^2*f - 6*I*a*b*d*e*f^2 + 6*I*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (-3*I*b^2*d^2*f^3*x^2 - 3*I*b^2*d^2*e^2*f + 6*I*a*b*d*e*f^2 - 6*I*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - (-3*I*b^2*d^2*f^3*x^2 - 3*I*b^2*d^2*e^2*f - 6*I*a*b*d*e*f^2 - 6*I*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (3*I*b^2*d^2*f^3*x^2 + 3*I*b^2*d^2*e^2*f + 6*I*a*b*d*e*f^2 + 6*I*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^3*e^3 - 3*(a^2 - b^2)*c*d^2*e^2*f + 3*(a^2 - b^2)*c^2*d*e*f^2 - (a^2 - b^2)*c^3*f^3)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d^3*f^3*x^3 + 3*(a^2 - b^2)*d^3*e*f^2*x^2 + 3*(a^2 - b^2)*d^3*e^2*f*x + 3*(a^2 - b^2)*c*d^2*e^2*f - 3*(a^2 - b^2)*c^2*d*e*f^2 + (a^2 - b^2)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2)*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2)*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 6*((a^2 - b^2)*d*f^3*x + (a^2 - b^2)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 6*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 6*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 6*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 6*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c))/(a^2*b*d^4*sin(d*x + c))","C",0
338,1,2529,0,2.054634," ","integrate((f*x+e)^2*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b d^{2} f^{2} x^{2} + 4 \, a b d^{2} e f x + 2 \, a b d^{2} e^{2} + 2 \, b^{2} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(a^{2} - b^{2}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - {\left(2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(-2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(-2 i \, {\left(a^{2} - b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{2} - b^{2}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(2 i \, b^{2} d f^{2} x + 2 i \, b^{2} d e f - 2 i \, a b f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-2 i \, b^{2} d f^{2} x - 2 i \, b^{2} d e f + 2 i \, a b f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-2 i \, b^{2} d f^{2} x - 2 i \, b^{2} d e f - 2 i \, a b f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(2 i \, b^{2} d f^{2} x + 2 i \, b^{2} d e f + 2 i \, a b f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} - b^{2}\right)} c d e f + {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} - b^{2}\right)} c d e f - {\left(a^{2} - b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{2 \, a^{2} b d^{3} \sin\left(d x + c\right)}"," ",0,"-1/2*(2*a*b*d^2*f^2*x^2 + 4*a*b*d^2*e*f*x + 2*a*b*d^2*e^2 + 2*b^2*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*b^2*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*b^2*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*b^2*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*(a^2 - b^2)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 2*(a^2 - b^2)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 2*(a^2 - b^2)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 2*(a^2 - b^2)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - (2*I*(a^2 - b^2)*d*f^2*x + 2*I*(a^2 - b^2)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (2*I*(a^2 - b^2)*d*f^2*x + 2*I*(a^2 - b^2)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (-2*I*(a^2 - b^2)*d*f^2*x - 2*I*(a^2 - b^2)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (-2*I*(a^2 - b^2)*d*f^2*x - 2*I*(a^2 - b^2)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (2*I*b^2*d*f^2*x + 2*I*b^2*d*e*f - 2*I*a*b*f^2)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (-2*I*b^2*d*f^2*x - 2*I*b^2*d*e*f + 2*I*a*b*f^2)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - (-2*I*b^2*d*f^2*x - 2*I*b^2*d*e*f - 2*I*a*b*f^2)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (2*I*b^2*d*f^2*x + 2*I*b^2*d*e*f + 2*I*a*b*f^2)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^2*e^2 - 2*(a^2 - b^2)*c*d*e*f + (a^2 - b^2)*c^2*f^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d^2*f^2*x^2 + 2*(a^2 - b^2)*d^2*e*f*x + 2*(a^2 - b^2)*c*d*e*f - (a^2 - b^2)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c)*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c)*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c))/(a^2*b*d^3*sin(d*x + c))","C",0
339,1,1419,0,2.173487," ","integrate((f*x+e)*cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b d f x - i \, b^{2} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + i \, b^{2} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + i \, b^{2} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - i \, b^{2} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, a b d e - i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + i \, {\left(a^{2} - b^{2}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d e - {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left({\left(a^{2} - b^{2}\right)} d f x + {\left(a^{2} - b^{2}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + {\left(b^{2} d f x + b^{2} d e + a b f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d f x + b^{2} d e + a b f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(b^{2} d f x + b^{2} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(b^{2} d f x + b^{2} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{2 \, a^{2} b d^{2} \sin\left(d x + c\right)}"," ",0,"-1/2*(2*a*b*d*f*x - I*b^2*f*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + I*b^2*f*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + I*b^2*f*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - I*b^2*f*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*a*b*d*e - I*(a^2 - b^2)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - I*(a^2 - b^2)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + I*(a^2 - b^2)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + I*(a^2 - b^2)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d*e - (a^2 - b^2)*c*f)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + ((a^2 - b^2)*d*f*x + (a^2 - b^2)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + (b^2*d*f*x + b^2*d*e + a*b*f)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d*f*x + b^2*d*e + a*b*f)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d*e - (b^2*c + a*b)*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + (b^2*d*e - (b^2*c + a*b)*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + (b^2*d*f*x + b^2*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + (b^2*d*f*x + b^2*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c))/(a^2*b*d^2*sin(d*x + c))","B",0
