1,1,86,0,0.358319," ","integrate(x^3*(b*x+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{4} x^{4} + a d^{4} x^{3} - 12 \, b d^{2} x^{2} - 6 \, a d^{2} x + 24 \, b\right)} \cos\left(d x + c\right)}{d^{5}} + \frac{{\left(4 \, b d^{3} x^{3} + 3 \, a d^{3} x^{2} - 24 \, b d x - 6 \, a d\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-(b*d^4*x^4 + a*d^4*x^3 - 12*b*d^2*x^2 - 6*a*d^2*x + 24*b)*cos(d*x + c)/d^5 + (4*b*d^3*x^3 + 3*a*d^3*x^2 - 24*b*d*x - 6*a*d)*sin(d*x + c)/d^5","A",0
2,1,68,0,0.417081," ","integrate(x^2*(b*x+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{3} x^{3} + a d^{3} x^{2} - 6 \, b d x - 2 \, a d\right)} \cos\left(d x + c\right)}{d^{4}} + \frac{{\left(3 \, b d^{2} x^{2} + 2 \, a d^{2} x - 6 \, b\right)} \sin\left(d x + c\right)}{d^{4}}"," ",0,"-(b*d^3*x^3 + a*d^3*x^2 - 6*b*d*x - 2*a*d)*cos(d*x + c)/d^4 + (3*b*d^2*x^2 + 2*a*d^2*x - 6*b)*sin(d*x + c)/d^4","A",0
3,1,49,0,0.511722," ","integrate(x*(b*x+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{2} x^{2} + a d^{2} x - 2 \, b\right)} \cos\left(d x + c\right)}{d^{3}} + \frac{{\left(2 \, b d x + a d\right)} \sin\left(d x + c\right)}{d^{3}}"," ",0,"-(b*d^2*x^2 + a*d^2*x - 2*b)*cos(d*x + c)/d^3 + (2*b*d*x + a*d)*sin(d*x + c)/d^3","A",0
4,1,31,0,1.054893," ","integrate((b*x+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d x + a d\right)} \cos\left(d x + c\right)}{d^{2}} + \frac{b \sin\left(d x + c\right)}{d^{2}}"," ",0,"-(b*d*x + a*d)*cos(d*x + c)/d^2 + b*sin(d*x + c)/d^2","A",0
5,1,339,0,0.481073," ","integrate((b*x+a)*sin(d*x+c)/x,x, algorithm=""giac"")","-\frac{a d \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - a d \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d \operatorname{Si}\left(d x\right) - 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b}{2 \, {\left(d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d \tan\left(\frac{1}{2} \, d x\right)^{2} + d \tan\left(\frac{1}{2} \, c\right)^{2} + d\right)}}"," ",0,"-1/2*(a*d*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a*d*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d*sin_integral(d*x)*tan(1/2*d*x)^2 + a*d*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d*sin_integral(d*x)*tan(1/2*c)^2 + 2*b*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d*real_part(cos_integral(-d*x))*tan(1/2*c) - a*d*imag_part(cos_integral(d*x)) + a*d*imag_part(cos_integral(-d*x)) - 2*a*d*sin_integral(d*x) - 2*b*tan(1/2*d*x)^2 - 8*b*tan(1/2*d*x)*tan(1/2*c) - 2*b*tan(1/2*c)^2 + 2*b)/(d*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*tan(1/2*d*x)^2 + d*tan(1/2*c)^2 + d)","C",0
6,1,569,0,0.488311," ","integrate((b*x+a)*sin(d*x+c)/x^2,x, algorithm=""giac"")","-\frac{a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, b x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x\right) \right) + b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, b x \operatorname{Si}\left(d x\right) + 4 \, a \tan\left(\frac{1}{2} \, d x\right) + 4 \, a \tan\left(\frac{1}{2} \, c\right)}{2 \, {\left(x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x \tan\left(\frac{1}{2} \, d x\right)^{2} + x \tan\left(\frac{1}{2} \, c\right)^{2} + x\right)}}"," ",0,"-1/2*(a*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + b*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - b*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*b*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*b*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + a*d*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - b*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + b*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*b*x*sin_integral(d*x)*tan(1/2*d*x)^2 + 2*a*d*x*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d*x*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d*x*sin_integral(d*x)*tan(1/2*c) + b*x*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - b*x*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*b*x*sin_integral(d*x)*tan(1/2*c)^2 - a*d*x*real_part(cos_integral(d*x)) - a*d*x*real_part(cos_integral(-d*x)) - 2*b*x*real_part(cos_integral(d*x))*tan(1/2*c) - 2*b*x*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*a*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*tan(1/2*d*x)*tan(1/2*c)^2 - b*x*imag_part(cos_integral(d*x)) + b*x*imag_part(cos_integral(-d*x)) - 2*b*x*sin_integral(d*x) + 4*a*tan(1/2*d*x) + 4*a*tan(1/2*c))/(x*tan(1/2*d*x)^2*tan(1/2*c)^2 + x*tan(1/2*d*x)^2 + x*tan(1/2*c)^2 + x)","C",0
7,1,796,0,0.539287," ","integrate((b*x+a)*sin(d*x+c)/x^3,x, algorithm=""giac"")","\frac{a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 8 \, b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) - 4 \, b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 8 \, b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 2 \, b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 8 \, b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x - 8 \, b x \tan\left(\frac{1}{2} \, d x\right) - 8 \, b x \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) - 4 \, a \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{2}\right)}}"," ",0,"1/4*(a*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 - 4*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 8*b*d*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + a*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 2*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 2*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) - 2*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 2*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(d*x)) + a*d^2*x^2*imag_part(cos_integral(-d*x)) - 2*a*d^2*x^2*sin_integral(d*x) - 4*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*c) + 4*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c) - 8*b*d*x^2*sin_integral(d*x)*tan(1/2*c) + 2*b*d*x^2*real_part(cos_integral(d*x)) + 2*b*d*x^2*real_part(cos_integral(-d*x)) + 2*a*d*x*tan(1/2*d*x)^2 + 8*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 8*b*x*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*d*x*tan(1/2*c)^2 + 8*b*x*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d*x - 8*b*x*tan(1/2*d*x) - 8*b*x*tan(1/2*c) - 4*a*tan(1/2*d*x) - 4*a*tan(1/2*c))/(x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^2*tan(1/2*d*x)^2 + x^2*tan(1/2*c)^2 + x^2)","C",0
8,1,961,0,0.537471," ","integrate((b*x+a)*sin(d*x+c)/x^4,x, algorithm=""giac"")","\frac{a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 6 \, b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 6 \, b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 6 \, b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 6 \, b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 6 \, b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) + 3 \, b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 6 \, b d^{2} x^{3} \operatorname{Si}\left(d x\right) - 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 6 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 6 \, b d x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b d x^{2} + 8 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x - 12 \, b x \tan\left(\frac{1}{2} \, d x\right) - 12 \, b x \tan\left(\frac{1}{2} \, c\right) - 8 \, a \tan\left(\frac{1}{2} \, d x\right) - 8 \, a \tan\left(\frac{1}{2} \, c\right)}{12 \, {\left(x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3}\right)}}"," ",0,"1/12*(a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^3*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + 3*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 3*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 6*b*d^2*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 6*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 6*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 3*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 3*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 6*b*d^2*x^3*sin_integral(d*x)*tan(1/2*d*x)^2 + 2*a*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d^3*x^3*sin_integral(d*x)*tan(1/2*c) + 3*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - 3*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 6*b*d^2*x^3*sin_integral(d*x)*tan(1/2*c)^2 - a*d^3*x^3*real_part(cos_integral(d*x)) - a*d^3*x^3*real_part(cos_integral(-d*x)) - 6*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*c) - 6*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*a*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 6*b*d*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 3*b*d^2*x^3*imag_part(cos_integral(d*x)) + 3*b*d^2*x^3*imag_part(cos_integral(-d*x)) - 6*b*d^2*x^3*sin_integral(d*x) - 2*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*d^2*x^2*tan(1/2*d*x) + 6*b*d*x^2*tan(1/2*d*x)^2 + 4*a*d^2*x^2*tan(1/2*c) + 24*b*d*x^2*tan(1/2*d*x)*tan(1/2*c) + 6*b*d*x^2*tan(1/2*c)^2 + 2*a*d*x*tan(1/2*d*x)^2 + 8*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 12*b*x*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*d*x*tan(1/2*c)^2 + 12*b*x*tan(1/2*d*x)*tan(1/2*c)^2 - 6*b*d*x^2 + 8*a*tan(1/2*d*x)^2*tan(1/2*c) + 8*a*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d*x - 12*b*x*tan(1/2*d*x) - 12*b*x*tan(1/2*c) - 8*a*tan(1/2*d*x) - 8*a*tan(1/2*c))/(x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^3*tan(1/2*d*x)^2 + x^3*tan(1/2*c)^2 + x^3)","C",0
9,1,1108,0,0.846145," ","integrate((b*x+a)*sin(d*x+c)/x^5,x, algorithm=""giac"")","-\frac{a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 16 \, b d^{3} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) - 8 \, b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 16 \, b d^{3} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 4 \, b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 16 \, b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} x^{3} - 16 \, b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) - 16 \, b d^{2} x^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 8 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) - 32 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 8 \, b d x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 32 \, b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} - 32 \, b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, b d x^{2} - 24 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d x + 32 \, b x \tan\left(\frac{1}{2} \, d x\right) + 32 \, b x \tan\left(\frac{1}{2} \, c\right) + 24 \, a \tan\left(\frac{1}{2} \, d x\right) + 24 \, a \tan\left(\frac{1}{2} \, c\right)}{48 \, {\left(x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4}\right)}}"," ",0,"-1/48*(a*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 - 8*b*d^3*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 8*b*d^3*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 16*b*d^3*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + a*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^4*x^4*sin_integral(d*x)*tan(1/2*c)^2 + 4*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 4*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 4*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a*d^3*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(d*x)) + a*d^4*x^4*imag_part(cos_integral(-d*x)) - 2*a*d^4*x^4*sin_integral(d*x) - 8*b*d^3*x^4*imag_part(cos_integral(d*x))*tan(1/2*c) + 8*b*d^3*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c) - 16*b*d^3*x^4*sin_integral(d*x)*tan(1/2*c) + 4*b*d^3*x^4*real_part(cos_integral(d*x)) + 4*b*d^3*x^4*real_part(cos_integral(-d*x)) + 2*a*d^3*x^3*tan(1/2*d*x)^2 + 8*a*d^3*x^3*tan(1/2*d*x)*tan(1/2*c) + 16*b*d^2*x^3*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*d^3*x^3*tan(1/2*c)^2 + 16*b*d^2*x^3*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 8*b*d*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^3*x^3 - 16*b*d^2*x^3*tan(1/2*d*x) - 16*b*d^2*x^3*tan(1/2*c) + 4*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*d^2*x^2*tan(1/2*d*x) - 8*b*d*x^2*tan(1/2*d*x)^2 - 4*a*d^2*x^2*tan(1/2*c) - 32*b*d*x^2*tan(1/2*d*x)*tan(1/2*c) - 8*b*d*x^2*tan(1/2*c)^2 - 4*a*d*x*tan(1/2*d*x)^2 - 16*a*d*x*tan(1/2*d*x)*tan(1/2*c) - 32*b*x*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*d*x*tan(1/2*c)^2 - 32*b*x*tan(1/2*d*x)*tan(1/2*c)^2 + 8*b*d*x^2 - 24*a*tan(1/2*d*x)^2*tan(1/2*c) - 24*a*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a*d*x + 32*b*x*tan(1/2*d*x) + 32*b*x*tan(1/2*c) + 24*a*tan(1/2*d*x) + 24*a*tan(1/2*c))/(x^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^4*tan(1/2*d*x)^2 + x^4*tan(1/2*c)^2 + x^4)","C",0
10,1,128,0,0.498273," ","integrate(x^2*(b*x+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{4} x^{4} + 2 \, a b d^{4} x^{3} + a^{2} d^{4} x^{2} - 12 \, b^{2} d^{2} x^{2} - 12 \, a b d^{2} x - 2 \, a^{2} d^{2} + 24 \, b^{2}\right)} \cos\left(d x + c\right)}{d^{5}} + \frac{2 \, {\left(2 \, b^{2} d^{3} x^{3} + 3 \, a b d^{3} x^{2} + a^{2} d^{3} x - 12 \, b^{2} d x - 6 \, a b d\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-(b^2*d^4*x^4 + 2*a*b*d^4*x^3 + a^2*d^4*x^2 - 12*b^2*d^2*x^2 - 12*a*b*d^2*x - 2*a^2*d^2 + 24*b^2)*cos(d*x + c)/d^5 + 2*(2*b^2*d^3*x^3 + 3*a*b*d^3*x^2 + a^2*d^3*x - 12*b^2*d*x - 6*a*b*d)*sin(d*x + c)/d^5","A",0
11,1,95,0,0.751989," ","integrate(x*(b*x+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{3} x^{3} + 2 \, a b d^{3} x^{2} + a^{2} d^{3} x - 6 \, b^{2} d x - 4 \, a b d\right)} \cos\left(d x + c\right)}{d^{4}} + \frac{{\left(3 \, b^{2} d^{2} x^{2} + 4 \, a b d^{2} x + a^{2} d^{2} - 6 \, b^{2}\right)} \sin\left(d x + c\right)}{d^{4}}"," ",0,"-(b^2*d^3*x^3 + 2*a*b*d^3*x^2 + a^2*d^3*x - 6*b^2*d*x - 4*a*b*d)*cos(d*x + c)/d^4 + (3*b^2*d^2*x^2 + 4*a*b*d^2*x + a^2*d^2 - 6*b^2)*sin(d*x + c)/d^4","A",0
12,1,65,0,0.569390," ","integrate((b*x+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)}{d^{3}} + \frac{2 \, {\left(b^{2} d x + a b d\right)} \sin\left(d x + c\right)}{d^{3}}"," ",0,"-(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2 - 2*b^2)*cos(d*x + c)/d^3 + 2*(b^2*d*x + a*b*d)*sin(d*x + c)/d^3","A",0
13,1,551,0,0.743807," ","integrate((b*x+a)^2*sin(d*x+c)/x,x, algorithm=""giac"")","-\frac{a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{2} \operatorname{Si}\left(d x\right) - 4 \, a b d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a b d \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d x + 4 \, a b d - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{2 \, {\left(d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + d^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2}\right)}}"," ",0,"-1/2*(a^2*d^2*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*a^2*d^2*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*d^2*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a^2*d^2*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*b^2*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^2*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2 + a^2*d^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2 - 2*a^2*d^2*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2 + a^2*d^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^2*sin_integral(d*x)*tan(1/2*c)^2 - 4*a*b*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*b^2*d*x*tan(1/2*d*x + 1/2*c)^2 - 2*a^2*d^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 2*b^2*d*x*tan(1/2*c)^2 - a^2*d^2*imag_part(cos_integral(d*x)) + a^2*d^2*imag_part(cos_integral(-d*x)) - 2*a^2*d^2*sin_integral(d*x) - 4*a*b*d*tan(1/2*d*x + 1/2*c)^2 + 4*a*b*d*tan(1/2*c)^2 - 4*b^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 2*b^2*d*x + 4*a*b*d - 4*b^2*tan(1/2*d*x + 1/2*c))/(d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + d^2*tan(1/2*d*x + 1/2*c)^2 + d^2*tan(1/2*c)^2 + d^2)","C",0
14,1,743,0,1.581745," ","integrate((b*x+a)^2*sin(d*x+c)/x^2,x, algorithm=""giac"")","-\frac{a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{2} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a b d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a b d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a b d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a b d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{2} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{2} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a b d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 4 \, a b d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b d x \Im \left( \operatorname{Ci}\left(d x\right) \right) + 2 \, a b d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 4 \, a b d x \operatorname{Si}\left(d x\right) - 2 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d \tan\left(\frac{1}{2} \, d x\right) + 4 \, a^{2} d \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} x}{2 \, {\left(d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d x \tan\left(\frac{1}{2} \, d x\right)^{2} + d x \tan\left(\frac{1}{2} \, c\right)^{2} + d x\right)}}"," ",0,"-1/2*(a^2*d^2*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^2*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^2*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^2*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^2*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*b*d*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*b*d*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*b*d*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a^2*d^2*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 4*a*b*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*b*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + a^2*d^2*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^2*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a*b*d*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 2*a*b*d*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 4*a*b*d*x*sin_integral(d*x)*tan(1/2*d*x)^2 + 2*a^2*d^2*x*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^2*x*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a^2*d^2*x*sin_integral(d*x)*tan(1/2*c) + 2*a*b*d*x*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - 2*a*b*d*x*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 4*a*b*d*x*sin_integral(d*x)*tan(1/2*c)^2 + 2*b^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x*real_part(cos_integral(d*x)) - a^2*d^2*x*real_part(cos_integral(-d*x)) - 4*a*b*d*x*real_part(cos_integral(d*x))*tan(1/2*c) - 4*a*b*d*x*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*a^2*d*tan(1/2*d*x)^2*tan(1/2*c) - 4*a^2*d*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*b*d*x*imag_part(cos_integral(d*x)) + 2*a*b*d*x*imag_part(cos_integral(-d*x)) - 4*a*b*d*x*sin_integral(d*x) - 2*b^2*x*tan(1/2*d*x)^2 - 8*b^2*x*tan(1/2*d*x)*tan(1/2*c) - 2*b^2*x*tan(1/2*c)^2 + 4*a^2*d*tan(1/2*d*x) + 4*a^2*d*tan(1/2*c) + 2*b^2*x)/(d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*x*tan(1/2*d*x)^2 + d*x*tan(1/2*c)^2 + d*x)","C",0
15,1,1182,0,0.992653," ","integrate((b*x+a)^2*sin(d*x+c)/x^3,x, algorithm=""giac"")","\frac{a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 16 \, a b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 16 \, a b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 4 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 16 \, a b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, a b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d x - 16 \, a b x \tan\left(\frac{1}{2} \, d x\right) - 16 \, a b x \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{2}\right)}}"," ",0,"1/4*(a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 - 8*a*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 8*a*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 16*a*b*d*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 4*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 4*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(d*x)) + a^2*d^2*x^2*imag_part(cos_integral(-d*x)) - 2*a^2*d^2*x^2*sin_integral(d*x) + 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 4*b^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 - 8*a*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*c) + 8*a*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c) - 16*a*b*d*x^2*sin_integral(d*x)*tan(1/2*c) - 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*b^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 4*a*b*d*x^2*real_part(cos_integral(d*x)) + 4*a*b*d*x^2*real_part(cos_integral(-d*x)) + 2*a^2*d*x*tan(1/2*d*x)^2 + 4*b^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) + 16*a*b*x*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d*x*tan(1/2*c)^2 + 16*a*b*x*tan(1/2*d*x)*tan(1/2*c)^2 + 2*b^2*x^2*imag_part(cos_integral(d*x)) - 2*b^2*x^2*imag_part(cos_integral(-d*x)) + 4*b^2*x^2*sin_integral(d*x) + 4*a^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d*x - 16*a*b*x*tan(1/2*d*x) - 16*a*b*x*tan(1/2*c) - 4*a^2*tan(1/2*d*x) - 4*a^2*tan(1/2*c))/(x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^2*tan(1/2*d*x)^2 + x^2*tan(1/2*c)^2 + x^2)","C",0
