1,1,170,0,0.400769," ","integrate((d*x+c)^4*cos(b*x+a),x, algorithm=""giac"")","\frac{4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d - 6 \, b d^{4} x - 6 \, b c d^{3}\right)} \cos\left(b x + a\right)}{b^{5}} + \frac{{\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} - 12 \, b^{2} d^{4} x^{2} - 24 \, b^{2} c d^{3} x - 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4}\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 + 3*b^3*c^2*d^2*x + b^3*c^3*d - 6*b*d^4*x - 6*b*c*d^3)*cos(b*x + a)/b^5 + (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 - 12*b^2*d^4*x^2 - 24*b^2*c*d^3*x - 12*b^2*c^2*d^2 + 24*d^4)*sin(b*x + a)/b^5","A",0
2,1,110,0,0.470575," ","integrate((d*x+c)^3*cos(b*x+a),x, algorithm=""giac"")","\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)}{b^{4}} + \frac{{\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} - 6 \, b d^{3} x - 6 \, b c d^{2}\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^4 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 - 6*b*d^3*x - 6*b*c*d^2)*sin(b*x + a)/b^4","A",0
3,1,64,0,0.402616," ","integrate((d*x+c)^2*cos(b*x+a),x, algorithm=""giac"")","\frac{2 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)}{b^{3}} + \frac{{\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \sin\left(b x + a\right)}{b^{3}}"," ",0,"2*(b*d^2*x + b*c*d)*cos(b*x + a)/b^3 + (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
4,1,30,0,0.432330," ","integrate((d*x+c)*cos(b*x+a),x, algorithm=""giac"")","\frac{d \cos\left(b x + a\right)}{b^{2}} + \frac{{\left(b d x + b c\right)} \sin\left(b x + a\right)}{b^{2}}"," ",0,"d*cos(b*x + a)/b^2 + (b*d*x + b*c)*sin(b*x + a)/b^2","A",0
5,1,577,0,0.636117," ","integrate(cos(b*x+a)/(d*x+c),x, algorithm=""giac"")","\frac{\Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 4 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 2 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 4 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) + 2 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right) + \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) + \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right)}{2 \, {\left(d \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{1}{2} \, a\right)^{2} + d \tan\left(\frac{b c}{2 \, d}\right)^{2} + d\right)}}"," ",0,"1/2*(real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 4*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d)^2 - real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 - real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 + 4*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 4*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 - real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 4*sin_integral((b*d*x + b*c)/d)*tan(1/2*a) + 2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 4*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d) + real_part(cos_integral(b*x + b*c/d)) + real_part(cos_integral(-b*x - b*c/d)))/(d*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d*tan(1/2*a)^2 + d*tan(1/2*b*c/d)^2 + d)","C",0
6,1,523,0,0.466644," ","integrate(cos(b*x+a)/(d*x+c)^2,x, algorithm=""giac"")","-\frac{{\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \operatorname{Ci}\left(\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) \sin\left(-\frac{b c - a d}{d}\right) + b^{3} c \operatorname{Ci}\left(\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) \sin\left(-\frac{b c - a d}{d}\right) - a b^{2} d \operatorname{Ci}\left(\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) \sin\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) - b^{3} c \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) + a b^{2} d \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) + b^{2} d \cos\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)}}{d}\right)\right)} d^{2}}{{\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} d^{4} + b c d^{4} - a d^{5}\right)} b}"," ",0,"-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos_integral(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-(b*c - a*d)/d) + b^3*c*cos_integral(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-(b*c - a*d)/d) - a*b^2*d*cos_integral(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-(b*c - a*d)/d) - (d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos(-(b*c - a*d)/d)*sin_integral(-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) - b^3*c*cos(-(b*c - a*d)/d)*sin_integral(-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + a*b^2*d*cos(-(b*c - a*d)/d)*sin_integral(-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + b^2*d*cos(-(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))/d))*d^2/(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*d^4 + b*c*d^4 - a*d^5)*b)","B",0
7,1,5518,0,1.114816," ","integrate(cos(b*x+a)/(d*x+c)^3,x, algorithm=""giac"")","-\frac{b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b d^{2} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b d^{2} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b c d \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b c d \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, d^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) + 4 \, b d^{2} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b d^{2} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b d^{2} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b d^{2} x \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) + 4 \, b c d \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 4 \, b c d \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, d^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b c d \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, d^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b c d \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 8 \, d^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, d^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) - 4 \, b d^{2} x \tan\left(\frac{1}{2} \, b x\right) - 4 \, b d^{2} x \tan\left(\frac{1}{2} \, a\right) - 4 \, b c d \tan\left(\frac{1}{2} \, b x\right) - 2 \, d^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} - 4 \, b c d \tan\left(\frac{1}{2} \, a\right) - 8 \, d^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, d^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, d^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, d^{2}}{4 \, {\left(d^{5} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{5} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + d^{5} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{5} x^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + c^{2} d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{5} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} + d^{5} x^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + c^{2} d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + d^{5} x^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + c^{2} d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + c^{2} d^{3} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{5} x^{2} + c^{2} d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} + c^{2} d^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + c^{2} d^{3} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + 4*b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 4*b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a) - 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d) - 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d)^2 + 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 + b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 - 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a) - b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 - b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 - b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 4*b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 4*b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 4*b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 4*b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d) - b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 - b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 + 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b*d^2*x*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 4*b*d^2*x*tan(1/2*b*x)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 + 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a) - 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a) - 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 - 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 + 2*b^2*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 2*b^2*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 4*b^2*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d) + 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d) - 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 - 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 + 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b*c*d*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*b*c*d*tan(1/2*b*x)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*d^2*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(b*x + b*c/d)) + b^2*d^2*x^2*real_part(cos_integral(-b*x - b*c/d)) + b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 + b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 - 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*a) + 4*b*d^2*x*tan(1/2*b*x)^2*tan(1/2*a) - b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 - b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 + 4*b*d^2*x*tan(1/2*b*x)*tan(1/2*a)^2 + 4*b^2*c*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 8*b^2*c*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d) + 4*b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 4*b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - b^2*c^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 - b^2*c^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - 4*b*d^2*x*tan(1/2*b*x)*tan(1/2*b*c/d)^2 - 4*b*d^2*x*tan(1/2*a)*tan(1/2*b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(b*x + b*c/d)) + 2*b^2*c*d*x*real_part(cos_integral(-b*x - b*c/d)) - 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a) + 4*b*c*d*tan(1/2*b*x)^2*tan(1/2*a) + 4*b*c*d*tan(1/2*b*x)*tan(1/2*a)^2 + 2*d^2*tan(1/2*b*x)^2*tan(1/2*a)^2 + 2*b^2*c^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 2*b^2*c^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 4*b^2*c^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d) - 4*b*c*d*tan(1/2*b*x)*tan(1/2*b*c/d)^2 - 2*d^2*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 4*b*c*d*tan(1/2*a)*tan(1/2*b*c/d)^2 - 8*d^2*tan(1/2*b*x)*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*d^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^2*c^2*real_part(cos_integral(b*x + b*c/d)) + b^2*c^2*real_part(cos_integral(-b*x - b*c/d)) - 4*b*d^2*x*tan(1/2*b*x) - 4*b*d^2*x*tan(1/2*a) - 4*b*c*d*tan(1/2*b*x) - 2*d^2*tan(1/2*b*x)^2 - 4*b*c*d*tan(1/2*a) - 8*d^2*tan(1/2*b*x)*tan(1/2*a) - 2*d^2*tan(1/2*a)^2 + 2*d^2*tan(1/2*b*c/d)^2 + 2*d^2)/(d^5*x^2*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*c*d^4*x*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d^5*x^2*tan(1/2*b*x)^2*tan(1/2*a)^2 + d^5*x^2*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + d^5*x^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + c^2*d^3*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*c*d^4*x*tan(1/2*b*x)^2*tan(1/2*a)^2 + 2*c*d^4*x*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 2*c*d^4*x*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d^5*x^2*tan(1/2*b*x)^2 + d^5*x^2*tan(1/2*a)^2 + c^2*d^3*tan(1/2*b*x)^2*tan(1/2*a)^2 + d^5*x^2*tan(1/2*b*c/d)^2 + c^2*d^3*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + c^2*d^3*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*c*d^4*x*tan(1/2*b*x)^2 + 2*c*d^4*x*tan(1/2*a)^2 + 2*c*d^4*x*tan(1/2*b*c/d)^2 + d^5*x^2 + c^2*d^3*tan(1/2*b*x)^2 + c^2*d^3*tan(1/2*a)^2 + c^2*d^3*tan(1/2*b*c/d)^2 + 2*c*d^4*x + c^2*d^3)","C",0
8,1,8378,0,1.464545," ","integrate(cos(b*x+a)/(d*x+c)^4,x, algorithm=""giac"")","\frac{b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 12 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 24 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 12 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 12 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 24 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{3} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 12 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 24 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 8 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) - b^{3} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) + 2 \, b^{3} d^{3} x^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 6 \, b^{3} c d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 12 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 24 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 16 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b d^{3} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b d^{3} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) - 3 \, b^{3} c d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) + 6 \, b^{3} c d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 8 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 6 \, b^{3} c^{2} d x \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) - 4 \, b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 8 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 2 \, b^{2} d^{3} x^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 8 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b c d^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, b c d^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) - 3 \, b^{3} c^{2} d x \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) + 6 \, b^{3} c^{2} d x \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 4 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, b x\right)^{2} + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 16 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 4 \, b d^{3} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 4 \, b^{2} c d^{2} x \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, b d^{3} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 2 \, b^{3} c^{3} \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 4 \, b^{2} c d^{2} x \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b d^{3} x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b d^{3} x \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, b^{2} d^{3} x^{2} + b^{3} c^{3} \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) - b^{3} c^{3} \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) + 2 \, b^{3} c^{3} \operatorname{Si}\left(\frac{b d x + b c}{d}\right) - 2 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, b x\right)^{2} - 8 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 4 \, b c d^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 2 \, b^{2} c^{2} d \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, b c d^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, b^{2} c^{2} d \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b c d^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b c d^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 16 \, d^{3} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, d^{3} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, b^{2} c d^{2} x + 4 \, b d^{3} x \tan\left(\frac{1}{2} \, b x\right) + 4 \, b d^{3} x \tan\left(\frac{1}{2} \, a\right) + 2 \, b^{2} c^{2} d + 4 \, b c d^{2} \tan\left(\frac{1}{2} \, b x\right) + 4 \, d^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} + 4 \, b c d^{2} \tan\left(\frac{1}{2} \, a\right) + 16 \, d^{3} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) + 4 \, d^{3} \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, d^{3} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, d^{3}}{12 \, {\left(d^{7} x^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{7} x^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + d^{7} x^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{7} x^{3} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c^{2} d^{5} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + c^{3} d^{4} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{7} x^{3} \tan\left(\frac{1}{2} \, b x\right)^{2} + d^{7} x^{3} \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, c^{2} d^{5} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + d^{7} x^{3} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c^{2} d^{5} x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c^{2} d^{5} x \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + c^{3} d^{4} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, c d^{6} x^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + c^{3} d^{4} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + c^{3} d^{4} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d^{7} x^{3} + 3 \, c^{2} d^{5} x \tan\left(\frac{1}{2} \, b x\right)^{2} + 3 \, c^{2} d^{5} x \tan\left(\frac{1}{2} \, a\right)^{2} + 3 \, c^{2} d^{5} x \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c d^{6} x^{2} + c^{3} d^{4} \tan\left(\frac{1}{2} \, b x\right)^{2} + c^{3} d^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + c^{3} d^{4} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/12*(b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2 + 4*b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 4*b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 8*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 12*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 12*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 24*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^2*d^3*x^2*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 - b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 + 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2 + 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 + b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 - 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2 - 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2 - 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 4*b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - 4*b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 8*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d) + 12*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 12*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 24*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 + b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d)^2 - 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 4*b^2*c*d^2*x*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 - 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 + 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2 + 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) + 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 - 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2 + 2*b^2*d^3*x^2*tan(1/2*b*x)^2*tan(1/2*a)^2 - b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 + b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)^2 - 2*b^3*d^3*x^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 2*b^3*d^3*x^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) - 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 12*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - 12*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 24*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d) + 4*b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) - 4*b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 8*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d) + 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d)^2 - 2*b^2*d^3*x^2*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 8*b^2*d^3*x^2*tan(1/2*b*x)*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^2*d^3*x^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*b^2*c^2*d*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + b^3*d^3*x^3*imag_part(cos_integral(b*x + b*c/d)) - b^3*d^3*x^3*imag_part(cos_integral(-b*x - b*c/d)) + 2*b^3*d^3*x^3*sin_integral((b*d*x + b*c)/d) + 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 - 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 + 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2 + 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) + 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) + 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*a) - 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 - 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2 + 4*b^2*c*d^2*x*tan(1/2*b*x)^2*tan(1/2*a)^2 - 6*b^3*c*d^2*x^2*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 6*b^3*c*d^2*x^2*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) - 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) - 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2*tan(1/2*b*c/d) + 12*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - 12*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 24*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d) + 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d)^2 - 4*b^2*c*d^2*x*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 16*b^2*c*d^2*x*tan(1/2*b*x)*tan(1/2*a)*tan(1/2*b*c/d)^2 - 4*b*d^3*x*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 4*b^2*c*d^2*x*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 4*b*d^3*x*tan(1/2*b*x)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*b^3*c*d^2*x^2*imag_part(cos_integral(b*x + b*c/d)) - 3*b^3*c*d^2*x^2*imag_part(cos_integral(-b*x - b*c/d)) + 6*b^3*c*d^2*x^2*sin_integral((b*d*x + b*c)/d) - 2*b^2*d^3*x^2*tan(1/2*b*x)^2 + b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*x)^2 - b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*x)^2 + 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*x)^2 + 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 8*b^2*d^3*x^2*tan(1/2*b*x)*tan(1/2*a) - 2*b^2*d^3*x^2*tan(1/2*a)^2 - b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 + b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 - 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2 + 2*b^2*c^2*d*tan(1/2*b*x)^2*tan(1/2*a)^2 - 6*b^3*c^2*d*x*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 6*b^3*c^2*d*x*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 4*b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) - 4*b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 8*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d) + 2*b^2*d^3*x^2*tan(1/2*b*c/d)^2 - b^3*c^3*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 + b^3*c^3*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 - 2*b^3*c^3*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d)^2 - 2*b^2*c^2*d*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 - 8*b^2*c^2*d*tan(1/2*b*x)*tan(1/2*a)*tan(1/2*b*c/d)^2 - 4*b*c*d^2*tan(1/2*b*x)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*b^2*c^2*d*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 4*b*c*d^2*tan(1/2*b*x)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 4*d^3*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*b^3*c^2*d*x*imag_part(cos_integral(b*x + b*c/d)) - 3*b^3*c^2*d*x*imag_part(cos_integral(-b*x - b*c/d)) + 6*b^3*c^2*d*x*sin_integral((b*d*x + b*c)/d) - 4*b^2*c*d^2*x*tan(1/2*b*x)^2 + 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 16*b^2*c*d^2*x*tan(1/2*b*x)*tan(1/2*a) - 4*b*d^3*x*tan(1/2*b*x)^2*tan(1/2*a) - 4*b^2*c*d^2*x*tan(1/2*a)^2 - 4*b*d^3*x*tan(1/2*b*x)*tan(1/2*a)^2 - 2*b^3*c^3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 2*b^3*c^3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 4*b^2*c*d^2*x*tan(1/2*b*c/d)^2 + 4*b*d^3*x*tan(1/2*b*x)*tan(1/2*b*c/d)^2 + 4*b*d^3*x*tan(1/2*a)*tan(1/2*b*c/d)^2 + 2*b^2*d^3*x^2 + b^3*c^3*imag_part(cos_integral(b*x + b*c/d)) - b^3*c^3*imag_part(cos_integral(-b*x - b*c/d)) + 2*b^3*c^3*sin_integral((b*d*x + b*c)/d) - 2*b^2*c^2*d*tan(1/2*b*x)^2 - 8*b^2*c^2*d*tan(1/2*b*x)*tan(1/2*a) - 4*b*c*d^2*tan(1/2*b*x)^2*tan(1/2*a) - 2*b^2*c^2*d*tan(1/2*a)^2 - 4*b*c*d^2*tan(1/2*b*x)*tan(1/2*a)^2 - 4*d^3*tan(1/2*b*x)^2*tan(1/2*a)^2 + 2*b^2*c^2*d*tan(1/2*b*c/d)^2 + 4*b*c*d^2*tan(1/2*b*x)*tan(1/2*b*c/d)^2 + 4*d^3*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 4*b*c*d^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 16*d^3*tan(1/2*b*x)*tan(1/2*a)*tan(1/2*b*c/d)^2 + 4*d^3*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 4*b^2*c*d^2*x + 4*b*d^3*x*tan(1/2*b*x) + 4*b*d^3*x*tan(1/2*a) + 2*b^2*c^2*d + 4*b*c*d^2*tan(1/2*b*x) + 4*d^3*tan(1/2*b*x)^2 + 4*b*c*d^2*tan(1/2*a) + 16*d^3*tan(1/2*b*x)*tan(1/2*a) + 4*d^3*tan(1/2*a)^2 - 4*d^3*tan(1/2*b*c/d)^2 - 4*d^3)/(d^7*x^3*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*c*d^6*x^2*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d^7*x^3*tan(1/2*b*x)^2*tan(1/2*a)^2 + d^7*x^3*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + d^7*x^3*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*c^2*d^5*x*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*c*d^6*x^2*tan(1/2*b*x)^2*tan(1/2*a)^2 + 3*c*d^6*x^2*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 3*c*d^6*x^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + c^3*d^4*tan(1/2*b*x)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d^7*x^3*tan(1/2*b*x)^2 + d^7*x^3*tan(1/2*a)^2 + 3*c^2*d^5*x*tan(1/2*b*x)^2*tan(1/2*a)^2 + d^7*x^3*tan(1/2*b*c/d)^2 + 3*c^2*d^5*x*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + 3*c^2*d^5*x*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*c*d^6*x^2*tan(1/2*b*x)^2 + 3*c*d^6*x^2*tan(1/2*a)^2 + c^3*d^4*tan(1/2*b*x)^2*tan(1/2*a)^2 + 3*c*d^6*x^2*tan(1/2*b*c/d)^2 + c^3*d^4*tan(1/2*b*x)^2*tan(1/2*b*c/d)^2 + c^3*d^4*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d^7*x^3 + 3*c^2*d^5*x*tan(1/2*b*x)^2 + 3*c^2*d^5*x*tan(1/2*a)^2 + 3*c^2*d^5*x*tan(1/2*b*c/d)^2 + 3*c*d^6*x^2 + c^3*d^4*tan(1/2*b*x)^2 + c^3*d^4*tan(1/2*a)^2 + c^3*d^4*tan(1/2*b*c/d)^2 + 3*c^2*d^5*x + c^3*d^4)","C",0