340,1,69,0,1.388457," ","integrate(cos(d*x+c)*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) + a b}{a^{2} b d \sin\left(d x + c\right)}"," ",0,"-(b^2*log(1/2*sin(d*x + c))*sin(d*x + c) + (a^2 - b^2)*log(b*sin(d*x + c) + a)*sin(d*x + c) + a*b)/(a^2*b*d*sin(d*x + c))","A",0
341,1,4702,0,3.882434," ","integrate((f*x+e)^3*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, a^{2} b d^{2} f^{3} x^{2} + 24 \, a^{2} b d^{2} e f^{2} x + 12 \, a^{2} b d^{2} e^{2} f - 12 i \, b^{3} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 i \, b^{3} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 i \, b^{3} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 i \, b^{3} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 i \, {\left(a^{2} b - b^{3}\right)} f^{3} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 24 \, a^{2} b f^{3} + 2 \, {\left(3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x + 3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(-3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x - 3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(-3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x - 3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f^{2} x + 3 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b - b^{3}\right)} c^{3} f^{3}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 \, {\left({\left(a^{2} b - b^{3}\right)} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d e f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f - 2 \, a^{2} b f^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(6 i \, b^{3} d^{2} f^{3} x^{2} + 6 i \, b^{3} d^{2} e^{2} f - 12 i \, a b^{2} d e f^{2} + 12 i \, {\left(b^{3} d^{2} e f^{2} - a b^{2} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(-6 i \, b^{3} d^{2} f^{3} x^{2} - 6 i \, b^{3} d^{2} e^{2} f + 12 i \, a b^{2} d e f^{2} - 12 i \, {\left(b^{3} d^{2} e f^{2} - a b^{2} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(6 i \, b^{3} d^{2} f^{3} x^{2} + 6 i \, b^{3} d^{2} e^{2} f + 12 i \, a b^{2} d e f^{2} + 12 i \, {\left(b^{3} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(-6 i \, b^{3} d^{2} f^{3} x^{2} - 6 i \, b^{3} d^{2} e^{2} f - 12 i \, a b^{2} d e f^{2} - 12 i \, {\left(b^{3} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + b^{3} d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{2} f + 3 \, {\left(b^{3} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + b^{3} d^{3} e^{3} + 3 \, a b^{2} d^{2} e^{2} f + 3 \, {\left(b^{3} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, {\left(b^{3} c + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} d e f^{2} - {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, {\left(b^{3} c + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} d e f^{2} - {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} c d^{2} e^{2} f - 3 \, {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} d e f^{2} + {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2}\right)} f^{3} + 3 \, {\left(b^{3} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} c d^{2} e^{2} f - 3 \, {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} d e f^{2} + {\left(b^{3} c^{3} + 3 \, a b^{2} c^{2}\right)} f^{3} + 3 \, {\left(b^{3} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} - a b^{2} f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} - a b^{2} f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} + a b^{2} f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} + a b^{2} f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + a b^{2} d^{3} e^{3}\right)} \cos\left(d x + c\right) - {\left(a^{3} d^{4} f^{3} x^{4} + 4 \, a^{3} d^{4} e f^{2} x^{3} + 6 \, a^{3} d^{4} e^{2} f x^{2} + 4 \, a^{3} d^{4} e^{3} x + 4 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + a^{2} b d^{3} e^{3} - 6 \, a^{2} b d e f^{2} + 3 \, {\left(a^{2} b d^{3} e^{2} f - 2 \, a^{2} b d f^{3}\right)} x\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, a^{2} b^{2} d^{4} \sin\left(d x + c\right)}"," ",0,"1/4*(12*a^2*b*d^2*f^3*x^2 + 24*a^2*b*d^2*e*f^2*x + 12*a^2*b*d^2*e^2*f - 12*I*b^3*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 12*I*b^3*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 12*I*b^3*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 12*I*b^3*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 12*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*I*(a^2*b - b^3)*f^3*sqrt(-(a^2 - b^2)/b^2)*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 24*a^2*b*f^3 + 2*(3*I*(a^2*b - b^3)*d^2*f^3*x^2 + 6*I*(a^2*b - b^3)*d^2*e*f^2*x + 3*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(-3*I*(a^2*b - b^3)*d^2*f^3*x^2 - 6*I*(a^2*b - b^3)*d^2*e*f^2*x - 3*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(-3*I*(a^2*b - b^3)*d^2*f^3*x^2 - 6*I*(a^2*b - b^3)*d^2*e*f^2*x - 3*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(3*I*(a^2*b - b^3)*d^2*f^3*x^2 + 6*I*(a^2*b - b^3)*d^2*e*f^2*x + 3*I*(a^2*b - b^3)*d^2*e^2*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 