16,1,1400,0,0.792892," ","integrate((b*x+a)^2*sin(d*x+c)/x^4,x, algorithm=""giac"")","\frac{a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 12 \, b^{2} d x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, b^{2} d x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) + 6 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 12 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) - 12 \, b^{2} d x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 24 \, b^{2} d x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 6 \, b^{2} d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 12 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) + 48 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 12 \, a b d x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 24 \, a b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, a b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d x^{2} - 24 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 24 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d x - 24 \, a b x \tan\left(\frac{1}{2} \, d x\right) - 24 \, a b x \tan\left(\frac{1}{2} \, c\right) - 8 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) - 8 \, a^{2} \tan\left(\frac{1}{2} \, c\right)}{12 \, {\left(x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3}\right)}}"," ",0,"1/12*(a^2*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^3*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + 6*a*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 6*a*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*a*b*d^2*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a^2*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 12*a*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 12*a*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + a^2*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 6*b^2*d*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 6*b^2*d*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 6*a*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 6*a*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 12*a*b*d^2*x^3*sin_integral(d*x)*tan(1/2*d*x)^2 + 2*a^2*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a^2*d^3*x^3*sin_integral(d*x)*tan(1/2*c) - 12*b^2*d*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 12*b^2*d*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 24*b^2*d*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + 6*a*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - 6*a*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 12*a*b*d^2*x^3*sin_integral(d*x)*tan(1/2*c)^2 - a^2*d^3*x^3*real_part(cos_integral(d*x)) - a^2*d^3*x^3*real_part(cos_integral(-d*x)) + 6*b^2*d*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 6*b^2*d*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 12*a*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*c) - 12*a*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*a^2*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 6*b^2*d*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 6*b^2*d*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*a^2*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 12*a*b*d*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 6*a*b*d^2*x^3*imag_part(cos_integral(d*x)) + 6*a*b*d^2*x^3*imag_part(cos_integral(-d*x)) - 12*a*b*d^2*x^3*sin_integral(d*x) - 12*b^2*d*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) + 12*b^2*d*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) - 24*b^2*d*x^3*sin_integral(d*x)*tan(1/2*c) - 2*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 6*b^2*d*x^3*real_part(cos_integral(d*x)) + 6*b^2*d*x^3*real_part(cos_integral(-d*x)) + 4*a^2*d^2*x^2*tan(1/2*d*x) + 12*a*b*d*x^2*tan(1/2*d*x)^2 + 4*a^2*d^2*x^2*tan(1/2*c) + 48*a*b*d*x^2*tan(1/2*d*x)*tan(1/2*c) + 24*b^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 12*a*b*d*x^2*tan(1/2*c)^2 + 24*b^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*a^2*d*x*tan(1/2*d*x)^2 + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) + 24*a*b*x*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d*x*tan(1/2*c)^2 + 24*a*b*x*tan(1/2*d*x)*tan(1/2*c)^2 - 12*a*b*d*x^2 - 24*b^2*x^2*tan(1/2*d*x) - 24*b^2*x^2*tan(1/2*c) + 8*a^2*tan(1/2*d*x)^2*tan(1/2*c) + 8*a^2*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d*x - 24*a*b*x*tan(1/2*d*x) - 24*a*b*x*tan(1/2*c) - 8*a^2*tan(1/2*d*x) - 8*a^2*tan(1/2*c))/(x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^3*tan(1/2*d*x)^2 + x^3*tan(1/2*c)^2 + x^3)","C",0
17,1,1712,0,0.428811," ","integrate((b*x+a)^2*sin(d*x+c)/x^5,x, algorithm=""giac"")","-\frac{a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 16 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 32 \, a b d^{3} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} d^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} d^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) + 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b^{2} d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 16 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 32 \, a b d^{3} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 8 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b^{2} d^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} d^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 32 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 32 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 12 \, b^{2} d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 24 \, b^{2} d^{2} x^{4} \operatorname{Si}\left(d x\right) + 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{3} x^{3} - 32 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) - 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} - 32 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, c\right) - 96 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 16 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) - 64 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 16 \, a b d x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d x^{3} - 4 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 64 \, a b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} - 64 \, a b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, a b d x^{2} + 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d x + 64 \, a b x \tan\left(\frac{1}{2} \, d x\right) + 64 \, a b x \tan\left(\frac{1}{2} \, c\right) + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) + 24 \, a^{2} \tan\left(\frac{1}{2} \, c\right)}{48 \, {\left(x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4}\right)}}"," ",0,"-1/48*(a^2*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 8*a*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 8*a*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 - 16*a*b*d^3*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 16*a*b*d^3*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 32*a*b*d^3*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + a^2*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^4*x^4*sin_integral(d*x)*tan(1/2*c)^2 - 12*b^2*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*b^2*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b^2*d^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*a*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 8*a*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) + 24*b^2*d^2*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 24*b^2*d^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 8*a*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 8*a*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a^2*d^3*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(d*x)) + a^2*d^4*x^4*imag_part(cos_integral(-d*x)) - 2*a^2*d^4*x^4*sin_integral(d*x) + 12*b^2*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 12*b^2*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 24*b^2*d^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 - 16*a*b*d^3*x^4*imag_part(cos_integral(d*x))*tan(1/2*c) + 16*a*b*d^3*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c) - 32*a*b*d^3*x^4*sin_integral(d*x)*tan(1/2*c) - 12*b^2*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 12*b^2*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 24*b^2*d^2*x^4*sin_integral(d*x)*tan(1/2*c)^2 + 8*a*b*d^3*x^4*real_part(cos_integral(d*x)) + 8*a*b*d^3*x^4*real_part(cos_integral(-d*x)) + 2*a^2*d^3*x^3*tan(1/2*d*x)^2 + 24*b^2*d^2*x^4*real_part(cos_integral(d*x))*tan(1/2*c) + 24*b^2*d^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a^2*d^3*x^3*tan(1/2*d*x)*tan(1/2*c) + 32*a*b*d^2*x^3*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d^3*x^3*tan(1/2*c)^2 + 32*a*b*d^2*x^3*tan(1/2*d*x)*tan(1/2*c)^2 + 24*b^2*d*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*b^2*d^2*x^4*imag_part(cos_integral(d*x)) - 12*b^2*d^2*x^4*imag_part(cos_integral(-d*x)) + 24*b^2*d^2*x^4*sin_integral(d*x) + 4*a^2*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 16*a*b*d*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^3*x^3 - 32*a*b*d^2*x^3*tan(1/2*d*x) - 24*b^2*d*x^3*tan(1/2*d*x)^2 - 32*a*b*d^2*x^3*tan(1/2*c) - 96*b^2*d*x^3*tan(1/2*d*x)*tan(1/2*c) - 24*b^2*d*x^3*tan(1/2*c)^2 + 4*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a^2*d^2*x^2*tan(1/2*d*x) - 16*a*b*d*x^2*tan(1/2*d*x)^2 - 4*a^2*d^2*x^2*tan(1/2*c) - 64*a*b*d*x^2*tan(1/2*d*x)*tan(1/2*c) - 48*b^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 16*a*b*d*x^2*tan(1/2*c)^2 - 48*b^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 24*b^2*d*x^3 - 4*a^2*d*x*tan(1/2*d*x)^2 - 16*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) - 64*a*b*x*tan(1/2*d*x)^2*tan(1/2*c) - 4*a^2*d*x*tan(1/2*c)^2 - 64*a*b*x*tan(1/2*d*x)*tan(1/2*c)^2 + 16*a*b*d*x^2 + 48*b^2*x^2*tan(1/2*d*x) + 48*b^2*x^2*tan(1/2*c) - 24*a^2*tan(1/2*d*x)^2*tan(1/2*c) - 24*a^2*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a^2*d*x + 64*a*b*x*tan(1/2*d*x) + 64*a*b*x*tan(1/2*c) + 24*a^2*tan(1/2*d*x) + 24*a^2*tan(1/2*c))/(x^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^4*tan(1/2*d*x)^2 + x^4*tan(1/2*c)^2 + x^4)","C",0
18,1,3337,0,2.513908," ","integrate(x^4*sin(d*x+c)/(b*x+a),x, algorithm=""giac"")","\frac{2 \, b^{4} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{4} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{4} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{4} d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 12 \, b^{4} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{4} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{4} d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b^{4} d^{3} x^{3} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, a b^{3} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 12 \, b^{4} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{4} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a b^{3} d^{3} x^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 12 \, b^{4} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a^{2} b^{2} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a b^{3} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{4} d^{3} x^{3} + 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b^{3} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b^{4} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{4} d^{4} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} b^{2} d^{3} x \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, a b^{3} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 12 \, b^{4} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 12 \, b^{4} d x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{3} d^{3} x^{2} + a^{4} d^{4} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - a^{4} d^{4} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 2 \, a^{4} d^{4} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 12 \, b^{4} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{3} b d^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} b^{2} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b^{3} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{3} b d^{3} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a^{2} b^{2} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a b^{3} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b^{3} d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 24 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} b^{2} d^{3} x - 8 \, a b^{3} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 12 \, b^{4} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{4} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{4} d x \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} b d^{3} + 4 \, a^{2} b^{2} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b^{3} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a b^{3} d \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b^{3} d \tan\left(\frac{a d}{2 \, b}\right)^{2} - 24 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 12 \, b^{4} d x - 4 \, a b^{3} d - 24 \, b^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{2 \, {\left(b^{5} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{5} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} d^{4} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{5} d^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{5} d^{4} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} d^{4}\right)}}"," ",0,"1/2*(2*b^4*d^3*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b^3*d^3*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^4*d^3*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*b^4*d^3*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^4*d^3*x^3*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*b^2*d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b^3*d^3*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) - 4*a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) + 8*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) - 2*a*b^3*d^3*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b^3*d^3*x^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 12*b^4*d^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^3*b*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^4*d^3*x^3*tan(1/2*d*x + 1/2*c)^2 + 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*b^4*d^3*x^3*tan(1/2*c)^2 + 2*a^2*b^2*d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b) - 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b) + 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*b^4*d^3*x^3*tan(1/2*a*d/b)^2 + 2*a^2*b^2*d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*b^2*d^3*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 8*a*b^3*d^2*x*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 12*b^4*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b^3*d^3*x^2*tan(1/2*d*x + 1/2*c)^2 + a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2 - a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2 + 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2 + 2*a*b^3*d^3*x^2*tan(1/2*c)^2 - a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 12*b^4*d^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 2*a^3*b*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) + 2*a*b^3*d^3*x^2*tan(1/2*a*d/b)^2 - a^4*d^4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + a^4*d^4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*a^4*d^4*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 + 12*b^4*d^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 - 2*a^3*b*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^3*b*d^3*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 4*a^2*b^2*d^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 4*a*b^3*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b^4*d^3*x^3 + 2*a^2*b^2*d^3*x*tan(1/2*d*x + 1/2*c)^2 + 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - 2*a^2*b^2*d^3*x*tan(1/2*c)^2 - 8*a*b^3*d^2*x*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 12*b^4*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^4*d^4*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*a^4*d^4*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) - 2*a^2*b^2*d^3*x*tan(1/2*a*d/b)^2 - 8*a*b^3*d^2*x*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 - 12*b^4*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 12*b^4*d*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b^3*d^3*x^2 + a^4*d^4*imag_part(cos_integral(d*x + a*d/b)) - a^4*d^4*imag_part(cos_integral(-d*x - a*d/b)) + 2*a^4*d^4*sin_integral((b*d*x + a*d)/b) + 12*b^4*d^2*x^2*tan(1/2*d*x + 1/2*c) - 2*a^3*b*d^3*tan(1/2*d*x + 1/2*c)^2 + 2*a^3*b*d^3*tan(1/2*c)^2 + 4*a^2*b^2*d^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 4*a*b^3*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*a^3*b*d^3*tan(1/2*a*d/b)^2 + 4*a^2*b^2*d^2*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 + 4*a*b^3*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 4*a*b^3*d*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 24*b^4*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*b^2*d^3*x - 8*a*b^3*d^2*x*tan(1/2*d*x + 1/2*c) - 12*b^4*d*x*tan(1/2*d*x + 1/2*c)^2 + 12*b^4*d*x*tan(1/2*c)^2 + 12*b^4*d*x*tan(1/2*a*d/b)^2 + 2*a^3*b*d^3 + 4*a^2*b^2*d^2*tan(1/2*d*x + 1/2*c) + 4*a*b^3*d*tan(1/2*d*x + 1/2*c)^2 - 4*a*b^3*d*tan(1/2*c)^2 - 24*b^4*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 4*a*b^3*d*tan(1/2*a*d/b)^2 - 24*b^4*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 + 12*b^4*d*x - 4*a*b^3*d - 24*b^4*tan(1/2*d*x + 1/2*c))/(b^5*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^5*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + b^5*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + b^5*d^4*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^5*d^4*tan(1/2*d*x + 1/2*c)^2 + b^5*d^4*tan(1/2*c)^2 + b^5*d^4*tan(1/2*a*d/b)^2 + b^5*d^4)","C",0
