1,1,169,0,0.760867," ","integrate((d*x+c)^4*cos(b*x+a),x, algorithm=""fricas"")","\frac{4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + b^{3} c^{3} d - 6 \, b c d^{3} + 3 \, {\left(b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right) + {\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)} \sin\left(b x + a\right)}{b^{5}}"," ",0,"(4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + b^3*c^3*d - 6*b*c*d^3 + 3*(b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a) + (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)*sin(b*x + a))/b^5","A",0
2,1,109,0,0.770239," ","integrate((d*x+c)^3*cos(b*x+a),x, algorithm=""fricas"")","\frac{3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sin\left(b x + a\right)}{b^{4}}"," ",0,"(3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cos(b*x + a) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*sin(b*x + a))/b^4","A",0
3,1,62,0,0.565655," ","integrate((d*x+c)^2*cos(b*x+a),x, algorithm=""fricas"")","\frac{2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{3}}"," ",0,"(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 - 2*d^2)*sin(b*x + a))/b^3","A",0
4,1,28,0,0.863013," ","integrate((d*x+c)*cos(b*x+a),x, algorithm=""fricas"")","\frac{d \cos\left(b x + a\right) + {\left(b d x + b c\right)} \sin\left(b x + a\right)}{b^{2}}"," ",0,"(d*cos(b*x + a) + (b*d*x + b*c)*sin(b*x + a))/b^2","A",0
5,1,78,0,0.757663," ","integrate(cos(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)} \cos\left(-\frac{b c - a d}{d}\right) - 2 \, \sin\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))*cos(-(b*c - a*d)/d) - 2*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
6,1,123,0,0.949482," ","integrate(cos(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b d x + b c\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 2 \, d \cos\left(b x + a\right) + {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*(b*d*x + b*c)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 2*d*cos(b*x + a) + ((b*d*x + b*c)*cos_integral((b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
7,1,209,0,0.664013," ","integrate(cos(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \cos\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \cos\left(-\frac{b c - a d}{d}\right) - 2 \, {\left(b d^{2} x + b c d\right)} \sin\left(b x + a\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*d^2*cos(b*x + a) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) - 2*(b*d^2*x + b*c*d)*sin(b*x + a))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
8,1,295,0,0.859933," ","integrate(cos(b*x+a)/(d*x+c)^4,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(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right) + 2 \, {\left(b d^{3} x + b c d^{2}\right)} \sin\left(b x + a\right) + {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(\frac{b d x + b c}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + b c}{d}\right)\right)} \sin\left(-\frac{b c - a d}{d}\right)}{12 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/12*(2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cos(b*x + a) + 2*(b*d^3*x + b*c*d^2)*sin(b*x + a) + ((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral((b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*cos_integral(-(b*d*x + b*c)/d))*sin(-(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
9,1,287,0,0.780246," ","integrate((d*x+c)^4*cos(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
10,1,190,0,0.919750," ","integrate((d*x+c)^3*cos(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
11,1,113,0,0.603858," ","integrate((d*x+c)^2*cos(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
12,1,53,0,0.823074," ","integrate((d*x+c)*cos(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
13,1,88,0,0.657707," ","integrate(cos(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
14,1,127,0,0.838328," ","integrate(cos(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 \, {\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))/(d^3*x + c*d^2)","A",0
15,1,218,0,0.697362," ","integrate(cos(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) + {\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) + ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-2*(b*d*x + b*c)/d))*cos(-2*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
16,1,350,0,0.881966," ","integrate((d*x+c)^4*cos(b*x+a)^3,x, algorithm=""fricas"")","\frac{12 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d - 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} - 2 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right)^{3} + 72 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d - 20 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} - 20 \, b d^{4}\right)} x\right)} \cos\left(b x + a\right) + {\left(54 \, b^{4} d^{4} x^{4} + 216 \, b^{4} c d^{3} x^{3} + 54 \, b^{4} c^{4} - 720 \, b^{2} c^{2} d^{2} + 1456 \, d^{4} + 36 \, {\left(9 \, b^{4} c^{2} d^{2} - 20 \, b^{2} d^{4}\right)} x^{2} + {\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} - 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} - 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d - 2 \, b^{2} c d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 72 \, {\left(3 \, b^{4} c^{3} d - 20 \, b^{2} c d^{3}\right)} x\right)} \sin\left(b x + a\right)}{81 \, b^{5}}"," ",0,"1/81*(12*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d - 2*b*c*d^3 + (9*b^3*c^2*d^2 - 2*b*d^4)*x)*cos(b*x + a)^3 + 72*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d - 20*b*c*d^3 + (9*b^3*c^2*d^2 - 20*b*d^4)*x)*cos(b*x + a) + (54*b^4*d^4*x^4 + 216*b^4*c*d^3*x^3 + 54*b^4*c^4 - 720*b^2*c^2*d^2 + 1456*d^4 + 36*(9*b^4*c^2*d^2 - 20*b^2*d^4)*x^2 + (27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 - 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 - 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d - 2*b^2*c*d^3)*x)*cos(b*x + a)^2 + 72*(3*b^4*c^3*d - 20*b^2*c*d^3)*x)*sin(b*x + a))/b^5","A",0
17,1,227,0,0.696552," ","integrate((d*x+c)^3*cos(b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 2 \, d^{3}\right)} \cos\left(b x + a\right)^{3} + 6 \, {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d - 20 \, d^{3}\right)} \cos\left(b x + a\right) + 3 \, {\left(6 \, b^{3} d^{3} x^{3} + 18 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{3} - 40 \, b c d^{2} + {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} - 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(9 \, b^{3} c^{2} d - 20 \, b d^{3}\right)} x\right)} \sin\left(b x + a\right)}{27 \, b^{4}}"," ",0,"1/27*((9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 2*d^3)*cos(b*x + a)^3 + 6*(9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 20*d^3)*cos(b*x + a) + 3*(6*b^3*d^3*x^3 + 18*b^3*c*d^2*x^2 + 6*b^3*c^3 - 40*b*c*d^2 + (3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 - 2*b*c*d^2 + (9*b^3*c^2*d - 2*b*d^3)*x)*cos(b*x + a)^2 + 2*(9*b^3*c^2*d - 20*b*d^3)*x)*sin(b*x + a))/b^4","A",0
18,1,128,0,0.724470," ","integrate((d*x+c)^2*cos(b*x+a)^3,x, algorithm=""fricas"")","\frac{6 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{3} + 36 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) + {\left(18 \, b^{2} d^{2} x^{2} + 36 \, b^{2} c d x + 18 \, b^{2} c^{2} + {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} - 2 \, d^{2}\right)} \cos\left(b x + a\right)^{2} - 40 \, d^{2}\right)} \sin\left(b x + a\right)}{27 \, b^{3}}"," ",0,"1/27*(6*(b*d^2*x + b*c*d)*cos(b*x + a)^3 + 36*(b*d^2*x + b*c*d)*cos(b*x + a) + (18*b^2*d^2*x^2 + 36*b^2*c*d*x + 18*b^2*c^2 + (9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 - 2*d^2)*cos(b*x + a)^2 - 40*d^2)*sin(b*x + a))/b^3","A",0
19,1,60,0,0.685162," ","integrate((d*x+c)*cos(b*x+a)^3,x, algorithm=""fricas"")","\frac{d \cos\left(b x + a\right)^{3} + 6 \, d \cos\left(b x + a\right) + 3 \, {\left(2 \, b d x + {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} + 2 \, b c\right)} \sin\left(b x + a\right)}{9 \, b^{2}}"," ",0,"1/9*(d*cos(b*x + a)^3 + 6*d*cos(b*x + a) + 3*(2*b*d*x + (b*d*x + b*c)*cos(b*x + a)^2 + 2*b*c)*sin(b*x + a))/b^2","A",0
20,1,153,0,0.490515," ","integrate(cos(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)} \cos\left(-\frac{b c - a d}{d}\right) + {\left(\operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 6 \, \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right)}{8 \, d}"," ",0,"1/8*(3*(cos_integral((b*d*x + b*c)/d) + cos_integral(-(b*d*x + b*c)/d))*cos(-(b*c - a*d)/d) + (cos_integral(3*(b*d*x + b*c)/d) + cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d) - 2*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 6*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d))/d","A",0
21,1,227,0,0.756611," ","integrate(cos(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{8 \, d \cos\left(b x + a\right)^{3} + 6 \, {\left(b d x + b c\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 6 \, {\left(b d x + b c\right)} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 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)} \sin\left(-\frac{b c - a d}{d}\right) + 3 \, {\left({\left(b d x + b c\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/8*(8*d*cos(b*x + a)^3 + 6*(b*d*x + b*c)*cos(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) + 6*(b*d*x + b*c)*cos(-(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))*sin(-(b*c - a*d)/d) + 3*((b*d*x + b*c)*cos_integral(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*cos_integral(-3*(b*d*x + b*c)/d))*sin(-3*(b*c - a*d)/d))/(d^3*x + c*d^2)","A",0
22,1,375,0,0.751139," ","integrate(cos(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{8 \, d^{2} \cos\left(b x + a\right)^{3} - 24 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) - 18 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 6 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 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)} \cos\left(-\frac{b c - a d}{d}\right) + 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \operatorname{Ci}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/16*(8*d^2*cos(b*x + a)^3 - 24*(b*d^2*x + b*c*d)*cos(b*x + a)^2*sin(b*x + a) - 18*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-3*(b*c - a*d)/d)*sin_integral(3*(b*d*x + b*c)/d) - 6*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(-(b*c - a*d)/d)*sin_integral((b*d*x + b*c)/d) + 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))*cos(-(b*c - a*d)/d) + 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos_integral(-3*(b*d*x + b*c)/d))*cos(-3*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
23,1,115,0,0.615928," ","integrate(x^3*cos(b*x+a)^4,x, algorithm=""fricas"")","\frac{12 \, b^{4} x^{4} + 3 \, {\left(8 \, b^{2} x^{2} - 1\right)} \cos\left(b x + a\right)^{4} - 45 \, b^{2} x^{2} + 9 \, {\left(8 \, b^{2} x^{2} - 5\right)} \cos\left(b x + a\right)^{2} + 2 \, {\left(2 \, {\left(8 \, b^{3} x^{3} - 3 \, b x\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(8 \, b^{3} x^{3} - 15 \, b x\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{128 \, b^{4}}"," ",0,"1/128*(12*b^4*x^4 + 3*(8*b^2*x^2 - 1)*cos(b*x + a)^4 - 45*b^2*x^2 + 9*(8*b^2*x^2 - 5)*cos(b*x + a)^2 + 2*(2*(8*b^3*x^3 - 3*b*x)*cos(b*x + a)^3 + 3*(8*b^3*x^3 - 15*b*x)*cos(b*x + a))*sin(b*x + a))/b^4","A",0