2*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*((a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2 - (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*d^3*e*f^2*x^2 + 3*(a^2*b - b^3)*d^3*e^2*f*x + 3*(a^2*b - b^3)*c*d^2*e^2*f - 3*(a^2*b - b^3)*c^2*d*e*f^2 + (a^2*b - b^3)*c^3*f^3)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*((a^2*b - b^3)*d*f^3*x + (a^2*b - b^3)*d*e*f^2)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f - 2*a^2*b*f^3)*cos(d*x + c)^2 + (6*I*b^3*d^2*f^3*x^2 + 6*I*b^3*d^2*e^2*f - 12*I*a*b^2*d*e*f^2 + 12*I*(b^3*d^2*e*f^2 - a*b^2*d*f^3)*x)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + (-6*I*b^3*d^2*f^3*x^2 - 6*I*b^3*d^2*e^2*f + 12*I*a*b^2*d*e*f^2 - 12*I*(b^3*d^2*e*f^2 - a*b^2*d*f^3)*x)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + (6*I*b^3*d^2*f^3*x^2 + 6*I*b^3*d^2*e^2*f + 12*I*a*b^2*d*e*f^2 + 12*I*(b^3*d^2*e*f^2 + a*b^2*d*f^3)*x)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + (-6*I*b^3*d^2*f^3*x^2 - 6*I*b^3*d^2*e^2*f - 12*I*a*b^2*d*e*f^2 - 12*I*(b^3*d^2*e*f^2 + a*b^2*d*f^3)*x)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*(b^3*d^3*f^3*x^3 + b^3*d^3*e^3 + 3*a*b^2*d^2*e^2*f + 3*(b^3*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 + 3*(b^3*d^3*e^2*f + 2*a*b^2*d^2*e*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*(b^3*d^3*f^3*x^3 + b^3*d^3*e^3 + 3*a*b^2*d^2*e^2*f + 3*(b^3*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 + 3*(b^3*d^3*e^2*f + 2*a*b^2*d^2*e*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 2*(b^3*d^3*e^3 - 3*(b^3*c + a*b^2)*d^2*e^2*f + 3*(b^3*c^2 + 2*a*b^2*c)*d*e*f^2 - (b^3*c^3 + 3*a*b^2*c^2)*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) - 2*(b^3*d^3*e^3 - 3*(b^3*c + a*b^2)*d^2*e^2*f + 3*(b^3*c^2 + 2*a*b^2*c)*d*e*f^2 - (b^3*c^3 + 3*a*b^2*c^2)*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*c*d^2*e^2*f - 3*(b^3*c^2 + 2*a*b^2*c)*d*e*f^2 + (b^3*c^3 + 3*a*b^2*c^2)*f^3 + 3*(b^3*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 3*(b^3*d^3*e^2*f - 2*a*b^2*d^2*e*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*c*d^2*e^2*f - 3*(b^3*c^2 + 2*a*b^2*c)*d*e*f^2 + (b^3*c^3 + 3*a*b^2*c^2)*f^3 + 3*(b^3*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 3*(b^3*d^3*e^2*f - 2*a*b^2*d^2*e*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 12*(b^3*d*f^3*x + b^3*d*e*f^2 - a*b^2*f^3)*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 12*(b^3*d*f^3*x + b^3*d*e*f^2 - a*b^2*f^3)*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 12*(b^3*d*f^3*x + b^3*d*e*f^2 + a*b^2*f^3)*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 12*(b^3*d*f^3*x + b^3*d*e*f^2 + a*b^2*f^3)*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 4*(a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + a*b^2*d^3*e^3)*cos(d*x + c) - (a^3*d^4*f^3*x^4 + 4*a^3*d^4*e*f^2*x^3 + 6*a^3*d^4*e^2*f*x^2 + 4*a^3*d^4*e^3*x + 4*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + a^2*b*d^3*e^3 - 6*a^2*b*d*e*f^2 + 3*(a^2*b*d^3*e^2*f - 2*a^2*b*d*f^3)*x)*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d^4*sin(d*x + c))","C",0
342,1,3071,0,2.502334," ","integrate((f*x+e)^2*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, a^{2} b d f^{2} x - 12 \, b^{3} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 12 \, b^{3} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 \, b^{3} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 12 \, b^{3} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 24 \, a^{2} b d e f + 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 12 \, {\left(a^{2} b - b^{3}\right)} f^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(-6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 \, {\left(6 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 6 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f - {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 24 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cos\left(d x + c\right)^{2} + {\left(12 i \, b^{3} d f^{2} x + 12 i \, b^{3} d e f - 12 i \, a b^{2} f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(-12 i \, b^{3} d f^{2} x - 12 i \, b^{3} d e f + 12 i \, a b^{2} f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(12 i \, b^{3} d f^{2} x + 12 i \, b^{3} d e f + 12 i \, a b^{2} f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(-12 i \, b^{3} d f^{2} x - 12 i \, b^{3} d e f - 12 i \, a b^{2} f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + b^{3} d^{2} e^{2} + 2 \, a b^{2} d e f + 2 \, {\left(b^{3} d^{2} e f + a b^{2} d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + b^{3} d^{2} e^{2} + 2 \, a b^{2} d e f + 2 \, {\left(b^{3} d^{2} e f + a b^{2} d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 6 \, {\left(b^{3} d^{2} e^{2} - 2 \, {\left(b^{3} c + a b^{2}\right)} d e f + {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 6 \, {\left(b^{3} d^{2} e^{2} - 2 \, {\left(b^{3} c + a b^{2}\right)} d e f + {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} c d e f - {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} f^{2} + 2 \, {\left(b^{3} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 6 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} c d e f - {\left(b^{3} c^{2} + 2 \, a b^{2} c\right)} f^{2} + 2 \, {\left(b^{3} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 12 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + a b^{2} d^{2} e^{2}\right)} \cos\left(d x + c\right) - 4 \, {\left(a^{3} d^{3} f^{2} x^{3} + 3 \, a^{3} d^{3} e f x^{2} + 3 \, a^{3} d^{3} e^{2} x + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + a^{2} b d^{2} e^{2} - 2 \, a^{2} b f^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, a^{2} b^{2} d^{3} \sin\left(d x + c\right)}"," ",0,"1/12*(24*a^2*b*d*f^2*x - 12*b^3*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 