19,1,2709,0,2.121787," ","integrate(x^3*sin(d*x+c)/(b*x+a),x, algorithm=""giac"")","\frac{2 \, b^{3} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b^{2} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{3} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 8 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{3} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{3} d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} b d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a b^{2} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a b^{2} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{2} d^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, b^{3} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{3} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{3} d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} b d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 8 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b^{3} d^{2} x^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} b d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} b d^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b^{2} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b^{2} d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a b^{2} d^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, b^{3} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{3} d^{3} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a b^{2} d^{2} x \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, b^{3} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{3} d^{2} x^{2} - a^{3} d^{3} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) + a^{3} d^{3} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) - 2 \, a^{3} d^{3} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 2 \, a^{2} b d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{2} b d^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b^{2} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} b d^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b^{2} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{2} d^{2} x + 8 \, b^{3} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 2 \, a^{2} b d^{2} - 4 \, a b^{2} d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 4 \, b^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, b^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{3} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{3}}{2 \, {\left(b^{4} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{4} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{4} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{4} d^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{4} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{4} d^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{4} d^{3} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{4} d^{3}\right)}}"," ",0,"1/2*(2*b^3*d^2*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a*b^2*d^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^3*d^2*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 4*a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) + 4*a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) - 8*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) + 2*b^3*d^2*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b^3*d^2*x^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*b*d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a*b^2*d^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b) + 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b) - 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*b^2*d^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a*b^2*d^2*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 8*b^3*d*x*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^3*d^2*x^2*tan(1/2*d*x + 1/2*c)^2 - a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2 + a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2 - 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2 - 2*b^3*d^2*x^2*tan(1/2*c)^2 + a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 - a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 + 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 2*a^2*b*d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 4*a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 4*a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 8*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) - 2*b^3*d^2*x^2*tan(1/2*a*d/b)^2 + a^3*d^3*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 - a^3*d^3*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 + 2*a^3*d^3*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 + 2*a^2*b*d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*b*d^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*a*b^2*d*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*b^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b^2*d^2*x*tan(1/2*d*x + 1/2*c)^2 - 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) - 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) + 2*a*b^2*d^2*x*tan(1/2*c)^2 + 8*b^3*d*x*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 2*a^3*d^3*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) + 2*a^3*d^3*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + 2*a*b^2*d^2*x*tan(1/2*a*d/b)^2 + 8*b^3*d*x*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 - 2*b^3*d^2*x^2 - a^3*d^3*imag_part(cos_integral(d*x + a*d/b)) + a^3*d^3*imag_part(cos_integral(-d*x - a*d/b)) - 2*a^3*d^3*sin_integral((b*d*x + a*d)/b) + 2*a^2*b*d^2*tan(1/2*d*x + 1/2*c)^2 - 2*a^2*b*d^2*tan(1/2*c)^2 - 4*a*b^2*d*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 4*b^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*b*d^2*tan(1/2*a*d/b)^2 - 4*a*b^2*d*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 - 4*b^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 4*b^3*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b^2*d^2*x + 8*b^3*d*x*tan(1/2*d*x + 1/2*c) - 2*a^2*b*d^2 - 4*a*b^2*d*tan(1/2*d*x + 1/2*c) - 4*b^3*tan(1/2*d*x + 1/2*c)^2 + 4*b^3*tan(1/2*c)^2 + 4*b^3*tan(1/2*a*d/b)^2 + 4*b^3)/(b^4*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^4*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + b^4*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + b^4*d^3*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^4*d^3*tan(1/2*d*x + 1/2*c)^2 + b^4*d^3*tan(1/2*c)^2 + b^4*d^3*tan(1/2*a*d/b)^2 + b^4*d^3)","C",0
20,1,2205,0,0.928602," ","integrate(x^2*sin(d*x+c)/(b*x+a),x, algorithm=""giac"")","\frac{a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a b d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b^{2} d x \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) - 2 \, a b d \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a b d \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d x + 2 \, a b d + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{2 \, {\left(b^{3} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{3} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{3} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{3} d^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{3} d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + b^{3} d^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{3} d^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{3} d^{2}\right)}}"," ",0,"1/2*(a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b^2*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) - 4*a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) + 8*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)*tan(1/2*a*d/b) - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*b^2*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b) - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*b^2*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*d*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x + 1/2*c)^2 - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x + 1/2*c)^2 - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 - 2*a*b*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 - 2*a*b*d*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b*d*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 4*b^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*d*x*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - 2*b^2*d*x*tan(1/2*c)^2 - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) - 2*b^2*d*x*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(d*x + a*d/b)) - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b)) + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b) - 2*a*b*d*tan(1/2*d*x + 1/2*c)^2 + 2*a*b*d*tan(1/2*c)^2 + 4*b^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 2*a*b*d*tan(1/2*a*d/b)^2 + 4*b^2*tan(1/2*d*x + 1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*d*x + 2*a*b*d + 4*b^2*tan(1/2*d*x + 1/2*c))/(b^3*d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^3*d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + b^3*d^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*a*d/b)^2 + b^3*d^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^3*d^2*tan(1/2*d*x + 1/2*c)^2 + b^3*d^2*tan(1/2*c)^2 + b^3*d^2*tan(1/2*a*d/b)^2 + b^3*d^2)","C",0
21,1,1647,0,0.838250," ","integrate(x*sin(d*x+c)/(b*x+a),x, algorithm=""giac"")","-\frac{a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a d \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + a d \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - a d \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 2 \, a d \operatorname{Si}\left(\frac{b d x + a d}{b}\right) - 2 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b}{2 \, {\left(b^{2} d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d \tan\left(\frac{1}{2} \, d x\right)^{2} + b^{2} d \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} d \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d\right)}}"," ",0,"-1/2*(a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - 4*a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 8*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) - 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) + 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2 - a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2 + 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2 - a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 2*b*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) - a*d*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + a*d*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*a*d*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 - 2*b*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 8*b*tan(1/2*d*x)*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - 2*a*d*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*a*d*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + a*d*imag_part(cos_integral(d*x + a*d/b)) - a*d*imag_part(cos_integral(-d*x - a*d/b)) + 2*a*d*sin_integral((b*d*x + a*d)/b) - 2*b*tan(1/2*d*x)^2 - 8*b*tan(1/2*d*x)*tan(1/2*c) - 2*b*tan(1/2*c)^2 + 2*b*tan(1/2*a*d/b)^2 + 2*b)/(b^2*d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^2*d*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*d*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + b^2*d*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^2*d*tan(1/2*d*x)^2 + b^2*d*tan(1/2*c)^2 + b^2*d*tan(1/2*a*d/b)^2 + b^2*d)","C",0
22,1,597,0,1.533841," ","integrate(sin(d*x+c)/(b*x+a),x, algorithm=""giac"")","\frac{\Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right)}{2 \, {\left(b \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b \tan\left(\frac{1}{2} \, c\right)^{2} + b \tan\left(\frac{a d}{2 \, b}\right)^{2} + b\right)}}"," ",0,"1/2*(imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) - imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 + 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + imag_part(cos_integral(d*x + a*d/b)) - imag_part(cos_integral(-d*x - a*d/b)) + 2*sin_integral((b*d*x + a*d)/b))/(b*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b*tan(1/2*c)^2 + b*tan(1/2*a*d/b)^2 + b)","C",0
23,1,838,0,2.055111," ","integrate(sin(d*x+c)/x/(b*x+a),x, algorithm=""giac"")","-\frac{\Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \operatorname{Si}\left(d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - \Im \left( \operatorname{Ci}\left(d x\right) \right) - \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, \operatorname{Si}\left(d x\right) + 2 \, \operatorname{Si}\left(\frac{b d x + a d}{b}\right)}{2 \, {\left(a \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a \tan\left(\frac{1}{2} \, c\right)^{2} + a \tan\left(\frac{a d}{2 \, b}\right)^{2} + a\right)}}"," ",0,"-1/2*(imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + imag_part(cos_integral(d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - imag_part(cos_integral(-d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*sin_integral(d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*real_part(cos_integral(d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*real_part(cos_integral(-d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 - imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + imag_part(cos_integral(d*x))*tan(1/2*c)^2 + imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*sin_integral(d*x)*tan(1/2*c)^2 - 2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 4*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) - imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 - imag_part(cos_integral(d*x))*tan(1/2*a*d/b)^2 + imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 + imag_part(cos_integral(-d*x))*tan(1/2*a*d/b)^2 - 2*sin_integral(d*x)*tan(1/2*a*d/b)^2 - 2*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 + 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) - 2*real_part(cos_integral(d*x))*tan(1/2*c) + 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - 2*real_part(cos_integral(-d*x))*tan(1/2*c) - 2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + imag_part(cos_integral(d*x + a*d/b)) - imag_part(cos_integral(d*x)) - imag_part(cos_integral(-d*x - a*d/b)) + imag_part(cos_integral(-d*x)) - 2*sin_integral(d*x) + 2*sin_integral((b*d*x + a*d)/b))/(a*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a*tan(1/2*c)^2 + a*tan(1/2*a*d/b)^2 + a)","C",0
24,1,2897,0,0.679759," ","integrate(sin(d*x+c)/x^2/(b*x+a),x, algorithm=""giac"")","-\frac{a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 8 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, b x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a d x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 8 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + b x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \operatorname{Si}\left(d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - a d x \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d x \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - b x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) + b x \Im \left( \operatorname{Ci}\left(d x\right) \right) + b x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) - b x \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, b x \operatorname{Si}\left(d x\right) - 2 \, b x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 4 \, a \tan\left(\frac{1}{2} \, d x\right) + 4 \, a \tan\left(\frac{1}{2} \, c\right)}{2 \, {\left(a^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} x \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} x\right)}}"," ",0,"-1/2*(a*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a*d*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*a*d*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - a*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - a*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + a*d*x*real_part(cos_integral(d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a*d*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*d*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 - b*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 + b*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 4*b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - 8*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + b*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*b*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*a*d*x*imag_part(cos_integral(d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a*d*x*imag_part(cos_integral(-d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*a*d*x*sin_integral(d*x)*tan(1/2*c)*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b*x*imag_part(cos_integral(-d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b*x*sin_integral(d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a*d*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 2*b*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 2*b*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + a*d*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) + 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) - 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - a*d*x*real_part(cos_integral(d*x))*tan(1/2*a*d/b)^2 - a*d*x*real_part(cos_integral(-d*x))*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b*x*real_part(cos_integral(-d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*a*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*a*tan(1/2*d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2 + b*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2 - b*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 2*b*x*sin_integral(d*x)*tan(1/2*d*x)^2 - 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2 + 2*a*d*x*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d*x*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d*x*sin_integral(d*x)*tan(1/2*c) + b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 - b*x*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 + b*x*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*b*x*sin_integral(d*x)*tan(1/2*c)^2 + 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 - 4*b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 4*b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 8*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) + b*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + b*x*imag_part(cos_integral(d*x))*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(-d*x))*tan(1/2*a*d/b)^2 + 2*b*x*sin_integral(d*x)*tan(1/2*a*d/b)^2 + 2*b*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 - a*d*x*real_part(cos_integral(d*x)) - a*d*x*real_part(cos_integral(-d*x)) - 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*b*x*real_part(cos_integral(d*x))*tan(1/2*c) - 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) + 2*b*x*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*a*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*tan(1/2*d*x)*tan(1/2*c)^2 + 2*b*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) + 2*b*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + 4*a*tan(1/2*d*x)*tan(1/2*a*d/b)^2 + 4*a*tan(1/2*c)*tan(1/2*a*d/b)^2 - b*x*imag_part(cos_integral(d*x + a*d/b)) + b*x*imag_part(cos_integral(d*x)) + b*x*imag_part(cos_integral(-d*x - a*d/b)) - b*x*imag_part(cos_integral(-d*x)) + 2*b*x*sin_integral(d*x) - 2*b*x*sin_integral((b*d*x + a*d)/b) + 4*a*tan(1/2*d*x) + 4*a*tan(1/2*c))/(a^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*x*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a^2*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*x*tan(1/2*d*x)^2 + a^2*x*tan(1/2*c)^2 + a^2*x*tan(1/2*a*d/b)^2 + a^2*x)","C",0
25,1,4565,0,0.715472," ","integrate(sin(d*x+c)/x^3/(b*x+a),x, algorithm=""giac"")","\frac{a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, a b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 16 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, a b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, a b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, a b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{2} x^{2} \operatorname{Si}\left(d x\right) - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 16 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) - 2 \, a b d x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 8 \, a b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, b^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d x \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, a b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 8 \, a b x \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) - 2 \, b^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, b^{2} x^{2} \operatorname{Si}\left(d x\right) - 4 \, b^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d x + 8 \, a b x \tan\left(\frac{1}{2} \, d x\right) + 8 \, a b x \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(a^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{3} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{3} x^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{3} x^{2}\right)}}"," ",0,"1/4*(a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 4*a*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*a*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 8*a*b*d*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*b^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 + 4*a*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 8*a*b*d*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 8*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 8*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - 16*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - a^2*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*a*d/b)^2 + a^2*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*a*d/b)^2 - 2*a^2*d^2*x^2*sin_integral(d*x)*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 4*b^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 4*a*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*a*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 8*a*b*d*x^2*sin_integral(d*x)*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*b^2*x^2*sin_integral(d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*c)^2 + 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) + 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) - 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*b*d*x^2*real_part(cos_integral(d*x))*tan(1/2*a*d/b)^2 - 2*a*b*d*x^2*real_part(cos_integral(-d*x))*tan(1/2*a*d/b)^2 + 2*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c)*tan(1/2*a*d/b)^2 + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c)*tan(1/2*a*d/b)^2 - 8*a*b*x*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a^2*d*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 8*a*b*x*tan(1/2*d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*x^2*imag_part(cos_integral(d*x)) + a^2*d^2*x^2*imag_part(cos_integral(-d*x)) - 2*a^2*d^2*x^2*sin_integral(d*x) - 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2 + 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 4*b^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 - 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2 + 4*a*b*d*x^2*imag_part(cos_integral(d*x))*tan(1/2*c) - 4*a*b*d*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c) + 8*a*b*d*x^2*sin_integral(d*x)*tan(1/2*c) + 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 + 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*b^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 - 8*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 16*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) + 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + 2*b^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*a*d/b)^2 + 4*b^2*x^2*sin_integral(d*x)*tan(1/2*a*d/b)^2 + 4*b^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 + 4*a^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 4*a^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b*d*x^2*real_part(cos_integral(d*x)) - 2*a*b*d*x^2*real_part(cos_integral(-d*x)) + 2*a^2*d*x*tan(1/2*d*x)^2 - 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) + 4*b^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) - 8*a*b*x*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d*x*tan(1/2*c)^2 - 8*a*b*x*tan(1/2*d*x)*tan(1/2*c)^2 + 4*b^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) + 4*b^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) - 2*a^2*d*x*tan(1/2*a*d/b)^2 + 8*a*b*x*tan(1/2*d*x)*tan(1/2*a*d/b)^2 + 8*a*b*x*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*x^2*imag_part(cos_integral(d*x + a*d/b)) + 2*b^2*x^2*imag_part(cos_integral(d*x)) + 2*b^2*x^2*imag_part(cos_integral(-d*x - a*d/b)) - 2*b^2*x^2*imag_part(cos_integral(-d*x)) + 4*b^2*x^2*sin_integral(d*x) - 4*b^2*x^2*sin_integral((b*d*x + a*d)/b) + 4*a^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*tan(1/2*d*x)*tan(1/2*c)^2 - 4*a^2*tan(1/2*d*x)*tan(1/2*a*d/b)^2 - 4*a^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d*x + 8*a*b*x*tan(1/2*d*x) + 8*a*b*x*tan(1/2*c) - 4*a^2*tan(1/2*d*x) - 4*a^2*tan(1/2*c))/(a^3*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^3*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^3*x^2*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a^3*x^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^3*x^2*tan(1/2*d*x)^2 + a^3*x^2*tan(1/2*c)^2 + a^3*x^2*tan(1/2*a*d/b)^2 + a^3*x^2)","C",0