24,1,88,0,0.658287," ","integrate(x^2*cos(b*x+a)^4,x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} + 8 \, b x \cos\left(b x + a\right)^{4} + 24 \, b x \cos\left(b x + a\right)^{2} - 15 \, b x + {\left(2 \, {\left(8 \, b^{2} x^{2} - 1\right)} \cos\left(b x + a\right)^{3} + 3 \, {\left(8 \, b^{2} x^{2} - 5\right)} \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{64 \, b^{3}}"," ",0,"1/64*(8*b^3*x^3 + 8*b*x*cos(b*x + a)^4 + 24*b*x*cos(b*x + a)^2 - 15*b*x + (2*(8*b^2*x^2 - 1)*cos(b*x + a)^3 + 3*(8*b^2*x^2 - 5)*cos(b*x + a))*sin(b*x + a))/b^3","A",0
25,1,63,0,0.859247," ","integrate(x*cos(b*x+a)^4,x, algorithm=""fricas"")","\frac{3 \, b^{2} x^{2} + \cos\left(b x + a\right)^{4} + 3 \, \cos\left(b x + a\right)^{2} + 2 \, {\left(2 \, b x \cos\left(b x + a\right)^{3} + 3 \, b x \cos\left(b x + a\right)\right)} \sin\left(b x + a\right)}{16 \, b^{2}}"," ",0,"1/16*(3*b^2*x^2 + cos(b*x + a)^4 + 3*cos(b*x + a)^2 + 2*(2*b*x*cos(b*x + a)^3 + 3*b*x*cos(b*x + a))*sin(b*x + a))/b^2","A",0
26,1,61,0,0.671296," ","integrate(cos(b*x+a)^4/x,x, algorithm=""fricas"")","\frac{1}{16} \, {\left(\operatorname{Ci}\left(4 \, b x\right) + \operatorname{Ci}\left(-4 \, b x\right)\right)} \cos\left(4 \, a\right) + \frac{1}{4} \, {\left(\operatorname{Ci}\left(2 \, b x\right) + \operatorname{Ci}\left(-2 \, b x\right)\right)} \cos\left(2 \, a\right) - \frac{1}{8} \, \sin\left(4 \, a\right) \operatorname{Si}\left(4 \, b x\right) - \frac{1}{2} \, \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x\right) + \frac{3}{8} \, \log\left(x\right)"," ",0,"1/16*(cos_integral(4*b*x) + cos_integral(-4*b*x))*cos(4*a) + 1/4*(cos_integral(2*b*x) + cos_integral(-2*b*x))*cos(2*a) - 1/8*sin(4*a)*sin_integral(4*b*x) - 1/2*sin(2*a)*sin_integral(2*b*x) + 3/8*log(x)","A",0
27,1,87,0,0.694839," ","integrate(cos(b*x+a)^4/x^2,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(b x + a\right)^{4} + 2 \, b x \cos\left(4 \, a\right) \operatorname{Si}\left(4 \, b x\right) + 4 \, b x \cos\left(2 \, a\right) \operatorname{Si}\left(2 \, b x\right) + {\left(b x \operatorname{Ci}\left(4 \, b x\right) + b x \operatorname{Ci}\left(-4 \, b x\right)\right)} \sin\left(4 \, a\right) + 2 \, {\left(b x \operatorname{Ci}\left(2 \, b x\right) + b x \operatorname{Ci}\left(-2 \, b x\right)\right)} \sin\left(2 \, a\right)}{4 \, x}"," ",0,"-1/4*(4*cos(b*x + a)^4 + 2*b*x*cos(4*a)*sin_integral(4*b*x) + 4*b*x*cos(2*a)*sin_integral(2*b*x) + (b*x*cos_integral(4*b*x) + b*x*cos_integral(-4*b*x))*sin(4*a) + 2*(b*x*cos_integral(2*b*x) + b*x*cos_integral(-2*b*x))*sin(2*a))/x","A",0
28,1,130,0,0.687326," ","integrate(cos(b*x+a)^4/x^3,x, algorithm=""fricas"")","\frac{4 \, b x \cos\left(b x + a\right)^{3} \sin\left(b x + a\right) + 2 \, b^{2} x^{2} \sin\left(4 \, a\right) \operatorname{Si}\left(4 \, b x\right) + 2 \, b^{2} x^{2} \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x\right) - \cos\left(b x + a\right)^{4} - {\left(b^{2} x^{2} \operatorname{Ci}\left(4 \, b x\right) + b^{2} x^{2} \operatorname{Ci}\left(-4 \, b x\right)\right)} \cos\left(4 \, a\right) - {\left(b^{2} x^{2} \operatorname{Ci}\left(2 \, b x\right) + b^{2} x^{2} \operatorname{Ci}\left(-2 \, b x\right)\right)} \cos\left(2 \, a\right)}{2 \, x^{2}}"," ",0,"1/2*(4*b*x*cos(b*x + a)^3*sin(b*x + a) + 2*b^2*x^2*sin(4*a)*sin_integral(4*b*x) + 2*b^2*x^2*sin(2*a)*sin_integral(2*b*x) - cos(b*x + a)^4 - (b^2*x^2*cos_integral(4*b*x) + b^2*x^2*cos_integral(-4*b*x))*cos(4*a) - (b^2*x^2*cos_integral(2*b*x) + b^2*x^2*cos_integral(-2*b*x))*cos(2*a))/x^2","A",0
29,1,966,0,1.025344," ","integrate((d*x+c)^3*sec(b*x+a),x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)}{2 \, b^{4}}"," ",0,"1/2*(6*I*d^3*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)))/b^4","C",0
30,1,598,0,0.897077," ","integrate((d*x+c)^2*sec(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{3}}"," ",0,"-1/2*(2*d^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) + sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(I*cos(b*x + a) - sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^3","C",0
31,1,306,0,0.938884," ","integrate((d*x+c)*sec(b*x+a),x, algorithm=""fricas"")","\frac{-i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b c - a d\right)} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b c - a d\right)} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right)}{2 \, b^{2}}"," ",0,"1/2*(-I*d*dilog(I*cos(b*x + a) + sin(b*x + a)) - I*d*dilog(I*cos(b*x + a) - sin(b*x + a)) + I*d*dilog(-I*cos(b*x + a) + sin(b*x + a)) + I*d*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b*c - a*d)*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b*c - a*d)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b*d*x + a*d)*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b*d*x + a*d)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b*c - a*d)*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b*c - a*d)*log(-cos(b*x + a) - I*sin(b*x + a) + I))/b^2","B",0
32,0,0,0,0.838603," ","integrate(sec(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)/(d*x + c), x)","F",0
33,1,786,0,1.223853," ","integrate((d*x+c)^3*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, d^{3} \cos\left(b x + a\right) {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(b x + a\right)}{2 \, b^{4} \cos\left(b x + a\right)}"," ",0,"1/2*(6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 6*d^3*cos(b*x + a)*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(b*x + a))/(b^4*cos(b*x + a))","C",0
34,1,450,0,0.920203," ","integrate((d*x+c)^2*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d^{2} \cos\left(b x + a\right) {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2}\right)} \cos\left(b x + a\right) \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b c d - a d^{2}\right)} \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(b x + a\right)}{b^{3} \cos\left(b x + a\right)}"," ",0,"(I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) + sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(I*cos(b*x + a) - sin(b*x + a)) - I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) + sin(b*x + a)) + I*d^2*cos(b*x + a)*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b*d^2*x + a*d^2)*cos(b*x + a)*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b*c*d - a*d^2)*cos(b*x + a)*log(-cos(b*x + a) - I*sin(b*x + a) + I) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(b*x + a))/(b^3*cos(b*x + a))","B",0
35,1,45,0,0.678123," ","integrate((d*x+c)*sec(b*x+a)^2,x, algorithm=""fricas"")","\frac{d \cos\left(b x + a\right) \log\left(-\cos\left(b x + a\right)\right) + {\left(b d x + b c\right)} \sin\left(b x + a\right)}{b^{2} \cos\left(b x + a\right)}"," ",0,"(d*cos(b*x + a)*log(-cos(b*x + a)) + (b*d*x + b*c)*sin(b*x + a))/(b^2*cos(b*x + a))","A",0
36,0,0,0,0.780353," ","integrate(sec(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)^2/(d*x + c), x)","F",0
37,1,1311,0,1.014475," ","integrate((d*x+c)^3*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 6 i \, d^{3} \cos\left(b x + a\right)^{2} {\rm polylog}\left(4, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} + 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} + 2\right)} b c d^{2} - {\left(a^{3} + 6 \, a\right)} d^{3}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - 6 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cos\left(b x + a\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \sin\left(b x + a\right)}{4 \, b^{4} \cos\left(b x + a\right)^{2}}"," ",0,"1/4*(6*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) + sin(b*x + a)) + 6*I*d^3*cos(b*x + a)^2*polylog(4, I*cos(b*x + a) - sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) + sin(b*x + a)) - 6*I*d^3*cos(b*x + a)^2*polylog(4, -I*cos(b*x + a) - sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d - 6*I*d^3)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + 6*I*d^3)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 2)*b*c*d^2 - (a^3 + 6*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 2)*b*c*d^2 - (a^3 + 6*a)*d^3)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 6*a)*d^3 + 3*(b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 6*a)*d^3 + 3*(b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 6*a)*d^3 + 3*(b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 + 6*a)*d^3 + 3*(b^3*c^2*d + 2*b*d^3)*x)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 2)*b*c*d^2 - (a^3 + 6*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 + 2)*b*c*d^2 - (a^3 + 6*a)*d^3)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) - 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - 6*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cos(b*x + a) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*sin(b*x + a))/(b^4*cos(b*x + a)^2)","C",0
38,1,795,0,1.239758," ","integrate((d*x+c)^2*sec(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - 2 \, d^{2} \cos\left(b x + a\right)^{2} {\rm polylog}\left(3, -i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} + 2\right)} d^{2}\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + 4 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right) - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \sin\left(b x + a\right)}{4 \, b^{3} \cos\left(b x + a\right)^{2}}"," ",0,"-1/4*(2*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, I*cos(b*x + a) - sin(b*x + a)) + 2*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) + sin(b*x + a)) - 2*d^2*cos(b*x + a)^2*polylog(3, -I*cos(b*x + a) - sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) - (-2*I*b*d^2*x - 2*I*b*c*d)*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) - (2*I*b*d^2*x + 2*I*b*c*d)*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 2)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + (a^2 + 2)*d^2)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + (a^2 + 2)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) + (b^2*c^2 - 2*a*b*c*d + (a^2 + 2)*d^2)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) + 4*(b*d^2*x + b*c*d)*cos(b*x + a) - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*sin(b*x + a))/(b^3*cos(b*x + a)^2)","C",0
39,1,435,0,0.962482," ","integrate((d*x+c)*sec(b*x+a)^3,x, algorithm=""fricas"")","\frac{-i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) - i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right)\right) + i \, d \cos\left(b x + a\right)^{2} {\rm Li}_2\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right)\right) + {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) + \sin\left(b x + a\right) + 1\right) - {\left(b d x + a d\right)} \cos\left(b x + a\right)^{2} \log\left(-i \, \cos\left(b x + a\right) - \sin\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) + i \, \sin\left(b x + a\right) + i\right) - {\left(b c - a d\right)} \cos\left(b x + a\right)^{2} \log\left(-\cos\left(b x + a\right) - i \, \sin\left(b x + a\right) + i\right) - 2 \, d \cos\left(b x + a\right) + 2 \, {\left(b d x + b c\right)} \sin\left(b x + a\right)}{4 \, b^{2} \cos\left(b x + a\right)^{2}}"," ",0,"1/4*(-I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) + sin(b*x + a)) - I*d*cos(b*x + a)^2*dilog(I*cos(b*x + a) - sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) + sin(b*x + a)) + I*d*cos(b*x + a)^2*dilog(-I*cos(b*x + a) - sin(b*x + a)) + (b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) + I*sin(b*x + a) + I) - (b*c - a*d)*cos(b*x + a)^2*log(cos(b*x + a) - I*sin(b*x + a) + I) + (b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*cos(b*x + a)^2*log(I*cos(b*x + a) - sin(b*x + a) + 1) + (b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) + sin(b*x + a) + 1) - (b*d*x + a*d)*cos(b*x + a)^2*log(-I*cos(b*x + a) - sin(b*x + a) + 1) + (b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) + I*sin(b*x + a) + I) - (b*c - a*d)*cos(b*x + a)^2*log(-cos(b*x + a) - I*sin(b*x + a) + I) - 2*d*cos(b*x + a) + 2*(b*d*x + b*c)*sin(b*x + a))/(b^2*cos(b*x + a)^2)","B",0