9,1,222,0,0.531630," ","integrate((d*x+c)^4*cos(b*x+a)^2,x, algorithm=""giac"")","\frac{1}{10} \, d^{4} x^{5} + \frac{1}{2} \, c d^{3} x^{4} + c^{2} d^{2} x^{3} + c^{3} d x^{2} + \frac{1}{2} \, c^{4} x + \frac{{\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 6 \, b^{3} c^{2} d^{2} x + 2 \, b^{3} c^{3} d - 3 \, b d^{4} x - 3 \, b c d^{3}\right)} \cos\left(2 \, b x + 2 \, a\right)}{4 \, b^{5}} + \frac{{\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 12 \, b^{4} c^{2} d^{2} x^{2} + 8 \, b^{4} c^{3} d x + 2 \, b^{4} c^{4} - 6 \, b^{2} d^{4} x^{2} - 12 \, b^{2} c d^{3} x - 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4}\right)} \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{5}}"," ",0,"1/10*d^4*x^5 + 1/2*c*d^3*x^4 + c^2*d^2*x^3 + c^3*d*x^2 + 1/2*c^4*x + 1/4*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 6*b^3*c^2*d^2*x + 2*b^3*c^3*d - 3*b*d^4*x - 3*b*c*d^3)*cos(2*b*x + 2*a)/b^5 + 1/8*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 12*b^4*c^2*d^2*x^2 + 8*b^4*c^3*d*x + 2*b^4*c^4 - 6*b^2*d^4*x^2 - 12*b^2*c*d^3*x - 6*b^2*c^2*d^2 + 3*d^4)*sin(2*b*x + 2*a)/b^5","A",0
10,1,153,0,0.421720," ","integrate((d*x+c)^3*cos(b*x+a)^2,x, algorithm=""giac"")","\frac{1}{8} \, d^{3} x^{4} + \frac{1}{2} \, c d^{2} x^{3} + \frac{3}{4} \, c^{2} d x^{2} + \frac{1}{2} \, c^{3} x + \frac{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(2 \, b x + 2 \, a\right)}{16 \, b^{4}} + \frac{{\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 6 \, b^{3} c^{2} d x + 2 \, b^{3} c^{3} - 3 \, b d^{3} x - 3 \, b c d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{4}}"," ",0,"1/8*d^3*x^4 + 1/2*c*d^2*x^3 + 3/4*c^2*d*x^2 + 1/2*c^3*x + 3/16*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d - d^3)*cos(2*b*x + 2*a)/b^4 + 1/8*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 6*b^3*c^2*d*x + 2*b^3*c^3 - 3*b*d^3*x - 3*b*c*d^2)*sin(2*b*x + 2*a)/b^4","A",0
11,1,94,0,0.527920," ","integrate((d*x+c)^2*cos(b*x+a)^2,x, algorithm=""giac"")","\frac{1}{6} \, d^{2} x^{3} + \frac{1}{2} \, c d x^{2} + \frac{1}{2} \, c^{2} x + \frac{{\left(b d^{2} x + b c d\right)} \cos\left(2 \, b x + 2 \, a\right)}{4 \, b^{3}} + \frac{{\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} - d^{2}\right)} \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{3}}"," ",0,"1/6*d^2*x^3 + 1/2*c*d*x^2 + 1/2*c^2*x + 1/4*(b*d^2*x + b*c*d)*cos(2*b*x + 2*a)/b^3 + 1/8*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 - d^2)*sin(2*b*x + 2*a)/b^3","A",0
12,1,48,0,0.567915," ","integrate((d*x+c)*cos(b*x+a)^2,x, algorithm=""giac"")","\frac{1}{4} \, d x^{2} + \frac{1}{2} \, c x + \frac{d \cos\left(2 \, b x + 2 \, a\right)}{8 \, b^{2}} + \frac{{\left(b d x + b c\right)} \sin\left(2 \, b x + 2 \, a\right)}{4 \, b^{2}}"," ",0,"1/4*d*x^2 + 1/2*c*x + 1/8*d*cos(2*b*x + 2*a)/b^2 + 1/4*(b*d*x + b*c)*sin(2*b*x + 2*a)/b^2","A",0
13,1,610,0,0.627522," ","integrate(cos(b*x+a)^2/(d*x+c),x, algorithm=""giac"")","\frac{2 \, \log\left({\left| d x + c \right|}\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 4 \, \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, \log\left({\left| d x + c \right|}\right) \tan\left(a\right)^{2} - \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} - \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 4 \, \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 2 \, \log\left({\left| d x + c \right|}\right) \tan\left(\frac{b c}{d}\right)^{2} - \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) + 2 \, \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) - 4 \, \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) + 2 \, \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) - 2 \, \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) + 4 \, \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{b c}{d}\right) + 2 \, \log\left({\left| d x + c \right|}\right) + \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) + \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right)}{4 \, {\left(d \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + d \tan\left(a\right)^{2} + d \tan\left(\frac{b c}{d}\right)^{2} + d\right)}}"," ",0,"1/4*(2*log(abs(d*x + c))*tan(a)^2*tan(b*c/d)^2 + real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 - 2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d) + 2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d) - 4*sin_integral(2*(b*d*x + b*c)/d)*tan(a)^2*tan(b*c/d) + 2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d)^2 - 2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d)^2 + 4*sin_integral(2*(b*d*x + b*c)/d)*tan(a)*tan(b*c/d)^2 + 2*log(abs(d*x + c))*tan(a)^2 - real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2 - real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2 + 4*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d) + 4*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d) + 2*log(abs(d*x + c))*tan(b*c/d)^2 - real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d)^2 - real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d)^2 - 2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a) + 2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a) - 4*sin_integral(2*(b*d*x + b*c)/d)*tan(a) + 2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d) - 2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d) + 4*sin_integral(2*(b*d*x + b*c)/d)*tan(b*c/d) + 2*log(abs(d*x + c)) + real_part(cos_integral(2*b*x + 2*b*c/d)) + real_part(cos_integral(-2*b*x - 2*b*c/d)))/(d*tan(a)^2*tan(b*c/d)^2 + d*tan(a)^2 + d*tan(b*c/d)^2 + d)","C",0
14,1,534,0,0.841800," ","integrate(cos(b*x+a)^2/(d*x+c)^2,x, algorithm=""giac"")","-\frac{{\left(2 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \operatorname{Ci}\left(\frac{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, b^{3} c \operatorname{Ci}\left(\frac{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, a b^{2} d \operatorname{Ci}\left(\frac{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) \sin\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) - 2 \, b^{3} c \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) + 2 \, a b^{2} d \cos\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) + b^{2} d \cos\left(-\frac{2 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)}}{d}\right) + b^{2} d\right)} d^{2}}{2 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} d^{4} + b c d^{4} - a d^{5}\right)} b}"," ",0,"-1/2*(2*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos_integral(2*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-2*(b*c - a*d)/d) + 2*b^3*c*cos_integral(2*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-2*(b*c - a*d)/d) - 2*a*b^2*d*cos_integral(2*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-2*(b*c - a*d)/d) - 2*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos(-2*(b*c - a*d)/d)*sin_integral(-2*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) - 2*b^3*c*cos(-2*(b*c - a*d)/d)*sin_integral(-2*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + 2*a*b^2*d*cos(-2*(b*c - a*d)/d)*sin_integral(-2*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + b^2*d*cos(-2*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))/d) + b^2*d)*d^2/(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*d^4 + b*c*d^4 - a*d^5)*b)","B",0
15,1,5136,0,1.350070," ","integrate(cos(b*x+a)^2/(d*x+c)^3,x, algorithm=""giac"")","-\frac{b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right) - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b d^{2} x \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b d^{2} x \tan\left(b x\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) - 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(a\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{b c}{d}\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 8 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b c d \tan\left(b x\right)^{2} \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b c d \tan\left(b x\right) \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + d^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) + b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(b x\right)^{2} - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) - 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) + 2 \, b d^{2} x \tan\left(b x\right)^{2} \tan\left(a\right) - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right)^{2} + 2 \, b d^{2} x \tan\left(b x\right) \tan\left(a\right)^{2} + 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) - 4 \, b^{2} c d x \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) + 8 \, b^{2} c d x \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right) - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b d^{2} x \tan\left(b x\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b d^{2} x \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) + 2 \, b^{2} c d x \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(a\right) - 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(a\right) + 2 \, b c d \tan\left(b x\right)^{2} \tan\left(a\right) + 2 \, b c d \tan\left(b x\right) \tan\left(a\right)^{2} + d^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) - 2 \, b^{2} c^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) \tan\left(\frac{b c}{d}\right) + 4 \, b^{2} c^{2} \operatorname{Si}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{b c}{d}\right) - 2 \, b c d \tan\left(b x\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, b c d \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} - 2 \, d^{2} \tan\left(b x\right) \tan\left(a\right) \tan\left(\frac{b c}{d}\right)^{2} + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(2 \, b x + \frac{2 \, b c}{d}\right) \right) + b^{2} c^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x - \frac{2 \, b c}{d}\right) \right) - 2 \, b d^{2} x \tan\left(b x\right) - 2 \, b d^{2} x \tan\left(a\right) - 2 \, b c d \tan\left(b x\right) - 2 \, b c d \tan\left(a\right) - 2 \, d^{2} \tan\left(b x\right) \tan\left(a\right) + d^{2} \tan\left(\frac{b c}{d}\right)^{2} + d^{2}}{2 \, {\left(d^{5} x^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, c d^{4} x \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + d^{5} x^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + d^{5} x^{2} \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + d^{5} x^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + c^{2} d^{3} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, c d^{4} x \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, c d^{4} x \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, c d^{4} x \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + d^{5} x^{2} \tan\left(b x\right)^{2} + d^{5} x^{2} \tan\left(a\right)^{2} + c^{2} d^{3} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + d^{5} x^{2} \tan\left(\frac{b c}{d}\right)^{2} + c^{2} d^{3} \tan\left(b x\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + c^{2} d^{3} \tan\left(a\right)^{2} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, c d^{4} x \tan\left(b x\right)^{2} + 2 \, c d^{4} x \tan\left(a\right)^{2} + 2 \, c d^{4} x \tan\left(\frac{b c}{d}\right)^{2} + d^{5} x^{2} + c^{2} d^{3} \tan\left(b x\right)^{2} + c^{2} d^{3} \tan\left(a\right)^{2} + c^{2} d^{3} \tan\left(\frac{b c}{d}\right)^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/2*(b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d) + 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d) - 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a)^2*tan(b*c/d) + 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 - b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2 - b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2 + 4*b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d) + 4*b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d) + 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d) - 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a)^2*tan(b*c/d) - b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(b*c/d)^2 - b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(b*c/d)^2 + 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d)^2 - 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a) + 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a) - 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a) - 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2 - 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2 + 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(b*c/d) - 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(b*c/d) + 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d) - 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d) + 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d) - 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(a)^2*tan(b*c/d) - 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d) + 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2*tan(b*c/d) - 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a)^2*tan(b*c/d) - 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(b*c/d)^2 - 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(b*c/d)^2 + 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d)^2 + 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(a)*tan(b*c/d)^2 + 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d)^2 - 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2 + b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2 - 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a) + 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a) - 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a) - b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2 - b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2 - b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)^2 - b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)^2 + 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(b*c/d) + 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(b*c/d) + 4*b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d) + 4*b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d) + 4*b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d) + 4*b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a)*tan(b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d) + 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d) - 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(a)^2*tan(b*c/d) - b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d)^2 - b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d)^2 - b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(b*c/d)^2 - b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(b*c/d)^2 + 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d)^2 - 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d)^2 + 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(a)*tan(b*c/d)^2 + 2*b*d^2*x*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d)^2 + 2*b*d^2*x*tan(b*x)*tan(a)^2*tan(b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2 + 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2 - 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a) + 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a) - 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(a) - 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(a) + 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(a) - 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(a) - 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2 - 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2 + 2*b^2*d^2*x^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d) - 2*b^2*d^2*x^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d) + 4*b^2*d^2*x^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*c/d) + 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2*tan(b*c/d) - 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2*tan(b*c/d) + 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*x)^2*tan(b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d) + 8*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d) - 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2*tan(b*c/d) + 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2*tan(b*c/d) - 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(a)^2*tan(b*c/d) - 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d)^2 - 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d)^2 + 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d)^2 - 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d)^2 + 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(a)*tan(b*c/d)^2 + 2*b*c*d*tan(b*x)^2*tan(a)*tan(b*c/d)^2 + 2*b*c*d*tan(b*x)*tan(a)^2*tan(b*c/d)^2 + d^2*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + b^2*d^2*x^2*real_part(cos_integral(2*b*x + 2*b*c/d)) + b^2*d^2*x^2*real_part(cos_integral(-2*b*x - 2*b*c/d)) + b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*x)^2 + b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*x)^2 - 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a) + 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a) - 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(a) + 2*b*d^2*x*tan(b*x)^2*tan(a) - b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)^2 - b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)^2 + 2*b*d^2*x*tan(b*x)*tan(a)^2 + 4*b^2*c*d*x*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d) - 4*b^2*c*d*x*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d) + 8*b^2*c*d*x*sin_integral(2*(b*d*x + b*c)/d)*tan(b*c/d) + 4*b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(a)*tan(b*c/d) + 4*b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a)*tan(b*c/d) - b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d)^2 - b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d)^2 - 2*b*d^2*x*tan(b*x)*tan(b*c/d)^2 - 2*b*d^2*x*tan(a)*tan(b*c/d)^2 + 2*b^2*c*d*x*real_part(cos_integral(2*b*x + 2*b*c/d)) + 2*b^2*c*d*x*real_part(cos_integral(-2*b*x - 2*b*c/d)) - 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(a) + 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(a) - 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(a) + 2*b*c*d*tan(b*x)^2*tan(a) + 2*b*c*d*tan(b*x)*tan(a)^2 + d^2*tan(b*x)^2*tan(a)^2 + 2*b^2*c^2*imag_part(cos_integral(2*b*x + 2*b*c/d))*tan(b*c/d) - 2*b^2*c^2*imag_part(cos_integral(-2*b*x - 2*b*c/d))*tan(b*c/d) + 4*b^2*c^2*sin_integral(2*(b*d*x + b*c)/d)*tan(b*c/d) - 2*b*c*d*tan(b*x)*tan(b*c/d)^2 - 2*b*c*d*tan(a)*tan(b*c/d)^2 - 2*d^2*tan(b*x)*tan(a)*tan(b*c/d)^2 + b^2*c^2*real_part(cos_integral(2*b*x + 2*b*c/d)) + b^2*c^2*real_part(cos_integral(-2*b*x - 2*b*c/d)) - 2*b*d^2*x*tan(b*x) - 2*b*d^2*x*tan(a) - 2*b*c*d*tan(b*x) - 2*b*c*d*tan(a) - 2*d^2*tan(b*x)*tan(a) + d^2*tan(b*c/d)^2 + d^2)/(d^5*x^2*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + 2*c*d^4*x*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + d^5*x^2*tan(b*x)^2*tan(a)^2 + d^5*x^2*tan(b*x)^2*tan(b*c/d)^2 + d^5*x^2*tan(a)^2*tan(b*c/d)^2 + c^2*d^3*tan(b*x)^2*tan(a)^2*tan(b*c/d)^2 + 2*c*d^4*x*tan(b*x)^2*tan(a)^2 + 2*c*d^4*x*tan(b*x)^2*tan(b*c/d)^2 + 2*c*d^4*x*tan(a)^2*tan(b*c/d)^2 + d^5*x^2*tan(b*x)^2 + d^5*x^2*tan(a)^2 + c^2*d^3*tan(b*x)^2*tan(a)^2 + d^5*x^2*tan(b*c/d)^2 + c^2*d^3*tan(b*x)^2*tan(b*c/d)^2 + c^2*d^3*tan(a)^2*tan(b*c/d)^2 + 2*c*d^4*x*tan(b*x)^2 + 2*c*d^4*x*tan(a)^2 + 2*c*d^4*x*tan(b*c/d)^2 + d^5*x^2 + c^2*d^3*tan(b*x)^2 + c^2*d^3*tan(a)^2 + c^2*d^3*tan(b*c/d)^2 + 2*c*d^4*x + c^2*d^3)","C",0
16,1,351,0,0.531168," ","integrate((d*x+c)^4*cos(b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 9 \, b^{3} c^{2} d^{2} x + 3 \, b^{3} c^{3} d - 2 \, b d^{4} x - 2 \, b c d^{3}\right)} \cos\left(3 \, b x + 3 \, a\right)}{27 \, b^{5}} + \frac{3 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{2} d^{2} x + b^{3} c^{3} d - 6 \, b d^{4} x - 6 \, b c d^{3}\right)} \cos\left(b x + a\right)}{b^{5}} + \frac{{\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 162 \, b^{4} c^{2} d^{2} x^{2} + 108 \, b^{4} c^{3} d x + 27 \, b^{4} c^{4} - 36 \, b^{2} d^{4} x^{2} - 72 \, b^{2} c d^{3} x - 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4}\right)} \sin\left(3 \, b x + 3 \, a\right)}{324 \, b^{5}} + \frac{3 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + 6 \, b^{4} c^{2} d^{2} x^{2} + 4 \, b^{4} c^{3} d x + b^{4} c^{4} - 12 \, b^{2} d^{4} x^{2} - 24 \, b^{2} c d^{3} x - 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4}\right)} \sin\left(b x + a\right)}{4 \, b^{5}}"," ",0,"1/27*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 9*b^3*c^2*d^2*x + 3*b^3*c^3*d - 2*b*d^4*x - 2*b*c*d^3)*cos(3*b*x + 3*a)/b^5 + 3*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + 3*b^3*c^2*d^2*x + b^3*c^3*d - 6*b*d^4*x - 6*b*c*d^3)*cos(b*x + a)/b^5 + 1/324*(27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 162*b^4*c^2*d^2*x^2 + 108*b^4*c^3*d*x + 27*b^4*c^4 - 36*b^2*d^4*x^2 - 72*b^2*c*d^3*x - 36*b^2*c^2*d^2 + 8*d^4)*sin(3*b*x + 3*a)/b^5 + 3/4*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + 6*b^4*c^2*d^2*x^2 + 4*b^4*c^3*d*x + b^4*c^4 - 12*b^2*d^4*x^2 - 24*b^2*c*d^3*x - 12*b^2*c^2*d^2 + 24*d^4)*sin(b*x + a)/b^5","A",0
17,1,231,0,0.415256," ","integrate((d*x+c)^3*cos(b*x+a)^3,x, algorithm=""giac"")","\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(3 \, b x + 3 \, a\right)}{108 \, b^{4}} + \frac{9 \, {\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)}{4 \, b^{4}} + \frac{{\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 9 \, b^{3} c^{2} d x + 3 \, b^{3} c^{3} - 2 \, b d^{3} x - 2 \, b c d^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)}{36 \, b^{4}} + \frac{3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3} - 6 \, b d^{3} x - 6 \, b c d^{2}\right)} \sin\left(b x + a\right)}{4 \, b^{4}}"," ",0,"1/108*(9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d - 2*d^3)*cos(3*b*x + 3*a)/b^4 + 9/4*(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^4 + 1/36*(3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 9*b^3*c^2*d*x + 3*b^3*c^3 - 2*b*d^3*x - 2*b*c*d^2)*sin(3*b*x + 3*a)/b^4 + 3/4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3 - 6*b*d^3*x - 6*b*c*d^2)*sin(b*x + a)/b^4","A",0
18,1,137,0,0.451489," ","integrate((d*x+c)^2*cos(b*x+a)^3,x, algorithm=""giac"")","\frac{{\left(b d^{2} x + b c d\right)} \cos\left(3 \, b x + 3 \, a\right)}{18 \, b^{3}} + \frac{3 \, {\left(b d^{2} x + b c d\right)} \cos\left(b x + a\right)}{2 \, b^{3}} + \frac{{\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} - 2 \, d^{2}\right)} \sin\left(3 \, b x + 3 \, a\right)}{108 \, b^{3}} + \frac{3 \, {\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)}{4 \, b^{3}}"," ",0,"1/18*(b*d^2*x + b*c*d)*cos(3*b*x + 3*a)/b^3 + 3/2*(b*d^2*x + b*c*d)*cos(b*x + a)/b^3 + 1/108*(9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 - 2*d^2)*sin(3*b*x + 3*a)/b^3 + 3/4*(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