26,1,1973,0,1.714132," ","integrate(x^4*sin(d*x+c)/(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left({\left(b x + a\right)} a^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{4} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a^{4} b c d^{4} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{5} d^{5} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} a^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{4} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a^{4} b c d^{4} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{5} d^{5} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 4 \, {\left(b x + a\right)} a^{3} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 4 \, a^{3} b^{2} c d^{3} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + 4 \, a^{4} b d^{4} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 4 \, {\left(b x + a\right)} a^{3} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 4 \, a^{3} b^{2} c d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - 4 \, a^{4} b d^{4} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{4} b d^{4} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - {\left(b x + a\right)}^{3} b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{3} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + 3 \, {\left(b x + a\right)}^{2} b^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} c \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 3 \, {\left(b x + a\right)} b^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c^{2} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + b^{5} c^{3} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + {\left(b x + a\right)}^{2} a b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, {\left(b x + a\right)} a b^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + a b^{4} c^{2} d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - {\left(b x + a\right)} a^{2} b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + a^{2} b^{3} c d^{2} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 3 \, a^{3} b^{2} d^{3} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, {\left(b x + a\right)}^{2} b^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + 4 \, {\left(b x + a\right)} b^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, b^{5} c^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + 2 \, a^{2} b^{3} d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + 2 \, {\left(b x + a\right)} b^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, b^{5} c \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + 2 \, a b^{4} d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b^{2}}{{\left({\left(b x + a\right)} b^{8} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} - b^{9} c d^{2} + a b^{8} d^{3}\right)} d}"," ",0,"((b*x + a)*a^4*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^4*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a^4*b*c*d^4*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^5*d^5*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a^4*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^4*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a^4*b*c*d^4*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^5*d^5*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 4*(b*x + a)*a^3*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 4*a^3*b^2*c*d^3*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + 4*a^4*b*d^4*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 4*(b*x + a)*a^3*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 4*a^3*b^2*c*d^3*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - 4*a^4*b*d^4*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^4*b*d^4*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - (b*x + a)^3*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^3*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + 3*(b*x + a)^2*b^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*c*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 3*(b*x + a)*b^4*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c^2*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + b^5*c^3*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + (b*x + a)^2*a*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*(b*x + a)*a*b^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + a*b^4*c^2*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - (b*x + a)*a^2*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + a^2*b^3*c*d^2*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 3*a^3*b^2*d^3*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*(b*x + a)^2*b^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + 4*(b*x + a)*b^4*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*b^5*c^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + 2*a^2*b^3*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + 2*(b*x + a)*b^4*(b*c/(b*x + a) - a*d/(b*x + a) + d)*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*b^5*c*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + 2*a*b^4*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b^2/(((b*x + a)*b^8*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2 - b^9*c*d^2 + a*b^8*d^3)*d)","B",0
27,1,1474,0,0.790757," ","integrate(x^3*sin(d*x+c)/(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(b x + a\right)} a^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a^{3} b c d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{4} d^{4} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} a^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a^{3} b c d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{4} d^{4} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 3 \, {\left(b x + a\right)} a^{2} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 3 \, a^{2} b^{2} c d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + 3 \, a^{3} b d^{3} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 3 \, {\left(b x + a\right)} a^{2} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 3 \, a^{2} b^{2} c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - 3 \, a^{3} b d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{3} b d^{3} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + {\left(b x + a\right)}^{2} b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, {\left(b x + a\right)} b^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + b^{4} c^{2} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - {\left(b x + a\right)} a b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + a b^{3} c d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, a^{2} b^{2} d^{2} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + {\left(b x + a\right)} b^{3} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - b^{4} c \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + a b^{3} d \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b^{2}}{{\left({\left(b x + a\right)} b^{7} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d - b^{8} c d + a b^{7} d^{2}\right)} d}"," ",0,"-((b*x + a)*a^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a^3*b*c*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^4*d^4*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a^3*b*c*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^4*d^4*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 3*(b*x + a)*a^2*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 3*a^2*b^2*c*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + 3*a^3*b*d^3*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 3*(b*x + a)*a^2*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 3*a^2*b^2*c*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - 3*a^3*b*d^3*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^3*b*d^3*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + (b*x + a)^2*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*(b*x + a)*b^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + b^4*c^2*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - (b*x + a)*a*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + a*b^3*c*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*a^2*b^2*d^2*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + (b*x + a)*b^3*(b*c/(b*x + a) - a*d/(b*x + a) + d)*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - b^4*c*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + a*b^3*d*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b^2/(((b*x + a)*b^7*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d - b^8*c*d + a*b^7*d^2)*d)","B",0
28,1,1120,0,0.748455," ","integrate(x^2*sin(d*x+c)/(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left({\left(b x + a\right)} a^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a^{2} b c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{3} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} a^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a^{2} b c d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{3} d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 2 \, {\left(b x + a\right)} a b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 2 \, a b^{2} c d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + 2 \, a^{2} b d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b x + a\right)} a b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 2 \, a b^{2} c d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - 2 \, a^{2} b d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{2} b d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - {\left(b x + a\right)} b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + b^{3} c \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - a b^{2} d \cos\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b^{2}}{{\left({\left(b x + a\right)} b^{6} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b^{7} c + a b^{6} d\right)} d}"," ",0,"((b*x + a)*a^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a^2*b*c*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^3*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a^2*b*c*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^3*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 2*(b*x + a)*a*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 2*a*b^2*c*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + 2*a^2*b*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 2*(b*x + a)*a*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 2*a*b^2*c*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - 2*a^2*b*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^2*b*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - (b*x + a)*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + b^3*c*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - a*b^2*d*cos(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b^2/(((b*x + a)*b^6*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b^7*c + a*b^6*d)*d)","B",0
29,1,951,0,0.809223," ","integrate(x*sin(d*x+c)/(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a b c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{2} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a b c d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{2} d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - b^{2} c d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + a b d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + b^{2} c d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a b d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a b d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b}{{\left({\left(b x + a\right)} b^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b^{5} c + a b^{4} d\right)} d}"," ",0,"-((b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a*b*c*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^2*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a*b*c*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^2*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - b^2*c*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + a*b*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - (b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + b^2*c*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a*b*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*b*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b/(((b*x + a)*b^4*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b^5*c + a*b^4*d)*d)","B",0
30,1,518,0,0.385073," ","integrate(sin(d*x+c)/(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left({\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - b c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - b c d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + b d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b^{2}}{{\left({\left(b x + a\right)} b^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b^{5} c + a b^{4} d\right)} d}"," ",0,"((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - b*c*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - b*c*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + b*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b^2/(((b*x + a)*b^4*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b^5*c + a*b^4*d)*d)","B",0
31,1,1281,0,0.793384," ","integrate(sin(d*x+c)/x/(b*x+a)^2,x, algorithm=""giac"")","-\frac{{\left({\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a b c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{2} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - a b c d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a^{2} d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) + b^{2} c d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) - a b d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) - {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + b^{2} c d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - a b d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) - b^{2} c d \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + a b d^{2} \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - b^{2} c d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a b d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a b d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b^{3}}{{\left({\left(b x + a\right)} a^{2} b^{4} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - a^{2} b^{5} c + a^{3} b^{4} d\right)} d}"," ",0,"-((b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a*b*c*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^2*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - a*b*c*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a^2*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - (b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) + b^2*c*d*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) - a*b*d^2*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) - (b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + b^2*c*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - a*b*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + (b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) - b^2*c*d*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + a*b*d^2*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + (b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - b^2*c*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*b*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*b*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b^3/(((b*x + a)*a^2*b^4*(b*c/(b*x + a) - a*d/(b*x + a) + d) - a^2*b^5*c + a^3*b^4*d)*d)","B",0
32,1,3180,0,1.737188," ","integrate(sin(d*x+c)/x^2/(b*x+a)^2,x, algorithm=""giac"")","\frac{{\left(\frac{{\left(b x + a\right)}^{2} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d^{2} \cos\left(c\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right)}{b} - 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d^{2} \cos\left(c\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) + a b c^{2} d^{2} \cos\left(c\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) + \frac{{\left(b x + a\right)} a^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \cos\left(c\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right)}{b} - a^{2} c d^{3} \cos\left(c\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) + \frac{{\left(b x + a\right)}^{2} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right)}{b} - 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a b c^{2} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + \frac{{\left(b x + a\right)} a^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right)}{b} - a^{2} c d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + \frac{{\left(b x + a\right)}^{2} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d^{2} \sin\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right)}{b} - 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d^{2} \sin\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + a b c^{2} d^{2} \sin\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + \frac{{\left(b x + a\right)} a^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \sin\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right)}{b} - a^{2} c d^{3} \sin\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + \frac{{\left(b x + a\right)}^{2} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right)}{b} - 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + a b c^{2} d^{2} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + \frac{{\left(b x + a\right)} a^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right)}{b} - a^{2} c d^{3} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - 2 \, {\left(b x + a\right)}^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) + 4 \, {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) - 2 \, b^{2} c^{2} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) - 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) + 2 \, a b c d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} - c\right) \sin\left(c\right) - 2 \, {\left(b x + a\right)}^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + 4 \, {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 2 \, b^{2} c^{2} d \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + 2 \, a b c d^{2} \operatorname{Ci}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) \sin\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(b x + a\right)}^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) - 4 \, {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + 2 \, b^{2} c^{2} d \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) - 2 \, a b c d^{2} \cos\left(c\right) \operatorname{Si}\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b} + c\right) + 2 \, {\left(b x + a\right)}^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - 4 \, {\left(b x + a\right)} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 2 \, b^{2} c^{2} d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) - 2 \, a b c d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} - b