40,0,0,0,0.776918," ","integrate(sec(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sec\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(sec(b*x + a)^2/(d*x + c), x)","F",0
41,1,190,0,1.071779," ","integrate((d*x+c)^(5/2)*cos(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{S}\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{C}\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(10 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) + {\left(4 \, b^{3} d^{2} x^{2} + 8 \, b^{3} c d x + 4 \, b^{3} c^{2} - 15 \, b d^{2}\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_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 15*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 2*sqrt(d*x + c)*(10*(b^2*d^2*x + b^2*c*d)*cos(b*x + a) + (4*b^3*d^2*x^2 + 8*b^3*c*d*x + 4*b^3*c^2 - 15*b*d^2)*sin(b*x + a)))/b^4","A",0
42,1,156,0,1.713062," ","integrate((d*x+c)^(3/2)*cos(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{C}\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{S}\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 \cos\left(b x + a\right) + 2 \, {\left(b^{2} d x + b^{2} c\right)} \sin\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_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 3*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 2*(3*b*d*cos(b*x + a) + 2*(b^2*d*x + b^2*c)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
43,1,126,0,0.658271," ","integrate((d*x+c)^(1/2)*cos(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{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - 2 \, \sqrt{d x + c} b \sin\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_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - 2*sqrt(d*x + c)*b*sin(b*x + a))/b^2","A",0
44,1,108,0,0.468665," ","integrate(cos(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{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - \sqrt{2} \pi \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)}{b}"," ",0,"(sqrt(2)*pi*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*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d))/b","A",0
45,1,144,0,0.616478," ","integrate(cos(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{S}\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{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} \cos\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_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + sqrt(2)*(pi*d*x + pi*c)*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)*cos(b*x + a))/(d^2*x + c*d)","A",0
46,1,208,0,0.761573," ","integrate(cos(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{C}\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{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(d \cos\left(b x + a\right) - 2 \, {\left(b d x + b c\right)} \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_cos(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_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(d*x + c)*(d*cos(b*x + a) - 2*(b*d*x + b*c)*sin(b*x + a)))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
47,1,296,0,0.664176," ","integrate(cos(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{S}\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{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({\left(4 \, b^{2} d^{2} x^{2} + 8 \, b^{2} c d x + 4 \, b^{2} c^{2} - 3 \, 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)\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_sin(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_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(d*x + c)*((4*b^2*d^2*x^2 + 8*b^2*c*d*x + 4*b^2*c^2 - 3*d^2)*cos(b*x + a) + 2*(b*d^2*x + b*c*d)*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
48,1,258,0,0.620483," ","integrate((d*x+c)^(5/2)*cos(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
49,1,195,0,0.556095," ","integrate((d*x+c)^(3/2)*cos(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
50,1,148,0,0.726215," ","integrate((d*x+c)^(1/2)*cos(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
51,1,114,0,0.503973," ","integrate(cos(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
52,1,136,0,0.548346," ","integrate(cos(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} \cos\left(b x + a\right)^{2}\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)/(d^2*x + c*d)","A",0
53,1,206,0,0.676339," ","integrate(cos(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)\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))*sqrt(d*x + c))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
54,1,323,0,0.818835," ","integrate(cos(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)\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))*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
55,1,417,0,0.710773," ","integrate(cos(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 - {\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 - (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
56,1,368,0,0.696508," ","integrate((d*x+c)^(5/2)*cos(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{S}\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{S}\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{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + 5 \, \sqrt{6} \pi d^{3} \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 24 \, {\left(10 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right)^{3} + 60 \, {\left(b^{2} d^{2} x + b^{2} c d\right)} \cos\left(b x + a\right) + {\left(24 \, b^{3} d^{2} x^{2} + 48 \, b^{3} c d x + 24 \, b^{3} c^{2} - 100 \, b d^{2} + {\left(12 \, b^{3} d^{2} x^{2} + 24 \, b^{3} c d x + 12 \, b^{3} c^{2} - 5 \, b d^{2}\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{864 \, b^{4}}"," ",0,"1/864*(5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 1215*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 1215*sqrt(2)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + 5*sqrt(6)*pi*d^3*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 24*(10*(b^2*d^2*x + b^2*c*d)*cos(b*x + a)^3 + 60*(b^2*d^2*x + b^2*c*d)*cos(b*x + a) + (24*b^3*d^2*x^2 + 48*b^3*c*d*x + 24*b^3*c^2 - 100*b*d^2 + (12*b^3*d^2*x^2 + 24*b^3*c*d*x + 12*b^3*c^2 - 5*b*d^2)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^4","A",0
57,1,299,0,0.566396," ","integrate((d*x+c)^(3/2)*cos(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{C}\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{C}\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{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) - \sqrt{6} \pi d^{2} \sqrt{\frac{b}{\pi d}} \operatorname{S}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(b d \cos\left(b x + a\right)^{3} + 6 \, b d \cos\left(b x + a\right) + 2 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c + {\left(b^{2} d x + b^{2} c\right)} \cos\left(b x + a\right)^{2}\right)} \sin\left(b x + a\right)\right)} \sqrt{d x + c}}{144 \, b^{3}}"," ",0,"-1/144*(sqrt(6)*pi*d^2*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 81*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 81*sqrt(2)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) - sqrt(6)*pi*d^2*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(b*d*cos(b*x + a)^3 + 6*b*d*cos(b*x + a) + 2*(2*b^2*d*x + 2*b^2*c + (b^2*d*x + b^2*c)*cos(b*x + a)^2)*sin(b*x + a))*sqrt(d*x + c))/b^3","A",0
58,1,245,0,0.471261," ","integrate((d*x+c)^(1/2)*cos(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{S}\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{S}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) + 27 \, \sqrt{2} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{b c - a d}{d}\right) + \sqrt{6} \pi d \sqrt{\frac{b}{\pi d}} \operatorname{C}\left(\sqrt{6} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 24 \, {\left(b \cos\left(b x + a\right)^{2} + 2 \, b\right)} \sqrt{d x + c} \sin\left(b x + a\right)}{72 \, b^{2}}"," ",0,"-1/72*(sqrt(6)*pi*d*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 27*sqrt(2)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-(b*c - a*d)/d) + sqrt(6)*pi*d*sqrt(b/(pi*d))*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) - 24*(b*cos(b*x + a)^2 + 2*b)*sqrt(d*x + c)*sin(b*x + a))/b^2","A",0
59,1,213,0,0.641477," ","integrate(cos(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{C}\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{C}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{\pi d}}\right) - 9 \, \sqrt{2} \pi \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 \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)}{12 \, b}"," ",0,"1/12*(sqrt(6)*pi*sqrt(b/(pi*d))*cos(-3*(b*c - a*d)/d)*fresnel_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 9*sqrt(2)*pi*sqrt(b/(pi*d))*cos(-(b*c - a*d)/d)*fresnel_cos(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) - 9*sqrt(2)*pi*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*sqrt(b/(pi*d))*fresnel_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d))/b","A",0
60,1,265,0,0.657512," ","integrate(cos(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{S}\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{S}\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{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} {\left(\pi d x + \pi c\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) + 4 \, \sqrt{d x + c} \cos\left(b x + a\right)^{3}}{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_sin(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_sin(sqrt(2)*sqrt(d*x + c)*sqrt(b/(pi*d))) + 3*sqrt(2)*(pi*d*x + pi*c)*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*x + pi*c)*sqrt(b/(pi*d))*fresnel_cos(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)^3)/(d^2*x + c*d)","A",0
61,1,367,0,0.751307," ","integrate(cos(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{C}\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{C}\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{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 d^{2} x^{2} + 2 \, \pi b c d x + \pi b c^{2}\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) + 2 \, {\left(d \cos\left(b x + a\right)^{3} - 6 \, {\left(b d x + b c\right)} \cos\left(b x + a\right)^{2} \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_cos(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_cos(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_sin(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_sin(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + 2*(d*cos(b*x + a)^3 - 6*(b*d*x + b*c)*cos(b*x + a)^2*sin(b*x + a))*sqrt(d*x + c))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