12*b^3*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 12*b^3*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 12*b^3*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 24*a^2*b*d*e*f + 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 12*(a^2*b - b^3)*f^2*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 2*(6*I*(a^2*b - b^3)*d*f^2*x + 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(-6*I*(a^2*b - b^3)*d*f^2*x - 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(-6*I*(a^2*b - b^3)*d*f^2*x - 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*(6*I*(a^2*b - b^3)*d*f^2*x + 6*I*(a^2*b - b^3)*d*e*f)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 6*((a^2*b - b^3)*d^2*e^2 - 2*(a^2*b - b^3)*c*d*e*f + (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 6*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*d^2*e*f*x + 2*(a^2*b - b^3)*c*d*e*f - (a^2*b - b^3)*c^2*f^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 24*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cos(d*x + c)^2 + (12*I*b^3*d*f^2*x + 12*I*b^3*d*e*f - 12*I*a*b^2*f^2)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + (-12*I*b^3*d*f^2*x - 12*I*b^3*d*e*f + 12*I*a*b^2*f^2)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + (12*I*b^3*d*f^2*x + 12*I*b^3*d*e*f + 12*I*a*b^2*f^2)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + (-12*I*b^3*d*f^2*x - 12*I*b^3*d*e*f - 12*I*a*b^2*f^2)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 6*(b^3*d^2*f^2*x^2 + b^3*d^2*e^2 + 2*a*b^2*d*e*f + 2*(b^3*d^2*e*f + a*b^2*d*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 6*(b^3*d^2*f^2*x^2 + b^3*d^2*e^2 + 2*a*b^2*d*e*f + 2*(b^3*d^2*e*f + a*b^2*d*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 6*(b^3*d^2*e^2 - 2*(b^3*c + a*b^2)*d*e*f + (b^3*c^2 + 2*a*b^2*c)*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) - 6*(b^3*d^2*e^2 - 2*(b^3*c + a*b^2)*d*e*f + (b^3*c^2 + 2*a*b^2*c)*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) - 6*(b^3*d^2*f^2*x^2 + 2*b^3*c*d*e*f - (b^3*c^2 + 2*a*b^2*c)*f^2 + 2*(b^3*d^2*e*f - a*b^2*d*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) - 6*(b^3*d^2*f^2*x^2 + 2*b^3*c*d*e*f - (b^3*c^2 + 2*a*b^2*c)*f^2 + 2*(b^3*d^2*e*f - a*b^2*d*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 12*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + a*b^2*d^2*e^2)*cos(d*x + c) - 4*(a^3*d^3*f^2*x^3 + 3*a^3*d^3*e*f*x^2 + 3*a^3*d^3*e^2*x + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + a^2*b*d^2*e^2 - 2*a^2*b*f^2)*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d^3*sin(d*x + c))","C",0
343,1,1760,0,2.092548," ","integrate((f*x+e)*cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a^{2} b f \cos\left(d x + c\right)^{2} - 2 i \, b^{3} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 i \, b^{3} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 i \, b^{3} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 i \, b^{3} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 i \, {\left(a^{2} b - b^{3}\right)} f \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 4 \, a^{2} b f - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d e - {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} c f\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d f x + b^{3} d e + a b^{2} f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left(b^{3} d f x + b^{3} d e + a b^{2} f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d e - {\left(b^{3} c + a b^{2}\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d e - {\left(b^{3} c + a b^{2}\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(a b^{2} d f x + a b^{2} d e\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{3} d^{2} f x^{2} + 2 \, a^{3} d^{2} e x + 2 \, {\left(a^{2} b d f x + a^{2} b d e\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, a^{2} b^{2} d^{2} \sin\left(d x + c\right)}"," ",0,"-1/4*(4*a^2*b*f*cos(d*x + c)^2 - 2*I*b^3*f*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*I*b^3*f*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 2*I*b^3*f*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*I*b^3*f*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*I*(a^2*b - b^3)*f*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 4*a^2*b*f - 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) + 2*((a^2*b - b^3)*d*e - (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*c*f)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*(b^3*d*f*x + b^3*d*e + a*b^2*f)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) - 2*(b^3*d*f*x + b^3*d*e + a*b^2*f)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 2*(b^3*d*e - (b^3*c + a*b^2)*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*(b^3*d*e - (b^3*c + a*b^2)*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*(b^3*d*f*x + b^3*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*(b^3*d*f*x + b^3*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(a*b^2*d*f*x + a*b^2*d*e)*cos(d*x + c) + 2*(a^3*d^2*f*x^2 + 2*a^3*d^2*e*x + 2*(a^2*b*d*f*x + a^2*b*d*e)*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d^2*sin(d*x + c))","B",0
344,1,396,0,1.854300," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{3} d x + a^{2} b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, a^{2} b^{2} d \sin\left(d x + c\right)}, \frac{b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a b^{2} \cos\left(d x + c\right) - 2 \, {\left(a^{2} - b^{2}\right)}^{\frac{3}{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{3} d x + a^{2} b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, a^{2} b^{2} d \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(b^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a*b^2*cos(d*x + c) - (a^2 - b^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 2*(a^3*d*x + a^2*b*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d*sin(d*x + c)), 1/2*(b^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a*b^2*cos(d*x + c) - 2*(a^2 - b^2)^(3/2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 2*(a^3*d*x + a^2*b*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d*sin(d*x + c))]","A",0