c + a d}{b}\right) + 2 \, {\left(b x + a\right)} a {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) - 2 \, a b c d^{2} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right) + a^{2} d^{3} \sin\left(-\frac{{\left(b x + a\right)} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}}{b}\right)\right)} b^{2}}{{\left({\left(b x + a\right)}^{2} a^{3} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)}^{2} - 2 \, {\left(b x + a\right)} a^{3} b^{2} {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} c + a^{3} b^{3} c^{2} + {\left(b x + a\right)} a^{4} b {\left(\frac{b c}{b x + a} - \frac{a d}{b x + a} + d\right)} d - a^{4} b^{2} c d\right)} d}"," ",0,"((b*x + a)^2*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d^2*cos(c)*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)/b - 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d^2*cos(c)*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c) + a*b*c^2*d^2*cos(c)*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c) + (b*x + a)*a^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*cos(c)*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)/b - a^2*c*d^3*cos(c)*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c) + (b*x + a)^2*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)/b - 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*b*c^2*d^2*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)/b - a^2*c*d^3*cos(-(b*c - a*d)/b)*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)^2*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d^2*sin(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c)/b - 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d^2*sin(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + a*b*c^2*d^2*sin(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + (b*x + a)*a^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*sin(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c)/b - a^2*c*d^3*sin(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + (b*x + a)^2*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)/b - 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + a*b*c^2*d^2*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + (b*x + a)*a^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)/b - a^2*c*d^3*sin(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - 2*(b*x + a)^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) + 4*(b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) - 2*b^2*c^2*d*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) - 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) + 2*a*b*c*d^2*cos_integral((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b - c)*sin(c) - 2*(b*x + a)^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + 4*(b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 2*b^2*c^2*d*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) - 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + 2*a*b*c*d^2*cos_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b)*sin(-(b*c - a*d)/b) + 2*(b*x + a)^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) - 4*(b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + 2*b^2*c^2*d*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) - 2*a*b*c*d^2*cos(c)*sin_integral(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b + c) + 2*(b*x + a)^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - 4*(b*x + a)*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 2*b^2*c^2*d*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) - 2*a*b*c*d^2*cos(-(b*c - a*d)/b)*sin_integral(((b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d) - b*c + a*d)/b) + 2*(b*x + a)*a*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) - 2*a*b*c*d^2*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b) + a^2*d^3*sin(-(b*x + a)*(b*c/(b*x + a) - a*d/(b*x + a) + d)/b))*b^2/(((b*x + a)^2*a^3*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)^2 - 2*(b*x + a)*a^3*b^2*(b*c/(b*x + a) - a*d/(b*x + a) + d)*c + a^3*b^3*c^2 + (b*x + a)*a^4*b*(b*c/(b*x + a) - a*d/(b*x + a) + d)*d - a^4*b^2*c*d)*d)","B",0
33,-1,0,0,0.000000," ","integrate(x^3*sin(d*x+c)/(b*x+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate(x^2*sin(d*x+c)/(b*x+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate(x*sin(d*x+c)/(b*x+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,1,5727,0,1.153640," ","integrate(sin(d*x+c)/(b*x+a)^3,x, algorithm=""giac"")","-\frac{b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 8 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 16 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 4 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, b^{2} d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 8 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 16 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - b^{2} d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 2 \, b^{2} d^{2} x^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a b d^{2} x \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - 4 \, a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) + 8 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right) - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 8 \, a b d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} - 2 \, a b d \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - 2 \, a b d^{2} x \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 4 \, a b d^{2} x \operatorname{Si}\left(\frac{b d x + a d}{b}\right) - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{1}{2} \, c\right) - 8 \, b^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) - 2 \, a^{2} d^{2} \Re \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) \tan\left(\frac{a d}{2 \, b}\right) + 2 \, b^{2} d x \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} d^{2} \Im \left( \operatorname{Ci}\left(d x + \frac{a d}{b}\right) \right) - a^{2} d^{2} \Im \left( \operatorname{Ci}\left(-d x - \frac{a d}{b}\right) \right) + 2 \, a^{2} d^{2} \operatorname{Si}\left(\frac{b d x + a d}{b}\right) - 2 \, a b d \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, a b d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a b d \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b d \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 4 \, b^{2} \tan\left(\frac{1}{2} \, c\right) \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, b^{2} d x + 2 \, a b d + 4 \, b^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, b^{2} \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(b^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} b^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + b^{5} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} b^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + b^{5} x^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} b^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + a^{2} b^{3} \tan\left(\frac{1}{2} \, c\right)^{2} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a b^{4} x \tan\left(\frac{a d}{2 \, b}\right)^{2} + b^{5} x^{2} + a^{2} b^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} b^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} b^{3} \tan\left(\frac{a d}{2 \, b}\right)^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/4*(b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - 4*b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 8*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) - 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) + 8*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - 8*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 16*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2 - b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2 + 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2 + 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) - b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) - 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) + 4*b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) + 4*a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) - 4*a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 8*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b) + 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b*d*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2 - 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2 + 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2 + 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 2*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*d^2*x^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*b^2*d^2*x^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2*tan(1/2*a*d/b) + 8*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 8*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 16*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2*tan(1/2*a*d/b) - 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 - 2*b^2*d*x*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b)^2 - 8*b^2*d*x*tan(1/2*d*x)*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*b^2*d*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^2*d^2*x^2*imag_part(cos_integral(d*x + a*d/b)) - b^2*d^2*x^2*imag_part(cos_integral(-d*x - a*d/b)) + 2*b^2*d^2*x^2*sin_integral((b*d*x + a*d)/b) + a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*d*x)^2 - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*d*x)^2 + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*d*x)^2 + 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)^2 + 2*a*b*d*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*b*d^2*x*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 4*a*b*d^2*x*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + 4*a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) - 4*a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*c)*tan(1/2*a*d/b) + 8*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*c)*tan(1/2*a*d/b) - a^2*d^2*imag_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b)^2 - 2*a^2*d^2*sin_integral((b*d*x + a*d)/b)*tan(1/2*a*d/b)^2 - 2*a*b*d*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 - 8*a*b*d*tan(1/2*d*x)*tan(1/2*c)*tan(1/2*a*d/b)^2 - 4*b^2*tan(1/2*d*x)^2*tan(1/2*c)*tan(1/2*a*d/b)^2 - 2*a*b*d*tan(1/2*c)^2*tan(1/2*a*d/b)^2 - 4*b^2*tan(1/2*d*x)*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b*d^2*x*imag_part(cos_integral(d*x + a*d/b)) - 2*a*b*d^2*x*imag_part(cos_integral(-d*x - a*d/b)) + 4*a*b*d^2*x*sin_integral((b*d*x + a*d)/b) - 2*b^2*d*x*tan(1/2*d*x)^2 + 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*c) + 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*c) - 8*b^2*d*x*tan(1/2*d*x)*tan(1/2*c) - 2*b^2*d*x*tan(1/2*c)^2 - 2*a^2*d^2*real_part(cos_integral(d*x + a*d/b))*tan(1/2*a*d/b) - 2*a^2*d^2*real_part(cos_integral(-d*x - a*d/b))*tan(1/2*a*d/b) + 2*b^2*d*x*tan(1/2*a*d/b)^2 + a^2*d^2*imag_part(cos_integral(d*x + a*d/b)) - a^2*d^2*imag_part(cos_integral(-d*x - a*d/b)) + 2*a^2*d^2*sin_integral((b*d*x + a*d)/b) - 2*a*b*d*tan(1/2*d*x)^2 - 8*a*b*d*tan(1/2*d*x)*tan(1/2*c) - 4*b^2*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*b*d*tan(1/2*c)^2 - 4*b^2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*a*b*d*tan(1/2*a*d/b)^2 + 4*b^2*tan(1/2*d*x)*tan(1/2*a*d/b)^2 + 4*b^2*tan(1/2*c)*tan(1/2*a*d/b)^2 + 2*b^2*d*x + 2*a*b*d + 4*b^2*tan(1/2*d*x) + 4*b^2*tan(1/2*c))/(b^5*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b^4*x*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^5*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^5*x^2*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + b^5*x^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + a^2*b^3*tan(1/2*d*x)^2*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b^4*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*b^4*x*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + 2*a*b^4*x*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + b^5*x^2*tan(1/2*d*x)^2 + b^5*x^2*tan(1/2*c)^2 + a^2*b^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + b^5*x^2*tan(1/2*a*d/b)^2 + a^2*b^3*tan(1/2*d*x)^2*tan(1/2*a*d/b)^2 + a^2*b^3*tan(1/2*c)^2*tan(1/2*a*d/b)^2 + 2*a*b^4*x*tan(1/2*d*x)^2 + 2*a*b^4*x*tan(1/2*c)^2 + 2*a*b^4*x*tan(1/2*a*d/b)^2 + b^5*x^2 + a^2*b^3*tan(1/2*d*x)^2 + a^2*b^3*tan(1/2*c)^2 + a^2*b^3*tan(1/2*a*d/b)^2 + 2*a*b^4*x + a^2*b^3)","C",0
37,-1,0,0,0.000000," ","integrate(sin(d*x+c)/x/(b*x+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(sin(d*x+c)/x^2/(b*x+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate(sin(d*x+c)/x^3/(b*x+a)^3,x, algorithm=""giac"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,97,0,1.874925," ","integrate(x^3*(b*x^2+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{5} x^{5} + a d^{5} x^{3} - 20 \, b d^{3} x^{3} - 6 \, a d^{3} x + 120 \, b d x\right)} \cos\left(d x + c\right)}{d^{6}} + \frac{{\left(5 \, b d^{4} x^{4} + 3 \, a d^{4} x^{2} - 60 \, b d^{2} x^{2} - 6 \, a d^{2} + 120 \, b\right)} \sin\left(d x + c\right)}{d^{6}}"," ",0,"-(b*d^5*x^5 + a*d^5*x^3 - 20*b*d^3*x^3 - 6*a*d^3*x + 120*b*d*x)*cos(d*x + c)/d^6 + (5*b*d^4*x^4 + 3*a*d^4*x^2 - 60*b*d^2*x^2 - 6*a*d^2 + 120*b)*sin(d*x + c)/d^6","A",0
41,1,79,0,0.623027," ","integrate(x^2*(b*x^2+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{4} x^{4} + a d^{4} x^{2} - 12 \, b d^{2} x^{2} - 2 \, a d^{2} + 24 \, b\right)} \cos\left(d x + c\right)}{d^{5}} + \frac{2 \, {\left(2 \, b d^{3} x^{3} + a d^{3} x - 12 \, b d x\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-(b*d^4*x^4 + a*d^4*x^2 - 12*b*d^2*x^2 - 2*a*d^2 + 24*b)*cos(d*x + c)/d^5 + 2*(2*b*d^3*x^3 + a*d^3*x - 12*b*d*x)*sin(d*x + c)/d^5","A",0
42,1,60,0,0.453916," ","integrate(x*(b*x^2+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{3} x^{3} + a d^{3} x - 6 \, b d x\right)} \cos\left(d x + c\right)}{d^{4}} + \frac{{\left(3 \, b d^{2} x^{2} + a d^{2} - 6 \, b\right)} \sin\left(d x + c\right)}{d^{4}}"," ",0,"-(b*d^3*x^3 + a*d^3*x - 6*b*d*x)*cos(d*x + c)/d^4 + (3*b*d^2*x^2 + a*d^2 - 6*b)*sin(d*x + c)/d^4","A",0
43,1,42,0,0.351347," ","integrate((b*x^2+a)*sin(d*x+c),x, algorithm=""giac"")","\frac{2 \, b x \sin\left(d x + c\right)}{d^{2}} - \frac{{\left(b d^{2} x^{2} + a d^{2} - 2 \, b\right)} \cos\left(d x + c\right)}{d^{3}}"," ",0,"2*b*x*sin(d*x + c)/d^2 - (b*d^2*x^2 + a*d^2 - 2*b)*cos(d*x + c)/d^3","A",0
44,1,432,0,0.768918," ","integrate((b*x^2+a)*sin(d*x+c)/x,x, algorithm=""giac"")","-\frac{a d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, b d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b d x \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 8 \, b d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b d x \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{2} \operatorname{Si}\left(d x\right) + 4 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b d x - 4 \, b \tan\left(\frac{1}{2} \, d x\right) - 4 \, b \tan\left(\frac{1}{2} \, c\right)}{2 \, {\left(d^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2}\right)}}"," ",0,"-1/2*(a*d^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 2*b*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^2*sin_integral(d*x)*tan(1/2*d*x)^2 + a*d^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^2*sin_integral(d*x)*tan(1/2*c)^2 - 2*b*d*x*tan(1/2*d*x)^2 - 2*a*d^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^2*real_part(cos_integral(-d*x))*tan(1/2*c) - 8*b*d*x*tan(1/2*d*x)*tan(1/2*c) - 2*b*d*x*tan(1/2*c)^2 - a*d^2*imag_part(cos_integral(d*x)) + a*d^2*imag_part(cos_integral(-d*x)) - 2*a*d^2*sin_integral(d*x) + 4*b*tan(1/2*d*x)^2*tan(1/2*c) + 4*b*tan(1/2*d*x)*tan(1/2*c)^2 + 2*b*d*x - 4*b*tan(1/2*d*x) - 4*b*tan(1/2*c))/(d^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^2*tan(1/2*d*x)^2 + d^2*tan(1/2*c)^2 + d^2)","C",0
45,1,411,0,0.348184," ","integrate((b*x^2+a)*sin(d*x+c)/x^2,x, algorithm=""giac"")","-\frac{a d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{2} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{2} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d^{2} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 4 \, a d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b x \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b x \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d \tan\left(\frac{1}{2} \, d x\right) + 4 \, a d \tan\left(\frac{1}{2} \, c\right) + 2 \, b x}{2 \, {\left(d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d x \tan\left(\frac{1}{2} \, d x\right)^{2} + d x \tan\left(\frac{1}{2} \, c\right)^{2} + d x\right)}}"," ",0,"-1/2*(a*d^2*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d^2*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^2*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^2*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^2*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a*d^2*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d^2*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + a*d^2*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d^2*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^2*x*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^2*x*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d^2*x*sin_integral(d*x)*tan(1/2*c) + 2*b*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*x*real_part(cos_integral(d*x)) - a*d^2*x*real_part(cos_integral(-d*x)) - 4*a*d*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*d*tan(1/2*d*x)*tan(1/2*c)^2 - 2*b*x*tan(1/2*d*x)^2 - 8*b*x*tan(1/2*d*x)*tan(1/2*c) - 2*b*x*tan(1/2*c)^2 + 4*a*d*tan(1/2*d*x) + 4*a*d*tan(1/2*c) + 2*b*x)/(d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*x*tan(1/2*d*x)^2 + d*x*tan(1/2*c)^2 + d*x)","C",0
46,1,766,0,0.317438," ","integrate((b*x^2+a)*sin(d*x+c)/x^3,x, algorithm=""giac"")","\frac{a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{2} x^{2} \operatorname{Si}\left(d x\right) + 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 2 \, b x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, b x^{2} \operatorname{Si}\left(d x\right) + 4 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x - 4 \, a \tan\left(\frac{1}{2} \, d x\right) - 4 \, a \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{2}\right)}}"," ",0,"1/4*(a*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 + a*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 - 2*b*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 4*b*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*b*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^2*x^2*imag_part(cos_integral(d*x)) + a*d^2*x^2*imag_part(cos_integral(-d*x)) - 2*a*d^2*x^2*sin_integral(d*x) + 2*b*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 2*b*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 4*b*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 - 2*b*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 2*b*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*b*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 2*a*d*x*tan(1/2*d*x)^2 + 4*b*x^2*real_part(cos_integral(d*x))*tan(1/2*c) + 4*b*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 2*a*d*x*tan(1/2*c)^2 + 2*b*x^2*imag_part(cos_integral(d*x)) - 2*b*x^2*imag_part(cos_integral(-d*x)) + 4*b*x^2*sin_integral(d*x) + 4*a*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d*x - 4*a*tan(1/2*d*x) - 4*a*tan(1/2*c))/(x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^2*tan(1/2*d*x)^2 + x^2*tan(1/2*c)^2 + x^2)","C",0
47,1,834,0,0.421510," ","integrate((b*x^2+a)*sin(d*x+c)/x^4,x, algorithm=""giac"")","\frac{a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 12 \, b d x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 12 \, b d x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, b d x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b d x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b d x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 24 \, b d x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 6 \, b d x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right) - 24 \, b x^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x - 8 \, a \tan\left(\frac{1}{2} \, d x\right) - 8 \, a \tan\left(\frac{1}{2} \, c\right)}{12 \, {\left(x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3}\right)}}"," ",0,"1/12*(a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^3*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 6*b*d*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 6*b*d*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d^3*x^3*sin_integral(d*x)*tan(1/2*c) - 12*b*d*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 12*b*d*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 24*b*d*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a*d^3*x^3*real_part(cos_integral(d*x)) - a*d^3*x^3*real_part(cos_integral(-d*x)) + 6*b*d*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 6*b*d*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 4*a*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 6*b*d*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 6*b*d*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*a*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 12*b*d*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) + 12*b*d*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) - 24*b*d*x^3*sin_integral(d*x)*tan(1/2*c) - 2*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 6*b*d*x^3*real_part(cos_integral(d*x)) + 6*b*d*x^3*real_part(cos_integral(-d*x)) + 4*a*d^2*x^2*tan(1/2*d*x) + 4*a*d^2*x^2*tan(1/2*c) + 24*b*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 24*b*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*a*d*x*tan(1/2*d*x)^2 + 8*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 2*a*d*x*tan(1/2*c)^2 - 24*b*x^2*tan(1/2*d*x) - 24*b*x^2*tan(1/2*c) + 8*a*tan(1/2*d*x)^2*tan(1/2*c) + 8*a*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d*x - 8*a*tan(1/2*d*x) - 8*a*tan(1/2*c))/(x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^3*tan(1/2*d*x)^2 + x^3*tan(1/2*c)^2 + x^3)","C",0