19,1,69,0,0.523838," ","integrate((d*x+c)*cos(b*x+a)^3,x, algorithm=""giac"")","\frac{d \cos\left(3 \, b x + 3 \, a\right)}{36 \, b^{2}} + \frac{3 \, d \cos\left(b x + a\right)}{4 \, b^{2}} + \frac{{\left(b d x + b c\right)} \sin\left(3 \, b x + 3 \, a\right)}{12 \, b^{2}} + \frac{3 \, {\left(b d x + b c\right)} \sin\left(b x + a\right)}{4 \, b^{2}}"," ",0,"1/36*d*cos(3*b*x + 3*a)/b^2 + 3/4*d*cos(b*x + a)/b^2 + 1/12*(b*d*x + b*c)*sin(3*b*x + 3*a)/b^2 + 3/4*(b*d*x + b*c)*sin(b*x + a)/b^2","A",0
20,1,6075,0,1.677646," ","integrate(cos(b*x+a)^3/(d*x+c),x, algorithm=""giac"")","\frac{\Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 12 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + 4 \, \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 12 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right) - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right) + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right) - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3 \, b c}{2 \, d}\right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right)^{2} + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right) + 4 \, \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) \tan\left(\frac{3 \, b c}{2 \, d}\right) - \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} - \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + 12 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) \tan\left(\frac{b c}{2 \, d}\right) + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) + 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3}{2} \, a\right) - 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3}{2} \, a\right) - 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) + 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{1}{2} \, a\right) - 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{1}{2} \, a\right) + 2 \, \Im \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right) - 2 \, \Im \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right) \tan\left(\frac{3 \, b c}{2 \, d}\right) + 4 \, \operatorname{Si}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \tan\left(\frac{3 \, b c}{2 \, d}\right) + 6 \, \Im \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) - 6 \, \Im \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) \tan\left(\frac{b c}{2 \, d}\right) + 12 \, \operatorname{Si}\left(\frac{b d x + b c}{d}\right) \tan\left(\frac{b c}{2 \, d}\right) + \Re \left( \operatorname{Ci}\left(3 \, b x + \frac{3 \, b c}{d}\right) \right) + 3 \, \Re \left( \operatorname{Ci}\left(b x + \frac{b c}{d}\right) \right) + 3 \, \Re \left( \operatorname{Ci}\left(-b x - \frac{b c}{d}\right) \right) + \Re \left( \operatorname{Ci}\left(-3 \, b x - \frac{3 \, b c}{d}\right) \right)}{8 \, {\left(d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + d \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{1}{2} \, a\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} \tan\left(\frac{b c}{2 \, d}\right)^{2} + d \tan\left(\frac{3}{2} \, a\right)^{2} + d \tan\left(\frac{1}{2} \, a\right)^{2} + d \tan\left(\frac{3 \, b c}{2 \, d}\right)^{2} + d \tan\left(\frac{b c}{2 \, d}\right)^{2} + d\right)}}"," ",0,"1/8*(real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2 + 12*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 12*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 4*real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 4*real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d) + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d) - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d) - 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2 + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2 - 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)*tan(3/2*b*c/d)^2 + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)^2 + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d) - 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 + 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a)*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(1/2*a)^2*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(1/2*a)^2*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*a)^2 + 4*real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d) + 4*real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2*tan(3/2*b*c/d) + real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d)^2 - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d)^2 + 12*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(1/2*b*c/d) + 12*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a)*tan(1/2*b*c/d) + 12*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 12*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*b*c/d)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(1/2*b*c/d)^2 + real_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + 4*real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 4*real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 - 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*a) + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*a) - 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*a) - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2 + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*a)^2 - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(1/2*a)^2 - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d) + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2*tan(3/2*b*c/d) - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)^2*tan(3/2*b*c/d) + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d) - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*a)^2*tan(3/2*b*c/d) + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(1/2*a)^2*tan(3/2*b*c/d) + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d)^2 - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d)^2 + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(3/2*b*c/d)^2 - 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(3/2*b*c/d)^2 + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(3/2*b*c/d)^2 - 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(3/2*b*c/d)^2 + 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2*tan(1/2*b*c/d) - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2*tan(1/2*b*c/d) + 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*a)^2*tan(1/2*b*c/d) - 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2*tan(1/2*b*c/d) - 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)^2*tan(1/2*b*c/d) + 6*imag_part(cos_integral(b*x + b*c/d))*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) + 12*sin_integral((b*d*x + b*c)/d)*tan(3/2*b*c/d)^2*tan(1/2*b*c/d) - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(1/2*b*c/d)^2 - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a)*tan(1/2*b*c/d)^2 + 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d)^2 + 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*a)*tan(1/2*b*c/d)^2 + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*b*c/d)*tan(1/2*b*c/d)^2 - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*a)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*a)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)^2 + real_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*a)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*a)^2 + 4*real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d) + 4*real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a)*tan(3/2*b*c/d) - real_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*b*c/d)^2 + 3*real_part(cos_integral(b*x + b*c/d))*tan(3/2*b*c/d)^2 + 3*real_part(cos_integral(-b*x - b*c/d))*tan(3/2*b*c/d)^2 - real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*b*c/d)^2 + 12*real_part(cos_integral(b*x + b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + 12*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*a)*tan(1/2*b*c/d) + real_part(cos_integral(3*b*x + 3*b*c/d))*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d)^2 - 3*real_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d)^2 + real_part(cos_integral(-3*b*x - 3*b*c/d))*tan(1/2*b*c/d)^2 - 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*a) + 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*a) - 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*a) - 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*a) + 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*a) - 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*a) + 2*imag_part(cos_integral(3*b*x + 3*b*c/d))*tan(3/2*b*c/d) - 2*imag_part(cos_integral(-3*b*x - 3*b*c/d))*tan(3/2*b*c/d) + 4*sin_integral(3*(b*d*x + b*c)/d)*tan(3/2*b*c/d) + 6*imag_part(cos_integral(b*x + b*c/d))*tan(1/2*b*c/d) - 6*imag_part(cos_integral(-b*x - b*c/d))*tan(1/2*b*c/d) + 12*sin_integral((b*d*x + b*c)/d)*tan(1/2*b*c/d) + real_part(cos_integral(3*b*x + 3*b*c/d)) + 3*real_part(cos_integral(b*x + b*c/d)) + 3*real_part(cos_integral(-b*x - b*c/d)) + real_part(cos_integral(-3*b*x - 3*b*c/d)))/(d*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + d*tan(3/2*a)^2*tan(1/2*a)^2*tan(3/2*b*c/d)^2 + d*tan(3/2*a)^2*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d*tan(3/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + d*tan(1/2*a)^2*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + d*tan(3/2*a)^2*tan(1/2*a)^2 + d*tan(3/2*a)^2*tan(3/2*b*c/d)^2 + d*tan(1/2*a)^2*tan(3/2*b*c/d)^2 + d*tan(3/2*a)^2*tan(1/2*b*c/d)^2 + d*tan(1/2*a)^2*tan(1/2*b*c/d)^2 + d*tan(3/2*b*c/d)^2*tan(1/2*b*c/d)^2 + d*tan(3/2*a)^2 + d*tan(1/2*a)^2 + d*tan(3/2*b*c/d)^2 + d*tan(1/2*b*c/d)^2 + d)","C",0
21,1,1000,0,1.036436," ","integrate(cos(b*x+a)^3/(d*x+c)^2,x, algorithm=""giac"")","-\frac{{\left(3 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \operatorname{Ci}\left(\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) \sin\left(-\frac{b c - a d}{d}\right) + 3 \, b^{3} c \operatorname{Ci}\left(\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) \sin\left(-\frac{b c - a d}{d}\right) - 3 \, a b^{2} d \operatorname{Ci}\left(\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) \sin\left(-\frac{b c - a d}{d}\right) + 3 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \operatorname{Ci}\left(\frac{3 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 3 \, b^{3} c \operatorname{Ci}\left(\frac{3 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 3 \, a b^{2} d \operatorname{Ci}\left(\frac{3 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) \sin\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 3 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) - 3 \, b^{3} c \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) + 3 \, a b^{2} d \cos\left(-\frac{b c - a d}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d}{d}\right) - 3 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} b^{2} \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(-\frac{3 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) - 3 \, b^{3} c \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(-\frac{3 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) + 3 \, a b^{2} d \cos\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) \operatorname{Si}\left(-\frac{3 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} + b c - a d\right)}}{d}\right) + 3 \, b^{2} d \cos\left(-\frac{{\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)}}{d}\right) + b^{2} d \cos\left(-\frac{3 \, {\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)}}{d}\right)\right)} d^{2}}{4 \, {\left({\left(d x + c\right)} {\left(b - \frac{b c}{d x + c} + \frac{a d}{d x + c}\right)} d^{4} + b c d^{4} - a d^{5}\right)} b}"," ",0,"-1/4*(3*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos_integral(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-(b*c - a*d)/d) + 3*b^3*c*cos_integral(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-(b*c - a*d)/d) - 3*a*b^2*d*cos_integral(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-(b*c - a*d)/d) + 3*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos_integral(3*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-3*(b*c - a*d)/d) + 3*b^3*c*cos_integral(3*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-3*(b*c - a*d)/d) - 3*a*b^2*d*cos_integral(3*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d)*sin(-3*(b*c - a*d)/d) - 3*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos(-(b*c - a*d)/d)*sin_integral(-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) - 3*b^3*c*cos(-(b*c - a*d)/d)*sin_integral(-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + 3*a*b^2*d*cos(-(b*c - a*d)/d)*sin_integral(-((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) - 3*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*b^2*cos(-3*(b*c - a*d)/d)*sin_integral(-3*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) - 3*b^3*c*cos(-3*(b*c - a*d)/d)*sin_integral(-3*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + 3*a*b^2*d*cos(-3*(b*c - a*d)/d)*sin_integral(-3*((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c)) + b*c - a*d)/d) + 3*b^2*d*cos(-(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))/d) + b^2*d*cos(-3*(d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))/d))*d^2/(((d*x + c)*(b - b*c/(d*x + c) + a*d/(d*x + c))*d^4 + b*c*d^4 - a*d^5)*b)","B",0
22,-1,0,0,0.000000," ","integrate(cos(b*x+a)^3/(d*x+c)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,1,108,0,0.441716," ","integrate(x^3*cos(b*x+a)^4,x, algorithm=""giac"")","\frac{3}{32} \, x^{4} + \frac{3 \, {\left(8 \, b^{2} x^{2} - 1\right)} \cos\left(4 \, b x + 4 \, a\right)}{1024 \, b^{4}} + \frac{3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \cos\left(2 \, b x + 2 \, a\right)}{16 \, b^{4}} + \frac{{\left(8 \, b^{3} x^{3} - 3 \, b x\right)} \sin\left(4 \, b x + 4 \, a\right)}{256 \, b^{4}} + \frac{{\left(2 \, b^{3} x^{3} - 3 \, b x\right)} \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{4}}"," ",0,"3/32*x^4 + 3/1024*(8*b^2*x^2 - 1)*cos(4*b*x + 4*a)/b^4 + 3/16*(2*b^2*x^2 - 1)*cos(2*b*x + 2*a)/b^4 + 1/256*(8*b^3*x^3 - 3*b*x)*sin(4*b*x + 4*a)/b^4 + 1/8*(2*b^3*x^3 - 3*b*x)*sin(2*b*x + 2*a)/b^4","A",0
24,1,84,0,0.360199," ","integrate(x^2*cos(b*x+a)^4,x, algorithm=""giac"")","\frac{1}{8} \, x^{3} + \frac{x \cos\left(4 \, b x + 4 \, a\right)}{64 \, b^{2}} + \frac{x \cos\left(2 \, b x + 2 \, a\right)}{4 \, b^{2}} + \frac{{\left(8 \, b^{2} x^{2} - 1\right)} \sin\left(4 \, b x + 4 \, a\right)}{256 \, b^{3}} + \frac{{\left(2 \, b^{2} x^{2} - 1\right)} \sin\left(2 \, b x + 2 \, a\right)}{8 \, b^{3}}"," ",0,"1/8*x^3 + 1/64*x*cos(4*b*x + 4*a)/b^2 + 1/4*x*cos(2*b*x + 2*a)/b^2 + 1/256*(8*b^2*x^2 - 1)*sin(4*b*x + 4*a)/b^3 + 1/8*(2*b^2*x^2 - 1)*sin(2*b*x + 2*a)/b^3","A",0
25,1,64,0,0.446577," ","integrate(x*cos(b*x+a)^4,x, algorithm=""giac"")","\frac{3}{16} \, x^{2} + \frac{x \sin\left(4 \, b x + 4 \, a\right)}{32 \, b} + \frac{x \sin\left(2 \, b x + 2 \, a\right)}{4 \, b} + \frac{\cos\left(4 \, b x + 4 \, a\right)}{128 \, b^{2}} + \frac{\cos\left(2 \, b x + 2 \, a\right)}{8 \, b^{2}}"," ",0,"3/16*x^2 + 1/32*x*sin(4*b*x + 4*a)/b + 1/4*x*sin(2*b*x + 2*a)/b + 1/128*cos(4*b*x + 4*a)/b^2 + 1/8*cos(2*b*x + 2*a)/b^2","A",0
26,1,428,0,0.492246," ","integrate(cos(b*x+a)^4/x,x, algorithm=""giac"")","\frac{6 \, \log\left({\left| x \right|}\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 4 \, \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 4 \, \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 8 \, \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 8 \, \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 16 \, \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 2 \, \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 4 \, \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 6 \, \log\left({\left| x \right|}\right) \tan\left(2 \, a\right)^{2} - \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 4 \, \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} - \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 6 \, \log\left({\left| x \right|}\right) \tan\left(a\right)^{2} + \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(a\right)^{2} - 4 \, \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(a\right)^{2} - 4 \, \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(a\right)^{2} + \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(a\right)^{2} - 2 \, \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right) + 2 \, \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right) - 4 \, \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, a\right) - 8 \, \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(a\right) + 8 \, \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(a\right) - 16 \, \operatorname{Si}\left(2 \, b x\right) \tan\left(a\right) + 6 \, \log\left({\left| x \right|}\right) + \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) + 4 \, \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) + 4 \, \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) + \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right)}{16 \, {\left(\tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + \tan\left(2 \, a\right)^{2} + \tan\left(a\right)^{2} + 1\right)}}"," ",0,"1/16*(6*log(abs(x))*tan(2*a)^2*tan(a)^2 - real_part(cos_integral(4*b*x))*tan(2*a)^2*tan(a)^2 - 4*real_part(cos_integral(2*b*x))*tan(2*a)^2*tan(a)^2 - 4*real_part(cos_integral(-2*b*x))*tan(2*a)^2*tan(a)^2 - real_part(cos_integral(-4*b*x))*tan(2*a)^2*tan(a)^2 - 8*imag_part(cos_integral(2*b*x))*tan(2*a)^2*tan(a) + 8*imag_part(cos_integral(-2*b*x))*tan(2*a)^2*tan(a) - 16*sin_integral(2*b*x)*tan(2*a)^2*tan(a) - 2*imag_part(cos_integral(4*b*x))*tan(2*a)*tan(a)^2 + 2*imag_part(cos_integral(-4*b*x))*tan(2*a)*tan(a)^2 - 4*sin_integral(4*b*x)*tan(2*a)*tan(a)^2 + 6*log(abs(x))*tan(2*a)^2 - real_part(cos_integral(4*b*x))*tan(2*a)^2 + 4*real_part(cos_integral(2*b*x))*tan(2*a)^2 + 4*real_part(cos_integral(-2*b*x))*tan(2*a)^2 - real_part(cos_integral(-4*b*x))*tan(2*a)^2 + 6*log(abs(x))*tan(a)^2 + real_part(cos_integral(4*b*x))*tan(a)^2 - 4*real_part(cos_integral(2*b*x))*tan(a)^2 - 4*real_part(cos_integral(-2*b*x))*tan(a)^2 + real_part(cos_integral(-4*b*x))*tan(a)^2 - 2*imag_part(cos_integral(4*b*x))*tan(2*a) + 2*imag_part(cos_integral(-4*b*x))*tan(2*a) - 4*sin_integral(4*b*x)*tan(2*a) - 8*imag_part(cos_integral(2*b*x))*tan(a) + 8*imag_part(cos_integral(-2*b*x))*tan(a) - 16*sin_integral(2*b*x)*tan(a) + 6*log(abs(x)) + real_part(cos_integral(4*b*x)) + 4*real_part(cos_integral(2*b*x)) + 4*real_part(cos_integral(-2*b*x)) + real_part(cos_integral(-4*b*x)))/(tan(2*a)^2*tan(a)^2 + tan(2*a)^2 + tan(a)^2 + 1)","C",0
27,1,3220,0,0.579242," ","integrate(cos(b*x+a)^4/x^2,x, algorithm=""giac"")","\frac{b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 4 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 8 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 3 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 3 \, \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(b x\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(b x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, a\right)^{2} - 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(a\right)^{2} + 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(a\right)^{2} - 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(a\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(a\right)^{2} - 2 \, b x \operatorname{Si}\left(4 \, b x\right) \tan\left(a\right)^{2} + 4 \, b x \operatorname{Si}\left(2 \, b x\right) \tan\left(a\right)^{2} + \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right) + 2 \, \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 4 \, \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b x \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(a\right) - 4 \, b x \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(a\right) + 8 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(a\right) + 8 \, \tan\left(b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) + \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - 4 \, \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} + \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - b x \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) - 2 \, b x \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) + 2 \, b x \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) + b x \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) - 2 \, b x \operatorname{Si}\left(4 \, b x\right) - 4 \, b x \operatorname{Si}\left(2 \, b x\right) - 3 \, \tan\left(2 \, b x\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(2 \, a\right) - 3 \, \tan\left(2 \, a\right)^{2} + 8 \, \tan\left(b x\right) \tan\left(a\right) - 4}{4 \, {\left(x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + x \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + x \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + x \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + x \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + x \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + x \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x \tan\left(2 \, b x\right)^{2} + x \tan\left(b x\right)^{2} + x \tan\left(2 \, a\right)^{2} + x \tan\left(a\right)^{2} + x\right)}}"," ",0,"1/4*(b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - 4*b*x*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a) - 2*b*x*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)*tan(a)^2 - 2*b*x*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)*tan(a)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 + 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 - 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 2*b*x*sin_integral(4*b*x)*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - 2*b*x*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a) - 2*b*x*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a) - 4*b*x*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a) - 4*b*x*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a) - 4*b*x*real_part(cos_integral(2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a) - 2*b*x*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a)*tan(a)^2 - 2*b*x*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a)*tan(a)^2 - 2*b*x*real_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a)*tan(a)^2 - 2*b*x*real_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a)*tan(a)^2 - 4*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2 - 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(b*x)^2 - 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(b*x)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(2*a)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(2*a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a)^2 + 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(2*a)^2 - 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(2*a)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(b*x)^2*tan(2*a)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(2*a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a)^2 + 2*b*x*sin_integral(4*b*x)*tan(b*x)^2*tan(2*a)^2 - 4*b*x*sin_integral(2*b*x)*tan(b*x)^2*tan(2*a)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(a)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(a)^2 - 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2*tan(a)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(b*x)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(b*x)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(a)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(a)^2 - 2*b*x*sin_integral(4*b*x)*tan(b*x)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(b*x)^2*tan(a)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(2*a)^2*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*a)^2*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(2*a)^2*tan(a)^2 + 2*b*x*sin_integral(4*b*x)*tan(2*a)^2*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(2*a)^2*tan(a)^2 - 2*b*x*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a) - 2*b*x*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a) - 2*b*x*real_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a) - 2*b*x*real_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a) - 4*b*x*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(a) - 4*b*x*real_part(cos_integral(2*b*x))*tan(b*x)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(a) - 4*b*x*real_part(cos_integral(2*b*x))*tan(2*a)^2*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(2*a)^2*tan(a) + 8*tan(2*b*x)^2*tan(b*x)*tan(2*a)^2*tan(a) - 3*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 - 2*b*x*real_part(cos_integral(4*b*x))*tan(2*a)*tan(a)^2 - 2*b*x*real_part(cos_integral(-4*b*x))*tan(2*a)*tan(a)^2 + 2*tan(2*b*x)*tan(b*x)^2*tan(2*a)*tan(a)^2 - 3*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2 - 2*b*x*sin_integral(4*b*x)*tan(2*b*x)^2 - 4*b*x*sin_integral(2*b*x)*tan(2*b*x)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(b*x)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(b*x)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(b*x)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(b*x)^2 - 2*b*x*sin_integral(4*b*x)*tan(b*x)^2 - 4*b*x*sin_integral(2*b*x)*tan(b*x)^2 + b*x*imag_part(cos_integral(4*b*x))*tan(2*a)^2 - 2*b*x*imag_part(cos_integral(2*b*x))*tan(2*a)^2 + 2*b*x*imag_part(cos_integral(-2*b*x))*tan(2*a)^2 - b*x*imag_part(cos_integral(-4*b*x))*tan(2*a)^2 + 2*b*x*sin_integral(4*b*x)*tan(2*a)^2 - 4*b*x*sin_integral(2*b*x)*tan(2*a)^2 - b*x*imag_part(cos_integral(4*b*x))*tan(a)^2 + 2*b*x*imag_part(cos_integral(2*b*x))*tan(a)^2 - 2*b*x*imag_part(cos_integral(-2*b*x))*tan(a)^2 + b*x*imag_part(cos_integral(-4*b*x))*tan(a)^2 - 2*b*x*sin_integral(4*b*x)*tan(a)^2 + 4*b*x*sin_integral(2*b*x)*tan(a)^2 + tan(2*b*x)^2*tan(b*x)^2 - 2*b*x*real_part(cos_integral(4*b*x))*tan(2*a) - 2*b*x*real_part(cos_integral(-4*b*x))*tan(2*a) + 2*tan(2*b*x)*tan(b*x)^2*tan(2*a) - 4*tan(2*b*x)^2*tan(2*a)^2 + tan(b*x)^2*tan(2*a)^2 - 4*b*x*real_part(cos_integral(2*b*x))*tan(a) - 4*b*x*real_part(cos_integral(-2*b*x))*tan(a) + 8*tan(2*b*x)^2*tan(b*x)*tan(a) + 8*tan(b*x)*tan(2*a)^2*tan(a) + tan(2*b*x)^2*tan(a)^2 - 4*tan(b*x)^2*tan(a)^2 + 2*tan(2*b*x)*tan(2*a)*tan(a)^2 + tan(2*a)^2*tan(a)^2 - b*x*imag_part(cos_integral(4*b*x)) - 2*b*x*imag_part(cos_integral(2*b*x)) + 2*b*x*imag_part(cos_integral(-2*b*x)) + b*x*imag_part(cos_integral(-4*b*x)) - 2*b*x*sin_integral(4*b*x) - 4*b*x*sin_integral(2*b*x) - 3*tan(2*b*x)^2 + 2*tan(2*b*x)*tan(2*a) - 3*tan(2*a)^2 + 8*tan(b*x)*tan(a) - 4)/(x*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + x*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 + x*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + x*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + x*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + x*tan(2*b*x)^2*tan(b*x)^2 + x*tan(2*b*x)^2*tan(2*a)^2 + x*tan(b*x)^2*tan(2*a)^2 + x*tan(2*b*x)^2*tan(a)^2 + x*tan(b*x)^2*tan(a)^2 + x*tan(2*a)^2*tan(a)^2 + x*tan(2*b*x)^2 + x*tan(b*x)^2 + x*tan(2*a)^2 + x*tan(a)^2 + x)","C",0