62,1,528,0,0.675648," ","integrate(cos(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{S}\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{S}\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{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^{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(\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({\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)^{3} + 2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)^{2} \sin\left(b x + a\right) - 8 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cos\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_sin(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_sin(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_cos(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_cos(sqrt(6)*sqrt(d*x + c)*sqrt(b/(pi*d)))*sin(-3*(b*c - a*d)/d) + ((12*b^2*d^2*x^2 + 24*b^2*c*d*x + 12*b^2*c^2 - d^2)*cos(b*x + a)^3 + 2*(b*d^2*x + b*c*d)*cos(b*x + a)^2*sin(b*x + a) - 8*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cos(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
63,1,35,0,0.893811," ","integrate(x^(3/2)*cos(x),x, algorithm=""fricas"")","-\frac{3}{4} \, \sqrt{2} \sqrt{\pi} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) + \frac{1}{2} \, {\left(2 \, x \sin\left(x\right) + 3 \, \cos\left(x\right)\right)} \sqrt{x}"," ",0,"-3/4*sqrt(2)*sqrt(pi)*fresnel_cos(sqrt(2)*sqrt(x)/sqrt(pi)) + 1/2*(2*x*sin(x) + 3*cos(x))*sqrt(x)","A",0
64,1,26,0,0.513801," ","integrate(x^(1/2)*cos(x),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\pi} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) + \sqrt{x} \sin\left(x\right)"," ",0,"-1/2*sqrt(2)*sqrt(pi)*fresnel_sin(sqrt(2)*sqrt(x)/sqrt(pi)) + sqrt(x)*sin(x)","A",0
65,1,18,0,0.628592," ","integrate(cos(x)/x^(1/2),x, algorithm=""fricas"")","\sqrt{2} \sqrt{\pi} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right)"," ",0,"sqrt(2)*sqrt(pi)*fresnel_cos(sqrt(2)*sqrt(x)/sqrt(pi))","A",0
66,1,31,0,0.463140," ","integrate(cos(x)/x^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\sqrt{2} \sqrt{\pi} x \operatorname{S}\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) + \sqrt{x} \cos\left(x\right)\right)}}{x}"," ",0,"-2*(sqrt(2)*sqrt(pi)*x*fresnel_sin(sqrt(2)*sqrt(x)/sqrt(pi)) + sqrt(x)*cos(x))/x","A",0
67,1,132,0,0.845190," ","integrate((d*x+c)^(4/3)*cos(b*x+a),x, algorithm=""fricas"")","\frac{-2 i \, d^{2} \left(\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b d x + i \, b c}{d}\right) + 2 i \, d^{2} \left(-\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{-i \, b d x - i \, b c}{d}\right) + 3 \, {\left(4 \, b d \cos\left(b x + a\right) + 3 \, {\left(b^{2} d x + b^{2} c\right)} \sin\left(b x + a\right)\right)} {\left(d x + c\right)}^{\frac{1}{3}}}{9 \, b^{3}}"," ",0,"1/9*(-2*I*d^2*(I*b/d)^(2/3)*e^((I*b*c - I*a*d)/d)*gamma(1/3, (I*b*d*x + I*b*c)/d) + 2*I*d^2*(-I*b/d)^(2/3)*e^((-I*b*c + I*a*d)/d)*gamma(1/3, (-I*b*d*x - I*b*c)/d) + 3*(4*b*d*cos(b*x + a) + 3*(b^2*d*x + b^2*c)*sin(b*x + a))*(d*x + c)^(1/3))/b^3","A",0
68,1,102,0,0.862060," ","integrate((d*x+c)^(2/3)*cos(b*x+a),x, algorithm=""fricas"")","\frac{d \left(\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b d x + i \, b c}{d}\right) + d \left(-\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{-i \, b d x - i \, b c}{d}\right) + 3 \, {\left(d x + c\right)}^{\frac{2}{3}} b \sin\left(b x + a\right)}{3 \, b^{2}}"," ",0,"1/3*(d*(I*b/d)^(1/3)*e^((I*b*c - I*a*d)/d)*gamma(2/3, (I*b*d*x + I*b*c)/d) + d*(-I*b/d)^(1/3)*e^((-I*b*c + I*a*d)/d)*gamma(2/3, (-I*b*d*x - I*b*c)/d) + 3*(d*x + c)^(2/3)*b*sin(b*x + a))/b^2","A",0
69,1,102,0,1.138289," ","integrate((d*x+c)^(1/3)*cos(b*x+a),x, algorithm=""fricas"")","\frac{d \left(\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b d x + i \, b c}{d}\right) + d \left(-\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{-i \, b d x - i \, b c}{d}\right) + 6 \, {\left(d x + c\right)}^{\frac{1}{3}} b \sin\left(b x + a\right)}{6 \, b^{2}}"," ",0,"1/6*(d*(I*b/d)^(2/3)*e^((I*b*c - I*a*d)/d)*gamma(1/3, (I*b*d*x + I*b*c)/d) + d*(-I*b/d)^(2/3)*e^((-I*b*c + I*a*d)/d)*gamma(1/3, (-I*b*d*x - I*b*c)/d) + 6*(d*x + c)^(1/3)*b*sin(b*x + a))/b^2","A",0
70,1,86,0,0.977171," ","integrate(cos(b*x+a)/(d*x+c)^(1/3),x, algorithm=""fricas"")","\frac{i \, \left(\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b d x + i \, b c}{d}\right) - i \, \left(-\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{-i \, b d x - i \, b c}{d}\right)}{2 \, b}"," ",0,"1/2*(I*(I*b/d)^(1/3)*e^((I*b*c - I*a*d)/d)*gamma(2/3, (I*b*d*x + I*b*c)/d) - I*(-I*b/d)^(1/3)*e^((-I*b*c + I*a*d)/d)*gamma(2/3, (-I*b*d*x - I*b*c)/d))/b","A",0
71,1,86,0,0.609386," ","integrate(cos(b*x+a)/(d*x+c)^(2/3),x, algorithm=""fricas"")","\frac{i \, \left(\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b d x + i \, b c}{d}\right) - i \, \left(-\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{-i \, b d x - i \, b c}{d}\right)}{2 \, b}"," ",0,"1/2*(I*(I*b/d)^(2/3)*e^((I*b*c - I*a*d)/d)*gamma(1/3, (I*b*d*x + I*b*c)/d) - I*(-I*b/d)^(2/3)*e^((-I*b*c + I*a*d)/d)*gamma(1/3, (-I*b*d*x - I*b*c)/d))/b","A",0
72,1,117,0,0.948355," ","integrate(cos(b*x+a)/(d*x+c)^(4/3),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(d x + c\right)} \left(\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b d x + i \, b c}{d}\right) + {\left(d x + c\right)} \left(-\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{-i \, b d x - i \, b c}{d}\right) - 2 \, {\left(d x + c\right)}^{\frac{2}{3}} \cos\left(b x + a\right)\right)}}{2 \, {\left(d^{2} x + c d\right)}}"," ",0,"3/2*((d*x + c)*(I*b/d)^(1/3)*e^((I*b*c - I*a*d)/d)*gamma(2/3, (I*b*d*x + I*b*c)/d) + (d*x + c)*(-I*b/d)^(1/3)*e^((-I*b*c + I*a*d)/d)*gamma(2/3, (-I*b*d*x - I*b*c)/d) - 2*(d*x + c)^(2/3)*cos(b*x + a))/(d^2*x + c*d)","A",0
73,1,117,0,0.904781," ","integrate(cos(b*x+a)/(d*x+c)^(5/3),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(d x + c\right)} \left(\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b d x + i \, b c}{d}\right) + {\left(d x + c\right)} \left(-\frac{i \, b}{d}\right)^{\frac{2}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{1}{3}, \frac{-i \, b d x - i \, b c}{d}\right) - 2 \, {\left(d x + c\right)}^{\frac{1}{3}} \cos\left(b x + a\right)\right)}}{4 \, {\left(d^{2} x + c d\right)}}"," ",0,"3/4*((d*x + c)*(I*b/d)^(2/3)*e^((I*b*c - I*a*d)/d)*gamma(1/3, (I*b*d*x + I*b*c)/d) + (d*x + c)*(-I*b/d)^(2/3)*e^((-I*b*c + I*a*d)/d)*gamma(1/3, (-I*b*d*x - I*b*c)/d) - 2*(d*x + c)^(1/3)*cos(b*x + a))/(d^2*x + c*d)","A",0
74,1,183,0,0.908723," ","integrate(cos(b*x+a)/(d*x+c)^(7/3),x, algorithm=""fricas"")","\frac{{\left(-9 i \, b d^{2} x^{2} - 18 i \, b c d x - 9 i \, b c^{2}\right)} \left(\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{i \, b c - i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b d x + i \, b c}{d}\right) + {\left(9 i \, b d^{2} x^{2} + 18 i \, b c d x + 9 i \, b c^{2}\right)} \left(-\frac{i \, b}{d}\right)^{\frac{1}{3}} e^{\left(\frac{-i \, b c + i \, a d}{d}\right)} \Gamma\left(\frac{2}{3}, \frac{-i \, b d x - i \, b c}{d}\right) - 6 \, {\left(d x + c\right)}^{\frac{2}{3}} {\left(d \cos\left(b x + a\right) - 3 \, {\left(b d x + b c\right)} \sin\left(b x + a\right)\right)}}{8 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)}}"," ",0,"1/8*((-9*I*b*d^2*x^2 - 18*I*b*c*d*x - 9*I*b*c^2)*(I*b/d)^(1/3)*e^((I*b*c - I*a*d)/d)*gamma(2/3, (I*b*d*x + I*b*c)/d) + (9*I*b*d^2*x^2 + 18*I*b*c*d*x + 9*I*b*c^2)*(-I*b/d)^(1/3)*e^((-I*b*c + I*a*d)/d)*gamma(2/3, (-I*b*d*x - I*b*c)/d) - 6*(d*x + c)^(2/3)*(d*cos(b*x + a) - 3*(b*d*x + b*c)*sin(b*x + a)))/(d^4*x^2 + 2*c*d^3*x + c^2*d^2)","A",0
75,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
76,0,0,0,0.622910," ","integrate(cos(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\cos\left(b x + a\right)}, x\right)"," ",0,"integral(sqrt(cos(b*x + a)), x)","F",0
77,-2,0,0,0.000000," ","integrate(cos(b*x+a)^(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
78,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
79,0,0,0,0.642083," ","integrate(cos(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\cos\left(b x + a\right)^{\frac{3}{2}}, x\right)"," ",0,"integral(cos(b*x + a)^(3/2), x)","F",0
80,-2,0,0,0.000000," ","integrate(cos(b*x+a)^(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
81,-2,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2)-1/3*x/cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
82,-2,0,0,0.000000," ","integrate(cos(x)^(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
83,-2,0,0,0.000000," ","integrate(x/cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
84,0,0,0,1.006148," ","integrate(1/cos(b*x+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\cos\left(b x + a\right)}}, x\right)"," ",0,"integral(1/sqrt(cos(b*x + a)), x)","F",0
85,-2,0,0,0.000000," ","integrate(1/x/cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
86,-2,0,0,0.000000," ","integrate(x/cos(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
87,0,0,0,0.918528," ","integrate(1/cos(b*x+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\cos\left(b x + a\right)^{\frac{3}{2}}}, x\right)"," ",0,"integral(cos(b*x + a)^(-3/2), x)","F",0
88,-2,0,0,0.000000," ","integrate(1/x/cos(b*x+a)^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
89,-2,0,0,0.000000," ","integrate(x/cos(b*x+a)^(3/2)+x*cos(b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
90,-2,0,0,0.000000," ","integrate(x/cos(x)^(3/2)+x*cos(x)^(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
91,1,15,0,0.908706," ","integrate(x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x \sin\left(x\right) - 2 \, \cos\left(x\right)\right)}}{3 \, \cos\left(x\right)^{\frac{3}{2}}}"," ",0,"2/3*(x*sin(x) - 2*cos(x))/cos(x)^(3/2)","A",0
92,-2,0,0,0.000000," ","integrate(x/cos(x)^(7/2)+3/5*x*cos(x)^(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^2/cos(x)^(3/2)+x^2*cos(x)^(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/sec(x)^(3/2)-1/3*x*sec(x)^(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,-2,0,0,0.000000," ","integrate(x/sec(x)^(5/2)-3/5*x/sec(x)^(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
96,-2,0,0,0.000000," ","integrate(x/sec(x)^(7/2)-5/21*x*sec(x)^(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
97,-2,0,0,0.000000," ","integrate(x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(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
98,0,0,0,0.657797," ","integrate((d*x+c)^m*(b*cos(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \left(b \cos\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*cos(f*x + e))^n, x)","F",0
99,1,186,0,0.921319," ","integrate((d*x+c)^m*cos(b*x+a)^3,x, algorithm=""fricas"")","\frac{i \, e^{\left(-\frac{d m \log\left(\frac{3 i \, b}{d}\right) - 3 i \, b c + 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{3 i \, b d x + 3 i \, b c}{d}\right) + 9 i \, e^{\left(-\frac{d m \log\left(\frac{i \, b}{d}\right) - i \, b c + i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{i \, b d x + i \, b c}{d}\right) - 9 i \, e^{\left(-\frac{d m \log\left(-\frac{i \, b}{d}\right) + i \, b c - i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-i \, b d x - i \, b c}{d}\right) - i \, e^{\left(-\frac{d m \log\left(-\frac{3 i \, b}{d}\right) + 3 i \, b c - 3 i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{-3 i \, b d x - 3 i \, b c}{d}\right)}{24 \, b}"," ",0,"1/24*(I*e^(-(d*m*log(3*I*b/d) - 3*I*b*c + 3*I*a*d)/d)*gamma(m + 1, (3*I*b*d*x + 3*I*b*c)/d) + 9*I*e^(-(d*m*log(I*b/d) - I*b*c + I*a*d)/d)*gamma(m + 1, (I*b*d*x + I*b*c)/d) - 9*I*e^(-(d*m*log(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d) - I*e^(-(d*m*log(-3*I*b/d) + 3*I*b*c - 3*I*a*d)/d)*gamma(m + 1, (-3*I*b*d*x - 3*I*b*c)/d))/b","A",0