48,1,1086,0,0.482262," ","integrate((b*x^2+a)*sin(d*x+c)/x^5,x, algorithm=""giac"")","-\frac{a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 24 \, b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{4} x^{4} \operatorname{Si}\left(d x\right) + 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 24 \, b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 12 \, b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 24 \, b d^{2} x^{4} \operatorname{Si}\left(d x\right) + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} x^{3} - 24 \, b d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} - 96 \, b d x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 24 \, b d x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) - 48 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 48 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b d x^{3} - 4 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right) + 48 \, b x^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d x + 24 \, a \tan\left(\frac{1}{2} \, d x\right) + 24 \, a \tan\left(\frac{1}{2} \, c\right)}{48 \, {\left(x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4}\right)}}"," ",0,"-1/48*(a*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 + a*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^4*x^4*sin_integral(d*x)*tan(1/2*c)^2 - 12*b*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*b*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b*d^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) + 24*b*d^2*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 24*b*d^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^4*x^4*imag_part(cos_integral(d*x)) + a*d^4*x^4*imag_part(cos_integral(-d*x)) - 2*a*d^4*x^4*sin_integral(d*x) + 12*b*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 12*b*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 24*b*d^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 - 12*b*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 12*b*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 24*b*d^2*x^4*sin_integral(d*x)*tan(1/2*c)^2 + 2*a*d^3*x^3*tan(1/2*d*x)^2 + 24*b*d^2*x^4*real_part(cos_integral(d*x))*tan(1/2*c) + 24*b*d^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a*d^3*x^3*tan(1/2*d*x)*tan(1/2*c) + 2*a*d^3*x^3*tan(1/2*c)^2 + 24*b*d*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*b*d^2*x^4*imag_part(cos_integral(d*x)) - 12*b*d^2*x^4*imag_part(cos_integral(-d*x)) + 24*b*d^2*x^4*sin_integral(d*x) + 4*a*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d^3*x^3 - 24*b*d*x^3*tan(1/2*d*x)^2 - 96*b*d*x^3*tan(1/2*d*x)*tan(1/2*c) - 24*b*d*x^3*tan(1/2*c)^2 + 4*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*d^2*x^2*tan(1/2*d*x) - 4*a*d^2*x^2*tan(1/2*c) - 48*b*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 48*b*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 24*b*d*x^3 - 4*a*d*x*tan(1/2*d*x)^2 - 16*a*d*x*tan(1/2*d*x)*tan(1/2*c) - 4*a*d*x*tan(1/2*c)^2 + 48*b*x^2*tan(1/2*d*x) + 48*b*x^2*tan(1/2*c) - 24*a*tan(1/2*d*x)^2*tan(1/2*c) - 24*a*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a*d*x + 24*a*tan(1/2*d*x) + 24*a*tan(1/2*c))/(x^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^4*tan(1/2*d*x)^2 + x^4*tan(1/2*c)^2 + x^4)","C",0
49,1,162,0,0.557925," ","integrate(x^2*(b*x^2+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{6} x^{6} + 2 \, a b d^{6} x^{4} + a^{2} d^{6} x^{2} - 30 \, b^{2} d^{4} x^{4} - 24 \, a b d^{4} x^{2} - 2 \, a^{2} d^{4} + 360 \, b^{2} d^{2} x^{2} + 48 \, a b d^{2} - 720 \, b^{2}\right)} \cos\left(d x + c\right)}{d^{7}} + \frac{2 \, {\left(3 \, b^{2} d^{5} x^{5} + 4 \, a b d^{5} x^{3} + a^{2} d^{5} x - 60 \, b^{2} d^{3} x^{3} - 24 \, a b d^{3} x + 360 \, b^{2} d x\right)} \sin\left(d x + c\right)}{d^{7}}"," ",0,"-(b^2*d^6*x^6 + 2*a*b*d^6*x^4 + a^2*d^6*x^2 - 30*b^2*d^4*x^4 - 24*a*b*d^4*x^2 - 2*a^2*d^4 + 360*b^2*d^2*x^2 + 48*a*b*d^2 - 720*b^2)*cos(d*x + c)/d^7 + 2*(3*b^2*d^5*x^5 + 4*a*b*d^5*x^3 + a^2*d^5*x - 60*b^2*d^3*x^3 - 24*a*b*d^3*x + 360*b^2*d*x)*sin(d*x + c)/d^7","A",0
50,1,129,0,1.004939," ","integrate(x*(b*x^2+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{5} x^{5} + 2 \, a b d^{5} x^{3} + a^{2} d^{5} x - 20 \, b^{2} d^{3} x^{3} - 12 \, a b d^{3} x + 120 \, b^{2} d x\right)} \cos\left(d x + c\right)}{d^{6}} + \frac{{\left(5 \, b^{2} d^{4} x^{4} + 6 \, a b d^{4} x^{2} + a^{2} d^{4} - 60 \, b^{2} d^{2} x^{2} - 12 \, a b d^{2} + 120 \, b^{2}\right)} \sin\left(d x + c\right)}{d^{6}}"," ",0,"-(b^2*d^5*x^5 + 2*a*b*d^5*x^3 + a^2*d^5*x - 20*b^2*d^3*x^3 - 12*a*b*d^3*x + 120*b^2*d*x)*cos(d*x + c)/d^6 + (5*b^2*d^4*x^4 + 6*a*b*d^4*x^2 + a^2*d^4 - 60*b^2*d^2*x^2 - 12*a*b*d^2 + 120*b^2)*sin(d*x + c)/d^6","A",0
51,1,99,0,0.414314," ","integrate((b*x^2+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{4} x^{4} + 2 \, a b d^{4} x^{2} + a^{2} d^{4} - 12 \, b^{2} d^{2} x^{2} - 4 \, a b d^{2} + 24 \, b^{2}\right)} \cos\left(d x + c\right)}{d^{5}} + \frac{4 \, {\left(b^{2} d^{3} x^{3} + a b d^{3} x - 6 \, b^{2} d x\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-(b^2*d^4*x^4 + 2*a*b*d^4*x^2 + a^2*d^4 - 12*b^2*d^2*x^2 - 4*a*b*d^2 + 24*b^2)*cos(d*x + c)/d^5 + 4*(b^2*d^3*x^3 + a*b*d^3*x - 6*b^2*d*x)*sin(d*x + c)/d^5","A",0
52,1,725,0,1.030089," ","integrate((b*x^2+a)^2*sin(d*x+c)/x,x, algorithm=""giac"")","\frac{2 \, b^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{3} x^{3} + 4 \, a b d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d^{3} x \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a^{2} d^{4} \operatorname{Si}\left(d x\right) + 12 \, b^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a b d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{3} x - 12 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d x - 24 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{2 \, {\left(d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + d^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{4}\right)}}"," ",0,"1/2*(2*b^2*d^3*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^4*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*d^4*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*b^2*d^3*x^3*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^4*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*a^2*d^4*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*b^2*d^3*x^3*tan(1/2*c)^2 + 4*a*b*d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^4*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2 - a^2*d^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^4*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2 - a^2*d^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a^2*d^4*sin_integral(d*x)*tan(1/2*c)^2 + 12*b^2*d^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 2*b^2*d^3*x^3 + 4*a*b*d^3*x*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^4*real_part(cos_integral(d*x))*tan(1/2*c) + 2*a^2*d^4*real_part(cos_integral(-d*x))*tan(1/2*c) - 4*a*b*d^3*x*tan(1/2*c)^2 - 12*b^2*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^4*imag_part(cos_integral(d*x)) - a^2*d^4*imag_part(cos_integral(-d*x)) + 2*a^2*d^4*sin_integral(d*x) + 12*b^2*d^2*x^2*tan(1/2*d*x + 1/2*c) + 8*a*b*d^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 4*a*b*d^3*x - 12*b^2*d*x*tan(1/2*d*x + 1/2*c)^2 + 12*b^2*d*x*tan(1/2*c)^2 + 8*a*b*d^2*tan(1/2*d*x + 1/2*c) - 24*b^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 12*b^2*d*x - 24*b^2*tan(1/2*d*x + 1/2*c))/(d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + d^4*tan(1/2*d*x + 1/2*c)^2 + d^4*tan(1/2*c)^2 + d^4)","C",0
53,1,1638,0,0.550847," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^2,x, algorithm=""giac"")","-\frac{a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{4} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) - 8 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 8 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{2} x^{3} - 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, c\right) + 4 \, a b d^{2} x + 4 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, b^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} x}{2 \, {\left(d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + d^{3} x \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{3} x \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} x\right)}}"," ",0,"-1/2*(a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^4*x*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^4*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^4*x*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) - 2*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 2*a^2*d^4*x*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a^2*d^4*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 4*a^2*d^4*x*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*a^2*d^4*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^4*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^4*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - 2*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*b^2*d^2*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*b*d^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2 - a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2 - a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 4*a^2*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) + a^2*d^4*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^4*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*a^2*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)*tan(1/2*c)^2 - 8*b^2*d*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2 + 2*b^2*d^2*x^3*tan(1/2*d*x)^2 - 4*a*b*d^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 2*a^2*d^4*x*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^4*x*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a^2*d^4*x*sin_integral(d*x)*tan(1/2*c) + 2*b^2*d^2*x^3*tan(1/2*c)^2 - 4*a*b*d^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a*b*d^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x*real_part(cos_integral(d*x)) - a^2*d^4*x*real_part(cos_integral(-d*x)) + 4*a^2*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x) - 8*b^2*d*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2 + 4*a^2*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 4*a^2*d^3*tan(1/2*d*x)^2*tan(1/2*c) - 8*b^2*d*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 4*a^2*d^3*tan(1/2*d*x)*tan(1/2*c)^2 + 2*b^2*d^2*x^3 - 4*a*b*d^2*x*tan(1/2*d*x + 1/2*c)^2 + 4*a*b*d^2*x*tan(1/2*d*x)^2 + 4*b^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 4*a*b*d^2*x*tan(1/2*c)^2 + 4*b^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 4*b^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 8*b^2*d*x^2*tan(1/2*d*x + 1/2*c) + 4*a^2*d^3*tan(1/2*d*x) + 4*a^2*d^3*tan(1/2*c) + 4*a*b*d^2*x + 4*b^2*x*tan(1/2*d*x + 1/2*c)^2 - 4*b^2*x*tan(1/2*d*x)^2 - 4*b^2*x*tan(1/2*c)^2 - 4*b^2*x)/(d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + d^3*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + d^3*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^3*x*tan(1/2*d*x + 1/2*c)^2 + d^3*x*tan(1/2*d*x)^2 + d^3*x*tan(1/2*c)^2 + d^3*x)","C",0
54,1,1058,0,0.315293," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^3,x, algorithm=""giac"")","\frac{a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{4} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{4} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{4} x^{2} \operatorname{Si}\left(d x\right) + 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a b d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{2} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a b d^{2} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a b d^{2} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 16 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 4 \, a b d^{2} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 8 \, a b d^{2} x^{2} \operatorname{Si}\left(d x\right) + 4 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 8 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{3} x - 4 \, b^{2} d x^{3} - 4 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, d x\right) + 8 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} x^{2}\right)}}"," ",0,"1/4*(a^2*d^4*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^4*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^4*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^4*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^4*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^4*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^4*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 + a^2*d^4*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^4*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^4*x^2*sin_integral(d*x)*tan(1/2*c)^2 - 4*a*b*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*b*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 8*a*b*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^4*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^4*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a*b*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 8*a*b*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^3*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b^2*d*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^2*imag_part(cos_integral(d*x)) + a^2*d^4*x^2*imag_part(cos_integral(-d*x)) - 2*a^2*d^4*x^2*sin_integral(d*x) + 4*a*b*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 4*a*b*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 8*a*b*d^2*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 - 4*a*b*d^2*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 4*a*b*d^2*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 8*a*b*d^2*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 2*a^2*d^3*x*tan(1/2*d*x)^2 + 4*b^2*d*x^3*tan(1/2*d*x)^2 + 8*a*b*d^2*x^2*real_part(cos_integral(d*x))*tan(1/2*c) + 8*a*b*d^2*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a^2*d^3*x*tan(1/2*d*x)*tan(1/2*c) + 16*b^2*d*x^3*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*d^3*x*tan(1/2*c)^2 + 4*b^2*d*x^3*tan(1/2*c)^2 + 4*a*b*d^2*x^2*imag_part(cos_integral(d*x)) - 4*a*b*d^2*x^2*imag_part(cos_integral(-d*x)) + 8*a*b*d^2*x^2*sin_integral(d*x) + 4*a^2*d^2*tan(1/2*d*x)^2*tan(1/2*c) - 8*b^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^2*tan(1/2*d*x)*tan(1/2*c)^2 - 8*b^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d^3*x - 4*b^2*d*x^3 - 4*a^2*d^2*tan(1/2*d*x) + 8*b^2*x^2*tan(1/2*d*x) - 4*a^2*d^2*tan(1/2*c) + 8*b^2*x^2*tan(1/2*c))/(d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^2*x^2*tan(1/2*d*x)^2 + d^2*x^2*tan(1/2*c)^2 + d^2*x^2)","C",0
55,1,1032,0,0.504255," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^4,x, algorithm=""giac"")","\frac{a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 24 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 48 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{4} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 24 \, a b d^{2} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 48 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) + 12 \, a b d^{2} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 4 \, a^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a^{2} d^{3} x^{2} \tan\left(\frac{1}{2} \, c\right) + 48 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 48 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 12 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a^{2} d^{2} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 48 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, a b d x^{2} \tan\left(\frac{1}{2} \, d x\right) - 48 \, a b d x^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{2} x - 12 \, b^{2} x^{3} - 8 \, a^{2} d \tan\left(\frac{1}{2} \, d x\right) - 8 \, a^{2} d \tan\left(\frac{1}{2} \, c\right)}{12 \, {\left(d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + d x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + d x^{3}\right)}}"," ",0,"1/12*(a^2*d^4*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^4*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^4*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^4*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^4*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^4*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a^2*d^4*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + a^2*d^4*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^4*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 12*a*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 12*a*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^4*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^4*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a^2*d^4*x^3*sin_integral(d*x)*tan(1/2*c) - 24*a*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 24*a*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 48*a*b*d^2*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^4*x^3*real_part(cos_integral(d*x)) - a^2*d^4*x^3*real_part(cos_integral(-d*x)) + 12*a*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 12*a*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 4*a^2*d^3*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 12*a*b*d^2*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 - 12*a*b*d^2*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 - 4*a^2*d^3*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 24*a*b*d^2*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) + 24*a*b*d^2*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) - 48*a*b*d^2*x^3*sin_integral(d*x)*tan(1/2*c) - 2*a^2*d^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 12*b^2*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*a*b*d^2*x^3*real_part(cos_integral(d*x)) + 12*a*b*d^2*x^3*real_part(cos_integral(-d*x)) + 4*a^2*d^3*x^2*tan(1/2*d*x) + 4*a^2*d^3*x^2*tan(1/2*c) + 48*a*b*d*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 48*a*b*d*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 2*a^2*d^2*x*tan(1/2*d*x)^2 + 12*b^2*x^3*tan(1/2*d*x)^2 + 8*a^2*d^2*x*tan(1/2*d*x)*tan(1/2*c) + 48*b^2*x^3*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*d^2*x*tan(1/2*c)^2 + 12*b^2*x^3*tan(1/2*c)^2 - 48*a*b*d*x^2*tan(1/2*d*x) - 48*a*b*d*x^2*tan(1/2*c) + 8*a^2*d*tan(1/2*d*x)^2*tan(1/2*c) + 8*a^2*d*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d^2*x - 12*b^2*x^3 - 8*a^2*d*tan(1/2*d*x) - 8*a^2*d*tan(1/2*c))/(d*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*x^3*tan(1/2*d*x)^2 + d*x^3*tan(1/2*c)^2 + d*x^3)","C",0