28,1,3920,0,0.759825," ","integrate(cos(b*x+a)^4/x^3,x, algorithm=""giac"")","\frac{4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 4 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 4 \, b x \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, b x\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 4 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(b x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(b x\right)^{2} - 4 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right)^{2} + 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(2 \, a\right)^{2} - 4 \, b x \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} - 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right) + 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 8 \, b x \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(a\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(a\right)^{2} - 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(a\right)^{2} + 4 \, b x \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(a\right)^{2} - 4 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} + 4 \, b x \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 4 \, b x \tan\left(2 \, b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 8 \, b x \tan\left(b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(4 \, b x\right) \right) \tan\left(2 \, a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-4 \, b x\right) \right) \tan\left(2 \, a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(4 \, b x\right) \tan\left(2 \, a\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(2 \, b x\right) \right) \tan\left(a\right) - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-2 \, b x\right) \right) \tan\left(a\right) + 16 \, b^{2} x^{2} \operatorname{Si}\left(2 \, b x\right) \tan\left(a\right) + 8 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) - 3 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) \tan\left(a\right)^{2} - 3 \, \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(4 \, b x\right) \right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(2 \, b x\right) \right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-2 \, b x\right) \right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-4 \, b x\right) \right) + 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) + 4 \, b x \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} - 4 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right) + 4 \, b x \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 4 \, b x \tan\left(2 \, b x\right) \tan\left(2 \, a\right)^{2} + 8 \, b x \tan\left(b x\right) \tan\left(2 \, a\right)^{2} + 8 \, b x \tan\left(2 \, b x\right)^{2} \tan\left(a\right) - 8 \, b x \tan\left(b x\right)^{2} \tan\left(a\right) + 8 \, b x \tan\left(2 \, a\right)^{2} \tan\left(a\right) + 4 \, b x \tan\left(2 \, b x\right) \tan\left(a\right)^{2} - 8 \, b x \tan\left(b x\right) \tan\left(a\right)^{2} + 4 \, b x \tan\left(2 \, a\right) \tan\left(a\right)^{2} + \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(b x\right)^{2} \tan\left(2 \, a\right) - 4 \, \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + 8 \, \tan\left(2 \, b x\right)^{2} \tan\left(b x\right) \tan\left(a\right) + 8 \, \tan\left(b x\right) \tan\left(2 \, a\right)^{2} \tan\left(a\right) + \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} - 4 \, \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(2 \, a\right) \tan\left(a\right)^{2} + \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + 4 \, b x \tan\left(2 \, b x\right) + 8 \, b x \tan\left(b x\right) + 4 \, b x \tan\left(2 \, a\right) + 8 \, b x \tan\left(a\right) - 3 \, \tan\left(2 \, b x\right)^{2} + 2 \, \tan\left(2 \, b x\right) \tan\left(2 \, a\right) - 3 \, \tan\left(2 \, a\right)^{2} + 8 \, \tan\left(b x\right) \tan\left(a\right) - 4}{8 \, {\left(x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(b x\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(2 \, a\right)^{2} + x^{2} \tan\left(b x\right)^{2} \tan\left(2 \, a\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(b x\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(2 \, a\right)^{2} \tan\left(a\right)^{2} + x^{2} \tan\left(2 \, b x\right)^{2} + x^{2} \tan\left(b x\right)^{2} + x^{2} \tan\left(2 \, a\right)^{2} + x^{2} \tan\left(a\right)^{2} + x^{2}\right)}}"," ",0,"1/8*(4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)*tan(a)^2 - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)*tan(a)^2 + 16*b^2*x^2*sin_integral(4*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a) - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(2*a) + 16*b^2*x^2*sin_integral(4*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(2*a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(2*b*x)^2*tan(b*x)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(2*a)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(2*b*x)^2*tan(2*a)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(2*a)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(b*x)^2*tan(2*a)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a)*tan(a)^2 - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a)*tan(a)^2 + 16*b^2*x^2*sin_integral(4*b*x)*tan(2*b*x)^2*tan(2*a)*tan(a)^2 + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a)*tan(a)^2 - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a)*tan(a)^2 + 16*b^2*x^2*sin_integral(4*b*x)*tan(b*x)^2*tan(2*a)*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(b*x)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(b*x)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(b*x)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(b*x)^2 + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(2*a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a)^2 + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(b*x)^2*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(2*a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a)^2 - 8*b*x*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a) - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(b*x)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(a)^2 - 4*b*x*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*a)^2*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*a)^2*tan(a)^2 - 8*b*x*tan(2*b*x)^2*tan(b*x)*tan(2*a)^2*tan(a)^2 - 4*b*x*tan(2*b*x)*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(2*b*x)^2*tan(2*a) - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(2*b*x)^2*tan(2*a) + 16*b^2*x^2*sin_integral(4*b*x)*tan(2*b*x)^2*tan(2*a) + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(b*x)^2*tan(2*a) - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(b*x)^2*tan(2*a) + 16*b^2*x^2*sin_integral(4*b*x)*tan(b*x)^2*tan(2*a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(2*b*x)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(2*b*x)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(2*b*x)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(b*x)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(b*x)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(b*x)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(2*a)^2*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(2*a)^2*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(2*a)^2*tan(a) + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(2*a)*tan(a)^2 - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(2*a)*tan(a)^2 + 16*b^2*x^2*sin_integral(4*b*x)*tan(2*a)*tan(a)^2 - 4*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*b*x)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*b*x)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*b*x)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*b*x)^2 - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(b*x)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(b*x)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(b*x)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(b*x)^2 - 4*b*x*tan(2*b*x)^2*tan(b*x)^2*tan(2*a) + 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(2*a)^2 - 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(2*a)^2 + 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(2*a)^2 + 8*b*x*tan(2*b*x)^2*tan(b*x)*tan(2*a)^2 - 4*b*x*tan(2*b*x)*tan(b*x)^2*tan(2*a)^2 - 8*b*x*tan(2*b*x)^2*tan(b*x)^2*tan(a) + 8*b*x*tan(2*b*x)^2*tan(2*a)^2*tan(a) - 8*b*x*tan(b*x)^2*tan(2*a)^2*tan(a) - 4*b^2*x^2*real_part(cos_integral(4*b*x))*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(2*b*x))*tan(a)^2 + 4*b^2*x^2*real_part(cos_integral(-2*b*x))*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(-4*b*x))*tan(a)^2 - 8*b*x*tan(2*b*x)^2*tan(b*x)*tan(a)^2 + 4*b*x*tan(2*b*x)*tan(b*x)^2*tan(a)^2 - 4*b*x*tan(2*b*x)^2*tan(2*a)*tan(a)^2 + 4*b*x*tan(b*x)^2*tan(2*a)*tan(a)^2 - 4*b*x*tan(2*b*x)*tan(2*a)^2*tan(a)^2 - 8*b*x*tan(b*x)*tan(2*a)^2*tan(a)^2 + 8*b^2*x^2*imag_part(cos_integral(4*b*x))*tan(2*a) - 8*b^2*x^2*imag_part(cos_integral(-4*b*x))*tan(2*a) + 16*b^2*x^2*sin_integral(4*b*x)*tan(2*a) + 8*b^2*x^2*imag_part(cos_integral(2*b*x))*tan(a) - 8*b^2*x^2*imag_part(cos_integral(-2*b*x))*tan(a) + 16*b^2*x^2*sin_integral(2*b*x)*tan(a) + 8*tan(2*b*x)^2*tan(b*x)*tan(2*a)^2*tan(a) - 3*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + 2*tan(2*b*x)*tan(b*x)^2*tan(2*a)*tan(a)^2 - 3*tan(b*x)^2*tan(2*a)^2*tan(a)^2 - 4*b^2*x^2*real_part(cos_integral(4*b*x)) - 4*b^2*x^2*real_part(cos_integral(2*b*x)) - 4*b^2*x^2*real_part(cos_integral(-2*b*x)) - 4*b^2*x^2*real_part(cos_integral(-4*b*x)) + 8*b*x*tan(2*b*x)^2*tan(b*x) + 4*b*x*tan(2*b*x)*tan(b*x)^2 - 4*b*x*tan(2*b*x)^2*tan(2*a) + 4*b*x*tan(b*x)^2*tan(2*a) - 4*b*x*tan(2*b*x)*tan(2*a)^2 + 8*b*x*tan(b*x)*tan(2*a)^2 + 8*b*x*tan(2*b*x)^2*tan(a) - 8*b*x*tan(b*x)^2*tan(a) + 8*b*x*tan(2*a)^2*tan(a) + 4*b*x*tan(2*b*x)*tan(a)^2 - 8*b*x*tan(b*x)*tan(a)^2 + 4*b*x*tan(2*a)*tan(a)^2 + tan(2*b*x)^2*tan(b*x)^2 + 2*tan(2*b*x)*tan(b*x)^2*tan(2*a) - 4*tan(2*b*x)^2*tan(2*a)^2 + tan(b*x)^2*tan(2*a)^2 + 8*tan(2*b*x)^2*tan(b*x)*tan(a) + 8*tan(b*x)*tan(2*a)^2*tan(a) + tan(2*b*x)^2*tan(a)^2 - 4*tan(b*x)^2*tan(a)^2 + 2*tan(2*b*x)*tan(2*a)*tan(a)^2 + tan(2*a)^2*tan(a)^2 + 4*b*x*tan(2*b*x) + 8*b*x*tan(b*x) + 4*b*x*tan(2*a) + 8*b*x*tan(a) - 3*tan(2*b*x)^2 + 2*tan(2*b*x)*tan(2*a) - 3*tan(2*a)^2 + 8*tan(b*x)*tan(a) - 4)/(x^2*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + x^2*tan(2*b*x)^2*tan(b*x)^2*tan(2*a)^2 + x^2*tan(2*b*x)^2*tan(b*x)^2*tan(a)^2 + x^2*tan(2*b*x)^2*tan(2*a)^2*tan(a)^2 + x^2*tan(b*x)^2*tan(2*a)^2*tan(a)^2 + x^2*tan(2*b*x)^2*tan(b*x)^2 + x^2*tan(2*b*x)^2*tan(2*a)^2 + x^2*tan(b*x)^2*tan(2*a)^2 + x^2*tan(2*b*x)^2*tan(a)^2 + x^2*tan(b*x)^2*tan(a)^2 + x^2*tan(2*a)^2*tan(a)^2 + x^2*tan(2*b*x)^2 + x^2*tan(b*x)^2 + x^2*tan(2*a)^2 + x^2*tan(a)^2 + x^2)","C",0
29,0,0,0,0.000000," ","integrate((d*x+c)^3*sec(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{3} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^3*sec(b*x + a), x)","F",0
30,0,0,0,0.000000," ","integrate((d*x+c)^2*sec(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^2*sec(b*x + a), x)","F",0
31,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)*sec(b*x + a), x)","F",0
32,0,0,0,0.000000," ","integrate(sec(b*x+a)/(d*x+c),x, algorithm=""giac"")","\int \frac{\sec\left(b x + a\right)}{d x + c}\,{d x}"," ",0,"integrate(sec(b*x + a)/(d*x + c), x)","F",0
33,0,0,0,0.000000," ","integrate((d*x+c)^3*sec(b*x+a)^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{3} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^3*sec(b*x + a)^2, x)","F",0
34,0,0,0,0.000000," ","integrate((d*x+c)^2*sec(b*x+a)^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^2*sec(b*x + a)^2, x)","F",0
35,1,1459,0,5.833938," ","integrate((d*x+c)*sec(b*x+a)^2,x, algorithm=""giac"")","-\frac{4 \, b d x \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 4 \, b d x \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{8} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 36 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 4 \, b c \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right) + 4 \, b c \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, b d x \tan\left(\frac{1}{2} \, b x\right) + d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{8} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 36 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x\right)^{2} - 4 \, b d x \tan\left(\frac{1}{2} \, a\right) + 4 \, d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{8} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 36 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) + d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{8} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 36 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, a\right)^{2} - 4 \, b c \tan\left(\frac{1}{2} \, b x\right) - 4 \, b c \tan\left(\frac{1}{2} \, a\right) - d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{4} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{8} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, b x\right)^{8} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{7} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{6} \tan\left(\frac{1}{2} \, a\right)^{2} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{4} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{5} \tan\left(\frac{1}{2} \, a\right) + 36 \, \tan\left(\frac{1}{2} \, b x\right)^{4} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right)^{3} - 2 \, \tan\left(\frac{1}{2} \, b x\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right)^{3} \tan\left(\frac{1}{2} \, a\right) + 16 \, \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right)^{3} + \tan\left(\frac{1}{2} \, a\right)^{4} - 8 \, \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1\right)}}{\tan\left(\frac{1}{2} \, a\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, a\right)^{2} + 1}\right)}{2 \, {\left(b^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} \tan\left(\frac{1}{2} \, a\right)^{2} - b^{2} \tan\left(\frac{1}{2} \, b x\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, b x\right) \tan\left(\frac{1}{2} \, a\right) - b^{2} \tan\left(\frac{1}{2} \, a\right)^{2} + b^{2}\right)}}"," ",0,"-1/2*(4*b*d*x*tan(1/2*b*x)^2*tan(1/2*a) + 4*b*d*x*tan(1/2*b*x)*tan(1/2*a)^2 - d*log(4*(tan(1/2*b*x)^8*tan(1/2*a)^4 - 2*tan(1/2*b*x)^8*tan(1/2*a)^2 - 8*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^8 + 8*tan(1/2*b*x)^7*tan(1/2*a) + 16*tan(1/2*b*x)^6*tan(1/2*a)^2 - 8*tan(1/2*b*x)^5*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + 8*tan(1/2*b*x)^5*tan(1/2*a) + 36*tan(1/2*b*x)^4*tan(1/2*a)^2 + 8*tan(1/2*b*x)^3*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4 - 8*tan(1/2*b*x)^3*tan(1/2*a) + 16*tan(1/2*b*x)^2*tan(1/2*a)^2 + 8*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*a)^4 - 8*tan(1/2*b*x)*tan(1/2*a) - 2*tan(1/2*a)^2 + 1)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*b*x)^2*tan(1/2*a)^2 + 4*b*c*tan(1/2*b*x)^2*tan(1/2*a) + 4*b*c*tan(1/2*b*x)*tan(1/2*a)^2 - 4*b*d*x*tan(1/2*b*x) + d*log(4*(tan(1/2*b*x)^8*tan(1/2*a)^4 - 2*tan(1/2*b*x)^8*tan(1/2*a)^2 - 8*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^8 + 8*tan(1/2*b*x)^7*tan(1/2*a) + 16*tan(1/2*b*x)^6*tan(1/2*a)^2 - 8*tan(1/2*b*x)^5*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + 8*tan(1/2*b*x)^5*tan(1/2*a) + 36*tan(1/2*b*x)^4*tan(1/2*a)^2 + 8*tan(1/2*b*x)^3*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4 - 8*tan(1/2*b*x)^3*tan(1/2*a) + 16*tan(1/2*b*x)^2*tan(1/2*a)^2 + 8*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*a)^4 - 8*tan(1/2*b*x)*tan(1/2*a) - 2*tan(1/2*a)^2 + 1)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*b*x)^2 - 4*b*d*x*tan(1/2*a) + 4*d*log(4*(tan(1/2*b*x)^8*tan(1/2*a)^4 - 2*tan(1/2*b*x)^8*tan(1/2*a)^2 - 8*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^8 + 8*tan(1/2*b*x)^7*tan(1/2*a) + 16*tan(1/2*b*x)^6*tan(1/2*a)^2 - 8*tan(1/2*b*x)^5*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + 8*tan(1/2*b*x)^5*tan(1/2*a) + 36*tan(1/2*b*x)^4*tan(1/2*a)^2 + 8*tan(1/2*b*x)^3*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4 - 8*tan(1/2*b*x)^3*tan(1/2*a) + 16*tan(1/2*b*x)^2*tan(1/2*a)^2 + 8*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*a)^4 - 8*tan(1/2*b*x)*tan(1/2*a) - 2*tan(1/2*a)^2 + 1)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*b*x)*tan(1/2*a) + d*log(4*(tan(1/2*b*x)^8*tan(1/2*a)^4 - 2*tan(1/2*b*x)^8*tan(1/2*a)^2 - 8*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^8 + 8*tan(1/2*b*x)^7*tan(1/2*a) + 16*tan(1/2*b*x)^6*tan(1/2*a)^2 - 8*tan(1/2*b*x)^5*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + 8*tan(1/2*b*x)^5*tan(1/2*a) + 36*tan(1/2*b*x)^4*tan(1/2*a)^2 + 8*tan(1/2*b*x)^3*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4 - 8*tan(1/2*b*x)^3*tan(1/2*a) + 16*tan(1/2*b*x)^2*tan(1/2*a)^2 + 8*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*a)^4 - 8*tan(1/2*b*x)*tan(1/2*a) - 2*tan(1/2*a)^2 + 1)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1))*tan(1/2*a)^2 - 4*b*c*tan(1/2*b*x) - 4*b*c*tan(1/2*a) - d*log(4*(tan(1/2*b*x)^8*tan(1/2*a)^4 - 2*tan(1/2*b*x)^8*tan(1/2*a)^2 - 8*tan(1/2*b*x)^7*tan(1/2*a)^3 + tan(1/2*b*x)^8 + 8*tan(1/2*b*x)^7*tan(1/2*a) + 16*tan(1/2*b*x)^6*tan(1/2*a)^2 - 8*tan(1/2*b*x)^5*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4*tan(1/2*a)^4 + 8*tan(1/2*b*x)^5*tan(1/2*a) + 36*tan(1/2*b*x)^4*tan(1/2*a)^2 + 8*tan(1/2*b*x)^3*tan(1/2*a)^3 - 2*tan(1/2*b*x)^4 - 8*tan(1/2*b*x)^3*tan(1/2*a) + 16*tan(1/2*b*x)^2*tan(1/2*a)^2 + 8*tan(1/2*b*x)*tan(1/2*a)^3 + tan(1/2*a)^4 - 8*tan(1/2*b*x)*tan(1/2*a) - 2*tan(1/2*a)^2 + 1)/(tan(1/2*a)^4 + 2*tan(1/2*a)^2 + 1)))/(b^2*tan(1/2*b*x)^2*tan(1/2*a)^2 - b^2*tan(1/2*b*x)^2 - 4*b^2*tan(1/2*b*x)*tan(1/2*a) - b^2*tan(1/2*a)^2 + b^2)","B",0
36,0,0,0,0.000000," ","integrate(sec(b*x+a)^2/(d*x+c),x, algorithm=""giac"")","\int \frac{\sec\left(b x + a\right)^{2}}{d x + c}\,{d x}"," ",0,"integrate(sec(b*x + a)^2/(d*x + c), x)","F",0
37,0,0,0,0.000000," ","integrate((d*x+c)^3*sec(b*x+a)^3,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{3} \sec\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^3*sec(b*x + a)^3, x)","F",0
38,0,0,0,0.000000," ","integrate((d*x+c)^2*sec(b*x+a)^3,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{2} \sec\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^2*sec(b*x + a)^3, x)","F",0
39,0,0,0,0.000000," ","integrate((d*x+c)*sec(b*x+a)^3,x, algorithm=""giac"")","\int {\left(d x + c\right)} \sec\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)*sec(b*x + a)^3, x)","F",0
40,0,0,0,0.000000," ","integrate(sec(b*x+a)^2/(d*x+c),x, algorithm=""giac"")","\int \frac{\sec\left(b x + a\right)^{2}}{d x + c}\,{d x}"," ",0,"integrate(sec(b*x + a)^2/(d*x + c), x)","F",0
41,1,1239,0,0.907559," ","integrate((d*x+c)^(5/2)*cos(b*x+a),x, algorithm=""giac"")","-\frac{8 \, {\left(\frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}\right)} c^{3} + 6 \, c d^{2} {\left(\frac{\frac{\sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} + 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(-2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 4 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b^{2}}}{d^{2}} + \frac{\frac{\sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} - 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 4 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b^{2}}}{d^{2}}\right)} - d^{3} {\left(\frac{\frac{\sqrt{2} \sqrt{\pi} {\left(8 \, b^{3} c^{3} + 12 i \, b^{2} c^{2} d - 18 \, b c d^{2} - 15 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{2 \, {\left(-4 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d + 12 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d - 12 i \, \sqrt{d x + c} b^{2} c^{2} d - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 18 \, \sqrt{d x + c} b c d^{2} + 15 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b^{3}}}{d^{3}} + \frac{\frac{\sqrt{2} \sqrt{\pi} {\left(8 \, b^{3} c^{3} - 12 i \, b^{2} c^{2} d - 18 \, b c d^{2} + 15 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{2 \, {\left(4 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d - 12 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d + 12 i \, \sqrt{d x + c} b^{2} c^{2} d - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 18 \, \sqrt{d x + c} b c d^{2} - 15 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b^{3}}}{d^{3}}\right)} - 12 \, {\left(\frac{\sqrt{2} \sqrt{\pi} {\left(2 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{\sqrt{2} \sqrt{\pi} {\left(2 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - \frac{2 i \, \sqrt{d x + c} d e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b} + \frac{2 i \, \sqrt{d x + c} d e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b}\right)} c^{2}}{16 \, d}"," ",0,"-1/16*(8*(sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))*c^3 + 6*c*d^2*((sqrt(2)*sqrt(pi)*(4*b^2*c^2 + 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(-2*I*(d*x + c)^(3/2)*b*d + 4*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b^2)/d^2 + (sqrt(2)*sqrt(pi)*(4*b^2*c^2 - 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(2*I*(d*x + c)^(3/2)*b*d - 4*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b^2)/d^2) - d^3*((sqrt(2)*sqrt(pi)*(8*b^3*c^3 + 12*I*b^2*c^2*d - 18*b*c*d^2 - 15*I*d^3)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 2*(-4*I*(d*x + c)^(5/2)*b^2*d + 12*I*(d*x + c)^(3/2)*b^2*c*d - 12*I*sqrt(d*x + c)*b^2*c^2*d - 10*(d*x + c)^(3/2)*b*d^2 + 18*sqrt(d*x + c)*b*c*d^2 + 15*I*sqrt(d*x + c)*d^3)*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b^3)/d^3 + (sqrt(2)*sqrt(pi)*(8*b^3*c^3 - 12*I*b^2*c^2*d - 18*b*c*d^2 + 15*I*d^3)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 2*(4*I*(d*x + c)^(5/2)*b^2*d - 12*I*(d*x + c)^(3/2)*b^2*c*d + 12*I*sqrt(d*x + c)*b^2*c^2*d - 10*(d*x + c)^(3/2)*b*d^2 + 18*sqrt(d*x + c)*b*c*d^2 - 15*I*sqrt(d*x + c)*d^3)*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b^3)/d^3) - 12*(sqrt(2)*sqrt(pi)*(2*b*c + I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + sqrt(2)*sqrt(pi)*(2*b*c - I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 2*I*sqrt(d*x + c)*d*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b + 2*I*sqrt(d*x + c)*d*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b)*c^2)/d","C",0