345,1,4916,0,3.771396," ","integrate((f*x+e)^3*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, {\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 24 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} x^{2} + 24 i \, b^{4} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 24 i \, b^{4} f^{3} {\rm polylog}\left(4, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 24 i \, b^{4} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 24 i \, b^{4} f^{3} {\rm polylog}\left(4, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 48 \, a^{3} b d e f^{2} + 8 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} + 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} {\rm polylog}\left(4, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} {\rm polylog}\left(4, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 3 \, {\left(2 \, a^{2} b^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} d^{2} e^{2} f - a^{2} b^{2} f^{3}\right)} \cos\left(d x + c\right)^{3} - 8 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + a^{3} b d^{3} e^{3} - 6 \, a^{3} b d e f^{2} + 3 \, {\left(a^{3} b d^{3} e^{2} f - 2 \, a^{3} b d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} - {\left(-12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(-12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(12 i \, b^{4} d^{2} f^{3} x^{2} + 12 i \, b^{4} d^{2} e^{2} f - 24 i \, a b^{3} d e f^{2} + 24 i \, {\left(b^{4} d^{2} e f^{2} - a b^{3} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-12 i \, b^{4} d^{2} f^{3} x^{2} - 12 i \, b^{4} d^{2} e^{2} f + 24 i \, a b^{3} d e f^{2} - 24 i \, {\left(b^{4} d^{2} e f^{2} - a b^{3} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-12 i \, b^{4} d^{2} f^{3} x^{2} - 12 i \, b^{4} d^{2} e^{2} f - 24 i \, a b^{3} d e f^{2} - 24 i \, {\left(b^{4} d^{2} e f^{2} + a b^{3} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(12 i \, b^{4} d^{2} f^{3} x^{2} + 12 i \, b^{4} d^{2} e^{2} f + 24 i \, a b^{3} d e f^{2} + 24 i \, {\left(b^{4} d^{2} e f^{2} + a b^{3} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{3} f^{3} x^{3} + b^{4} d^{3} e^{3} + 3 \, a b^{3} d^{2} e^{2} f + 3 \, {\left(b^{4} d^{3} e f^{2} + a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e^{2} f + 2 \, a b^{3} d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{3} f^{3} x^{3} + b^{4} d^{3} e^{3} + 3 \, a b^{3} d^{2} e^{2} f + 3 \, {\left(b^{4} d^{3} e f^{2} + a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e^{2} f + 2 \, a b^{3} d^{2} e f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{3} e^{3} - 3 \, {\left(b^{4} c + a b^{3}\right)} d^{2} e^{2} f + 3 \, {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} d e f^{2} - {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{3} e^{3} - 3 \, {\left(b^{4} c + a b^{3}\right)} d^{2} e^{2} f + 3 \, {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} d e f^{2} - {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2}\right)} f^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} c d^{2} e^{2} f - 3 \, {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} d e f^{2} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2}\right)} f^{3} + 3 \, {\left(b^{4} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e^{2} f - 2 \, a b^{3} d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} c d^{2} e^{2} f - 3 \, {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} d e f^{2} + {\left(b^{4} c^{3} + 3 \, a b^{3} c^{2}\right)} f^{3} + 3 \, {\left(b^{4} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{4} d^{3} e^{2} f - 2 \, a b^{3} d^{2} e f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 24 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 24 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 24 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 24 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 24 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2} - a b^{3} f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 24 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2} - a b^{3} f^{3}\right)} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 24 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2} + a b^{3} f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 24 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2} + a b^{3} f^{3}\right)} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 24 \, {\left(2 \, a^{3} b d f^{3} - {\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f\right)} x - 3 \, {\left(2 \, a^{2} b^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} d^{2} e^{2} f - a^{2} b^{2} f^{3}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 6 \, a^{2} b^{2} d^{3} e f^{2} x^{2} + 2 \, a^{2} b^{2} d^{3} e^{3} - 3 \, a^{2} b^{2} d e f^{2} - 2 \, {\left(2 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 6 \, a^{2} b^{2} d^{3} e f^{2} x^{2} + 2 \, a^{2} b^{2} d^{3} e^{3} - 3 \, a^{2} b^{2} d e f^{2} + 3 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - a^{2} b^{2} d f^{3}\right)} x\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - a^{2} b^{2} d f^{3}\right)} x - 24 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f - 2 \, a^{3} b f^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, a^{2} b^{3} d^{4} \sin\left(d x + c\right)}"," ",0,"-1/8*(8*(a^3*b + a*b^3)*d^3*f^3*x^3 + 24*(a^3*b + a*b^3)*d^3*e*f^2*x^2 + 24*I*b^4*f^3*polylog(4, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 