56,1,1497,0,0.697120," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^5,x, algorithm=""giac"")","-\frac{a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, a b d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{4} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 48 \, a b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 48 \, a b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{4} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{4} x^{4} \operatorname{Si}\left(d x\right) + 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 48 \, a b d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, a b d^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 48 \, a b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 48 \, a b d^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, a b d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 24 \, a b d^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 48 \, a b d^{2} x^{4} \operatorname{Si}\left(d x\right) - 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 48 \, b^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b^{2} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{3} x^{3} - 48 \, a b d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} - 48 \, b^{2} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 192 \, a b d x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 48 \, a b d x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) + 24 \, b^{2} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 48 \, b^{2} x^{4} \operatorname{Si}\left(d x\right) - 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) - 96 \, a b x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 96 \, a b x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, a b d x^{3} - 4 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right)^{2} - 16 \, a^{2} d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 96 \, a b x^{2} \tan\left(\frac{1}{2} \, d x\right) + 96 \, a b x^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d x + 24 \, a^{2} \tan\left(\frac{1}{2} \, d x\right) + 24 \, a^{2} \tan\left(\frac{1}{2} \, c\right)}{48 \, {\left(x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{4}\right)}}"," ",0,"-1/48*(a^2*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^4*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 + a^2*d^4*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^4*x^4*sin_integral(d*x)*tan(1/2*c)^2 - 24*a*b*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 24*a*b*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 48*a*b*d^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^4*x^4*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^4*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) + 48*a*b*d^2*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 48*a*b*d^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^3*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^4*x^4*imag_part(cos_integral(d*x)) + a^2*d^4*x^4*imag_part(cos_integral(-d*x)) - 2*a^2*d^4*x^4*sin_integral(d*x) + 24*a*b*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 24*a*b*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 48*a*b*d^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 - 24*a*b*d^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 24*a*b*d^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 48*a*b*d^2*x^4*sin_integral(d*x)*tan(1/2*c)^2 + 24*b^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 48*b^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^3*x^3*tan(1/2*d*x)^2 + 48*a*b*d^2*x^4*real_part(cos_integral(d*x))*tan(1/2*c) + 48*a*b*d^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a^2*d^3*x^3*tan(1/2*d*x)*tan(1/2*c) - 48*b^2*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 48*b^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d^3*x^3*tan(1/2*c)^2 + 48*a*b*d*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 24*a*b*d^2*x^4*imag_part(cos_integral(d*x)) - 24*a*b*d^2*x^4*imag_part(cos_integral(-d*x)) + 48*a*b*d^2*x^4*sin_integral(d*x) - 24*b^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + 24*b^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 48*b^2*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 + 4*a^2*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 24*b^2*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - 24*b^2*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 48*b^2*x^4*sin_integral(d*x)*tan(1/2*c)^2 + 4*a^2*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d^3*x^3 - 48*a*b*d*x^3*tan(1/2*d*x)^2 - 48*b^2*x^4*real_part(cos_integral(d*x))*tan(1/2*c) - 48*b^2*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) - 192*a*b*d*x^3*tan(1/2*d*x)*tan(1/2*c) - 48*a*b*d*x^3*tan(1/2*c)^2 + 4*a^2*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b^2*x^4*imag_part(cos_integral(d*x)) + 24*b^2*x^4*imag_part(cos_integral(-d*x)) - 48*b^2*x^4*sin_integral(d*x) - 4*a^2*d^2*x^2*tan(1/2*d*x) - 4*a^2*d^2*x^2*tan(1/2*c) - 96*a*b*x^2*tan(1/2*d*x)^2*tan(1/2*c) - 96*a*b*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 48*a*b*d*x^3 - 4*a^2*d*x*tan(1/2*d*x)^2 - 16*a^2*d*x*tan(1/2*d*x)*tan(1/2*c) - 4*a^2*d*x*tan(1/2*c)^2 + 96*a*b*x^2*tan(1/2*d*x) + 96*a*b*x^2*tan(1/2*c) - 24*a^2*tan(1/2*d*x)^2*tan(1/2*c) - 24*a^2*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a^2*d*x + 24*a^2*tan(1/2*d*x) + 24*a^2*tan(1/2*c))/(x^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^4*tan(1/2*d*x)^2 + x^4*tan(1/2*c)^2 + x^4)","C",0
57,0,0,0,0.000000," ","integrate(x^4*sin(d*x+c)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{x^{4} \sin\left(d x + c\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(x^4*sin(d*x + c)/(b*x^2 + a), x)","F",0
58,0,0,0,0.000000," ","integrate(x^3*sin(d*x+c)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{x^{3} \sin\left(d x + c\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(x^3*sin(d*x + c)/(b*x^2 + a), x)","F",0
59,0,0,0,0.000000," ","integrate(x^2*sin(d*x+c)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{x^{2} \sin\left(d x + c\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(x^2*sin(d*x + c)/(b*x^2 + a), x)","F",0
60,0,0,0,0.000000," ","integrate(x*sin(d*x+c)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{x \sin\left(d x + c\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(x*sin(d*x + c)/(b*x^2 + a), x)","F",0
61,0,0,0,0.000000," ","integrate(sin(d*x+c)/(b*x^2+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{b x^{2} + a}\,{d x}"," ",0,"integrate(sin(d*x + c)/(b*x^2 + a), x)","F",0
62,0,0,0,0.000000," ","integrate(sin(d*x+c)/x/(b*x^2+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)} x}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)*x), x)","F",0
63,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^2/(b*x^2+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)} x^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)*x^2), x)","F",0
64,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^3/(b*x^2+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)} x^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)*x^3), x)","F",0
65,0,0,0,0.000000," ","integrate(x^4*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{x^{4} \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^4*sin(d*x + c)/(b*x^2 + a)^2, x)","F",0
66,0,0,0,0.000000," ","integrate(x^3*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{x^{3} \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*sin(d*x + c)/(b*x^2 + a)^2, x)","F",0
67,0,0,0,0.000000," ","integrate(x^2*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{x^{2} \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^2*sin(d*x + c)/(b*x^2 + a)^2, x)","F",0
68,0,0,0,0.000000," ","integrate(x*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{x \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x*sin(d*x + c)/(b*x^2 + a)^2, x)","F",0
69,0,0,0,0.000000," ","integrate(sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(b*x^2 + a)^2, x)","F",0
70,0,0,0,0.000000," ","integrate(sin(d*x+c)/x/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2} x}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)^2*x), x)","F",0
71,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^2/(b*x^2+a)^2,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{2} x^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)^2*x^2), x)","F",0
72,0,0,0,0.000000," ","integrate(x^3*sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{x^{3} \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^3*sin(d*x + c)/(b*x^2 + a)^3, x)","F",0
73,0,0,0,0.000000," ","integrate(x^2*sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{x^{2} \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x^2*sin(d*x + c)/(b*x^2 + a)^3, x)","F",0
74,0,0,0,0.000000," ","integrate(x*sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{x \sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate(x*sin(d*x + c)/(b*x^2 + a)^3, x)","F",0
75,0,0,0,0.000000," ","integrate(sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)/(b*x^2 + a)^3, x)","F",0
76,0,0,0,0.000000," ","integrate(sin(d*x+c)/x/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3} x}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)^3*x), x)","F",0
77,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^2/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3} x^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)^3*x^2), x)","F",0
78,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^3/(b*x^2+a)^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{2} + a\right)}^{3} x^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^2 + a)^3*x^3), x)","F",0
79,1,106,0,0.522321," ","integrate(x^3*(b*x^3+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{6} x^{6} + a d^{6} x^{3} - 30 \, b d^{4} x^{4} - 6 \, a d^{4} x + 360 \, b d^{2} x^{2} - 720 \, b\right)} \cos\left(d x + c\right)}{d^{7}} + \frac{3 \, {\left(2 \, b d^{5} x^{5} + a d^{5} x^{2} - 40 \, b d^{3} x^{3} - 2 \, a d^{3} + 240 \, b d x\right)} \sin\left(d x + c\right)}{d^{7}}"," ",0,"-(b*d^6*x^6 + a*d^6*x^3 - 30*b*d^4*x^4 - 6*a*d^4*x + 360*b*d^2*x^2 - 720*b)*cos(d*x + c)/d^7 + 3*(2*b*d^5*x^5 + a*d^5*x^2 - 40*b*d^3*x^3 - 2*a*d^3 + 240*b*d*x)*sin(d*x + c)/d^7","A",0
80,1,88,0,0.415590," ","integrate(x^2*(b*x^3+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{5} x^{5} + a d^{5} x^{2} - 20 \, b d^{3} x^{3} - 2 \, a d^{3} + 120 \, b d x\right)} \cos\left(d x + c\right)}{d^{6}} + \frac{{\left(5 \, b d^{4} x^{4} + 2 \, a d^{4} x - 60 \, b d^{2} x^{2} + 120 \, b\right)} \sin\left(d x + c\right)}{d^{6}}"," ",0,"-(b*d^5*x^5 + a*d^5*x^2 - 20*b*d^3*x^3 - 2*a*d^3 + 120*b*d*x)*cos(d*x + c)/d^6 + (5*b*d^4*x^4 + 2*a*d^4*x - 60*b*d^2*x^2 + 120*b)*sin(d*x + c)/d^6","A",0
81,1,69,0,0.417092," ","integrate(x*(b*x^3+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{4} x^{4} + a d^{4} x - 12 \, b d^{2} x^{2} + 24 \, b\right)} \cos\left(d x + c\right)}{d^{5}} + \frac{{\left(4 \, b d^{3} x^{3} + a d^{3} - 24 \, b d x\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-(b*d^4*x^4 + a*d^4*x - 12*b*d^2*x^2 + 24*b)*cos(d*x + c)/d^5 + (4*b*d^3*x^3 + a*d^3 - 24*b*d*x)*sin(d*x + c)/d^5","A",0
82,1,54,0,0.638606," ","integrate((b*x^3+a)*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b d^{3} x^{3} + a d^{3} - 6 \, b d x\right)} \cos\left(d x + c\right)}{d^{4}} + \frac{3 \, {\left(b d^{2} x^{2} - 2 \, b\right)} \sin\left(d x + c\right)}{d^{4}}"," ",0,"-(b*d^3*x^3 + a*d^3 - 6*b*d*x)*cos(d*x + c)/d^4 + 3*(b*d^2*x^2 - 2*b)*sin(d*x + c)/d^4","A",0
83,1,510,0,0.380456," ","integrate((b*x^3+a)*sin(d*x+c)/x,x, algorithm=""giac"")","-\frac{2 \, b d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - a d^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 2 \, b d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, b d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, b d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b d^{2} x^{2} - a d^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{3} \operatorname{Si}\left(d x\right) - 4 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, b d x \tan\left(\frac{1}{2} \, d x\right) - 8 \, b d x \tan\left(\frac{1}{2} \, c\right) + 4 \, b \tan\left(\frac{1}{2} \, d x\right)^{2} + 16 \, b \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, b \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b}{2 \, {\left(d^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3}\right)}}"," ",0,"-1/2*(2*b*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*b*d^2*x^2*tan(1/2*d*x)^2 - a*d^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^3*sin_integral(d*x)*tan(1/2*d*x)^2 - 8*b*d^2*x^2*tan(1/2*d*x)*tan(1/2*c) - 2*b*d^2*x^2*tan(1/2*c)^2 + a*d^3*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^3*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^3*sin_integral(d*x)*tan(1/2*c)^2 - 2*a*d^3*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^3*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*b*d*x*tan(1/2*d*x)^2*tan(1/2*c) + 8*b*d*x*tan(1/2*d*x)*tan(1/2*c)^2 + 2*b*d^2*x^2 - a*d^3*imag_part(cos_integral(d*x)) + a*d^3*imag_part(cos_integral(-d*x)) - 2*a*d^3*sin_integral(d*x) - 4*b*tan(1/2*d*x)^2*tan(1/2*c)^2 - 8*b*d*x*tan(1/2*d*x) - 8*b*d*x*tan(1/2*c) + 4*b*tan(1/2*d*x)^2 + 16*b*tan(1/2*d*x)*tan(1/2*c) + 4*b*tan(1/2*c)^2 - 4*b)/(d^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^3*tan(1/2*d*x)^2 + d^3*tan(1/2*c)^2 + d^3)","C",0
84,1,489,0,0.557699," ","integrate((b*x^3+a)*sin(d*x+c)/x^2,x, algorithm=""giac"")","-\frac{a d^{3} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{3} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d^{3} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{3} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - a d^{3} x \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d^{3} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 8 \, b d x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a d^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b d x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a d^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b d x^{2} + 4 \, a d^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a d^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, b x \tan\left(\frac{1}{2} \, d x\right) - 4 \, b x \tan\left(\frac{1}{2} \, c\right)}{2 \, {\left(d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} x\right)}}"," ",0,"-1/2*(a*d^3*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d^3*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^3*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a*d^3*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d^3*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + a*d^3*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d^3*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*b*d*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^3*x*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d^3*x*sin_integral(d*x)*tan(1/2*c) - a*d^3*x*real_part(cos_integral(d*x)) - a*d^3*x*real_part(cos_integral(-d*x)) - 2*b*d*x^2*tan(1/2*d*x)^2 - 8*b*d*x^2*tan(1/2*d*x)*tan(1/2*c) - 4*a*d^2*tan(1/2*d*x)^2*tan(1/2*c) - 2*b*d*x^2*tan(1/2*c)^2 - 4*a*d^2*tan(1/2*d*x)*tan(1/2*c)^2 + 4*b*x*tan(1/2*d*x)^2*tan(1/2*c) + 4*b*x*tan(1/2*d*x)*tan(1/2*c)^2 + 2*b*d*x^2 + 4*a*d^2*tan(1/2*d*x) + 4*a*d^2*tan(1/2*c) - 4*b*x*tan(1/2*d*x) - 4*b*x*tan(1/2*c))/(d^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^2*x*tan(1/2*d*x)^2 + d^2*x*tan(1/2*c)^2 + d^2*x)","C",0
85,1,564,0,0.331418," ","integrate((b*x^3+a)*sin(d*x+c)/x^3,x, algorithm=""giac"")","\frac{a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a d^{3} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{3} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a d^{3} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a d^{3} x^{2} \operatorname{Si}\left(d x\right) - 4 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a d^{2} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a d^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 16 \, b x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d^{2} x - 4 \, b x^{2} - 4 \, a d \tan\left(\frac{1}{2} \, d x\right) - 4 \, a d \tan\left(\frac{1}{2} \, c\right)}{4 \, {\left(d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d x^{2}\right)}}"," ",0,"1/4*(a*d^3*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^3*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a*d^3*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a*d^3*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a*d^3*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a*d^3*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 + a*d^3*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a*d^3*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^3*x^2*sin_integral(d*x)*tan(1/2*c)^2 - 2*a*d^3*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^3*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) - 2*a*d^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^3*x^2*imag_part(cos_integral(d*x)) + a*d^3*x^2*imag_part(cos_integral(-d*x)) - 2*a*d^3*x^2*sin_integral(d*x) - 4*b*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^2*x*tan(1/2*d*x)^2 + 8*a*d^2*x*tan(1/2*d*x)*tan(1/2*c) + 2*a*d^2*x*tan(1/2*c)^2 + 4*b*x^2*tan(1/2*d*x)^2 + 16*b*x^2*tan(1/2*d*x)*tan(1/2*c) + 4*a*d*tan(1/2*d*x)^2*tan(1/2*c) + 4*b*x^2*tan(1/2*c)^2 + 4*a*d*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d^2*x - 4*b*x^2 - 4*a*d*tan(1/2*d*x) - 4*a*d*tan(1/2*c))/(d*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d*x^2*tan(1/2*d*x)^2 + d*x^2*tan(1/2*c)^2 + d*x^2)","C",0
86,1,796,0,0.502325," ","integrate((b*x^3+a)*sin(d*x+c)/x^4,x, algorithm=""giac"")","\frac{a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) - a d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 12 \, b x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 12 \, b x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 12 \, b x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a d^{2} x^{2} \tan\left(\frac{1}{2} \, c\right) + 12 \, b x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 6 \, b x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 12 \, b x^{3} \operatorname{Si}\left(d x\right) + 2 \, a d x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a d x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a d x \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a d x - 8 \, a \tan\left(\frac{1}{2} \, d x\right) - 8 \, a \tan\left(\frac{1}{2} \, c\right)}{12 \, {\left(x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + x^{3}\right)}}"," ",0,"1/12*(a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a*d^3*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + a*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a*d^3*x^3*sin_integral(d*x)*tan(1/2*c) - 6*b*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 6*b*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 12*b*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a*d^3*x^3*real_part(cos_integral(d*x)) - a*d^3*x^3*real_part(cos_integral(-d*x)) - 4*a*d^2*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 12*b*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 12*b*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*d^2*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 6*b*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 6*b*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 12*b*x^3*sin_integral(d*x)*tan(1/2*d*x)^2 - 6*b*x^3*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 6*b*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 12*b*x^3*sin_integral(d*x)*tan(1/2*c)^2 - 2*a*d*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*d^2*x^2*tan(1/2*d*x) + 4*a*d^2*x^2*tan(1/2*c) + 12*b*x^3*real_part(cos_integral(d*x))*tan(1/2*c) + 12*b*x^3*real_part(cos_integral(-d*x))*tan(1/2*c) + 6*b*x^3*imag_part(cos_integral(d*x)) - 6*b*x^3*imag_part(cos_integral(-d*x)) + 12*b*x^3*sin_integral(d*x) + 2*a*d*x*tan(1/2*d*x)^2 + 8*a*d*x*tan(1/2*d*x)*tan(1/2*c) + 2*a*d*x*tan(1/2*c)^2 + 8*a*tan(1/2*d*x)^2*tan(1/2*c) + 8*a*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a*d*x - 8*a*tan(1/2*d*x) - 8*a*tan(1/2*c))/(x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + x^3*tan(1/2*d*x)^2 + x^3*tan(1/2*c)^2 + x^3)","C",0
87,1,161,0,0.532782," ","integrate(x*(b*x^3+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{7} x^{7} + 2 \, a b d^{7} x^{4} - 42 \, b^{2} d^{5} x^{5} + a^{2} d^{7} x - 24 \, a b d^{5} x^{2} + 840 \, b^{2} d^{3} x^{3} + 48 \, a b d^{3} - 5040 \, b^{2} d x\right)} \cos\left(d x + c\right)}{d^{8}} + \frac{{\left(7 \, b^{2} d^{6} x^{6} + 8 \, a b d^{6} x^{3} - 210 \, b^{2} d^{4} x^{4} + a^{2} d^{6} - 48 \, a b d^{4} x + 2520 \, b^{2} d^{2} x^{2} - 5040 \, b^{2}\right)} \sin\left(d x + c\right)}{d^{8}}"," ",0,"-(b^2*d^7*x^7 + 2*a*b*d^7*x^4 - 42*b^2*d^5*x^5 + a^2*d^7*x - 24*a*b*d^5*x^2 + 840*b^2*d^3*x^3 + 48*a*b*d^3 - 5040*b^2*d*x)*cos(d*x + c)/d^8 + (7*b^2*d^6*x^6 + 8*a*b*d^6*x^3 - 210*b^2*d^4*x^4 + a^2*d^6 - 48*a*b*d^4*x + 2520*b^2*d^2*x^2 - 5040*b^2)*sin(d*x + c)/d^8","A",0
88,1,131,0,0.406591," ","integrate((b*x^3+a)^2*sin(d*x+c),x, algorithm=""giac"")","-\frac{{\left(b^{2} d^{6} x^{6} + 2 \, a b d^{6} x^{3} - 30 \, b^{2} d^{4} x^{4} + a^{2} d^{6} - 12 \, a b d^{4} x + 360 \, b^{2} d^{2} x^{2} - 720 \, b^{2}\right)} \cos\left(d x + c\right)}{d^{7}} + \frac{6 \, {\left(b^{2} d^{5} x^{5} + a b d^{5} x^{2} - 20 \, b^{2} d^{3} x^{3} - 2 \, a b d^{3} + 120 \, b^{2} d x\right)} \sin\left(d x + c\right)}{d^{7}}"," ",0,"-(b^2*d^6*x^6 + 2*a*b*d^6*x^3 - 30*b^2*d^4*x^4 + a^2*d^6 - 12*a*b*d^4*x + 360*b^2*d^2*x^2 - 720*b^2)*cos(d*x + c)/d^7 + 6*(b^2*d^5*x^5 + a*b*d^5*x^2 - 20*b^2*d^3*x^3 - 2*a*b*d^3 + 120*b^2*d*x)*sin(d*x + c)/d^7","A",0