42,1,773,0,0.610127," ","integrate((d*x+c)^(3/2)*cos(b*x+a),x, algorithm=""giac"")","-\frac{4 \, {\left(\frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}\right)} c^{2} + d^{2} {\left(\frac{\frac{\sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} + 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(-2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 4 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b^{2}}}{d^{2}} + \frac{\frac{\sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} - 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 4 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b^{2}}}{d^{2}}\right)} - 4 \, {\left(\frac{\sqrt{2} \sqrt{\pi} {\left(2 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{\sqrt{2} \sqrt{\pi} {\left(2 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - \frac{2 i \, \sqrt{d x + c} d e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b} + \frac{2 i \, \sqrt{d x + c} d e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b}\right)} c}{8 \, d}"," ",0,"-1/8*(4*(sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))*c^2 + d^2*((sqrt(2)*sqrt(pi)*(4*b^2*c^2 + 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(-2*I*(d*x + c)^(3/2)*b*d + 4*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b^2)/d^2 + (sqrt(2)*sqrt(pi)*(4*b^2*c^2 - 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(2*I*(d*x + c)^(3/2)*b*d - 4*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b^2)/d^2) - 4*(sqrt(2)*sqrt(pi)*(2*b*c + I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + sqrt(2)*sqrt(pi)*(2*b*c - I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 2*I*sqrt(d*x + c)*d*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b + 2*I*sqrt(d*x + c)*d*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b)*c)/d","C",0
43,1,422,0,0.512950," ","integrate((d*x+c)^(1/2)*cos(b*x+a),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} \sqrt{\pi} {\left(2 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{\sqrt{2} \sqrt{\pi} {\left(2 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - 2 \, {\left(\frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}\right)} c - \frac{2 i \, \sqrt{d x + c} d e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b} + \frac{2 i \, \sqrt{d x + c} d e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b}}{4 \, d}"," ",0,"1/4*(sqrt(2)*sqrt(pi)*(2*b*c + I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + sqrt(2)*sqrt(pi)*(2*b*c - I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 2*(sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))*c - 2*I*sqrt(d*x + c)*d*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b + 2*I*sqrt(d*x + c)*d*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b)/d","C",0
44,1,166,0,0.500041," ","integrate(cos(b*x+a)/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}}{2 \, d}"," ",0,"-1/2*(sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))/d","C",0
45,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(3/2), x)","F",0
46,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(5/2), x)","F",0
47,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(7/2), x)","F",0
48,1,1311,0,0.837322," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^2,x, algorithm=""giac"")","-\frac{2240 \, {\left(\frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} - 4 \, \sqrt{d x + c}\right)} c^{3} - 28 \, c d^{2} {\left(\frac{64 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)}}{d^{2}} - \frac{15 \, {\left(\frac{\sqrt{\pi} {\left(16 \, b^{2} c^{2} + 8 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(-4 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 8 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-2 i \, {\left(d x + c\right)} b + 2 i \, b c - 2 i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}} - \frac{15 \, {\left(\frac{\sqrt{\pi} {\left(16 \, b^{2} c^{2} - 8 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(4 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 8 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{2 i \, {\left(d x + c\right)} b - 2 i \, b c + 2 i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}}\right)} - d^{3} {\left(\frac{256 \, {\left(5 \, {\left(d x + c\right)}^{\frac{7}{2}} - 21 \, {\left(d x + c\right)}^{\frac{5}{2}} c + 35 \, {\left(d x + c\right)}^{\frac{3}{2}} c^{2} - 35 \, \sqrt{d x + c} c^{3}\right)}}{d^{3}} + \frac{35 \, {\left(\frac{\sqrt{\pi} {\left(64 \, b^{3} c^{3} + 48 i \, b^{2} c^{2} d - 36 \, b c d^{2} - 15 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{2 \, {\left(-16 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d + 48 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d - 48 i \, \sqrt{d x + c} b^{2} c^{2} d - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 36 \, \sqrt{d x + c} b c d^{2} + 15 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{-2 i \, {\left(d x + c\right)} b + 2 i \, b c - 2 i \, a d}{d}\right)}}{b^{3}}\right)}}{d^{3}} + \frac{35 \, {\left(\frac{\sqrt{\pi} {\left(64 \, b^{3} c^{3} - 48 i \, b^{2} c^{2} d - 36 \, b c d^{2} + 15 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{2 \, {\left(16 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d - 48 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d + 48 i \, \sqrt{d x + c} b^{2} c^{2} d - 20 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 36 \, \sqrt{d x + c} b c d^{2} - 15 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{2 i \, {\left(d x + c\right)} b - 2 i \, b c + 2 i \, a d}{d}\right)}}{b^{3}}\right)}}{d^{3}}\right)} - 560 \, {\left(\frac{3 \, \sqrt{\pi} {\left(4 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{3 \, \sqrt{\pi} {\left(4 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + 16 \, {\left(d x + c\right)}^{\frac{3}{2}} - 48 \, \sqrt{d x + c} c - \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{2 i \, {\left(d x + c\right)} b - 2 i \, b c + 2 i \, a d}{d}\right)}}{b} + \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{-2 i \, {\left(d x + c\right)} b + 2 i \, b c - 2 i \, a d}{d}\right)}}{b}\right)} c^{2}}{8960 \, d}"," ",0,"-1/8960*(2240*(sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) - 4*sqrt(d*x + c))*c^3 - 28*c*d^2*(64*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)/d^2 - 15*(sqrt(pi)*(16*b^2*c^2 + 8*I*b*c*d - 3*d^2)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(-4*I*(d*x + c)^(3/2)*b*d + 8*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((-2*I*(d*x + c)*b + 2*I*b*c - 2*I*a*d)/d)/b^2)/d^2 - 15*(sqrt(pi)*(16*b^2*c^2 - 8*I*b*c*d - 3*d^2)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(4*I*(d*x + c)^(3/2)*b*d - 8*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((2*I*(d*x + c)*b - 2*I*b*c + 2*I*a*d)/d)/b^2)/d^2) - d^3*(256*(5*(d*x + c)^(7/2) - 21*(d*x + c)^(5/2)*c + 35*(d*x + c)^(3/2)*c^2 - 35*sqrt(d*x + c)*c^3)/d^3 + 35*(sqrt(pi)*(64*b^3*c^3 + 48*I*b^2*c^2*d - 36*b*c*d^2 - 15*I*d^3)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 2*(-16*I*(d*x + c)^(5/2)*b^2*d + 48*I*(d*x + c)^(3/2)*b^2*c*d - 48*I*sqrt(d*x + c)*b^2*c^2*d - 20*(d*x + c)^(3/2)*b*d^2 + 36*sqrt(d*x + c)*b*c*d^2 + 15*I*sqrt(d*x + c)*d^3)*e^((-2*I*(d*x + c)*b + 2*I*b*c - 2*I*a*d)/d)/b^3)/d^3 + 35*(sqrt(pi)*(64*b^3*c^3 - 48*I*b^2*c^2*d - 36*b*c*d^2 + 15*I*d^3)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 2*(16*I*(d*x + c)^(5/2)*b^2*d - 48*I*(d*x + c)^(3/2)*b^2*c*d + 48*I*sqrt(d*x + c)*b^2*c^2*d - 20*(d*x + c)^(3/2)*b*d^2 + 36*sqrt(d*x + c)*b*c*d^2 - 15*I*sqrt(d*x + c)*d^3)*e^((2*I*(d*x + c)*b - 2*I*b*c + 2*I*a*d)/d)/b^3)/d^3) - 560*(3*sqrt(pi)*(4*b*c + I*d)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 3*sqrt(pi)*(4*b*c - I*d)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) + 16*(d*x + c)^(3/2) - 48*sqrt(d*x + c)*c - 6*I*sqrt(d*x + c)*d*e^((2*I*(d*x + c)*b - 2*I*b*c + 2*I*a*d)/d)/b + 6*I*sqrt(d*x + c)*d*e^((-2*I*(d*x + c)*b + 2*I*b*c - 2*I*a*d)/d)/b)*c^2)/d","C",0
49,1,807,0,1.038673," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^2,x, algorithm=""giac"")","-\frac{240 \, {\left(\frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} - 4 \, \sqrt{d x + c}\right)} c^{2} - d^{2} {\left(\frac{64 \, {\left(3 \, {\left(d x + c\right)}^{\frac{5}{2}} - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} c + 15 \, \sqrt{d x + c} c^{2}\right)}}{d^{2}} - \frac{15 \, {\left(\frac{\sqrt{\pi} {\left(16 \, b^{2} c^{2} + 8 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(-4 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 8 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-2 i \, {\left(d x + c\right)} b + 2 i \, b c - 2 i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}} - \frac{15 \, {\left(\frac{\sqrt{\pi} {\left(16 \, b^{2} c^{2} - 8 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(4 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 8 i \, \sqrt{d x + c} b c d - 3 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{2 i \, {\left(d x + c\right)} b - 2 i \, b c + 2 i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}}\right)} - 40 \, {\left(\frac{3 \, \sqrt{\pi} {\left(4 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{3 \, \sqrt{\pi} {\left(4 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + 16 \, {\left(d x + c\right)}^{\frac{3}{2}} - 48 \, \sqrt{d x + c} c - \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{2 i \, {\left(d x + c\right)} b - 2 i \, b c + 2 i \, a d}{d}\right)}}{b} + \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{-2 i \, {\left(d x + c\right)} b + 2 i \, b c - 2 i \, a d}{d}\right)}}{b}\right)} c}{960 \, d}"," ",0,"-1/960*(240*(sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) - 4*sqrt(d*x + c))*c^2 - d^2*(64*(3*(d*x + c)^(5/2) - 10*(d*x + c)^(3/2)*c + 15*sqrt(d*x + c)*c^2)/d^2 - 15*(sqrt(pi)*(16*b^2*c^2 + 8*I*b*c*d - 3*d^2)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(-4*I*(d*x + c)^(3/2)*b*d + 8*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((-2*I*(d*x + c)*b + 2*I*b*c - 2*I*a*d)/d)/b^2)/d^2 - 15*(sqrt(pi)*(16*b^2*c^2 - 8*I*b*c*d - 3*d^2)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(4*I*(d*x + c)^(3/2)*b*d - 8*I*sqrt(d*x + c)*b*c*d - 3*sqrt(d*x + c)*d^2)*e^((2*I*(d*x + c)*b - 2*I*b*c + 2*I*a*d)/d)/b^2)/d^2) - 40*(3*sqrt(pi)*(4*b*c + I*d)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 3*sqrt(pi)*(4*b*c - I*d)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) + 16*(d*x + c)^(3/2) - 48*sqrt(d*x + c)*c - 6*I*sqrt(d*x + c)*d*e^((2*I*(d*x + c)*b - 2*I*b*c + 2*I*a*d)/d)/b + 6*I*sqrt(d*x + c)*d*e^((-2*I*(d*x + c)*b + 2*I*b*c - 2*I*a*d)/d)/b)*c)/d","C",0
50,1,428,0,2.029650," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^2,x, algorithm=""giac"")","-\frac{12 \, {\left(\frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} - 4 \, \sqrt{d x + c}\right)} c - \frac{3 \, \sqrt{\pi} {\left(4 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - \frac{3 \, \sqrt{\pi} {\left(4 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - 16 \, {\left(d x + c\right)}^{\frac{3}{2}} + 48 \, \sqrt{d x + c} c + \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{2 i \, {\left(d x + c\right)} b - 2 i \, b c + 2 i \, a d}{d}\right)}}{b} - \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{-2 i \, {\left(d x + c\right)} b + 2 i \, b c - 2 i \, a d}{d}\right)}}{b}}{48 \, d}"," ",0,"-1/48*(12*(sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) - 4*sqrt(d*x + c))*c - 3*sqrt(pi)*(4*b*c + I*d)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) - 3*sqrt(pi)*(4*b*c - I*d)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 16*(d*x + c)^(3/2) + 48*sqrt(d*x + c)*c + 6*I*sqrt(d*x + c)*d*e^((2*I*(d*x + c)*b - 2*I*b*c + 2*I*a*d)/d)/b - 6*I*sqrt(d*x + c)*d*e^((-2*I*(d*x + c)*b + 2*I*b*c - 2*I*a*d)/d)/b)/d","C",0
51,1,163,0,0.485517," ","integrate(cos(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{2 i \, b c - 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{d}\right) e^{\left(\frac{-2 i \, b c + 2 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} - 4 \, \sqrt{d x + c}}{4 \, d}"," ",0,"-1/4*(sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((2*I*b*c - 2*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(pi)*d*erf(-sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-2*I*b*c + 2*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) - 4*sqrt(d*x + c))/d","C",0
52,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{{\left(d x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/(d*x + c)^(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{{\left(d x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/(d*x + c)^(5/2), x)","F",0
54,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{{\left(d x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/(d*x + c)^(7/2), x)","F",0
55,0,0,0,0.000000," ","integrate(cos(b*x+a)^2/(d*x+c)^(9/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{2}}{{\left(d x + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^2/(d*x + c)^(9/2), x)","F",0
56,1,2457,0,1.921171," ","integrate((d*x+c)^(5/2)*cos(b*x+a)^3,x, algorithm=""giac"")","-\frac{72 \, {\left(\frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}\right)} c^{3} + 18 \, c d^{2} {\left(\frac{\frac{\sqrt{6} \sqrt{\pi} {\left(12 \, b^{2} c^{2} + 4 i \, b c d - d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{6 \, {\left(-2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 4 i \, \sqrt{d x + c} b c d - \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-3 i \, {\left(d x + c\right)} b + 3 i \, b c - 3 i \, a d}{d}\right)}}{b^{2}}}{d^{2}} + \frac{9 \, {\left(\frac{3 \, \sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} + 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(-6 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 12 i \, \sqrt{d x + c} b c d - 9 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}} + \frac{9 \, {\left(\frac{3 \, \sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} - 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(6 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 12 i \, \sqrt{d x + c} b c d - 9 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}} + \frac{\frac{\sqrt{6} \sqrt{\pi} {\left(12 \, b^{2} c^{2} - 4 i \, b c d - d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{6 \, {\left(2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 4 i \, \sqrt{d x + c} b c d - \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{3 i \, {\left(d x + c\right)} b - 3 i \, b c + 3 i \, a d}{d}\right)}}{b^{2}}}{d^{2}}\right)} - d^{3} {\left(\frac{\frac{\sqrt{6} \sqrt{\pi} {\left(72 \, b^{3} c^{3} + 36 i \, b^{2} c^{2} d - 18 \, b c d^{2} - 5 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{6 \, {\left(-12 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d + 36 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d - 36 i \, \sqrt{d x + c} b^{2} c^{2} d - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 18 \, \sqrt{d x + c} b c d^{2} + 5 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{-3 i \, {\left(d x + c\right)} b + 3 i \, b c - 3 i \, a d}{d}\right)}}{b^{3}}}{d^{3}} + \frac{27 \, {\left(\frac{\sqrt{2} \sqrt{\pi} {\left(24 \, b^{3} c^{3} + 36 i \, b^{2} c^{2} d - 54 \, b c d^{2} - 45 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{2 \, {\left(-12 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d + 36 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d - 36 i \, \sqrt{d x + c} b^{2} c^{2} d - 30 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 54 \, \sqrt{d x + c} b c d^{2} + 45 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b^{3}}\right)}}{d^{3}} + \frac{27 \, {\left(\frac{\sqrt{2} \sqrt{\pi} {\left(24 \, b^{3} c^{3} - 36 i \, b^{2} c^{2} d - 54 \, b c d^{2} + 45 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{2 \, {\left(12 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d - 36 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d + 36 i \, \sqrt{d x + c} b^{2} c^{2} d - 30 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 54 \, \sqrt{d x + c} b c d^{2} - 45 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b^{3}}\right)}}{d^{3}} + \frac{\frac{\sqrt{6} \sqrt{\pi} {\left(72 \, b^{3} c^{3} - 36 i \, b^{2} c^{2} d - 18 \, b c d^{2} + 5 i \, d^{3}\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{3}} - \frac{6 \, {\left(12 i \, {\left(d x + c\right)}^{\frac{5}{2}} b^{2} d - 36 i \, {\left(d x + c\right)}^{\frac{3}{2}} b^{2} c d + 36 i \, \sqrt{d x + c} b^{2} c^{2} d - 10 \, {\left(d x + c\right)}^{\frac{3}{2}} b d^{2} + 18 \, \sqrt{d x + c} b c d^{2} - 5 i \, \sqrt{d x + c} d^{3}\right)} e^{\left(\frac{3 i \, {\left(d x + c\right)} b - 3 i \, b c + 3 i \, a d}{d}\right)}}{b^{3}}}{d^{3}}\right)} - 36 \, {\left(\frac{\sqrt{6} \sqrt{\pi} {\left(6 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{9 \, \sqrt{2} \sqrt{\pi} {\left(6 \, b c + 3 i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{9 \, \sqrt{2} \sqrt{\pi} {\left(6 \, b c - 3 i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{\sqrt{6} \sqrt{\pi} {\left(6 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{3 i \, {\left(d x + c\right)} b - 3 i \, b c + 3 i \, a d}{d}\right)}}{b} - \frac{54 i \, \sqrt{d x + c} d e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b} + \frac{54 i \, \sqrt{d x + c} d e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b} + \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{-3 i \, {\left(d x + c\right)} b + 3 i \, b c - 3 i \, a d}{d}\right)}}{b}\right)} c^{2}}{1728 \, d}"," ",0,"-1/1728*(72*(sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))*c^3 + 18*c*d^2*((sqrt(6)*sqrt(pi)*(12*b^2*c^2 + 4*I*b*c*d - d^2)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 6*(-2*I*(d*x + c)^(3/2)*b*d + 4*I*sqrt(d*x + c)*b*c*d - sqrt(d*x + c)*d^2)*e^((-3*I*(d*x + c)*b + 3*I*b*c - 3*I*a*d)/d)/b^2)/d^2 + 9*(3*sqrt(2)*sqrt(pi)*(4*b^2*c^2 + 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(-6*I*(d*x + c)^(3/2)*b*d + 12*I*sqrt(d*x + c)*b*c*d - 9*sqrt(d*x + c)*d^2)*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b^2)/d^2 + 9*(3*sqrt(2)*sqrt(pi)*(4*b^2*c^2 - 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(6*I*(d*x + c)^(3/2)*b*d - 12*I*sqrt(d*x + c)*b*c*d - 9*sqrt(d*x + c)*d^2)*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b^2)/d^2 + (sqrt(6)*sqrt(pi)*(12*b^2*c^2 - 4*I*b*c*d - d^2)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 6*(2*I*(d*x + c)^(3/2)*b*d - 4*I*sqrt(d*x + c)*b*c*d - sqrt(d*x + c)*d^2)*e^((3*I*(d*x + c)*b - 3*I*b*c + 3*I*a*d)/d)/b^2)/d^2) - d^3*((sqrt(6)*sqrt(pi)*(72*b^3*c^3 + 36*I*b^2*c^2*d - 18*b*c*d^2 - 5*I*d^3)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 6*(-12*I*(d*x + c)^(5/2)*b^2*d + 36*I*(d*x + c)^(3/2)*b^2*c*d - 36*I*sqrt(d*x + c)*b^2*c^2*d - 10*(d*x + c)^(3/2)*b*d^2 + 18*sqrt(d*x + c)*b*c*d^2 + 5*I*sqrt(d*x + c)*d^3)*e^((-3*I*(d*x + c)*b + 3*I*b*c - 3*I*a*d)/d)/b^3)/d^3 + 27*(sqrt(2)*sqrt(pi)*(24*b^3*c^3 + 36*I*b^2*c^2*d - 54*b*c*d^2 - 45*I*d^3)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 2*(-12*I*(d*x + c)^(5/2)*b^2*d + 36*I*(d*x + c)^(3/2)*b^2*c*d - 36*I*sqrt(d*x + c)*b^2*c^2*d - 30*(d*x + c)^(3/2)*b*d^2 + 54*sqrt(d*x + c)*b*c*d^2 + 45*I*sqrt(d*x + c)*d^3)*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b^3)/d^3 + 27*(sqrt(2)*sqrt(pi)*(24*b^3*c^3 - 36*I*b^2*c^2*d - 54*b*c*d^2 + 45*I*d^3)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 2*(12*I*(d*x + c)^(5/2)*b^2*d - 36*I*(d*x + c)^(3/2)*b^2*c*d + 36*I*sqrt(d*x + c)*b^2*c^2*d - 30*(d*x + c)^(3/2)*b*d^2 + 54*sqrt(d*x + c)*b*c*d^2 - 45*I*sqrt(d*x + c)*d^3)*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b^3)/d^3 + (sqrt(6)*sqrt(pi)*(72*b^3*c^3 - 36*I*b^2*c^2*d - 18*b*c*d^2 + 5*I*d^3)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^3) - 6*(12*I*(d*x + c)^(5/2)*b^2*d - 36*I*(d*x + c)^(3/2)*b^2*c*d + 36*I*sqrt(d*x + c)*b^2*c^2*d - 10*(d*x + c)^(3/2)*b*d^2 + 18*sqrt(d*x + c)*b*c*d^2 - 5*I*sqrt(d*x + c)*d^3)*e^((3*I*(d*x + c)*b - 3*I*b*c + 3*I*a*d)/d)/b^3)/d^3) - 36*(sqrt(6)*sqrt(pi)*(6*b*c + I*d)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 9*sqrt(2)*sqrt(pi)*(6*b*c + 3*I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 9*sqrt(2)*sqrt(pi)*(6*b*c - 3*I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) + sqrt(6)*sqrt(pi)*(6*b*c - I*d)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 6*I*sqrt(d*x + c)*d*e^((3*I*(d*x + c)*b - 3*I*b*c + 3*I*a*d)/d)/b - 54*I*sqrt(d*x + c)*d*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b + 54*I*sqrt(d*x + c)*d*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b + 6*I*sqrt(d*x + c)*d*e^((-3*I*(d*x + c)*b + 3*I*b*c - 3*I*a*d)/d)/b)*c^2)/d","C",0
57,1,1533,0,2.180538," ","integrate((d*x+c)^(3/2)*cos(b*x+a)^3,x, algorithm=""giac"")","-\frac{12 \, {\left(\frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}\right)} c^{2} + d^{2} {\left(\frac{\frac{\sqrt{6} \sqrt{\pi} {\left(12 \, b^{2} c^{2} + 4 i \, b c d - d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{6 \, {\left(-2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 4 i \, \sqrt{d x + c} b c d - \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-3 i \, {\left(d x + c\right)} b + 3 i \, b c - 3 i \, a d}{d}\right)}}{b^{2}}}{d^{2}} + \frac{9 \, {\left(\frac{3 \, \sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} + 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(-6 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d + 12 i \, \sqrt{d x + c} b c d - 9 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}} + \frac{9 \, {\left(\frac{3 \, \sqrt{2} \sqrt{\pi} {\left(4 \, b^{2} c^{2} - 4 i \, b c d - 3 \, d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{2 \, {\left(6 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 12 i \, \sqrt{d x + c} b c d - 9 \, \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b^{2}}\right)}}{d^{2}} + \frac{\frac{\sqrt{6} \sqrt{\pi} {\left(12 \, b^{2} c^{2} - 4 i \, b c d - d^{2}\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b^{2}} + \frac{6 \, {\left(2 i \, {\left(d x + c\right)}^{\frac{3}{2}} b d - 4 i \, \sqrt{d x + c} b c d - \sqrt{d x + c} d^{2}\right)} e^{\left(\frac{3 i \, {\left(d x + c\right)} b - 3 i \, b c + 3 i \, a d}{d}\right)}}{b^{2}}}{d^{2}}\right)} - 4 \, {\left(\frac{\sqrt{6} \sqrt{\pi} {\left(6 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{9 \, \sqrt{2} \sqrt{\pi} {\left(6 \, b c + 3 i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{9 \, \sqrt{2} \sqrt{\pi} {\left(6 \, b c - 3 i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{\sqrt{6} \sqrt{\pi} {\left(6 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{3 i \, {\left(d x + c\right)} b - 3 i \, b c + 3 i \, a d}{d}\right)}}{b} - \frac{54 i \, \sqrt{d x + c} d e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b} + \frac{54 i \, \sqrt{d x + c} d e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b} + \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{-3 i \, {\left(d x + c\right)} b + 3 i \, b c - 3 i \, a d}{d}\right)}}{b}\right)} c}{288 \, d}"," ",0,"-1/288*(12*(sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))*c^2 + d^2*((sqrt(6)*sqrt(pi)*(12*b^2*c^2 + 4*I*b*c*d - d^2)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 6*(-2*I*(d*x + c)^(3/2)*b*d + 4*I*sqrt(d*x + c)*b*c*d - sqrt(d*x + c)*d^2)*e^((-3*I*(d*x + c)*b + 3*I*b*c - 3*I*a*d)/d)/b^2)/d^2 + 9*(3*sqrt(2)*sqrt(pi)*(4*b^2*c^2 + 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(-6*I*(d*x + c)^(3/2)*b*d + 12*I*sqrt(d*x + c)*b*c*d - 9*sqrt(d*x + c)*d^2)*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b^2)/d^2 + 9*(3*sqrt(2)*sqrt(pi)*(4*b^2*c^2 - 4*I*b*c*d - 3*d^2)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 2*(6*I*(d*x + c)^(3/2)*b*d - 12*I*sqrt(d*x + c)*b*c*d - 9*sqrt(d*x + c)*d^2)*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b^2)/d^2 + (sqrt(6)*sqrt(pi)*(12*b^2*c^2 - 4*I*b*c*d - d^2)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b^2) + 6*(2*I*(d*x + c)^(3/2)*b*d - 4*I*sqrt(d*x + c)*b*c*d - sqrt(d*x + c)*d^2)*e^((3*I*(d*x + c)*b - 3*I*b*c + 3*I*a*d)/d)/b^2)/d^2) - 4*(sqrt(6)*sqrt(pi)*(6*b*c + I*d)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 9*sqrt(2)*sqrt(pi)*(6*b*c + 3*I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 9*sqrt(2)*sqrt(pi)*(6*b*c - 3*I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) + sqrt(6)*sqrt(pi)*(6*b*c - I*d)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 6*I*sqrt(d*x + c)*d*e^((3*I*(d*x + c)*b - 3*I*b*c + 3*I*a*d)/d)/b - 54*I*sqrt(d*x + c)*d*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b + 54*I*sqrt(d*x + c)*d*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b + 6*I*sqrt(d*x + c)*d*e^((-3*I*(d*x + c)*b + 3*I*b*c - 3*I*a*d)/d)/b)*c)/d","C",0