100,1,134,0,1.770964," ","integrate((d*x+c)^m*cos(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
101,1,96,0,1.037491," ","integrate((d*x+c)^m*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-\frac{d m \log\left(\frac{i \, b}{d}\right) - i \, b c + i \, a d}{d}\right)} \Gamma\left(m + 1, \frac{i \, b d x + i \, b c}{d}\right) - i \, e^{\left(-\frac{d m \log\left(-\frac{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*(I*e^(-(d*m*log(I*b/d) - I*b*c + I*a*d)/d)*gamma(m + 1, (I*b*d*x + I*b*c)/d) - I*e^(-(d*m*log(-I*b/d) + I*b*c - I*a*d)/d)*gamma(m + 1, (-I*b*d*x - I*b*c)/d))/b","A",0
102,0,0,0,1.075423," ","integrate((d*x+c)^m*sec(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sec\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*sec(b*x + a), x)","F",0
103,0,0,0,1.138032," ","integrate((d*x+c)^m*sec(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \sec\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*sec(b*x + a)^2, x)","F",0
104,1,54,0,0.532467," ","integrate(x^(3+m)*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-{\left(m + 3\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 4, i \, b x\right) - i \, 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*(I*e^(-(m + 3)*log(I*b) - I*a)*gamma(m + 4, I*b*x) - I*e^(-(m + 3)*log(-I*b) + I*a)*gamma(m + 4, -I*b*x))/b","A",0
105,1,54,0,1.404995," ","integrate(x^(2+m)*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-{\left(m + 2\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 3, i \, b x\right) - i \, 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*(I*e^(-(m + 2)*log(I*b) - I*a)*gamma(m + 3, I*b*x) - I*e^(-(m + 2)*log(-I*b) + I*a)*gamma(m + 3, -I*b*x))/b","A",0
106,1,54,0,0.441937," ","integrate(x^(1+m)*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-{\left(m + 1\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 2, i \, b x\right) - i \, 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*(I*e^(-(m + 1)*log(I*b) - I*a)*gamma(m + 2, I*b*x) - I*e^(-(m + 1)*log(-I*b) + I*a)*gamma(m + 2, -I*b*x))/b","A",0
107,1,50,0,0.758895," ","integrate(x^m*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-m \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 1, i \, b x\right) - i \, e^{\left(-m \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m + 1, -i \, b x\right)}{2 \, b}"," ",0,"1/2*(I*e^(-m*log(I*b) - I*a)*gamma(m + 1, I*b*x) - I*e^(-m*log(-I*b) + I*a)*gamma(m + 1, -I*b*x))/b","A",0
108,1,50,0,0.683038," ","integrate(x^(-1+m)*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-{\left(m - 1\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m, i \, b x\right) - i \, 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*(I*e^(-(m - 1)*log(I*b) - I*a)*gamma(m, I*b*x) - I*e^(-(m - 1)*log(-I*b) + I*a)*gamma(m, -I*b*x))/b","A",0
109,1,54,0,0.703351," ","integrate(x^(-2+m)*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-{\left(m - 2\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m - 1, i \, b x\right) - i \, 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*(I*e^(-(m - 2)*log(I*b) - I*a)*gamma(m - 1, I*b*x) - I*e^(-(m - 2)*log(-I*b) + I*a)*gamma(m - 1, -I*b*x))/b","A",0
110,1,54,0,0.492242," ","integrate(x^(-3+m)*cos(b*x+a),x, algorithm=""fricas"")","\frac{i \, e^{\left(-{\left(m - 3\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m - 2, i \, b x\right) - i \, 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*(I*e^(-(m - 3)*log(I*b) - I*a)*gamma(m - 2, I*b*x) - I*e^(-(m - 3)*log(-I*b) + I*a)*gamma(m - 2, -I*b*x))/b","A",0
111,1,77,0,0.666826," ","integrate(x^(3+m)*cos(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
112,1,77,0,0.628081," ","integrate(x^(2+m)*cos(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
113,1,77,0,0.750461," ","integrate(x^(1+m)*cos(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
114,1,69,0,0.495339," ","integrate(x^m*cos(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
115,1,64,0,0.683091," ","integrate(x^(-1+m)*cos(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
116,1,77,0,1.045903," ","integrate(x^(-2+m)*cos(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
117,1,77,0,0.710191," ","integrate(x^(-3+m)*cos(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
118,1,168,0,0.623418," ","integrate((d*x+c)^3*(a+a*cos(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 + 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)} \cos\left(f x + e\right) + 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)} \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 + 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)*cos(f*x + e) + 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)*sin(f*x + e))/f^4","A",0
119,1,102,0,0.728496," ","integrate((d*x+c)^2*(a+a*cos(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 + 6 \, {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right) + 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)} \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 + 6*(a*d^2*f*x + a*c*d*f)*cos(f*x + e) + 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2 - 2*a*d^2)*sin(f*x + e))/f^3","A",0
120,1,51,0,0.682552," ","integrate((d*x+c)*(a+a*cos(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x + 2 \, a d \cos\left(f x + e\right) + 2 \, {\left(a d f x + a c f\right)} \sin\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*cos(f*x + e) + 2*(a*d*f*x + a*c*f)*sin(f*x + e))/f^2","A",0
121,1,92,0,0.725106," ","integrate((a+a*cos(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{2 \, a \sin\left(-\frac{d e - c f}{d}\right) \operatorname{Si}\left(\frac{d f x + c f}{d}\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)} \cos\left(-\frac{d e - c f}{d}\right) + 2 \, a \log\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(2*a*sin(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + (a*cos_integral((d*f*x + c*f)/d) + a*cos_integral(-(d*f*x + c*f)/d))*cos(-(d*e - c*f)/d) + 2*a*log(d*x + c))/d","A",0
122,1,135,0,0.858267," ","integrate((a+a*cos(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, a d \cos\left(f x + e\right) + 2 \, {\left(a d f x + a c f\right)} \cos\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)} \sin\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*a*d*cos(f*x + e) + 2*(a*d*f*x + a*c*f)*cos(-(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))*sin(-(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
123,1,369,0,0.573219," ","integrate((d*x+c)^3*(a+a*cos(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 + 48 \, {\left(a^{2} d^{3} f^{2} x^{2} + 2 \, a^{2} c d^{2} f^{2} x + a^{2} c^{2} d f^{2} - 2 \, a^{2} d^{3}\right)} \cos\left(f x + e\right) + 2 \, {\left(8 \, a^{2} d^{3} f^{3} x^{3} + 24 \, a^{2} c d^{2} f^{3} x^{2} + 8 \, a^{2} c^{3} f^{3} - 48 \, a^{2} c d^{2} f + 24 \, {\left(a^{2} c^{2} d f^{3} - 2 \, a^{2} d^{3} f\right)} x + {\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 + 48*(a^2*d^3*f^2*x^2 + 2*a^2*c*d^2*f^2*x + a^2*c^2*d*f^2 - 2*a^2*d^3)*cos(f*x + e) + 2*(8*a^2*d^3*f^3*x^3 + 24*a^2*c*d^2*f^3*x^2 + 8*a^2*c^3*f^3 - 48*a^2*c*d^2*f + 24*(a^2*c^2*d*f^3 - 2*a^2*d^3*f)*x + (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
124,1,212,0,0.582655," ","integrate((d*x+c)^2*(a+a*cos(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 + 16 \, {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cos\left(f x + e\right) + {\left(8 \, a^{2} d^{2} f^{2} x^{2} + 16 \, a^{2} c d f^{2} x + 8 \, a^{2} c^{2} f^{2} - 16 \, a^{2} d^{2} + {\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 + 16*(a^2*d^2*f*x + a^2*c*d*f)*cos(f*x + e) + (8*a^2*d^2*f^2*x^2 + 16*a^2*c*d*f^2*x + 8*a^2*c^2*f^2 - 16*a^2*d^2 + (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
125,1,98,0,0.594908," ","integrate((d*x+c)*(a+a*cos(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 \, a^{2} d \cos\left(f x + e\right) + 2 \, {\left(4 \, a^{2} d f x + 4 \, a^{2} c f + {\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*cos(f*x + e) + 2*(4*a^2*d*f*x + 4*a^2*c*f + (a^2*d*f*x + a^2*c*f)*cos(f*x + e))*sin(f*x + e))/f^2","A",0
126,1,186,0,0.583230," ","integrate((a+a*cos(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} \sin\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) + 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)} \cos\left(-\frac{d e - c f}{d}\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 \, 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*sin(-(d*e - c*f)/d)*sin_integral((d*f*x + c*f)/d) + 6*a^2*log(d*x + c) + 4*(a^2*cos_integral((d*f*x + c*f)/d) + a^2*cos_integral(-(d*f*x + c*f)/d))*cos(-(d*e - c*f)/d) + (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))/d","A",0
127,1,284,0,0.688962," ","integrate((a+a*cos(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 \cos\left(f x + e\right) + 2 \, 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)} \cos\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)} \sin\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*cos(f*x + e) + 2*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)*cos(-(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))*sin(-(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
128,1,418,0,0.651526," ","integrate((d*x+c)^3/(a+a*cos(f*x+e)),x, algorithm=""fricas"")","\frac{{\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)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \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)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) + 6 \, {\left(d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) + 6 \, {\left(d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) - i \, \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}}"," ",0,"((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))*dilog(-cos(f*x + e) + I*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))*dilog(-cos(f*x + e) - I*sin(f*x + e)) + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) + 6*(d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) + I*sin(f*x + e)) + 6*(d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) - I*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)","C",0
129,1,222,0,0.658991," ","integrate((d*x+c)^2/(a+a*cos(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 i \, d^{2} \cos\left(f x + e\right) + 2 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) + {\left(-2 i \, d^{2} \cos\left(f x + e\right) - 2 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) + 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) + 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\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}}"," ",0,"((2*I*d^2*cos(f*x + e) + 2*I*d^2)*dilog(-cos(f*x + e) + I*sin(f*x + e)) + (-2*I*d^2*cos(f*x + e) - 2*I*d^2)*dilog(-cos(f*x + e) - I*sin(f*x + e)) + 2*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) + 2*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) + (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)","B",0