24*I*b^4*f^3*polylog(4, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 24*I*b^4*f^3*polylog(4, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 24*I*b^4*f^3*polylog(4, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 48*a^3*b*d*e*f^2 + 8*(a^3*b + a*b^3)*d^3*e^3 + 24*I*(a^4 - 2*a^2*b^2 + b^4)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 24*I*(a^4 - 2*a^2*b^2 + b^4)*f^3*polylog(4, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 24*I*(a^4 - 2*a^2*b^2 + b^4)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 24*I*(a^4 - 2*a^2*b^2 + b^4)*f^3*polylog(4, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 3*(2*a^2*b^2*d^2*f^3*x^2 + 4*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*d^2*e^2*f - a^2*b^2*f^3)*cos(d*x + c)^3 - 8*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + a^3*b*d^3*e^3 - 6*a^3*b*d*e*f^2 + 3*(a^3*b*d^3*e^2*f - 2*a^3*b*d*f^3)*x)*cos(d*x + c)^2 - (-12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*f^3*x^2 - 24*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f^2*x - 12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (-12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*f^3*x^2 - 24*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f^2*x - 12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e^2*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 24*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f^2*x + 12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 24*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f^2*x + 12*I*(a^4 - 2*a^2*b^2 + b^4)*d^2*e^2*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (12*I*b^4*d^2*f^3*x^2 + 12*I*b^4*d^2*e^2*f - 24*I*a*b^3*d*e*f^2 + 24*I*(b^4*d^2*e*f^2 - a*b^3*d*f^3)*x)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (-12*I*b^4*d^2*f^3*x^2 - 12*I*b^4*d^2*e^2*f + 24*I*a*b^3*d*e*f^2 - 24*I*(b^4*d^2*e*f^2 - a*b^3*d*f^3)*x)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - (-12*I*b^4*d^2*f^3*x^2 - 12*I*b^4*d^2*e^2*f - 24*I*a*b^3*d*e*f^2 - 24*I*(b^4*d^2*e*f^2 + a*b^3*d*f^3)*x)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (12*I*b^4*d^2*f^3*x^2 + 12*I*b^4*d^2*e^2*f + 24*I*a*b^3*d*e*f^2 + 24*I*(b^4*d^2*e*f^2 + a*b^3*d*f^3)*x)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 - 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 - 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 - 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 - 2*a^2*b^2 + b^4)*c^3*f^3)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 4*(b^4*d^3*f^3*x^3 + b^4*d^3*e^3 + 3*a*b^3*d^2*e^2*f + 3*(b^4*d^3*e*f^2 + a*b^3*d^2*f^3)*x^2 + 3*(b^4*d^3*e^2*f + 2*a*b^3*d^2*e*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(b^4*d^3*f^3*x^3 + b^4*d^3*e^3 + 3*a*b^3*d^2*e^2*f + 3*(b^4*d^3*e*f^2 + a*b^3*d^2*f^3)*x^2 + 3*(b^4*d^3*e^2*f + 2*a*b^3*d^2*e*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(b^4*d^3*e^3 - 3*(b^4*c + a*b^3)*d^2*e^2*f + 3*(b^4*c^2 + 2*a*b^3*c)*d*e*f^2 - (b^4*c^3 + 3*a*b^3*c^2)*f^3)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 4*(b^4*d^3*e^3 - 3*(b^4*c + a*b^3)*d^2*e^2*f + 3*(b^4*c^2 + 2*a*b^3*c)*d*e*f^2 - (b^4*c^3 + 3*a*b^3*c^2)*f^3)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 4*(b^4*d^3*f^3*x^3 + 3*b^4*c*d^2*e^2*f - 3*(b^4*c^2 + 2*a*b^3*c)*d*e*f^2 + (b^4*c^3 + 3*a*b^3*c^2)*f^3 + 3*(b^4*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(b^4*d^3*e^2*f - 2*a*b^3*d^2*e*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(b^4*d^3*f^3*x^3 + 3*b^4*c*d^2*e^2*f - 3*(b^4*c^2 + 2*a*b^3*c)*d*e*f^2 + (b^4*c^3 + 3*a*b^3*c^2)*f^3 + 3*(b^4*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(b^4*d^3*e^2*f - 2*a*b^3*d^2*e*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 24*((a^4 - 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 - 2*a^2*b^2 + b^4)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 24*((a^4 - 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 - 2*a^2*b^2 + b^4)*d*e*f^2)*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 24*((a^4 - 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 - 2*a^2*b^2 + b^4)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 24*((a^4 - 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 - 2*a^2*b^2 + b^4)*d*e*f^2)*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 24*(b^4*d*f^3*x + b^4*d*e*f^2 - a*b^3*f^3)*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 24*(b^4*d*f^3*x + b^4*d*e*f^2 - a*b^3*f^3)*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 24*(b^4*d*f^3*x + b^4*d*e*f^2 + a*b^3*f^3)*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 24*(b^4*d*f^3*x + b^4*d*e*f^2 + a*b^3*f^3)*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 24*(2*a^3*b*d*f^3 - (a^3*b + a*b^3)*d^3*e^2*f)*x - 3*(2*a^2*b^2*d^2*f^3*x^2 + 4*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*d^2*e^2*f - a^2*b^2*f^3)*cos(d*x + c) - (2*a^2*b^2*d^3*f^3*x^3 + 6*a^2*b^2*d^3*e*f^2*x^2 + 2*a^2*b^2*d^3*e^3 - 3*a^2*b^2*d*e*f^2 - 2*(2*a^2*b^2*d^3*f^3*x^3 + 6*a^2*b^2*d^3*e*f^2*x^2 + 2*a^2*b^2*d^3*e^3 - 3*a^2*b^2*d*e*f^2 + 3*(2*a^2*b^2*d^3*e^2*f - a^2*b^2*d*f^3)*x)*cos(d*x + c)^2 + 3*(2*a^2*b^2*d^3*e^2*f - a^2*b^2*d*f^3)*x - 24*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f - 2*a^3*b*f^3)*cos(d*x + c))*sin(d*x + c))/(a^2*b^3*d^4*sin(d*x + c))","C",0