58,1,838,0,3.155915," ","integrate((d*x+c)^(1/2)*cos(b*x+a)^3,x, algorithm=""giac"")","\frac{\frac{\sqrt{6} \sqrt{\pi} {\left(6 \, b c + i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{9 \, \sqrt{2} \sqrt{\pi} {\left(6 \, b c + 3 i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{9 \, \sqrt{2} \sqrt{\pi} {\left(6 \, b c - 3 i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} + \frac{\sqrt{6} \sqrt{\pi} {\left(6 \, b c - i \, d\right)} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)} b} - 6 \, {\left(\frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}\right)} c - \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{3 i \, {\left(d x + c\right)} b - 3 i \, b c + 3 i \, a d}{d}\right)}}{b} - \frac{54 i \, \sqrt{d x + c} d e^{\left(\frac{i \, {\left(d x + c\right)} b - i \, b c + i \, a d}{d}\right)}}{b} + \frac{54 i \, \sqrt{d x + c} d e^{\left(\frac{-i \, {\left(d x + c\right)} b + i \, b c - i \, a d}{d}\right)}}{b} + \frac{6 i \, \sqrt{d x + c} d e^{\left(\frac{-3 i \, {\left(d x + c\right)} b + 3 i \, b c - 3 i \, a d}{d}\right)}}{b}}{144 \, d}"," ",0,"1/144*(sqrt(6)*sqrt(pi)*(6*b*c + I*d)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 9*sqrt(2)*sqrt(pi)*(6*b*c + 3*I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)*b) + 9*sqrt(2)*sqrt(pi)*(6*b*c - 3*I*d)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) + sqrt(6)*sqrt(pi)*(6*b*c - I*d)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)*b) - 6*(sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))*c - 6*I*sqrt(d*x + c)*d*e^((3*I*(d*x + c)*b - 3*I*b*c + 3*I*a*d)/d)/b - 54*I*sqrt(d*x + c)*d*e^((I*(d*x + c)*b - I*b*c + I*a*d)/d)/b + 54*I*sqrt(d*x + c)*d*e^((-I*(d*x + c)*b + I*b*c - I*a*d)/d)/b + 6*I*sqrt(d*x + c)*d*e^((-3*I*(d*x + c)*b + 3*I*b*c - 3*I*a*d)/d)/b)/d","C",0
59,1,328,0,0.616614," ","integrate(cos(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""giac"")","-\frac{\frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{3 i \, b c - 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{i \, b c - i \, a d}{d}\right)}}{\sqrt{b d} {\left(\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{9 \, \sqrt{2} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{2} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-i \, b c + i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}} + \frac{\sqrt{6} \sqrt{\pi} d \operatorname{erf}\left(-\frac{\sqrt{6} \sqrt{b d} \sqrt{d x + c} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}{2 \, d}\right) e^{\left(\frac{-3 i \, b c + 3 i \, a d}{d}\right)}}{\sqrt{b d} {\left(-\frac{i \, b d}{\sqrt{b^{2} d^{2}}} + 1\right)}}}{24 \, d}"," ",0,"-1/24*(sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((3*I*b*c - 3*I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((I*b*c - I*a*d)/d)/(sqrt(b*d)*(I*b*d/sqrt(b^2*d^2) + 1)) + 9*sqrt(2)*sqrt(pi)*d*erf(-1/2*sqrt(2)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-I*b*c + I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)) + sqrt(6)*sqrt(pi)*d*erf(-1/2*sqrt(6)*sqrt(b*d)*sqrt(d*x + c)*(-I*b*d/sqrt(b^2*d^2) + 1)/d)*e^((-3*I*b*c + 3*I*a*d)/d)/(sqrt(b*d)*(-I*b*d/sqrt(b^2*d^2) + 1)))/d","C",0
60,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{{\left(d x + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/(d*x + c)^(3/2), x)","F",0
61,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{{\left(d x + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/(d*x + c)^(5/2), x)","F",0
62,0,0,0,0.000000," ","integrate(cos(b*x+a)^3/(d*x+c)^(7/2),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{3}}{{\left(d x + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^3/(d*x + c)^(7/2), x)","F",0
63,1,69,0,0.488084," ","integrate(x^(3/2)*cos(x),x, algorithm=""giac"")","\left(\frac{3}{16} i + \frac{3}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) - \left(\frac{3}{16} i - \frac{3}{16}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) - \frac{1}{4} \, {\left(2 i \, x^{\frac{3}{2}} - 3 \, \sqrt{x}\right)} e^{\left(i \, x\right)} - \frac{1}{4} \, {\left(-2 i \, x^{\frac{3}{2}} - 3 \, \sqrt{x}\right)} e^{\left(-i \, x\right)}"," ",0,"(3/16*I + 3/16)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x)) - (3/16*I - 3/16)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x)) - 1/4*(2*I*x^(3/2) - 3*sqrt(x))*e^(I*x) - 1/4*(-2*I*x^(3/2) - 3*sqrt(x))*e^(-I*x)","C",0
64,1,53,0,0.441829," ","integrate(x^(1/2)*cos(x),x, algorithm=""giac"")","-\left(\frac{1}{8} i - \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) + \left(\frac{1}{8} i + \frac{1}{8}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) - \frac{1}{2} i \, \sqrt{x} e^{\left(i \, x\right)} + \frac{1}{2} i \, \sqrt{x} e^{\left(-i \, x\right)}"," ",0,"-(1/8*I - 1/8)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x)) + (1/8*I + 1/8)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x)) - 1/2*I*sqrt(x)*e^(I*x) + 1/2*I*sqrt(x)*e^(-I*x)","C",0
65,1,35,0,0.340020," ","integrate(cos(x)/x^(1/2),x, algorithm=""giac"")","-\left(\frac{1}{4} i + \frac{1}{4}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(\left(\frac{1}{2} i - \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right) + \left(\frac{1}{4} i - \frac{1}{4}\right) \, \sqrt{2} \sqrt{\pi} \operatorname{erf}\left(-\left(\frac{1}{2} i + \frac{1}{2}\right) \, \sqrt{2} \sqrt{x}\right)"," ",0,"-(1/4*I + 1/4)*sqrt(2)*sqrt(pi)*erf((1/2*I - 1/2)*sqrt(2)*sqrt(x)) + (1/4*I - 1/4)*sqrt(2)*sqrt(pi)*erf(-(1/2*I + 1/2)*sqrt(2)*sqrt(x))","C",0
66,0,0,0,0.000000," ","integrate(cos(x)/x^(3/2),x, algorithm=""giac"")","\int \frac{\cos\left(x\right)}{x^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(x)/x^(3/2), x)","F",0
67,0,0,0,0.000000," ","integrate((d*x+c)^(4/3)*cos(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{\frac{4}{3}} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^(4/3)*cos(b*x + a), x)","F",0
68,0,0,0,0.000000," ","integrate((d*x+c)^(2/3)*cos(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{\frac{2}{3}} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^(2/3)*cos(b*x + a), x)","F",0
69,0,0,0,0.000000," ","integrate((d*x+c)^(1/3)*cos(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{\frac{1}{3}} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^(1/3)*cos(b*x + a), x)","F",0
70,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(1/3),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(1/3), x)","F",0
71,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(2/3),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{2}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(2/3), x)","F",0
72,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(4/3),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(4/3), x)","F",0
73,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(5/3),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{5}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(5/3), x)","F",0
74,0,0,0,0.000000," ","integrate(cos(b*x+a)/(d*x+c)^(7/3),x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)}{{\left(d x + c\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(cos(b*x + a)/(d*x + c)^(7/3), x)","F",0
75,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int x \sqrt{\cos\left(b x + a\right)}\,{d x}"," ",0,"integrate(x*sqrt(cos(b*x + a)), x)","F",0
76,0,0,0,0.000000," ","integrate(cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int \sqrt{\cos\left(b x + a\right)}\,{d x}"," ",0,"integrate(sqrt(cos(b*x + a)), x)","F",0
77,0,0,0,0.000000," ","integrate(cos(b*x+a)^(1/2)/x,x, algorithm=""giac"")","\int \frac{\sqrt{\cos\left(b x + a\right)}}{x}\,{d x}"," ",0,"integrate(sqrt(cos(b*x + a))/x, x)","F",0
78,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2),x, algorithm=""giac"")","\int x \cos\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)^(3/2), x)","F",0
79,0,0,0,0.000000," ","integrate(cos(b*x+a)^(3/2),x, algorithm=""giac"")","\int \cos\left(b x + a\right)^{\frac{3}{2}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(3/2), x)","F",0
80,0,0,0,0.000000," ","integrate(cos(b*x+a)^(3/2)/x,x, algorithm=""giac"")","\int \frac{\cos\left(b x + a\right)^{\frac{3}{2}}}{x}\,{d x}"," ",0,"integrate(cos(b*x + a)^(3/2)/x, x)","F",0
81,0,0,0,0.000000," ","integrate(x*cos(b*x+a)^(3/2)-1/3*x/cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int x \cos\left(b x + a\right)^{\frac{3}{2}} - \frac{x}{3 \, \sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x*cos(b*x + a)^(3/2) - 1/3*x/sqrt(cos(b*x + a)), x)","F",0
82,0,0,0,0.000000," ","integrate(cos(x)^(3/2)/x^3,x, algorithm=""giac"")","\int \frac{\cos\left(x\right)^{\frac{3}{2}}}{x^{3}}\,{d x}"," ",0,"integrate(cos(x)^(3/2)/x^3, x)","F",0
83,0,0,0,0.000000," ","integrate(x/cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(x/sqrt(cos(b*x + a)), x)","F",0
84,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/sqrt(cos(b*x + a)), x)","F",0
85,0,0,0,0.000000," ","integrate(1/x/cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int \frac{1}{x \sqrt{\cos\left(b x + a\right)}}\,{d x}"," ",0,"integrate(1/(x*sqrt(cos(b*x + a))), x)","F",0
86,0,0,0,0.000000," ","integrate(x/cos(b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{x}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/cos(b*x + a)^(3/2), x)","F",0
87,0,0,0,0.000000," ","integrate(1/cos(b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(b*x + a)^(-3/2), x)","F",0
88,0,0,0,0.000000," ","integrate(1/x/cos(b*x+a)^(3/2),x, algorithm=""giac"")","\int \frac{1}{x \cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(x*cos(b*x + a)^(3/2)), x)","F",0
89,0,0,0,0.000000," ","integrate(x/cos(b*x+a)^(3/2)+x*cos(b*x+a)^(1/2),x, algorithm=""giac"")","\int x \sqrt{\cos\left(b x + a\right)} + \frac{x}{\cos\left(b x + a\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sqrt(cos(b*x + a)) + x/cos(b*x + a)^(3/2), x)","F",0
90,0,0,0,0.000000," ","integrate(x/cos(x)^(3/2)+x*cos(x)^(1/2),x, algorithm=""giac"")","\int x \sqrt{\cos\left(x\right)} + \frac{x}{\cos\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x*sqrt(cos(x)) + x/cos(x)^(3/2), x)","F",0
91,0,0,0,0.000000," ","integrate(x/cos(x)^(5/2)-1/3*x/cos(x)^(1/2),x, algorithm=""giac"")","\int -\frac{x}{3 \, \sqrt{\cos\left(x\right)}} + \frac{x}{\cos\left(x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-1/3*x/sqrt(cos(x)) + x/cos(x)^(5/2), x)","F",0
92,0,0,0,0.000000," ","integrate(x/cos(x)^(7/2)+3/5*x*cos(x)^(1/2),x, algorithm=""giac"")","\int \frac{3}{5} \, x \sqrt{\cos\left(x\right)} + \frac{x}{\cos\left(x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(3/5*x*sqrt(cos(x)) + x/cos(x)^(7/2), x)","F",0
93,0,0,0,0.000000," ","integrate(x^2/cos(x)^(3/2)+x^2*cos(x)^(1/2),x, algorithm=""giac"")","\int x^{2} \sqrt{\cos\left(x\right)} + \frac{x^{2}}{\cos\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2*sqrt(cos(x)) + x^2/cos(x)^(3/2), x)","F",0
94,0,0,0,0.000000," ","integrate(x/sec(x)^(3/2)-1/3*x*sec(x)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{3} \, x \sqrt{\sec\left(x\right)} + \frac{x}{\sec\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/3*x*sqrt(sec(x)) + x/sec(x)^(3/2), x)","F",0
95,0,0,0,0.000000," ","integrate(x/sec(x)^(5/2)-3/5*x/sec(x)^(1/2),x, algorithm=""giac"")","\int -\frac{3 \, x}{5 \, \sqrt{\sec\left(x\right)}} + \frac{x}{\sec\left(x\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(-3/5*x/sqrt(sec(x)) + x/sec(x)^(5/2), x)","F",0
96,0,0,0,0.000000," ","integrate(x/sec(x)^(7/2)-5/21*x*sec(x)^(1/2),x, algorithm=""giac"")","\int -\frac{5}{21} \, x \sqrt{\sec\left(x\right)} + \frac{x}{\sec\left(x\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(-5/21*x*sqrt(sec(x)) + x/sec(x)^(7/2), x)","F",0
97,0,0,0,0.000000," ","integrate(x^2/sec(x)^(3/2)-1/3*x^2*sec(x)^(1/2),x, algorithm=""giac"")","\int -\frac{1}{3} \, x^{2} \sqrt{\sec\left(x\right)} + \frac{x^{2}}{\sec\left(x\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(-1/3*x^2*sqrt(sec(x)) + x^2/sec(x)^(3/2), x)","F",0
98,0,0,0,0.000000," ","integrate((d*x+c)^m*(b*cos(f*x+e))^n,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{m} \left(b \cos\left(f x + e\right)\right)^{n}\,{d x}"," ",0,"integrate((d*x + c)^m*(b*cos(f*x + e))^n, x)","F",0
99,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^3,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{3}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^3, x)","F",0
100,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a)^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a)^2, x)","F",0
101,0,0,0,0.000000," ","integrate((d*x+c)^m*cos(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{m} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*cos(b*x + a), x)","F",0
102,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a),x, algorithm=""giac"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right)\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a), x)","F",0
103,0,0,0,0.000000," ","integrate((d*x+c)^m*sec(b*x+a)^2,x, algorithm=""giac"")","\int {\left(d x + c\right)}^{m} \sec\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate((d*x + c)^m*sec(b*x + a)^2, x)","F",0
104,0,0,0,0.000000," ","integrate(x^(3+m)*cos(b*x+a),x, algorithm=""giac"")","\int x^{m + 3} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 3)*cos(b*x + a), x)","F",0
105,0,0,0,0.000000," ","integrate(x^(2+m)*cos(b*x+a),x, algorithm=""giac"")","\int x^{m + 2} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 2)*cos(b*x + a), x)","F",0
106,0,0,0,0.000000," ","integrate(x^(1+m)*cos(b*x+a),x, algorithm=""giac"")","\int x^{m + 1} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m + 1)*cos(b*x + a), x)","F",0
107,0,0,0,0.000000," ","integrate(x^m*cos(b*x+a),x, algorithm=""giac"")","\int x^{m} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^m*cos(b*x + a), x)","F",0
108,0,0,0,0.000000," ","integrate(x^(-1+m)*cos(b*x+a),x, algorithm=""giac"")","\int x^{m - 1} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 1)*cos(b*x + a), x)","F",0
109,0,0,0,0.000000," ","integrate(x^(-2+m)*cos(b*x+a),x, algorithm=""giac"")","\int x^{m - 2} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 2)*cos(b*x + a), x)","F",0
110,0,0,0,0.000000," ","integrate(x^(-3+m)*cos(b*x+a),x, algorithm=""giac"")","\int x^{m - 3} \cos\left(b x + a\right)\,{d x}"," ",0,"integrate(x^(m - 3)*cos(b*x + a), x)","F",0
111,0,0,0,0.000000," ","integrate(x^(3+m)*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m + 3} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^(m + 3)*cos(b*x + a)^2, x)","F",0
112,0,0,0,0.000000," ","integrate(x^(2+m)*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m + 2} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^(m + 2)*cos(b*x + a)^2, x)","F",0
113,0,0,0,0.000000," ","integrate(x^(1+m)*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m + 1} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^(m + 1)*cos(b*x + a)^2, x)","F",0
114,0,0,0,0.000000," ","integrate(x^m*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^m*cos(b*x + a)^2, x)","F",0
115,0,0,0,0.000000," ","integrate(x^(-1+m)*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m - 1} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^(m - 1)*cos(b*x + a)^2, x)","F",0
116,0,0,0,0.000000," ","integrate(x^(-2+m)*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m - 2} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^(m - 2)*cos(b*x + a)^2, x)","F",0
117,0,0,0,0.000000," ","integrate(x^(-3+m)*cos(b*x+a)^2,x, algorithm=""giac"")","\int x^{m - 3} \cos\left(b x + a\right)^{2}\,{d x}"," ",0,"integrate(x^(m - 3)*cos(b*x + a)^2, x)","F",0
118,1,156,0,0.449042," ","integrate((d*x+c)^3*(a+a*cos(f*x+e)),x, algorithm=""giac"")","\frac{1}{4} \, a d^{3} x^{4} + a c d^{2} x^{3} + \frac{3}{2} \, a c^{2} d x^{2} + a c^{3} x + \frac{3 \, {\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)}{f^{4}} + \frac{{\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + 3 \, a c^{2} d f^{3} x + a c^{3} f^{3} - 6 \, a d^{3} f x - 6 \, a c d^{2} f\right)} \sin\left(f x + e\right)}{f^{4}}"," ",0,"1/4*a*d^3*x^4 + a*c*d^2*x^3 + 3/2*a*c^2*d*x^2 + a*c^3*x + 3*(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)/f^4 + (a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + 3*a*c^2*d*f^3*x + a*c^3*f^3 - 6*a*d^3*f*x - 6*a*c*d^2*f)*sin(f*x + e)/f^4","A",0
119,1,94,0,0.440453," ","integrate((d*x+c)^2*(a+a*cos(f*x+e)),x, algorithm=""giac"")","\frac{1}{3} \, a d^{2} x^{3} + a c d x^{2} + a c^{2} x + \frac{2 \, {\left(a d^{2} f x + a c d f\right)} \cos\left(f x + e\right)}{f^{3}} + \frac{{\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)}{f^{3}}"," ",0,"1/3*a*d^2*x^3 + a*c*d*x^2 + a*c^2*x + 2*(a*d^2*f*x + a*c*d*f)*cos(f*x + e)/f^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
120,1,46,0,0.418741," ","integrate((d*x+c)*(a+a*cos(f*x+e)),x, algorithm=""giac"")","\frac{1}{2} \, a d x^{2} + a c x + \frac{a d \cos\left(f x + e\right)}{f^{2}} + \frac{{\left(a d f x + a c f\right)} \sin\left(f x + e\right)}{f^{2}}"," ",0,"1/2*a*d*x^2 + a*c*x + a*d*cos(f*x + e)/f^2 + (a*d*f*x + a*c*f)*sin(f*x + e)/f^2","A",0
121,1,692,0,0.487516," ","integrate((a+a*cos(f*x+e))/(d*x+c),x, algorithm=""giac"")","\frac{2 \, a \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + a \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + a \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 2 \, a \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) + 4 \, a \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 2 \, a \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} - 4 \, a \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} - a \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} - a \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} + 4 \, a \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) + 4 \, a \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) + 2 \, a \log\left({\left| d x + c \right|}\right) \tan\left(\frac{1}{2} \, e\right)^{2} - a \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} - a \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) - 2 \, a \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) + 4 \, a \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right) - 2 \, a \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right) + 2 \, a \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right) - 4 \, a \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{1}{2} \, e\right) + 2 \, a \log\left({\left| d x + c \right|}\right) + a \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) + a \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right)}{2 \, {\left(d \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + d \tan\left(\frac{c f}{2 \, d}\right)^{2} + d \tan\left(\frac{1}{2} \, e\right)^{2} + d\right)}}"," ",0,"1/2*(2*a*log(abs(d*x + c))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + a*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + a*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 2*a*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e) - 2*a*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e) + 4*a*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)^2*tan(1/2*e) - 2*a*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)^2 + 2*a*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)^2 - 4*a*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)*tan(1/2*e)^2 + 2*a*log(abs(d*x + c))*tan(1/2*c*f/d)^2 - a*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2 - a*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2 + 4*a*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(1/2*e) + 4*a*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(1/2*e) + 2*a*log(abs(d*x + c))*tan(1/2*e)^2 - a*real_part(cos_integral(f*x + c*f/d))*tan(1/2*e)^2 - a*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*e)^2 + 2*a*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d) - 2*a*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d) + 4*a*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d) - 2*a*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*e) + 2*a*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*e) - 4*a*sin_integral((d*f*x + c*f)/d)*tan(1/2*e) + 2*a*log(abs(d*x + c)) + a*real_part(cos_integral(f*x + c*f/d)) + a*real_part(cos_integral(-f*x - c*f/d)))/(d*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + d*tan(1/2*c*f/d)^2 + d*tan(1/2*e)^2 + d)","C",0
122,1,578,0,0.542023," ","integrate((a+a*cos(f*x+e))/(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} f^{2} \operatorname{Ci}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) \sin\left(\frac{c f - d e}{d}\right) - c f^{3} \operatorname{Ci}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) \sin\left(\frac{c f - d e}{d}\right) + d f^{2} \operatorname{Ci}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) e \sin\left(\frac{c f - d e}{d}\right) - {\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} f^{2} \cos\left(\frac{c f - d e}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) + c f^{3} \cos\left(\frac{c f - d e}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) - d f^{2} \cos\left(\frac{c f - d e}{d}\right) e \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) + d f^{2} \cos\left(\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)}}{d}\right)\right)} a d^{2}}{{\left({\left(d x + c\right)} d^{4} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c d^{4} f + d^{5} e\right)} f} - \frac{a}{{\left(d x + c\right)} d}"," ",0,"((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c))*f^2*cos_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*sin((c*f - d*e)/d) - c*f^3*cos_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*sin((c*f - d*e)/d) + d*f^2*cos_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*e*sin((c*f - d*e)/d) - (d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c))*f^2*cos((c*f - d*e)/d)*sin_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) + c*f^3*cos((c*f - d*e)/d)*sin_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) - d*f^2*cos((c*f - d*e)/d)*e*sin_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) + d*f^2*cos((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c))/d))*a*d^2/(((d*x + c)*d^4*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*d^4*f + d^5*e)*f) - a/((d*x + c)*d)","B",0
123,1,339,0,0.715928," ","integrate((d*x+c)^3*(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{8} \, a^{2} d^{3} x^{4} + \frac{3}{2} \, a^{2} c d^{2} x^{3} + \frac{9}{4} \, a^{2} c^{2} d x^{2} + \frac{3}{2} \, a^{2} c^{3} x + \frac{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(2 \, f x + 2 \, e\right)}{16 \, f^{4}} + \frac{6 \, {\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)}{f^{4}} + \frac{{\left(2 \, a^{2} d^{3} f^{3} x^{3} + 6 \, a^{2} c d^{2} f^{3} x^{2} + 6 \, a^{2} c^{2} d f^{3} x + 2 \, a^{2} c^{3} f^{3} - 3 \, a^{2} d^{3} f x - 3 \, a^{2} c d^{2} f\right)} \sin\left(2 \, f x + 2 \, e\right)}{8 \, f^{4}} + \frac{2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3} - 6 \, a^{2} d^{3} f x - 6 \, a^{2} c d^{2} f\right)} \sin\left(f x + e\right)}{f^{4}}"," ",0,"3/8*a^2*d^3*x^4 + 3/2*a^2*c*d^2*x^3 + 9/4*a^2*c^2*d*x^2 + 3/2*a^2*c^3*x + 3/16*(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(2*f*x + 2*e)/f^4 + 6*(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)/f^4 + 1/8*(2*a^2*d^3*f^3*x^3 + 6*a^2*c*d^2*f^3*x^2 + 6*a^2*c^2*d*f^3*x + 2*a^2*c^3*f^3 - 3*a^2*d^3*f*x - 3*a^2*c*d^2*f)*sin(2*f*x + 2*e)/f^4 + 2*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3 - 6*a^2*d^3*f*x - 6*a^2*c*d^2*f)*sin(f*x + e)/f^4","A",0
124,1,207,0,0.807409," ","integrate((d*x+c)^2*(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\frac{1}{2} \, a^{2} d^{2} x^{3} + \frac{3}{2} \, a^{2} c d x^{2} + \frac{3}{2} \, a^{2} c^{2} x + \frac{{\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cos\left(2 \, f x + 2 \, e\right)}{4 \, f^{3}} + \frac{4 \, {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cos\left(f x + e\right)}{f^{3}} + \frac{{\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)} \sin\left(2 \, f x + 2 \, e\right)}{8 \, f^{3}} + \frac{2 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2} - 2 \, a^{2} d^{2}\right)} \sin\left(f x + e\right)}{f^{3}}"," ",0,"1/2*a^2*d^2*x^3 + 3/2*a^2*c*d*x^2 + 3/2*a^2*c^2*x + 1/4*(a^2*d^2*f*x + a^2*c*d*f)*cos(2*f*x + 2*e)/f^3 + 4*(a^2*d^2*f*x + a^2*c*d*f)*cos(f*x + e)/f^3 + 1/8*(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)*sin(2*f*x + 2*e)/f^3 + 2*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2 - 2*a^2*d^2)*sin(f*x + e)/f^3","A",0
125,1,107,0,0.390966," ","integrate((d*x+c)*(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\frac{3}{4} \, a^{2} d x^{2} + \frac{3}{2} \, a^{2} c x + \frac{a^{2} d \cos\left(2 \, f x + 2 \, e\right)}{8 \, f^{2}} + \frac{2 \, a^{2} d \cos\left(f x + e\right)}{f^{2}} + \frac{{\left(a^{2} d f x + a^{2} c f\right)} \sin\left(2 \, f x + 2 \, e\right)}{4 \, f^{2}} + \frac{2 \, {\left(a^{2} d f x + a^{2} c f\right)} \sin\left(f x + e\right)}{f^{2}}"," ",0,"3/4*a^2*d*x^2 + 3/2*a^2*c*x + 1/8*a^2*d*cos(2*f*x + 2*e)/f^2 + 2*a^2*d*cos(f*x + e)/f^2 + 1/4*(a^2*d*f*x + a^2*c*f)*sin(2*f*x + 2*e)/f^2 + 2*(a^2*d*f*x + a^2*c*f)*sin(f*x + e)/f^2","A",0