130,1,58,0,0.740147," ","integrate((d*x+c)/(a+a*cos(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(d \cos\left(f x + e\right) + d\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\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}}"," ",0,"((d*cos(f*x + e) + d)*log(1/2*cos(f*x + e) + 1/2) + (d*f*x + c*f)*sin(f*x + e))/(a*f^2*cos(f*x + e) + a*f^2)","A",0
131,0,0,0,0.712209," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(a d x + a c\right)} \cos\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (a*d*x + a*c)*cos(f*x + e)), x)","F",0
132,0,0,0,0.653710," ","integrate(1/(d*x+c)^2/(a+a*cos(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)} \cos\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)*cos(f*x + e)), x)","F",0
133,1,769,0,0.660181," ","integrate((d*x+c)^3/(a+a*cos(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, d^{3} f^{2} x^{2} + 6 \, c d^{2} f^{2} x + 3 \, c^{2} d f^{2} + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\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)^{2} + {\left(12 i \, d^{3} f x + 12 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \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)^{2} + {\left(-12 i \, d^{3} f x - 12 i \, c d^{2} f\right)} \cos\left(f x + e\right)\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 2 \, d^{3} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) - 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 2 \, d^{3} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) - 6 \, {\left(d^{3} \cos\left(f x + e\right)^{2} + 2 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) - 6 \, {\left(d^{3} \cos\left(f x + e\right)^{2} + 2 \, d^{3} \cos\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - {\left(2 \, d^{3} f^{3} x^{3} + 6 \, c d^{2} f^{3} x^{2} + 2 \, c^{3} f^{3} + 6 \, c d^{2} f + 6 \, {\left(c^{2} d f^{3} + d^{3} f\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} + 2 \, a^{2} f^{4} \cos\left(f x + e\right) + a^{2} f^{4}\right)}}"," ",0,"-1/3*(3*d^3*f^2*x^2 + 6*c*d^2*f^2*x + 3*c^2*d*f^2 + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*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)^2 + (12*I*d^3*f*x + 12*I*c*d^2*f)*cos(f*x + e))*dilog(-cos(f*x + e) + I*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)^2 + (-12*I*d^3*f*x - 12*I*c*d^2*f)*cos(f*x + e))*dilog(-cos(f*x + e) - I*sin(f*x + e)) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 2*d^3 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 2*d^3)*cos(f*x + e)^2 + 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 2*d^3)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 2*d^3 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 2*d^3)*cos(f*x + e)^2 + 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + 2*d^3)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) - 6*(d^3*cos(f*x + e)^2 + 2*d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) + I*sin(f*x + e)) - 6*(d^3*cos(f*x + e)^2 + 2*d^3*cos(f*x + e) + d^3)*polylog(3, -cos(f*x + e) - I*sin(f*x + e)) - (2*d^3*f^3*x^3 + 6*c*d^2*f^3*x^2 + 2*c^3*f^3 + 6*c*d^2*f + 6*(c^2*d*f^3 + d^3*f)*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 + 2*a^2*f^4*cos(f*x + e) + a^2*f^4)","C",0
134,1,390,0,1.217094," ","integrate((d*x+c)^2/(a+a*cos(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, d^{2} f x + 2 \, c d f + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right) - {\left(2 i \, d^{2} \cos\left(f x + e\right)^{2} + 4 i \, d^{2} \cos\left(f x + e\right) + 2 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) - {\left(-2 i \, d^{2} \cos\left(f x + e\right)^{2} - 4 i \, d^{2} \cos\left(f x + e\right) - 2 i \, d^{2}\right)} {\rm Li}_2\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) - 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) - 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cos\left(f x + e\right)\right)} \log\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) - {\left(2 \, d^{2} f^{2} x^{2} + 4 \, c d f^{2} x + 2 \, c^{2} f^{2} + 2 \, d^{2} + {\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} + 2 \, a^{2} f^{3} \cos\left(f x + e\right) + a^{2} f^{3}\right)}}"," ",0,"-1/3*(2*d^2*f*x + 2*c*d*f + 2*(d^2*f*x + c*d*f)*cos(f*x + e) - (2*I*d^2*cos(f*x + e)^2 + 4*I*d^2*cos(f*x + e) + 2*I*d^2)*dilog(-cos(f*x + e) + I*sin(f*x + e)) - (-2*I*d^2*cos(f*x + e)^2 - 4*I*d^2*cos(f*x + e) - 2*I*d^2)*dilog(-cos(f*x + e) - I*sin(f*x + e)) - 2*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e)^2 + 2*(d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) + I*sin(f*x + e) + 1) - 2*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cos(f*x + e)^2 + 2*(d^2*f*x + c*d*f)*cos(f*x + e))*log(cos(f*x + e) - I*sin(f*x + e) + 1) - (2*d^2*f^2*x^2 + 4*c*d*f^2*x + 2*c^2*f^2 + 2*d^2 + (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 + 2*a^2*f^3*cos(f*x + e) + a^2*f^3)","B",0
135,1,118,0,0.546132," ","integrate((d*x+c)/(a+a*cos(f*x+e))^2,x, algorithm=""fricas"")","-\frac{d \cos\left(f x + e\right) - {\left(d \cos\left(f x + e\right)^{2} + 2 \, d \cos\left(f x + e\right) + d\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) - {\left(2 \, d f x + 2 \, c f + {\left(d f x + c f\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right) + d}{3 \, {\left(a^{2} f^{2} \cos\left(f x + e\right)^{2} + 2 \, a^{2} f^{2} \cos\left(f x + e\right) + a^{2} f^{2}\right)}}"," ",0,"-1/3*(d*cos(f*x + e) - (d*cos(f*x + e)^2 + 2*d*cos(f*x + e) + d)*log(1/2*cos(f*x + e) + 1/2) - (2*d*f*x + 2*c*f + (d*f*x + c*f)*cos(f*x + e))*sin(f*x + e) + d)/(a^2*f^2*cos(f*x + e)^2 + 2*a^2*f^2*cos(f*x + e) + a^2*f^2)","A",0
136,0,0,0,0.622778," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + 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)} \cos\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (a^2*d*x + a^2*c)*cos(f*x + e)^2 + 2*(a^2*d*x + a^2*c)*cos(f*x + e)), x)","F",0
137,0,0,0,1.079236," ","integrate(1/(d*x+c)^2/(a+a*cos(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + 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)} \cos\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + 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)*cos(f*x + e)), x)","F",0
138,1,467,0,0.830938," ","integrate((d*x+c)^3/(a-a*cos(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} - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) \sin\left(f x + e\right) - 6 \, d^{3} {\rm polylog}\left(3, \cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) \sin\left(f x + e\right) - {\left(-6 i \, d^{3} f x - 6 i \, c d^{2} f\right)} {\rm Li}_2\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) \sin\left(f x + e\right) - {\left(6 i \, d^{3} f x + 6 i \, c d^{2} f\right)} {\rm Li}_2\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) \sin\left(f x + e\right) - 3 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2} i \, \sin\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) - 3 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) - \frac{1}{2} i \, \sin\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\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\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) \sin\left(f x + e\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\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) \sin\left(f x + e\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)} \cos\left(f x + e\right)}{a f^{4} \sin\left(f x + e\right)}"," ",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 - 6*d^3*polylog(3, cos(f*x + e) + I*sin(f*x + e))*sin(f*x + e) - 6*d^3*polylog(3, cos(f*x + e) - I*sin(f*x + e))*sin(f*x + e) - (-6*I*d^3*f*x - 6*I*c*d^2*f)*dilog(cos(f*x + e) + I*sin(f*x + e))*sin(f*x + e) - (6*I*d^3*f*x + 6*I*c*d^2*f)*dilog(cos(f*x + e) - I*sin(f*x + e))*sin(f*x + e) - 3*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*log(-1/2*cos(f*x + e) + 1/2*I*sin(f*x + e) + 1/2)*sin(f*x + e) - 3*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*log(-1/2*cos(f*x + e) - 1/2*I*sin(f*x + e) + 1/2)*sin(f*x + e) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*log(-cos(f*x + e) + I*sin(f*x + e) + 1)*sin(f*x + e) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*log(-cos(f*x + e) - I*sin(f*x + e) + 1)*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)*cos(f*x + e))/(a*f^4*sin(f*x + e))","C",0
139,1,283,0,0.647362," ","integrate((d*x+c)^2/(a-a*cos(f*x+e)),x, algorithm=""fricas"")","-\frac{d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2} + 2 i \, d^{2} {\rm Li}_2\left(\cos\left(f x + e\right) + i \, \sin\left(f x + e\right)\right) \sin\left(f x + e\right) - 2 i \, d^{2} {\rm Li}_2\left(\cos\left(f x + e\right) - i \, \sin\left(f x + e\right)\right) \sin\left(f x + e\right) + 2 \, {\left(d^{2} e - c d f\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2} i \, \sin\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) + 2 \, {\left(d^{2} e - c d f\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) - \frac{1}{2} i \, \sin\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) - 2 \, {\left(d^{2} f x + d^{2} e\right)} \log\left(-\cos\left(f x + e\right) + i \, \sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) - 2 \, {\left(d^{2} f x + d^{2} e\right)} \log\left(-\cos\left(f x + e\right) - i \, \sin\left(f x + e\right) + 1\right) \sin\left(f x + e\right) + {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x + c^{2} f^{2}\right)} \cos\left(f x + e\right)}{a f^{3} \sin\left(f x + e\right)}"," ",0,"-(d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2 + 2*I*d^2*dilog(cos(f*x + e) + I*sin(f*x + e))*sin(f*x + e) - 2*I*d^2*dilog(cos(f*x + e) - I*sin(f*x + e))*sin(f*x + e) + 2*(d^2*e - c*d*f)*log(-1/2*cos(f*x + e) + 1/2*I*sin(f*x + e) + 1/2)*sin(f*x + e) + 2*(d^2*e - c*d*f)*log(-1/2*cos(f*x + e) - 1/2*I*sin(f*x + e) + 1/2)*sin(f*x + e) - 2*(d^2*f*x + d^2*e)*log(-cos(f*x + e) + I*sin(f*x + e) + 1)*sin(f*x + e) - 2*(d^2*f*x + d^2*e)*log(-cos(f*x + e) - I*sin(f*x + e) + 1)*sin(f*x + e) + (d^2*f^2*x^2 + 2*c*d*f^2*x + c^2*f^2)*cos(f*x + e))/(a*f^3*sin(f*x + e))","B",0
140,1,59,0,0.569873," ","integrate((d*x+c)/(a-a*cos(f*x+e)),x, algorithm=""fricas"")","-\frac{d f x - d \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) + c f + {\left(d f x + c f\right)} \cos\left(f x + e\right)}{a f^{2} \sin\left(f x + e\right)}"," ",0,"-(d*f*x - d*log(-1/2*cos(f*x + e) + 1/2)*sin(f*x + e) + c*f + (d*f*x + c*f)*cos(f*x + e))/(a*f^2*sin(f*x + e))","A",0
141,0,0,0,0.597098," ","integrate(1/(d*x+c)/(a-a*cos(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c - {\left(a d x + a c\right)} \cos\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c - (a*d*x + a*c)*cos(f*x + e)), x)","F",0
142,0,0,0,0.586406," ","integrate(1/(d*x+c)^2/(a-a*cos(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)} \cos\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)*cos(f*x + e)), x)","F",0
143,-2,0,0,0.000000," ","integrate(x^3*(a+a*cos(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
144,-2,0,0,0.000000," ","integrate(x^2*(a+a*cos(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
145,-2,0,0,0.000000," ","integrate(x*(a+a*cos(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
146,1,32,0,0.762266," ","integrate((a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) + d}"," ",0,"2*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/(d*cos(d*x + c) + d)","A",0
147,-2,0,0,0.000000," ","integrate((a+a*cos(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