346,1,3131,0,2.926694," ","integrate((f*x+e)^2*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, b^{4} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 8 \, b^{4} f^{2} {\rm polylog}\left(3, \cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 8 \, b^{4} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 8 \, b^{4} f^{2} {\rm polylog}\left(3, -\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 8 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} - 16 \, a^{3} b f^{2} + 16 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 8 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 8 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 8 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 8 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) - 8 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x + c\right) + a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) \sin\left(d x + c\right) + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} d e f\right)} \cos\left(d x + c\right)^{3} - 8 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + a^{3} b d^{2} e^{2} - 2 \, a^{3} b f^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(-8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x - 8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(-8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x - 8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + 8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + 8 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - {\left(8 i \, b^{4} d f^{2} x + 8 i \, b^{4} d e f - 8 i \, a b^{3} f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-8 i \, b^{4} d f^{2} x - 8 i \, b^{4} d e f + 8 i \, a b^{3} f^{2}\right)} {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(-8 i \, b^{4} d f^{2} x - 8 i \, b^{4} d e f - 8 i \, a b^{3} f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(8 i \, b^{4} d f^{2} x + 8 i \, b^{4} d e f + 8 i \, a b^{3} f^{2}\right)} {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + b^{4} d^{2} e^{2} + 2 \, a b^{3} d e f + 2 \, {\left(b^{4} d^{2} e f + a b^{3} d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + b^{4} d^{2} e^{2} + 2 \, a b^{3} d e f + 2 \, {\left(b^{4} d^{2} e f + a b^{3} d f^{2}\right)} x\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{2} e^{2} - 2 \, {\left(b^{4} c + a b^{3}\right)} d e f + {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{2} e^{2} - 2 \, {\left(b^{4} c + a b^{3}\right)} d e f + {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} c d e f - {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} f^{2} + 2 \, {\left(b^{4} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} c d e f - {\left(b^{4} c^{2} + 2 \, a b^{3} c\right)} f^{2} + 2 \, {\left(b^{4} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} d e f\right)} \cos\left(d x + c\right) - {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 4 \, a^{2} b^{2} d^{2} e f x + 2 \, a^{2} b^{2} d^{2} e^{2} - a^{2} b^{2} f^{2} - 2 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 4 \, a^{2} b^{2} d^{2} e f x + 2 \, a^{2} b^{2} d^{2} e^{2} - a^{2} b^{2} f^{2}\right)} \cos\left(d x + c\right)^{2} - 16 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, a^{2} b^{3} d^{3} \sin\left(d x + c\right)}"," ",0,"-1/8*(8*b^4*f^2*polylog(3, cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 8*b^4*f^2*polylog(3, cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 8*b^4*f^2*polylog(3, -cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 8*b^4*f^2*polylog(3, -cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 8*(a^3*b + a*b^3)*d^2*f^2*x^2 - 16*a^3*b*f^2 + 16*(a^3*b + a*b^3)*d^2*e*f*x + 8*(a^3*b + a*b^3)*d^2*e^2 - 8*(a^4 - 2*a^2*b^2 + b^4)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 8*(a^4 - 2*a^2*b^2 + b^4)*f^2*polylog(3, -(I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 8*(a^4 - 2*a^2*b^2 + b^4)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) - 8*(a^4 - 2*a^2*b^2 + b^4)*f^2*polylog(3, -(-I*a*cos(d*x + c) + a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2))/b)*sin(d*x + c) + 4*(a^2*b^2*d*f^2*x + a^2*b^2*d*e*f)*cos(d*x + c)^3 - 8*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + a^3*b*d^2*e^2 - 2*a^3*b*f^2)*cos(d*x + c)^2 - (-8*I*(a^4 - 2*a^2*b^2 + b^4)*d*f^2*x - 8*I*(a^4 - 2*a^2*b^2 + b^4)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (-8*I*(a^4 - 2*a^2*b^2 + b^4)*d*f^2*x - 8*I*(a^4 - 2*a^2*b^2 + b^4)*d*e*f)*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (8*I*(a^4 - 2*a^2*b^2 + b^4)*d*f^2*x + 8*I*(a^4 - 2*a^2*b^2 + b^4)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (8*I*(a^4 - 2*a^2*b^2 + b^4)*d*f^2*x + 8*I*(a^4 - 2*a^2*b^2 + b^4)*d*e*f)*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - (8*I*b^4*d*f^2*x + 8*I*b^4*d*e*f - 8*I*a*b^3*f^2)*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (-8*I*b^4*d*f^2*x - 8*I*b^4*d*e*f + 8*I*a*b^3*f^2)*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - (-8*I*b^4*d*f^2*x - 8*I*b^4*d*e*f - 8*I*a*b^3*f^2)*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - (8*I*b^4*d*f^2*x + 8*I*b^4*d*e*f + 8*I*a*b^3*f^2)*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 4*((a^4 - 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 - 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 - 2*a^2*b^2 + b^4)*c^2*f^2)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 4*(b^4*d^2*f^2*x^2 + b^4*d^2*e^2 + 2*a*b^3*d*e*f + 2*(b^4*d^2*e*f + a*b^3*d*f^2)*x)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(b^4*d^2*f^2*x^2 + b^4*d^2*e^2 + 2*a*b^3*d*e*f + 2*(b^4*d^2*e*f + a*b^3*d*f^2)*x)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(b^4*d^2*e^2 - 2*(b^4*c + a*b^3)*d*e*f + (b^4*c^2 + 2*a*b^3*c)*f^2)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 4*(b^4*d^2*e^2 - 2*(b^4*c + a*b^3)*d*e*f + (b^4*c^2 + 2*a*b^3*c)*f^2)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 4*(b^4*d^2*f^2*x^2 + 2*b^4*c*d*e*f - (b^4*c^2 + 2*a*b^3*c)*f^2 + 2*(b^4*d^2*e*f - a*b^3*d*f^2)*x)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 4*(b^4*d^2*f^2*x^2 + 2*b^4*c*d*e*f - (b^4*c^2 + 2*a*b^3*c)*f^2 + 2*(b^4*d^2*e*f - a*b^3*d*f^2)*x)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - 4*(a^2*b^2*d*f^2*x + a^2*b^2*d*e*f)*cos(d*x + c) - (2*a^2*b^2*d^2*f^2*x^2 + 4*a^2*b^2*d^2*e*f*x + 2*a^2*b^2*d^2*e^2 - a^2*b^2*f^2 - 2*(2*a^2*b^2*d^2*f^2*x^2 + 4*a^2*b^2*d^2*e*f*x + 2*a^2*b^2*d^2*e^2 - a^2*b^2*f^2)*cos(d*x + c)^2 - 16*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cos(d*x + c))*sin(d*x + c))/(a^2*b^3*d^3*sin(d*x + c))","C",0