126,1,6933,0,2.032223," ","integrate((a+a*cos(f*x+e))^2/(d*x+c),x, algorithm=""giac"")","\frac{6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(e\right)^{2} + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(e\right)^{2} - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right) + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(e\right)^{2} - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(e\right)^{2} + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(e\right)^{2} - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{1}{2} \, e\right) \tan\left(e\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{d}\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right)^{2} + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{c f}{2 \, d}\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right)^{2} + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) + 16 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) \tan\left(\frac{1}{2} \, e\right) + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(\frac{1}{2} \, e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} - 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(e\right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) \tan\left(e\right) + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(e\right)^{2} + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(e\right)^{2} - a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(e\right)^{2} + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(\frac{c f}{d}\right) + 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(\frac{c f}{d}\right) + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{c f}{2 \, d}\right) + 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{c f}{2 \, d}\right) - 8 \, a^{2} \Im \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right) + 8 \, a^{2} \Im \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) \tan\left(\frac{1}{2} \, e\right) - 16 \, a^{2} \operatorname{Si}\left(\frac{d f x + c f}{d}\right) \tan\left(\frac{1}{2} \, e\right) - 2 \, a^{2} \Im \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) \tan\left(e\right) + 2 \, a^{2} \Im \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right) \tan\left(e\right) - 4 \, a^{2} \operatorname{Si}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \tan\left(e\right) + 6 \, a^{2} \log\left({\left| d x + c \right|}\right) + a^{2} \Re \left( \operatorname{Ci}\left(2 \, f x + \frac{2 \, c f}{d}\right) \right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(f x + \frac{c f}{d}\right) \right) + 4 \, a^{2} \Re \left( \operatorname{Ci}\left(-f x - \frac{c f}{d}\right) \right) + a^{2} \Re \left( \operatorname{Ci}\left(-2 \, f x - \frac{2 \, c f}{d}\right) \right)}{4 \, {\left(d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{c f}{2 \, d}\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + d \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{c f}{2 \, d}\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{1}{2} \, e\right)^{2} \tan\left(e\right)^{2} + d \tan\left(\frac{c f}{d}\right)^{2} + d \tan\left(\frac{c f}{2 \, d}\right)^{2} + d \tan\left(\frac{1}{2} \, e\right)^{2} + d \tan\left(e\right)^{2} + d\right)}}"," ",0,"1/4*(6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)*tan(e)^2 - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)*tan(e)^2 + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)*tan(e)^2 - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)^2*tan(e)^2 + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)^2*tan(e)^2 - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)^2*tan(e)^2 - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) + 4*a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e)^2 + 16*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)*tan(e)^2 + 16*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e) - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e) + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e) - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)^2 + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)^2 - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e)^2 + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2 - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e) - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e) + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e) + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e) - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2*tan(e) + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*e)^2*tan(e) - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e) + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(e)^2 - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(e)^2 + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(e)^2 - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(e)^2 + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(e)^2 - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(e)^2 - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*e)*tan(e)^2 + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*e)*tan(e)^2 - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*e)*tan(e)^2 + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)*tan(e)^2 - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)*tan(e)^2 + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)^2*tan(1/2*e)*tan(e)^2 - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*e)^2*tan(e)^2 + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*e)^2*tan(e)^2 - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(1/2*e)^2*tan(e)^2 - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)^2*tan(e)^2 + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)^2*tan(e)^2 - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)*tan(1/2*e)^2*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(1/2*c*f/d)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)^2 + 16*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e) + 16*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d)*tan(1/2*e) + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(1/2*e)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(1/2*e)^2 + 6*a^2*log(abs(d*x + c))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(e) + 4*a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2*tan(e) + 4*a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*e)^2*tan(e) + 4*a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*e)^2*tan(e) + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2*tan(e)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(e)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(e)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(e)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(1/2*c*f/d)^2*tan(e)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*c*f/d)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(e)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*c*f/d)^2*tan(e)^2 + 16*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)*tan(e)^2 + 16*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(1/2*e)^2*tan(e)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*e)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*e)^2*tan(e)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*e)^2*tan(e)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*e)^2*tan(e)^2 + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d) - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*c*f/d) + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*c*f/d) + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2 - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*c*f/d)^2 + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(1/2*c*f/d)^2 - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2*tan(1/2*e) + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2*tan(1/2*e) - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(c*f/d)^2*tan(1/2*e) + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e) - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2*tan(1/2*e) + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)^2*tan(1/2*e) + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(1/2*e)^2 - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(1/2*e)^2 + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(1/2*e)^2 - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)^2 + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(1/2*e)^2 - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)*tan(1/2*e)^2 + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2*tan(e) - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2*tan(e) + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)^2*tan(e) - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*c*f/d)^2*tan(e) + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*c*f/d)^2*tan(e) - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(1/2*c*f/d)^2*tan(e) - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*e)^2*tan(e) + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*e)^2*tan(e) - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(1/2*e)^2*tan(e) - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(e)^2 + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(e)^2 - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d)*tan(e)^2 + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(e)^2 - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(e)^2 + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d)*tan(e)^2 - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*e)*tan(e)^2 + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*e)*tan(e)^2 - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*e)*tan(e)^2 + 6*a^2*log(abs(d*x + c))*tan(c*f/d)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(c*f/d)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(c*f/d)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)^2 + 6*a^2*log(abs(d*x + c))*tan(1/2*c*f/d)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*c*f/d)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*c*f/d)^2 + 16*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d)*tan(1/2*e) + 16*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d)*tan(1/2*e) + 6*a^2*log(abs(d*x + c))*tan(1/2*e)^2 + a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(1/2*e)^2 - 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(1/2*e)^2 - 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(1/2*e)^2 + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(1/2*e)^2 + 4*a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d)*tan(e) + 4*a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d)*tan(e) + 6*a^2*log(abs(d*x + c))*tan(e)^2 - a^2*real_part(cos_integral(2*f*x + 2*c*f/d))*tan(e)^2 + 4*a^2*real_part(cos_integral(f*x + c*f/d))*tan(e)^2 + 4*a^2*real_part(cos_integral(-f*x - c*f/d))*tan(e)^2 - a^2*real_part(cos_integral(-2*f*x - 2*c*f/d))*tan(e)^2 + 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(c*f/d) - 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(c*f/d) + 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(c*f/d) + 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*c*f/d) - 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*c*f/d) + 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*c*f/d) - 8*a^2*imag_part(cos_integral(f*x + c*f/d))*tan(1/2*e) + 8*a^2*imag_part(cos_integral(-f*x - c*f/d))*tan(1/2*e) - 16*a^2*sin_integral((d*f*x + c*f)/d)*tan(1/2*e) - 2*a^2*imag_part(cos_integral(2*f*x + 2*c*f/d))*tan(e) + 2*a^2*imag_part(cos_integral(-2*f*x - 2*c*f/d))*tan(e) - 4*a^2*sin_integral(2*(d*f*x + c*f)/d)*tan(e) + 6*a^2*log(abs(d*x + c)) + a^2*real_part(cos_integral(2*f*x + 2*c*f/d)) + 4*a^2*real_part(cos_integral(f*x + c*f/d)) + 4*a^2*real_part(cos_integral(-f*x - c*f/d)) + a^2*real_part(cos_integral(-2*f*x - 2*c*f/d)))/(d*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + d*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + d*tan(c*f/d)^2*tan(1/2*c*f/d)^2*tan(e)^2 + d*tan(c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + d*tan(1/2*c*f/d)^2*tan(1/2*e)^2*tan(e)^2 + d*tan(c*f/d)^2*tan(1/2*c*f/d)^2 + d*tan(c*f/d)^2*tan(1/2*e)^2 + d*tan(1/2*c*f/d)^2*tan(1/2*e)^2 + d*tan(c*f/d)^2*tan(e)^2 + d*tan(1/2*c*f/d)^2*tan(e)^2 + d*tan(1/2*e)^2*tan(e)^2 + d*tan(c*f/d)^2 + d*tan(1/2*c*f/d)^2 + d*tan(1/2*e)^2 + d*tan(e)^2 + d)","C",0
127,1,1133,0,1.000386," ","integrate((a+a*cos(f*x+e))^2/(d*x+c)^2,x, algorithm=""giac"")","\frac{{\left(2 \, {\left(d x + c\right)} a^{2} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} f^{2} \operatorname{Ci}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e\right)}}{d}\right) \sin\left(\frac{2 \, {\left(c f - d e\right)}}{d}\right) - 2 \, a^{2} c f^{3} \operatorname{Ci}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e\right)}}{d}\right) \sin\left(\frac{2 \, {\left(c f - d e\right)}}{d}\right) + 2 \, a^{2} d f^{2} \operatorname{Ci}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e\right)}}{d}\right) e \sin\left(\frac{2 \, {\left(c f - d e\right)}}{d}\right) + 4 \, {\left(d x + c\right)} a^{2} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} f^{2} \operatorname{Ci}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) \sin\left(\frac{c f - d e}{d}\right) - 4 \, a^{2} c f^{3} \operatorname{Ci}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) \sin\left(\frac{c f - d e}{d}\right) + 4 \, a^{2} d f^{2} \operatorname{Ci}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) e \sin\left(\frac{c f - d e}{d}\right) - 4 \, {\left(d x + c\right)} a^{2} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} f^{2} \cos\left(\frac{c f - d e}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) + 4 \, a^{2} c f^{3} \cos\left(\frac{c f - d e}{d}\right) \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) - 4 \, a^{2} d f^{2} \cos\left(\frac{c f - d e}{d}\right) e \operatorname{Si}\left(-\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e}{d}\right) - 2 \, {\left(d x + c\right)} a^{2} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} f^{2} \cos\left(\frac{2 \, {\left(c f - d e\right)}}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e\right)}}{d}\right) + 2 \, a^{2} c f^{3} \cos\left(\frac{2 \, {\left(c f - d e\right)}}{d}\right) \operatorname{Si}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e\right)}}{d}\right) - 2 \, a^{2} d f^{2} \cos\left(\frac{2 \, {\left(c f - d e\right)}}{d}\right) e \operatorname{Si}\left(-\frac{2 \, {\left({\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c f + d e\right)}}{d}\right) + a^{2} d f^{2} \cos\left(\frac{2 \, {\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)}}{d}\right) + 4 \, a^{2} d f^{2} \cos\left(\frac{{\left(d x + c\right)} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)}}{d}\right) + 3 \, a^{2} d f^{2}\right)} d^{2}}{2 \, {\left({\left(d x + c\right)} d^{4} {\left(\frac{c f}{d x + c} - f - \frac{d e}{d x + c}\right)} - c d^{4} f + d^{5} e\right)} f}"," ",0,"1/2*(2*(d*x + c)*a^2*(c*f/(d*x + c) - f - d*e/(d*x + c))*f^2*cos_integral(-2*((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*sin(2*(c*f - d*e)/d) - 2*a^2*c*f^3*cos_integral(-2*((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*sin(2*(c*f - d*e)/d) + 2*a^2*d*f^2*cos_integral(-2*((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*e*sin(2*(c*f - d*e)/d) + 4*(d*x + c)*a^2*(c*f/(d*x + c) - f - d*e/(d*x + c))*f^2*cos_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*sin((c*f - d*e)/d) - 4*a^2*c*f^3*cos_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*sin((c*f - d*e)/d) + 4*a^2*d*f^2*cos_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d)*e*sin((c*f - d*e)/d) - 4*(d*x + c)*a^2*(c*f/(d*x + c) - f - d*e/(d*x + c))*f^2*cos((c*f - d*e)/d)*sin_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) + 4*a^2*c*f^3*cos((c*f - d*e)/d)*sin_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) - 4*a^2*d*f^2*cos((c*f - d*e)/d)*e*sin_integral(-((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) - 2*(d*x + c)*a^2*(c*f/(d*x + c) - f - d*e/(d*x + c))*f^2*cos(2*(c*f - d*e)/d)*sin_integral(-2*((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) + 2*a^2*c*f^3*cos(2*(c*f - d*e)/d)*sin_integral(-2*((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) - 2*a^2*d*f^2*cos(2*(c*f - d*e)/d)*e*sin_integral(-2*((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*f + d*e)/d) + a^2*d*f^2*cos(2*(d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c))/d) + 4*a^2*d*f^2*cos((d*x + c)*(c*f/(d*x + c) - f - d*e/(d*x + c))/d) + 3*a^2*d*f^2)*d^2/(((d*x + c)*d^4*(c*f/(d*x + c) - f - d*e/(d*x + c)) - c*d^4*f + d^5*e)*f)","B",0
128,0,0,0,0.000000," ","integrate((d*x+c)^3/(a+a*cos(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{3}}{a \cos\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^3/(a*cos(f*x + e) + a), x)","F",0
129,0,0,0,0.000000," ","integrate((d*x+c)^2/(a+a*cos(f*x+e)),x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{2}}{a \cos\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*x + c)^2/(a*cos(f*x + e) + a), x)","F",0
130,1,234,0,0.610786," ","integrate((d*x+c)/(a+a*cos(f*x+e)),x, algorithm=""giac"")","-\frac{d f x \tan\left(\frac{1}{2} \, f x\right) + d f x \tan\left(\frac{1}{2} \, e\right) - d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 1\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + c f \tan\left(\frac{1}{2} \, f x\right) + c f \tan\left(\frac{1}{2} \, e\right) + d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 1\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right)}{a f^{2} \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) - a f^{2}}"," ",0,"-(d*f*x*tan(1/2*f*x) + d*f*x*tan(1/2*e) - d*log(4*(tan(1/2*f*x)^4*tan(1/2*e)^2 - 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 - 2*tan(1/2*f*x)*tan(1/2*e) + 1)/(tan(1/2*e)^2 + 1))*tan(1/2*f*x)*tan(1/2*e) + c*f*tan(1/2*f*x) + c*f*tan(1/2*e) + d*log(4*(tan(1/2*f*x)^4*tan(1/2*e)^2 - 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 - 2*tan(1/2*f*x)*tan(1/2*e) + 1)/(tan(1/2*e)^2 + 1)))/(a*f^2*tan(1/2*f*x)*tan(1/2*e) - a*f^2)","B",0
131,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)} {\left(a \cos\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x + c)*(a*cos(f*x + e) + a)), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*cos(f*x+e)),x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)}^{2} {\left(a \cos\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(1/((d*x + c)^2*(a*cos(f*x + e) + a)), x)","F",0
133,0,0,0,0.000000," ","integrate((d*x+c)^3/(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{3}}{{\left(a \cos\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^3/(a*cos(f*x + e) + a)^2, x)","F",0
134,0,0,0,0.000000," ","integrate((d*x+c)^2/(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\int \frac{{\left(d x + c\right)}^{2}}{{\left(a \cos\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*x + c)^2/(a*cos(f*x + e) + a)^2, x)","F",0
135,1,757,0,3.029073," ","integrate((d*x+c)/(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","-\frac{3 \, d f x \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right)^{2} + 3 \, d f x \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{3} - 2 \, d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 1\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right)^{3} + 3 \, c f \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right)^{2} + 3 \, c f \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{3} + d \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right)^{3} + d f x \tan\left(\frac{1}{2} \, f x\right)^{3} - 3 \, d f x \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right) - 3 \, d f x \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right)^{2} + 6 \, d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 1\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + d f x \tan\left(\frac{1}{2} \, e\right)^{3} + c f \tan\left(\frac{1}{2} \, f x\right)^{3} - 3 \, c f \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right) + d \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) - 3 \, c f \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right)^{2} - d \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + c f \tan\left(\frac{1}{2} \, e\right)^{3} + d \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right)^{3} + 3 \, d f x \tan\left(\frac{1}{2} \, f x\right) + 3 \, d f x \tan\left(\frac{1}{2} \, e\right) - 6 \, d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 1\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 3 \, c f \tan\left(\frac{1}{2} \, f x\right) - d \tan\left(\frac{1}{2} \, f x\right)^{2} + 3 \, c f \tan\left(\frac{1}{2} \, e\right) + d \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) - d \tan\left(\frac{1}{2} \, e\right)^{2} + 2 \, d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} \tan\left(\frac{1}{2} \, e\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} - 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + 1\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) - d}{6 \, {\left(a^{2} f^{2} \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right)^{3} - 3 \, a^{2} f^{2} \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + 3 \, a^{2} f^{2} \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) - a^{2} f^{2}\right)}}"," ",0,"-1/6*(3*d*f*x*tan(1/2*f*x)^3*tan(1/2*e)^2 + 3*d*f*x*tan(1/2*f*x)^2*tan(1/2*e)^3 - 2*d*log(4*(tan(1/2*f*x)^4*tan(1/2*e)^2 - 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 - 2*tan(1/2*f*x)*tan(1/2*e) + 1)/(tan(1/2*e)^2 + 1))*tan(1/2*f*x)^3*tan(1/2*e)^3 + 3*c*f*tan(1/2*f*x)^3*tan(1/2*e)^2 + 3*c*f*tan(1/2*f*x)^2*tan(1/2*e)^3 + d*tan(1/2*f*x)^3*tan(1/2*e)^3 + d*f*x*tan(1/2*f*x)^3 - 3*d*f*x*tan(1/2*f*x)^2*tan(1/2*e) - 3*d*f*x*tan(1/2*f*x)*tan(1/2*e)^2 + 6*d*log(4*(tan(1/2*f*x)^4*tan(1/2*e)^2 - 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 - 2*tan(1/2*f*x)*tan(1/2*e) + 1)/(tan(1/2*e)^2 + 1))*tan(1/2*f*x)^2*tan(1/2*e)^2 + d*f*x*tan(1/2*e)^3 + c*f*tan(1/2*f*x)^3 - 3*c*f*tan(1/2*f*x)^2*tan(1/2*e) + d*tan(1/2*f*x)^3*tan(1/2*e) - 3*c*f*tan(1/2*f*x)*tan(1/2*e)^2 - d*tan(1/2*f*x)^2*tan(1/2*e)^2 + c*f*tan(1/2*e)^3 + d*tan(1/2*f*x)*tan(1/2*e)^3 + 3*d*f*x*tan(1/2*f*x) + 3*d*f*x*tan(1/2*e) - 6*d*log(4*(tan(1/2*f*x)^4*tan(1/2*e)^2 - 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 - 2*tan(1/2*f*x)*tan(1/2*e) + 1)/(tan(1/2*e)^2 + 1))*tan(1/2*f*x)*tan(1/2*e) + 3*c*f*tan(1/2*f*x) - d*tan(1/2*f*x)^2 + 3*c*f*tan(1/2*e) + d*tan(1/2*f*x)*tan(1/2*e) - d*tan(1/2*e)^2 + 2*d*log(4*(tan(1/2*f*x)^4*tan(1/2*e)^2 - 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 - 2*tan(1/2*f*x)*tan(1/2*e) + 1)/(tan(1/2*e)^2 + 1)) - d)/(a^2*f^2*tan(1/2*f*x)^3*tan(1/2*e)^3 - 3*a^2*f^2*tan(1/2*f*x)^2*tan(1/2*e)^2 + 3*a^2*f^2*tan(1/2*f*x)*tan(1/2*e) - a^2*f^2)","B",0
136,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)} {\left(a \cos\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*x + c)*(a*cos(f*x + e) + a)^2), x)","F",0
137,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a+a*cos(f*x+e))^2,x, algorithm=""giac"")","\int \frac{1}{{\left(d x + c\right)}^{2} {\left(a \cos\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(1/((d*x + c)^2*(a*cos(f*x + e) + a)^2), x)","F",0
138,0,0,0,0.000000," ","integrate((d*x+c)^3/(a-a*cos(f*x+e)),x, algorithm=""giac"")","\int -\frac{{\left(d x + c\right)}^{3}}{a \cos\left(f x + e\right) - a}\,{d x}"," ",0,"integrate(-(d*x + c)^3/(a*cos(f*x + e) - a), x)","F",0
139,0,0,0,0.000000," ","integrate((d*x+c)^2/(a-a*cos(f*x+e)),x, algorithm=""giac"")","\int -\frac{{\left(d x + c\right)}^{2}}{a \cos\left(f x + e\right) - a}\,{d x}"," ",0,"integrate(-(d*x + c)^2/(a*cos(f*x + e) - a), x)","F",0
140,1,229,0,0.604628," ","integrate((d*x+c)/(a-a*cos(f*x+e)),x, algorithm=""giac"")","\frac{d f x \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + c f \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) - d f x + d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, e\right)^{2}\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, f x\right) + d \log\left(\frac{4 \, {\left(\tan\left(\frac{1}{2} \, f x\right)^{4} + 2 \, \tan\left(\frac{1}{2} \, f x\right)^{3} \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, f x\right)^{2} \tan\left(\frac{1}{2} \, e\right)^{2} + \tan\left(\frac{1}{2} \, f x\right)^{2} + 2 \, \tan\left(\frac{1}{2} \, f x\right) \tan\left(\frac{1}{2} \, e\right) + \tan\left(\frac{1}{2} \, e\right)^{2}\right)}}{\tan\left(\frac{1}{2} \, e\right)^{2} + 1}\right) \tan\left(\frac{1}{2} \, e\right) - c f}{a f^{2} \tan\left(\frac{1}{2} \, f x\right) + a f^{2} \tan\left(\frac{1}{2} \, e\right)}"," ",0,"(d*f*x*tan(1/2*f*x)*tan(1/2*e) + c*f*tan(1/2*f*x)*tan(1/2*e) - d*f*x + d*log(4*(tan(1/2*f*x)^4 + 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 + 2*tan(1/2*f*x)*tan(1/2*e) + tan(1/2*e)^2)/(tan(1/2*e)^2 + 1))*tan(1/2*f*x) + d*log(4*(tan(1/2*f*x)^4 + 2*tan(1/2*f*x)^3*tan(1/2*e) + tan(1/2*f*x)^2*tan(1/2*e)^2 + tan(1/2*f*x)^2 + 2*tan(1/2*f*x)*tan(1/2*e) + tan(1/2*e)^2)/(tan(1/2*e)^2 + 1))*tan(1/2*e) - c*f)/(a*f^2*tan(1/2*f*x) + a*f^2*tan(1/2*e))","B",0