148,-2,0,0,0.000000," ","integrate((a+a*cos(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
149,-2,0,0,0.000000," ","integrate((a+a*cos(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
150,-2,0,0,0.000000," ","integrate(x^3*(a+a*cos(x))^(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
151,-2,0,0,0.000000," ","integrate(x^2*(a+a*cos(x))^(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
152,-2,0,0,0.000000," ","integrate(x*(a+a*cos(x))^(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
153,1,18,0,0.676391," ","integrate((a+a*cos(x))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \cos\left(x\right) + a} \sin\left(x\right)}{\cos\left(x\right) + 1}"," ",0,"2*sqrt(a*cos(x) + a)*sin(x)/(cos(x) + 1)","A",0
154,-2,0,0,0.000000," ","integrate((a+a*cos(x))^(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
155,-2,0,0,0.000000," ","integrate((a+a*cos(x))^(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
156,-2,0,0,0.000000," ","integrate((a+a*cos(x))^(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
157,-2,0,0,0.000000," ","integrate(x^3*(a-a*cos(x))^(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
158,-2,0,0,0.000000," ","integrate(x^2*(a-a*cos(x))^(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
159,-2,0,0,0.000000," ","integrate(x*(a-a*cos(x))^(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
160,1,19,0,0.581978," ","integrate((a-a*cos(x))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{-a \cos\left(x\right) + a} {\left(\cos\left(x\right) + 1\right)}}{\sin\left(x\right)}"," ",0,"-2*sqrt(-a*cos(x) + a)*(cos(x) + 1)/sin(x)","A",0
161,-2,0,0,0.000000," ","integrate((a-a*cos(x))^(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
162,-2,0,0,0.000000," ","integrate((a-a*cos(x))^(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
163,-2,0,0,0.000000," ","integrate((a-a*cos(x))^(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
164,-2,0,0,0.000000," ","integrate(x^3*(a+a*cos(x))^(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
165,-2,0,0,0.000000," ","integrate(x^2*(a+a*cos(x))^(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
166,-2,0,0,0.000000," ","integrate(x*(a+a*cos(x))^(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
167,-2,0,0,0.000000," ","integrate((a+a*cos(x))^(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
168,-2,0,0,0.000000," ","integrate((a+a*cos(x))^(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
169,-2,0,0,0.000000," ","integrate((a+a*cos(x))^(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
170,0,0,0,0.557397," ","integrate(x^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{a \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x^3/sqrt(a*cos(d*x + c) + a), x)","F",0
171,0,0,0,0.620089," ","integrate(x^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{a \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x^2/sqrt(a*cos(d*x + c) + a), x)","F",0
172,0,0,0,0.657429," ","integrate(x/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{a \cos\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x/sqrt(a*cos(d*x + c) + a), x)","F",0
173,1,126,0,0.672527," ","integrate(1/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{\cos\left(d x + c\right)^{2} - \frac{2 \, \sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sin\left(d x + c\right)}{\sqrt{a}} - 2 \, \cos\left(d x + c\right) - 3}{\cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 1}\right)}{2 \, \sqrt{a} d}, -\frac{\sqrt{2} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \cos\left(d x + c\right) + a} \sqrt{-\frac{1}{a}}}{\sin\left(d x + c\right)}\right)}{d}\right]"," ",0,"[1/2*sqrt(2)*log(-(cos(d*x + c)^2 - 2*sqrt(2)*sqrt(a*cos(d*x + c) + a)*sin(d*x + c)/sqrt(a) - 2*cos(d*x + c) - 3)/(cos(d*x + c)^2 + 2*cos(d*x + c) + 1))/(sqrt(a)*d), -sqrt(2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt(a*cos(d*x + c) + a)*sqrt(-1/a)/sin(d*x + c))/d]","A",0
174,0,0,0,0.558224," ","integrate(1/x/(a+a*cos(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(d x + c\right) + a}}{a x \cos\left(d x + c\right) + a x}, x\right)"," ",0,"integral(sqrt(a*cos(d*x + c) + a)/(a*x*cos(d*x + c) + a*x), x)","F",0
175,0,0,0,0.723329," ","integrate(x^3/(a-a*cos(x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a \cos\left(x\right) + a} x^{3}}{a \cos\left(x\right) - a}, x\right)"," ",0,"integral(-sqrt(-a*cos(x) + a)*x^3/(a*cos(x) - a), x)","F",0
176,0,0,0,0.548567," ","integrate(x^2/(a-a*cos(x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a \cos\left(x\right) + a} x^{2}}{a \cos\left(x\right) - a}, x\right)"," ",0,"integral(-sqrt(-a*cos(x) + a)*x^2/(a*cos(x) - a), x)","F",0
177,0,0,0,0.804448," ","integrate(x/(a-a*cos(x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a \cos\left(x\right) + a} x}{a \cos\left(x\right) - a}, x\right)"," ",0,"integral(-sqrt(-a*cos(x) + a)*x/(a*cos(x) - a), x)","F",0
178,1,87,0,0.681326," ","integrate(1/(a-a*cos(x))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{{\left(\cos\left(x\right) + 3\right)} \sin\left(x\right) - \frac{2 \, \sqrt{2} \sqrt{-a \cos\left(x\right) + a} {\left(\cos\left(x\right) + 1\right)}}{\sqrt{a}}}{{\left(\cos\left(x\right) - 1\right)} \sin\left(x\right)}\right)}{2 \, \sqrt{a}}, \sqrt{2} \sqrt{-\frac{1}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{-a \cos\left(x\right) + a} \sqrt{-\frac{1}{a}}}{\sin\left(x\right)}\right)\right]"," ",0,"[1/2*sqrt(2)*log(-((cos(x) + 3)*sin(x) - 2*sqrt(2)*sqrt(-a*cos(x) + a)*(cos(x) + 1)/sqrt(a))/((cos(x) - 1)*sin(x)))/sqrt(a), sqrt(2)*sqrt(-1/a)*arctan(sqrt(2)*sqrt(-a*cos(x) + a)*sqrt(-1/a)/sin(x))]","A",0
179,0,0,0,0.945041," ","integrate(1/x/(a-a*cos(x))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-a \cos\left(x\right) + a}}{a x \cos\left(x\right) - a x}, x\right)"," ",0,"integral(-sqrt(-a*cos(x) + a)/(a*x*cos(x) - a*x), x)","F",0
180,0,0,0,0.732399," ","integrate(x^3/(a+a*cos(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(x\right) + a} x^{3}}{a^{2} \cos\left(x\right)^{2} + 2 \, a^{2} \cos\left(x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*cos(x) + a)*x^3/(a^2*cos(x)^2 + 2*a^2*cos(x) + a^2), x)","F",0
181,0,0,0,0.607470," ","integrate(x^2/(a+a*cos(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(x\right) + a} x^{2}}{a^{2} \cos\left(x\right)^{2} + 2 \, a^{2} \cos\left(x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*cos(x) + a)*x^2/(a^2*cos(x)^2 + 2*a^2*cos(x) + a^2), x)","F",0
182,0,0,0,1.605132," ","integrate(x/(a+a*cos(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(x\right) + a} x}{a^{2} \cos\left(x\right)^{2} + 2 \, a^{2} \cos\left(x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*cos(x) + a)*x/(a^2*cos(x)^2 + 2*a^2*cos(x) + a^2), x)","F",0
183,0,0,0,0.561530," ","integrate(1/x/(a+a*cos(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cos\left(x\right) + a}}{a^{2} x \cos\left(x\right)^{2} + 2 \, a^{2} x \cos\left(x\right) + a^{2} x}, x\right)"," ",0,"integral(sqrt(a*cos(x) + a)/(a^2*x*cos(x)^2 + 2*a^2*x*cos(x) + a^2*x), x)","F",0
184,-2,0,0,0.000000," ","integrate((a+a*cos(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
185,1,1074,0,0.748939," ","integrate(x^3/(a+b*cos(x)),x, algorithm=""fricas"")","-\frac{2 i \, b x^{3} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b}\right) - 2 i \, b x^{3} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b}\right) - 2 i \, b x^{3} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b}\right) + 2 i \, b x^{3} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b}\right) + 6 \, b x^{2} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b} + 1\right) - 6 \, b x^{2} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b} + 1\right) + 6 \, b x^{2} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b} + 1\right) - 6 \, b x^{2} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, b}{2 \, b} + 1\right) + 12 i \, b x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) - 12 i \, b x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) - 12 i \, b x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) + 12 i \, b x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) - 12 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) + 12 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{2 \, a \cos\left(x\right) + 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) + i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) - 12 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) + 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right) + 12 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{2 \, a \cos\left(x\right) - 2 i \, a \sin\left(x\right) - 2 \, {\left(b \cos\left(x\right) - i \, b \sin\left(x\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{2 \, b}\right)}{4 \, {\left(a^{2} - b^{2}\right)}}"," ",0,"-1/4*(2*I*b*x^3*sqrt((a^2 - b^2)/b^2)*log(1/2*(2*a*cos(x) + 2*I*a*sin(x) + 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b) - 2*I*b*x^3*sqrt((a^2 - b^2)/b^2)*log(1/2*(2*a*cos(x) + 2*I*a*sin(x) - 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b) - 2*I*b*x^3*sqrt((a^2 - b^2)/b^2)*log(1/2*(2*a*cos(x) - 2*I*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b) + 2*I*b*x^3*sqrt((a^2 - b^2)/b^2)*log(1/2*(2*a*cos(x) - 2*I*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b) + 6*b*x^2*sqrt((a^2 - b^2)/b^2)*dilog(-1/2*(2*a*cos(x) + 2*I*a*sin(x) + 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b + 1) - 6*b*x^2*sqrt((a^2 - b^2)/b^2)*dilog(-1/2*(2*a*cos(x) + 2*I*a*sin(x) - 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b + 1) + 6*b*x^2*sqrt((a^2 - b^2)/b^2)*dilog(-1/2*(2*a*cos(x) - 2*I*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b + 1) - 6*b*x^2*sqrt((a^2 - b^2)/b^2)*dilog(-1/2*(2*a*cos(x) - 2*I*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2) + 2*b)/b + 1) + 12*I*b*x*sqrt((a^2 - b^2)/b^2)*polylog(3, -1/2*(2*a*cos(x) + 2*I*a*sin(x) + 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) - 12*I*b*x*sqrt((a^2 - b^2)/b^2)*polylog(3, -1/2*(2*a*cos(x) + 2*I*a*sin(x) - 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) - 12*I*b*x*sqrt((a^2 - b^2)/b^2)*polylog(3, -1/2*(2*a*cos(x) - 2*I*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) + 12*I*b*x*sqrt((a^2 - b^2)/b^2)*polylog(3, -1/2*(2*a*cos(x) - 2*I*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) - 12*b*sqrt((a^2 - b^2)/b^2)*polylog(4, -1/2*(2*a*cos(x) + 2*I*a*sin(x) + 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) + 12*b*sqrt((a^2 - b^2)/b^2)*polylog(4, -1/2*(2*a*cos(x) + 2*I*a*sin(x) - 2*(b*cos(x) + I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) - 12*b*sqrt((a^2 - b^2)/b^2)*polylog(4, -1/2*(2*a*cos(x) - 2*I*a*sin(x) + 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b) + 12*b*sqrt((a^2 - b^2)/b^2)*polylog(4, -1/2*(2*a*cos(x) - 2*I*a*sin(x) - 2*(b*cos(x) - I*b*sin(x))*sqrt((a^2 - b^2)/b^2))/b))/(a^2 - b^2)","C",0