347,1,1707,0,1.859054," ","integrate((f*x+e)*cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a^{2} b^{2} f \cos\left(d x + c\right)^{3} - 2 i \, b^{4} f {\rm Li}_2\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 i \, b^{4} f {\rm Li}_2\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 2 i \, b^{4} f {\rm Li}_2\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 2 i \, b^{4} f {\rm Li}_2\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - a^{2} b^{2} f \cos\left(d x + c\right) + 4 \, {\left(a^{3} b + a b^{3}\right)} d f x + 2 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 2 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f {\rm Li}_2\left(\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) - 2 i \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} f {\rm Li}_2\left(\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) \sin\left(d x + c\right) + 4 \, {\left(a^{3} b + a b^{3}\right)} d e - 4 \, {\left(a^{3} b d f x + a^{3} b d e\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) + 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(-2 \, b \cos\left(d x + c\right) - 2 i \, b \sin\left(d x + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(-\frac{i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) + i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) - 2 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \log\left(-\frac{-i \, a \cos\left(d x + c\right) - a \sin\left(d x + c\right) - {\left(b \cos\left(d x + c\right) - i \, b \sin\left(d x + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{4} d f x + b^{4} d e + a b^{3} f\right)} \log\left(\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{4} d f x + b^{4} d e + a b^{3} f\right)} \log\left(\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{4} d e - {\left(b^{4} c + a b^{3}\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{4} d e - {\left(b^{4} c + a b^{3}\right)} f\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) - \frac{1}{2} i \, \sin\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \log\left(-\cos\left(d x + c\right) + i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \log\left(-\cos\left(d x + c\right) - i \, \sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - {\left(a^{2} b^{2} d f x + a^{2} b^{2} d e - 4 \, a^{3} b f \cos\left(d x + c\right) - 2 \, {\left(a^{2} b^{2} d f x + a^{2} b^{2} d e\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, a^{2} b^{3} d^{2} \sin\left(d x + c\right)}"," ",0,"-1/4*(a^2*b^2*f*cos(d*x + c)^3 - 2*I*b^4*f*dilog(cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) + 2*I*b^4*f*dilog(cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) + 2*I*b^4*f*dilog(-cos(d*x + c) + I*sin(d*x + c))*sin(d*x + c) - 2*I*b^4*f*dilog(-cos(d*x + c) - I*sin(d*x + c))*sin(d*x + c) - a^2*b^2*f*cos(d*x + c) + 4*(a^3*b + a*b^3)*d*f*x + 2*I*(a^4 - 2*a^2*b^2 + b^4)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 2*I*(a^4 - 2*a^2*b^2 + b^4)*f*dilog((I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*I*(a^4 - 2*a^2*b^2 + b^4)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) - 2*I*(a^4 - 2*a^2*b^2 + b^4)*f*dilog((-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1)*sin(d*x + c) + 4*(a^3*b + a*b^3)*d*e - 4*(a^3*b*d*f*x + a^3*b*d*e)*cos(d*x + c)^2 - 2*((a^4 - 2*a^2*b^2 + b^4)*d*e - (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*e - (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*e - (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(-2*b*cos(d*x + c) + 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*e - (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(-2*b*cos(d*x + c) - 2*I*b*sin(d*x + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*f*x + (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*f*x + (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(-(I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*f*x + (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) - 2*((a^4 - 2*a^2*b^2 + b^4)*d*f*x + (a^4 - 2*a^2*b^2 + b^4)*c*f)*log(-(-I*a*cos(d*x + c) - a*sin(d*x + c) - (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b)*sin(d*x + c) + 2*(b^4*d*f*x + b^4*d*e + a*b^3*f)*log(cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*(b^4*d*f*x + b^4*d*e + a*b^3*f)*log(cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) + 2*(b^4*d*e - (b^4*c + a*b^3)*f)*log(-1/2*cos(d*x + c) + 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*(b^4*d*e - (b^4*c + a*b^3)*f)*log(-1/2*cos(d*x + c) - 1/2*I*sin(d*x + c) + 1/2)*sin(d*x + c) + 2*(b^4*d*f*x + b^4*c*f)*log(-cos(d*x + c) + I*sin(d*x + c) + 1)*sin(d*x + c) + 2*(b^4*d*f*x + b^4*c*f)*log(-cos(d*x + c) - I*sin(d*x + c) + 1)*sin(d*x + c) - (a^2*b^2*d*f*x + a^2*b^2*d*e - 4*a^3*b*f*cos(d*x + c) - 2*(a^2*b^2*d*f*x + a^2*b^2*d*e)*cos(d*x + c)^2)*sin(d*x + c))/(a^2*b^3*d^2*sin(d*x + c))","B",0
348,1,133,0,0.947655," ","integrate(cos(d*x+c)^3*cot(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a^{3} b \cos\left(d x + c\right)^{2} - 4 \, b^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, a^{3} b - 4 \, a b^{3} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) - {\left(2 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} - a^{2} b^{2}\right)} \sin\left(d x + c\right)}{4 \, a^{2} b^{3} d \sin\left(d x + c\right)}"," ",0,"1/4*(4*a^3*b*cos(d*x + c)^2 - 4*b^4*log(1/2*sin(d*x + c))*sin(d*x + c) - 4*a^3*b - 4*a*b^3 + 4*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)*sin(d*x + c) - (2*a^2*b^2*cos(d*x + c)^2 - a^2*b^2)*sin(d*x + c))/(a^2*b^3*d*sin(d*x + c))","A",0