141,0,0,0,0.000000," ","integrate(1/(d*x+c)/(a-a*cos(f*x+e)),x, algorithm=""giac"")","\int -\frac{1}{{\left(d x + c\right)} {\left(a \cos\left(f x + e\right) - a\right)}}\,{d x}"," ",0,"integrate(-1/((d*x + c)*(a*cos(f*x + e) - a)), x)","F",0
142,0,0,0,0.000000," ","integrate(1/(d*x+c)^2/(a-a*cos(f*x+e)),x, algorithm=""giac"")","\int -\frac{1}{{\left(d x + c\right)}^{2} {\left(a \cos\left(f x + e\right) - a\right)}}\,{d x}"," ",0,"integrate(-1/((d*x + c)^2*(a*cos(f*x + e) - a)), x)","F",0
143,1,98,0,0.471594," ","integrate(x^3*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} \sqrt{a} {\left(\frac{6 \, {\left(d^{2} x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d^{4}} + \frac{{\left(d^{3} x^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 24 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d^{4}}\right)}"," ",0,"2*sqrt(2)*sqrt(a)*(6*(d^2*x^2*sgn(cos(1/2*d*x + 1/2*c)) - 8*sgn(cos(1/2*d*x + 1/2*c)))*cos(1/2*d*x + 1/2*c)/d^4 + (d^3*x^3*sgn(cos(1/2*d*x + 1/2*c)) - 24*d*x*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d^4)","A",0
144,1,77,0,0.561312," ","integrate(x^2*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} \sqrt{a} {\left(\frac{4 \, x \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d^{2}} + \frac{{\left(d^{2} x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d^{3}}\right)}"," ",0,"2*sqrt(2)*sqrt(a)*(4*x*cos(1/2*d*x + 1/2*c)*sgn(cos(1/2*d*x + 1/2*c))/d^2 + (d^2*x^2*sgn(cos(1/2*d*x + 1/2*c)) - 8*sgn(cos(1/2*d*x + 1/2*c)))*sin(1/2*d*x + 1/2*c)/d^3)","A",0
145,1,57,0,0.442488," ","integrate(x*(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} {\left(\frac{x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d} + \frac{2 \, \cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}{d^{2}}\right)} \sqrt{a}"," ",0,"2*sqrt(2)*(x*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d + 2*cos(1/2*d*x + 1/2*c)*sgn(cos(1/2*d*x + 1/2*c))/d^2)*sqrt(a)","A",0
146,1,30,0,1.011727," ","integrate((a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{2 \, \sqrt{2} \sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{d}"," ",0,"2*sqrt(2)*sqrt(a)*sgn(cos(1/2*d*x + 1/2*c))*sin(1/2*d*x + 1/2*c)/d","A",0
147,1,166,0,0.536764," ","integrate((a+a*cos(d*x+c))^(1/2)/x,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(\Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 2 \, \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - 2 \, \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + 4 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{4} \, c\right) - \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sqrt{a}}{2 \, {\left(\tan\left(\frac{1}{4} \, c\right)^{2} + 1\right)}}"," ",0,"-1/2*sqrt(2)*(real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 2*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) - 2*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) + 4*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x)*tan(1/4*c) - real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c)) - real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c)))*sqrt(a)/(tan(1/4*c)^2 + 1)","C",0
148,1,560,0,1.077340," ","integrate((a+a*cos(d*x+c))^(1/2)/x^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(d x \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - d x \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 2 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - 2 \, d x \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 2 \, d x \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right) - d x \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} + d x \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} - 2 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{4} \, d x\right)^{2} + d x \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - d x \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 2 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 2 \, d x \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - 2 \, d x \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - 4 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} - d x \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) + d x \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 2 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) + 4 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} + 16 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right) \tan\left(\frac{1}{4} \, c\right) + 4 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 4 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sqrt{a}}{4 \, {\left(x \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + x \tan\left(\frac{1}{4} \, d x\right)^{2} + x \tan\left(\frac{1}{4} \, c\right)^{2} + x\right)}}"," ",0,"1/4*sqrt(2)*(d*x*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c)^2 - d*x*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c)^2 + 2*d*x*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x)*tan(1/4*d*x)^2*tan(1/4*c)^2 - 2*d*x*real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c) - 2*d*x*real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c) - d*x*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2 + d*x*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2 - 2*d*x*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x)*tan(1/4*d*x)^2 + d*x*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 - d*x*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 2*d*x*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x)*tan(1/4*c)^2 - 2*d*x*real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) - 2*d*x*real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) - 4*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c)^2 - d*x*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c)) + d*x*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c)) - 2*d*x*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x) + 4*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2 + 16*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)*tan(1/4*c) + 4*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 - 4*sgn(cos(1/2*d*x + 1/2*c)))*sqrt(a)/(x*tan(1/4*d*x)^2*tan(1/4*c)^2 + x*tan(1/4*d*x)^2 + x*tan(1/4*c)^2 + x)","C",0
149,1,662,0,1.230683," ","integrate((a+a*cos(d*x+c))^(1/2)/x^3,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(d^{2} x^{2} \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 2 \, d^{2} x^{2} \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 2 \, d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right) + 4 \, d^{2} x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right) - d^{2} x^{2} \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} - d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} + d^{2} x^{2} \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} + 2 \, d^{2} x^{2} \Im \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) - 2 \, d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + 4 \, d^{2} x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \operatorname{Si}\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{4} \, c\right) - d^{2} x^{2} \Re \left( \operatorname{Ci}\left(\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-\frac{1}{2} \, d x\right) \right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) - 8 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right) - 8 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + 8 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right) + 8 \, d x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right) + 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right)^{2} + 32 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, d x\right) \tan\left(\frac{1}{4} \, c\right) + 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right) \tan\left(\frac{1}{4} \, c\right)^{2} - 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)\right)} \sqrt{a}}{16 \, {\left(x^{2} \tan\left(\frac{1}{4} \, d x\right)^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + x^{2} \tan\left(\frac{1}{4} \, d x\right)^{2} + x^{2} \tan\left(\frac{1}{4} \, c\right)^{2} + x^{2}\right)}}"," ",0,"1/16*sqrt(2)*(d^2*x^2*real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c)^2 + d^2*x^2*real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c)^2 + 2*d^2*x^2*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c) - 2*d^2*x^2*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c) + 4*d^2*x^2*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x)*tan(1/4*d*x)^2*tan(1/4*c) - d^2*x^2*real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2 - d^2*x^2*real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2 + d^2*x^2*real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + d^2*x^2*real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 + 2*d^2*x^2*imag_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) - 2*d^2*x^2*imag_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) + 4*d^2*x^2*sgn(cos(1/2*d*x + 1/2*c))*sin_integral(1/2*d*x)*tan(1/4*c) - d^2*x^2*real_part(cos_integral(1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c)) - d^2*x^2*real_part(cos_integral(-1/2*d*x))*sgn(cos(1/2*d*x + 1/2*c)) - 8*d*x*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c) - 8*d*x*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)*tan(1/4*c)^2 - 8*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2*tan(1/4*c)^2 + 8*d*x*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x) + 8*d*x*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c) + 8*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)^2 + 32*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*d*x)*tan(1/4*c) + 8*sgn(cos(1/2*d*x + 1/2*c))*tan(1/4*c)^2 - 8*sgn(cos(1/2*d*x + 1/2*c)))*sqrt(a)/(x^2*tan(1/4*d*x)^2*tan(1/4*c)^2 + x^2*tan(1/4*d*x)^2 + x^2*tan(1/4*c)^2 + x^2)","C",0
150,1,55,0,0.414841," ","integrate(x^3*(a+a*cos(x))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} {\left(6 \, {\left(x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \cos\left(\frac{1}{2} \, x\right) + {\left(x^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 24 \, x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"2*sqrt(2)*(6*(x^2*sgn(cos(1/2*x)) - 8*sgn(cos(1/2*x)))*cos(1/2*x) + (x^3*sgn(cos(1/2*x)) - 24*x*sgn(cos(1/2*x)))*sin(1/2*x))*sqrt(a)","A",0
151,1,43,0,0.419158," ","integrate(x^2*(a+a*cos(x))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} {\left(4 \, x \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + {\left(x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"2*sqrt(2)*(4*x*cos(1/2*x)*sgn(cos(1/2*x)) + (x^2*sgn(cos(1/2*x)) - 8*sgn(cos(1/2*x)))*sin(1/2*x))*sqrt(a)","A",0
152,1,31,0,0.396226," ","integrate(x*(a+a*cos(x))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} {\left(x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) + 2 \, \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}"," ",0,"2*sqrt(2)*(x*sgn(cos(1/2*x))*sin(1/2*x) + 2*cos(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)","A",0
153,1,17,0,1.372313," ","integrate((a+a*cos(x))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} \sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)"," ",0,"2*sqrt(2)*sqrt(a)*sgn(cos(1/2*x))*sin(1/2*x)","A",0
154,1,16,0,0.435494," ","integrate((a+a*cos(x))^(1/2)/x,x, algorithm=""giac"")","\sqrt{2} \sqrt{a} \operatorname{Ci}\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)"," ",0,"sqrt(2)*sqrt(a)*cos_integral(1/2*x)*sgn(cos(1/2*x))","A",0
155,1,34,0,0.437401," ","integrate((a+a*cos(x))^(1/2)/x^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \operatorname{Si}\left(\frac{1}{2} \, x\right) + 2 \, \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}}{2 \, x}"," ",0,"-1/2*sqrt(2)*(x*sgn(cos(1/2*x))*sin_integral(1/2*x) + 2*cos(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)/x","A",0
156,1,48,0,0.412203," ","integrate((a+a*cos(x))^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(x^{2} \operatorname{Ci}\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 2 \, x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) + 4 \, \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}}{8 \, x^{2}}"," ",0,"-1/8*sqrt(2)*(x^2*cos_integral(1/2*x)*sgn(cos(1/2*x)) - 2*x*sgn(cos(1/2*x))*sin(1/2*x) + 4*cos(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)/x^2","A",0
157,1,55,0,0.469043," ","integrate(x^3*(a-a*cos(x))^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{2} {\left({\left(x^{3} \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) - 24 \, x \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right)\right)} \cos\left(\frac{1}{2} \, x\right) - 6 \, {\left(x^{2} \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) - 8 \, \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"-2*sqrt(2)*((x^3*sgn(sin(1/2*x)) - 24*x*sgn(sin(1/2*x)))*cos(1/2*x) - 6*(x^2*sgn(sin(1/2*x)) - 8*sgn(sin(1/2*x)))*sin(1/2*x))*sqrt(a)","A",0
158,1,51,0,0.373111," ","integrate(x^2*(a-a*cos(x))^(1/2),x, algorithm=""giac"")","2 \, \sqrt{2} {\left(4 \, x \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) - {\left(x^{2} \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) - 8 \, \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right)\right)} \cos\left(\frac{1}{2} \, x\right) - 8 \, \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}"," ",0,"2*sqrt(2)*(4*x*sgn(sin(1/2*x))*sin(1/2*x) - (x^2*sgn(sin(1/2*x)) - 8*sgn(sin(1/2*x)))*cos(1/2*x) - 8*sgn(sin(1/2*x)))*sqrt(a)","A",0
159,1,31,0,0.421553," ","integrate(x*(a-a*cos(x))^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{2} {\left(x \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) - 2 \, \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"-2*sqrt(2)*(x*cos(1/2*x)*sgn(sin(1/2*x)) - 2*sgn(sin(1/2*x))*sin(1/2*x))*sqrt(a)","A",0
160,1,26,0,0.411765," ","integrate((a-a*cos(x))^(1/2),x, algorithm=""giac"")","-2 \, \sqrt{2} {\left(\cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) - \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}"," ",0,"-2*sqrt(2)*(cos(1/2*x)*sgn(sin(1/2*x)) - sgn(sin(1/2*x)))*sqrt(a)","A",0
161,1,16,0,0.398815," ","integrate((a-a*cos(x))^(1/2)/x,x, algorithm=""giac"")","\sqrt{2} \sqrt{a} \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) \operatorname{Si}\left(\frac{1}{2} \, x\right)"," ",0,"sqrt(2)*sqrt(a)*sgn(sin(1/2*x))*sin_integral(1/2*x)","A",0
162,1,34,0,2.645846," ","integrate((a-a*cos(x))^(1/2)/x^2,x, algorithm=""giac"")","\frac{\sqrt{2} {\left(x \operatorname{Ci}\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) - 2 \, \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}}{2 \, x}"," ",0,"1/2*sqrt(2)*(x*cos_integral(1/2*x)*sgn(sin(1/2*x)) - 2*sgn(sin(1/2*x))*sin(1/2*x))*sqrt(a)/x","A",0
163,1,48,0,0.453795," ","integrate((a-a*cos(x))^(1/2)/x^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(x^{2} \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) \operatorname{Si}\left(\frac{1}{2} \, x\right) + 2 \, x \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) + 4 \, \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}}{8 \, x^{2}}"," ",0,"-1/8*sqrt(2)*(x^2*sgn(sin(1/2*x))*sin_integral(1/2*x) + 2*x*cos(1/2*x)*sgn(sin(1/2*x)) + 4*sgn(sin(1/2*x))*sin(1/2*x))*sqrt(a)/x^2","A",0
164,1,113,0,0.478985," ","integrate(x^3*(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{2} {\left(2 \, {\left(9 \, a x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \cos\left(\frac{3}{2} \, x\right) + 486 \, {\left(a x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \cos\left(\frac{1}{2} \, x\right) + 3 \, {\left(3 \, a x^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{3}{2} \, x\right) + 81 \, {\left(a x^{3} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 24 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"1/27*sqrt(2)*(2*(9*a*x^2*sgn(cos(1/2*x)) - 8*a*sgn(cos(1/2*x)))*cos(3/2*x) + 486*(a*x^2*sgn(cos(1/2*x)) - 8*a*sgn(cos(1/2*x)))*cos(1/2*x) + 3*(3*a*x^3*sgn(cos(1/2*x)) - 8*a*x*sgn(cos(1/2*x)))*sin(3/2*x) + 81*(a*x^3*sgn(cos(1/2*x)) - 24*a*x*sgn(cos(1/2*x)))*sin(1/2*x))*sqrt(a)","A",0
165,1,85,0,0.373732," ","integrate(x^2*(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\frac{1}{27} \, \sqrt{2} {\left(12 \, a x \cos\left(\frac{3}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 324 \, a x \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + {\left(9 \, a x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{3}{2} \, x\right) + 81 \, {\left(a x^{2} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 8 \, a \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sin\left(\frac{1}{2} \, x\right)\right)} \sqrt{a}"," ",0,"1/27*sqrt(2)*(12*a*x*cos(3/2*x)*sgn(cos(1/2*x)) + 324*a*x*cos(1/2*x)*sgn(cos(1/2*x)) + (9*a*x^2*sgn(cos(1/2*x)) - 8*a*sgn(cos(1/2*x)))*sin(3/2*x) + 81*(a*x^2*sgn(cos(1/2*x)) - 8*a*sgn(cos(1/2*x)))*sin(1/2*x))*sqrt(a)","A",0
166,1,59,0,0.479996," ","integrate(x*(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\frac{1}{9} \, \sqrt{2} {\left(3 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{3}{2} \, x\right) + 27 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) + 2 \, a \cos\left(\frac{3}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 54 \, a \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}"," ",0,"1/9*sqrt(2)*(3*a*x*sgn(cos(1/2*x))*sin(3/2*x) + 27*a*x*sgn(cos(1/2*x))*sin(1/2*x) + 2*a*cos(3/2*x)*sgn(cos(1/2*x)) + 54*a*cos(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)","A",0
167,1,32,0,0.424594," ","integrate((a+a*cos(x))^(3/2)/x,x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{2} {\left(a \operatorname{Ci}\left(\frac{3}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 3 \, a \operatorname{Ci}\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}"," ",0,"1/2*sqrt(2)*(a*cos_integral(3/2*x)*sgn(cos(1/2*x)) + 3*a*cos_integral(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)","A",0
168,1,62,0,0.424380," ","integrate((a+a*cos(x))^(3/2)/x^2,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(3 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \operatorname{Si}\left(\frac{3}{2} \, x\right) + 3 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \operatorname{Si}\left(\frac{1}{2} \, x\right) + 2 \, a \cos\left(\frac{3}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 6 \, a \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}}{4 \, x}"," ",0,"-1/4*sqrt(2)*(3*a*x*sgn(cos(1/2*x))*sin_integral(3/2*x) + 3*a*x*sgn(cos(1/2*x))*sin_integral(1/2*x) + 2*a*cos(3/2*x)*sgn(cos(1/2*x)) + 6*a*cos(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)/x","A",0
169,1,92,0,0.518328," ","integrate((a+a*cos(x))^(3/2)/x^3,x, algorithm=""giac"")","-\frac{\sqrt{2} {\left(9 \, a x^{2} \operatorname{Ci}\left(\frac{3}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 3 \, a x^{2} \operatorname{Ci}\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) - 6 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{3}{2} \, x\right) - 6 \, a x \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) \sin\left(\frac{1}{2} \, x\right) + 4 \, a \cos\left(\frac{3}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right) + 12 \, a \cos\left(\frac{1}{2} \, x\right) \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, x\right)\right)\right)} \sqrt{a}}{16 \, x^{2}}"," ",0,"-1/16*sqrt(2)*(9*a*x^2*cos_integral(3/2*x)*sgn(cos(1/2*x)) + 3*a*x^2*cos_integral(1/2*x)*sgn(cos(1/2*x)) - 6*a*x*sgn(cos(1/2*x))*sin(3/2*x) - 6*a*x*sgn(cos(1/2*x))*sin(1/2*x) + 4*a*cos(3/2*x)*sgn(cos(1/2*x)) + 12*a*cos(1/2*x)*sgn(cos(1/2*x)))*sqrt(a)/x^2","A",0
170,0,0,0,0.000000," ","integrate(x^3/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(a*cos(d*x + c) + a), x)","F",0
171,0,0,0,0.000000," ","integrate(x^2/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(a*cos(d*x + c) + a), x)","F",0
172,0,0,0,0.000000," ","integrate(x/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{a \cos\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(a*cos(d*x + c) + a), x)","F",0
173,1,93,0,1.859889," ","integrate(1/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\frac{\frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 2 \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)} - \frac{\sqrt{2} \log\left({\left| \frac{1}{\sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)} + \sin\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\cos\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)\right)}}{4 \, d}"," ",0,"1/4*(sqrt(2)*log(abs(1/sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c) + 2))/(sqrt(a)*sgn(cos(1/2*d*x + 1/2*c))) - sqrt(2)*log(abs(1/sin(1/2*d*x + 1/2*c) + sin(1/2*d*x + 1/2*c) - 2))/(sqrt(a)*sgn(cos(1/2*d*x + 1/2*c))))/d","B",0
174,0,0,0,0.000000," ","integrate(1/x/(a+a*cos(d*x+c))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{a \cos\left(d x + c\right) + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(a*cos(d*x + c) + a)*x), x)","F",0
175,0,0,0,0.000000," ","integrate(x^3/(a-a*cos(x))^(1/2),x, algorithm=""giac"")","\int \frac{x^{3}}{\sqrt{-a \cos\left(x\right) + a}}\,{d x}"," ",0,"integrate(x^3/sqrt(-a*cos(x) + a), x)","F",0
176,0,0,0,0.000000," ","integrate(x^2/(a-a*cos(x))^(1/2),x, algorithm=""giac"")","\int \frac{x^{2}}{\sqrt{-a \cos\left(x\right) + a}}\,{d x}"," ",0,"integrate(x^2/sqrt(-a*cos(x) + a), x)","F",0
177,0,0,0,0.000000," ","integrate(x/(a-a*cos(x))^(1/2),x, algorithm=""giac"")","\int \frac{x}{\sqrt{-a \cos\left(x\right) + a}}\,{d x}"," ",0,"integrate(x/sqrt(-a*cos(x) + a), x)","F",0
178,1,20,0,0.488555," ","integrate(1/(a-a*cos(x))^(1/2),x, algorithm=""giac"")","\frac{\sqrt{2} \log\left({\left| \tan\left(\frac{1}{4} \, x\right) \right|}\right)}{\sqrt{a} \mathrm{sgn}\left(\sin\left(\frac{1}{2} \, x\right)\right)}"," ",0,"sqrt(2)*log(abs(tan(1/4*x)))/(sqrt(a)*sgn(sin(1/2*x)))","A",0
179,0,0,0,0.000000," ","integrate(1/x/(a-a*cos(x))^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-a \cos\left(x\right) + a} x}\,{d x}"," ",0,"integrate(1/(sqrt(-a*cos(x) + a)*x), x)","F",0
180,0,0,0,0.000000," ","integrate(x^3/(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\int \frac{x^{3}}{{\left(a \cos\left(x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^3/(a*cos(x) + a)^(3/2), x)","F",0
181,0,0,0,0.000000," ","integrate(x^2/(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\int \frac{x^{2}}{{\left(a \cos\left(x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x^2/(a*cos(x) + a)^(3/2), x)","F",0
182,0,0,0,0.000000," ","integrate(x/(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\int \frac{x}{{\left(a \cos\left(x\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(x/(a*cos(x) + a)^(3/2), x)","F",0
183,0,0,0,0.000000," ","integrate(1/x/(a+a*cos(x))^(3/2),x, algorithm=""giac"")","\int \frac{1}{{\left(a \cos\left(x\right) + a\right)}^{\frac{3}{2}} x}\,{d x}"," ",0,"integrate(1/((a*cos(x) + a)^(3/2)*x), x)","F",0
184,0,0,0,0.000000," ","integrate((a+a*cos(d*x+c))^(1/3)/x,x, algorithm=""giac"")","\int \frac{{\left(a \cos\left(d x + c\right) + a\right)}^{\frac{1}{3}}}{x}\,{d x}"," ",0,"integrate((a*cos(d*x + c) + a)^(1/3)/x, x)","F",0
185,0,0,0,0.000000," ","integrate(x^3/(a+b*cos(x)),x, algorithm=""giac"")","\int \frac{x^{3}}{b \cos\left(x\right) + a}\,{d x}"," ",0,"integrate(x^3/(b*cos(x) + a), x)","F",0
186,0,0,0,0.000000," ","integrate(x^2/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{x^{2}}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(x^2/(b*cos(d*x + c) + a), x)","F",0
187,0,0,0,0.000000," ","integrate(x/(a+b*cos(d*x+c)),x, algorithm=""giac"")","\int \frac{x}{b \cos\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(x/(b*cos(d*x + c) + a), x)","F",0
188,0,0,0,0.000000," ","integrate(1/x/(a+b*cos(x)),x, algorithm=""giac"")","\int \frac{1}{{\left(b \cos\left(x\right) + a\right)} x}\,{d x}"," ",0,"integrate(1/((b*cos(x) + a)*x), x)","F",0
189,0,0,0,0.000000," ","integrate((f*x+e)/(a+b*cos(d*x+c))^2,x, algorithm=""giac"")","\int \frac{f x + e}{{\left(b \cos\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((f*x + e)/(b*cos(d*x + c) + a)^2, x)","F",0