186,1,1267,0,0.791865," ","integrate(x^2/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, b d x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \cos\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 d x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \cos\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 d x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \cos\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 d x \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \cos\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 c^{2} \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 \, a\right) + 2 i \, b c^{2} \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 \, a\right) - 2 i \, b c^{2} \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 \, a\right) + 2 i \, b c^{2} \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 \, a\right) + 2 \, {\left(i \, b d^{2} x^{2} - i \, b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \cos\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(-i \, b d^{2} x^{2} + i \, b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \cos\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(-i \, b d^{2} x^{2} + i \, b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \cos\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(i \, b d^{2} x^{2} - i \, b c^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \cos\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 i \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \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 i \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \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 i \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \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 i \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \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)} d^{3}}"," ",0,"-1/4*(4*b*d*x*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) + I*a*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*d*x*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) + I*a*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*d*x*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) - I*a*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*d*x*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) - I*a*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*c^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*a) + 2*I*b*c^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*a) - 2*I*b*c^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*a) + 2*I*b*c^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*a) + 2*(I*b*d^2*x^2 - I*b*c^2)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) + I*a*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*(-I*b*d^2*x^2 + I*b*c^2)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) + I*a*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*(-I*b*d^2*x^2 + I*b*c^2)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) - I*a*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*(I*b*d^2*x^2 - I*b*c^2)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) - I*a*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*b*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cos(d*x + c) + I*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*I*b*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cos(d*x + c) + I*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*I*b*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cos(d*x + c) - I*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*I*b*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cos(d*x + c) - I*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)*d^3)","C",0
187,1,917,0,0.957938," ","integrate(x/(a+b*cos(d*x+c)),x, algorithm=""fricas"")","-\frac{2 i \, b c \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 \, a\right) - 2 i \, b c \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 \, a\right) + 2 i \, b c \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 \, a\right) - 2 i \, b c \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 \, a\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \cos\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 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \cos\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 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \cos\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 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \cos\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(i \, b d x + i \, b c\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \cos\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(-i \, b d x - i \, b c\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \cos\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(-i \, b d x - i \, b c\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \cos\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(i \, b d x + i \, b c\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \cos\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^{2}\right)} d^{2}}"," ",0,"-1/4*(2*I*b*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*a) - 2*I*b*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*a) + 2*I*b*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*a) - 2*I*b*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*a) + 2*b*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) + I*a*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*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) + I*a*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*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) - I*a*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*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) - I*a*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*x + I*b*c)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) + I*a*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*(-I*b*d*x - I*b*c)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) + I*a*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*(-I*b*d*x - I*b*c)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) - I*a*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*(I*b*d*x + I*b*c)*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) - I*a*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)","B",0
188,0,0,0,0.628316," ","integrate(1/x/(a+b*cos(x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \cos\left(x\right) + a x}, x\right)"," ",0,"integral(1/(b*x*cos(x) + a*x), x)","F",0
189,1,1482,0,1.592949," ","integrate((f*x+e)/(a+b*cos(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a b^{2} f \cos\left(d x + c\right) + a^{2} b f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \cos\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^{2} f \cos\left(d x + c\right) + a^{2} b f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \cos\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^{2} f \cos\left(d x + c\right) + a^{2} b f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \cos\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^{2} f \cos\left(d x + c\right) + a^{2} b f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \cos\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^{2} b d f x - i \, a^{2} b c f + {\left(-i \, a b^{2} d f x - i \, a b^{2} c f\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) + {\left(b \cos\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(i \, a^{2} b d f x + i \, a^{2} b c f + {\left(i \, a b^{2} d f x + i \, a b^{2} c f\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) + i \, a \sin\left(d x + c\right) - {\left(b \cos\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(i \, a^{2} b d f x + i \, a^{2} b c f + {\left(i \, a b^{2} d f x + i \, a b^{2} c f\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) + {\left(b \cos\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(-i \, a^{2} b d f x - i \, a^{2} b c f + {\left(-i \, a b^{2} d f x - i \, a b^{2} c f\right)} \cos\left(d x + c\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cos\left(d x + c\right) - i \, a \sin\left(d x + c\right) - {\left(b \cos\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 - b^{3}\right)} f \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} f - {\left(i \, a^{2} b d e - i \, a^{2} b c f + {\left(i \, a b^{2} d e - i \, a b^{2} c f\right)} \cos\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 \, a\right) + {\left({\left(a^{2} b - b^{3}\right)} f \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} f - {\left(-i \, a^{2} b d e + i \, a^{2} b c f + {\left(-i \, a b^{2} d e + i \, a b^{2} c f\right)} \cos\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 \, a\right) + {\left({\left(a^{2} b - b^{3}\right)} f \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} f - {\left(i \, a^{2} b d e - i \, a^{2} b c f + {\left(i \, a b^{2} d e - i \, a b^{2} c f\right)} \cos\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 \, a\right) + {\left({\left(a^{2} b - b^{3}\right)} f \cos\left(d x + c\right) + {\left(a^{3} - a b^{2}\right)} f - {\left(-i \, a^{2} b d e + i \, a^{2} b c f + {\left(-i \, a b^{2} d e + i \, a b^{2} c f\right)} \cos\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 \, a\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cos\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2}\right)}}"," ",0,"-1/2*((a*b^2*f*cos(d*x + c) + a^2*b*f)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) + I*a*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^2*f*cos(d*x + c) + a^2*b*f)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) + I*a*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^2*f*cos(d*x + c) + a^2*b*f)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) - I*a*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^2*f*cos(d*x + c) + a^2*b*f)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cos(d*x + c) - I*a*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*d*f*x - I*a^2*b*c*f + (-I*a*b^2*d*f*x - I*a*b^2*c*f)*cos(d*x + c))*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) + I*a*sin(d*x + c) + (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt((a^2 - b^2)/b^2) + b)/b) - (I*a^2*b*d*f*x + I*a^2*b*c*f + (I*a*b^2*d*f*x + I*a*b^2*c*f)*cos(d*x + c))*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) + I*a*sin(d*x + c) - (b*cos(d*x + c) + I*b*sin(d*x + c))*sqrt((a^2 - b^2)/b^2) + b)/b) - (I*a^2*b*d*f*x + I*a^2*b*c*f + (I*a*b^2*d*f*x + I*a*b^2*c*f)*cos(d*x + c))*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) - I*a*sin(d*x + c) + (b*cos(d*x + c) - I*b*sin(d*x + c))*sqrt((a^2 - b^2)/b^2) + b)/b) - (-I*a^2*b*d*f*x - I*a^2*b*c*f + (-I*a*b^2*d*f*x - I*a*b^2*c*f)*cos(d*x + c))*sqrt((a^2 - b^2)/b^2)*log((a*cos(d*x + c) - I*a*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)*f*cos(d*x + c) + (a^3 - a*b^2)*f - (I*a^2*b*d*e - I*a^2*b*c*f + (I*a*b^2*d*e - I*a*b^2*c*f)*cos(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*a) + ((a^2*b - b^3)*f*cos(d*x + c) + (a^3 - a*b^2)*f - (-I*a^2*b*d*e + I*a^2*b*c*f + (-I*a*b^2*d*e + I*a*b^2*c*f)*cos(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*a) + ((a^2*b - b^3)*f*cos(d*x + c) + (a^3 - a*b^2)*f - (I*a^2*b*d*e - I*a^2*b*c*f + (I*a*b^2*d*e - I*a*b^2*c*f)*cos(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*a) + ((a^2*b - b^3)*f*cos(d*x + c) + (a^3 - a*b^2)*f - (-I*a^2*b*d*e + I*a^2*b*c*f + (-I*a*b^2*d*e + I*a*b^2*c*f)*cos(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*a) + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d^2*cos(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d^2)","B",0