89,1,921,0,0.357786," ","integrate((b*x^3+a)^2*sin(d*x+c)/x,x, algorithm=""giac"")","\frac{2 \, b^{2} d^{5} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{5} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{5} x^{5} \tan\left(\frac{1}{2} \, c\right)^{2} + 20 \, b^{2} d^{4} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{5} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{6} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{5} x^{5} + 2 \, a^{2} d^{6} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{6} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 40 \, b^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 20 \, b^{2} d^{4} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b d^{5} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} d^{6} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{6} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a b d^{5} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{6} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 40 \, b^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{6} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 40 \, b^{2} d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, a b d^{4} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{5} x^{2} + a^{2} d^{6} \Im \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{6} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 2 \, a^{2} d^{6} \operatorname{Si}\left(d x\right) - 240 \, b^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 40 \, b^{2} d^{3} x^{3} + 16 \, a b d^{4} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 240 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 240 \, b^{2} d^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) - 8 \, a b d^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 240 \, b^{2} d x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 240 \, b^{2} d x \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} + 480 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 240 \, b^{2} d x + 480 \, b^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{2 \, {\left(d^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{6} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + d^{6} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{6}\right)}}"," ",0,"1/2*(2*b^2*d^5*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*b^2*d^5*x^5*tan(1/2*d*x + 1/2*c)^2 - 2*b^2*d^5*x^5*tan(1/2*c)^2 + 20*b^2*d^4*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 4*a*b*d^5*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^6*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^6*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*d^6*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*b^2*d^5*x^5 + 2*a^2*d^6*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*a^2*d^6*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 40*b^2*d^3*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 20*b^2*d^4*x^4*tan(1/2*d*x + 1/2*c) + 4*a*b*d^5*x^2*tan(1/2*d*x + 1/2*c)^2 + a^2*d^6*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2 - a^2*d^6*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^6*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2 - 4*a*b*d^5*x^2*tan(1/2*c)^2 - a^2*d^6*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^6*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 2*a^2*d^6*sin_integral(d*x)*tan(1/2*c)^2 - 40*b^2*d^3*x^3*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^6*real_part(cos_integral(d*x))*tan(1/2*c) + 2*a^2*d^6*real_part(cos_integral(-d*x))*tan(1/2*c) + 40*b^2*d^3*x^3*tan(1/2*c)^2 + 16*a*b*d^4*x*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 4*a*b*d^5*x^2 + a^2*d^6*imag_part(cos_integral(d*x)) - a^2*d^6*imag_part(cos_integral(-d*x)) + 2*a^2*d^6*sin_integral(d*x) - 240*b^2*d^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 8*a*b*d^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 40*b^2*d^3*x^3 + 16*a*b*d^4*x*tan(1/2*d*x + 1/2*c) + 240*b^2*d*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 240*b^2*d^2*x^2*tan(1/2*d*x + 1/2*c) - 8*a*b*d^3*tan(1/2*d*x + 1/2*c)^2 + 8*a*b*d^3*tan(1/2*c)^2 + 240*b^2*d*x*tan(1/2*d*x + 1/2*c)^2 - 240*b^2*d*x*tan(1/2*c)^2 + 8*a*b*d^3 + 480*b^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 - 240*b^2*d*x + 480*b^2*tan(1/2*d*x + 1/2*c))/(d^6*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + d^6*tan(1/2*d*x + 1/2*c)^2 + d^6*tan(1/2*c)^2 + d^6)","C",0
90,1,2038,0,1.341395," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^2,x, algorithm=""giac"")","\frac{2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{6} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, b^{2} d^{3} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{6} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{6} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, b^{2} d^{4} x^{5} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 16 \, b^{2} d^{3} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 16 \, b^{2} d^{3} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, b^{2} d^{4} x^{5} - 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{6} x \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{6} x \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{6} x \Re \left( \operatorname{Ci}\left(-d x\right) \right) + 16 \, b^{2} d^{3} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a b d^{4} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 96 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a b d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b^{2} d^{2} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a b d^{4} x^{2} - 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, d x\right) - 96 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{5} \tan\left(\frac{1}{2} \, c\right) - 96 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d^{2} x^{3} + 8 \, a b d^{3} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 48 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 96 \, b^{2} d x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 48 \, b^{2} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 48 \, b^{2} x \tan\left(\frac{1}{2} \, d x\right)^{2} - 48 \, b^{2} x \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, b^{2} x}{2 \, {\left(d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{5} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + d^{5} x \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{5} x \tan\left(\frac{1}{2} \, c\right)^{2} + d^{5} x\right)}}"," ",0,"1/2*(2*b^2*d^4*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b^2*d^4*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - 2*a^2*d^6*x*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d^6*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) - 4*a^2*d^6*x*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) + 2*b^2*d^4*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*b^2*d^4*x^5*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 16*b^2*d^3*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a*b*d^4*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*b^2*d^4*x^5*tan(1/2*d*x + 1/2*c)^2 - 2*b^2*d^4*x^5*tan(1/2*d*x)^2 - 2*a^2*d^6*x*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 2*a^2*d^6*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 4*a^2*d^6*x*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a^2*d^6*x*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d^6*x*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a^2*d^6*x*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - 2*b^2*d^4*x^5*tan(1/2*c)^2 - 24*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2 + a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2 + a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 16*b^2*d^3*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2 + 4*a*b*d^4*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 4*a^2*d^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^6*x*real_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^6*x*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 16*b^2*d^3*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 4*a*b*d^4*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a^2*d^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)*tan(1/2*c)^2 - 4*a*b*d^4*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*b^2*d^4*x^5 - 24*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - 2*a^2*d^6*x*imag_part(cos_integral(d*x))*tan(1/2*c) + 2*a^2*d^6*x*imag_part(cos_integral(-d*x))*tan(1/2*c) - 4*a^2*d^6*x*sin_integral(d*x)*tan(1/2*c) - 24*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 24*b^2*d^2*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*a*b*d^3*x*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^6*x*real_part(cos_integral(d*x)) + a^2*d^6*x*real_part(cos_integral(-d*x)) + 16*b^2*d^3*x^4*tan(1/2*d*x + 1/2*c) + 4*a*b*d^4*x^2*tan(1/2*d*x + 1/2*c)^2 - 4*a^2*d^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x) - 4*a*b*d^4*x^2*tan(1/2*d*x)^2 - 4*a^2*d^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 4*a^2*d^5*tan(1/2*d*x)^2*tan(1/2*c) - 4*a*b*d^4*x^2*tan(1/2*c)^2 + 4*a^2*d^5*tan(1/2*d*x)*tan(1/2*c)^2 - 96*b^2*d*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b^2*d^2*x^3*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*d^2*x^3*tan(1/2*d*x)^2 + 8*a*b*d^3*x*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2 + 24*b^2*d^2*x^3*tan(1/2*c)^2 + 8*a*b*d^3*x*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 48*b^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a*b*d^4*x^2 - 4*a^2*d^5*tan(1/2*d*x) - 96*b^2*d*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2 - 4*a^2*d^5*tan(1/2*c) - 96*b^2*d*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 24*b^2*d^2*x^3 + 8*a*b*d^3*x*tan(1/2*d*x + 1/2*c) + 48*b^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 48*b^2*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 48*b^2*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 96*b^2*d*x^2*tan(1/2*d*x + 1/2*c) + 48*b^2*x*tan(1/2*d*x + 1/2*c)^2 - 48*b^2*x*tan(1/2*d*x)^2 - 48*b^2*x*tan(1/2*c)^2 - 48*b^2*x)/(d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + d^5*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^5*x*tan(1/2*d*x + 1/2*c)^2 + d^5*x*tan(1/2*d*x)^2 + d^5*x*tan(1/2*c)^2 + d^5*x)","C",0
91,1,2171,0,1.150793," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^3,x, algorithm=""giac"")","\frac{a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d^{2} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} + 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{2} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, b^{2} d^{3} x^{5} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{6} x^{2} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{6} x^{2} \operatorname{Si}\left(d x\right) + 24 \, b^{2} d^{2} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} d^{2} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, b^{2} d^{3} x^{5} - 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x\right)^{2} - 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{5} x \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d^{2} x^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) + 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right) - 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 8 \, a b d^{3} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{5} x - 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, b^{2} d x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a b d^{3} x^{2} - 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, d x\right) - 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 4 \, a^{2} d^{4} \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} d x^{3} - 48 \, b^{2} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)}{4 \, {\left(d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{4} x^{2} \tan\left(\frac{1}{2} \, d x + \frac{1}{2} \, c\right)^{2} + d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{4} x^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{4} x^{2}\right)}}"," ",0,"1/4*(a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^6*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^6*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*b^2*d^3*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*d^3*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - 2*a^2*d^6*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a^2*d^6*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) - 2*a^2*d^6*x^2*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^6*x^2*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*b^2*d^3*x^5*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 4*b^2*d^3*x^5*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x + 1/2*c)^2 + a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x + 1/2*c)^2 - 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*d*x + 1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*d*x)^2 + a^2*d^6*x^2*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^6*x^2*sin_integral(d*x)*tan(1/2*c)^2 + 24*b^2*d^2*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2*tan(1/2*c)^2 + 8*a*b*d^3*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*b^2*d^3*x^5*tan(1/2*d*x + 1/2*c)^2 - 4*b^2*d^3*x^5*tan(1/2*d*x)^2 + 2*a^2*d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 - 2*a^2*d^6*x^2*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^6*x^2*real_part(cos_integral(-d*x))*tan(1/2*c) + 8*a^2*d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)*tan(1/2*c) - 4*b^2*d^3*x^5*tan(1/2*c)^2 + 2*a^2*d^5*x*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 - 2*a^2*d^5*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*b^2*d*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^2*imag_part(cos_integral(d*x)) + a^2*d^6*x^2*imag_part(cos_integral(-d*x)) - 2*a^2*d^6*x^2*sin_integral(d*x) + 24*b^2*d^2*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2 + 8*a*b*d^3*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 4*a^2*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c) + 24*b^2*d^2*x^4*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 8*a*b*d^3*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 4*a^2*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)*tan(1/2*c)^2 - 8*a*b*d^3*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*b^2*d^3*x^5 - 2*a^2*d^5*x*tan(1/2*d*x + 1/2*c)^2 + 2*a^2*d^5*x*tan(1/2*d*x)^2 - 24*b^2*d*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + 8*a^2*d^5*x*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*d^5*x*tan(1/2*c)^2 - 24*b^2*d*x^3*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + 24*b^2*d*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 24*b^2*d^2*x^4*tan(1/2*d*x + 1/2*c) + 8*a*b*d^3*x^2*tan(1/2*d*x + 1/2*c)^2 - 4*a^2*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x) - 8*a*b*d^3*x^2*tan(1/2*d*x)^2 - 4*a^2*d^4*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c) + 4*a^2*d^4*tan(1/2*d*x)^2*tan(1/2*c) - 8*a*b*d^3*x^2*tan(1/2*c)^2 + 4*a^2*d^4*tan(1/2*d*x)*tan(1/2*c)^2 - 48*b^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^5*x - 24*b^2*d*x^3*tan(1/2*d*x + 1/2*c)^2 + 24*b^2*d*x^3*tan(1/2*d*x)^2 + 24*b^2*d*x^3*tan(1/2*c)^2 - 8*a*b*d^3*x^2 - 4*a^2*d^4*tan(1/2*d*x) - 48*b^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*d*x)^2 - 4*a^2*d^4*tan(1/2*c) - 48*b^2*x^2*tan(1/2*d*x + 1/2*c)*tan(1/2*c)^2 + 24*b^2*d*x^3 - 48*b^2*x^2*tan(1/2*d*x + 1/2*c))/(d^4*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^4*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*d*x)^2 + d^4*x^2*tan(1/2*d*x + 1/2*c)^2*tan(1/2*c)^2 + d^4*x^2*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^4*x^2*tan(1/2*d*x + 1/2*c)^2 + d^4*x^2*tan(1/2*d*x)^2 + d^4*x^2*tan(1/2*c)^2 + d^4*x^2)","C",0
92,1,1181,0,0.952269," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^4,x, algorithm=""giac"")","\frac{a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{6} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{6} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) - 12 \, b^{2} d^{2} x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, a b d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) - a^{2} d^{6} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 4 \, a^{2} d^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, a b d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, a b d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, b^{2} d^{2} x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} + 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 24 \, a b d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 48 \, b^{2} d^{2} x^{5} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 12 \, b^{2} d^{2} x^{5} \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - 24 \, a b d^{3} x^{3} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{5} x^{2} \tan\left(\frac{1}{2} \, d x\right) + 4 \, a^{2} d^{5} x^{2} \tan\left(\frac{1}{2} \, c\right) + 24 \, a b d^{3} x^{3} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 24 \, a b d^{3} x^{3} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} d x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} d x^{4} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 12 \, b^{2} d^{2} x^{5} + 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(d x\right) \right) - 12 \, a b d^{3} x^{3} \Im \left( \operatorname{Ci}\left(-d x\right) \right) + 24 \, a b d^{3} x^{3} \operatorname{Si}\left(d x\right) + 2 \, a^{2} d^{4} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a^{2} d^{4} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{4} x \tan\left(\frac{1}{2} \, c\right)^{2} + 24 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b^{2} d x^{4} \tan\left(\frac{1}{2} \, d x\right) + 48 \, b^{2} d x^{4} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 8 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{4} x - 24 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} - 96 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 24 \, b^{2} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} - 8 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, d x\right) - 8 \, a^{2} d^{3} \tan\left(\frac{1}{2} \, c\right) + 24 \, b^{2} x^{3}}{12 \, {\left(d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{3} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{3} x^{3}\right)}}"," ",0,"1/12*(a^2*d^6*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + a^2*d^6*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^6*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^6*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^6*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^6*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - a^2*d^6*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + a^2*d^6*x^3*real_part(cos_integral(d*x))*tan(1/2*c)^2 + a^2*d^6*x^3*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^6*x^3*imag_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^6*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c) + 4*a^2*d^6*x^3*sin_integral(d*x)*tan(1/2*c) - 12*b^2*d^2*x^5*tan(1/2*d*x)^2*tan(1/2*c)^2 - 12*a*b*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 12*a*b*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - 24*a*b*d^3*x^3*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^3*real_part(cos_integral(d*x)) - a^2*d^6*x^3*real_part(cos_integral(-d*x)) - 4*a^2*d^5*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 24*a*b*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 24*a*b*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 4*a^2*d^5*x^2*tan(1/2*d*x)*tan(1/2*c)^2 + 12*b^2*d^2*x^5*tan(1/2*d*x)^2 + 12*a*b*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 12*a*b*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 24*a*b*d^3*x^3*sin_integral(d*x)*tan(1/2*d*x)^2 + 48*b^2*d^2*x^5*tan(1/2*d*x)*tan(1/2*c) + 12*b^2*d^2*x^5*tan(1/2*c)^2 - 12*a*b*d^3*x^3*imag_part(cos_integral(d*x))*tan(1/2*c)^2 + 12*a*b*d^3*x^3*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 - 24*a*b*d^3*x^3*sin_integral(d*x)*tan(1/2*c)^2 - 2*a^2*d^4*x*tan(1/2*d*x)^2*tan(1/2*c)^2 + 4*a^2*d^5*x^2*tan(1/2*d*x) + 4*a^2*d^5*x^2*tan(1/2*c) + 24*a*b*d^3*x^3*real_part(cos_integral(d*x))*tan(1/2*c) + 24*a*b*d^3*x^3*real_part(cos_integral(-d*x))*tan(1/2*c) - 48*b^2*d*x^4*tan(1/2*d*x)^2*tan(1/2*c) - 48*b^2*d*x^4*tan(1/2*d*x)*tan(1/2*c)^2 - 12*b^2*d^2*x^5 + 12*a*b*d^3*x^3*imag_part(cos_integral(d*x)) - 12*a*b*d^3*x^3*imag_part(cos_integral(-d*x)) + 24*a*b*d^3*x^3*sin_integral(d*x) + 2*a^2*d^4*x*tan(1/2*d*x)^2 + 8*a^2*d^4*x*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*d^4*x*tan(1/2*c)^2 + 24*b^2*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 48*b^2*d*x^4*tan(1/2*d*x) + 48*b^2*d*x^4*tan(1/2*c) + 8*a^2*d^3*tan(1/2*d*x)^2*tan(1/2*c) + 8*a^2*d^3*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d^4*x - 24*b^2*x^3*tan(1/2*d*x)^2 - 96*b^2*x^3*tan(1/2*d*x)*tan(1/2*c) - 24*b^2*x^3*tan(1/2*c)^2 - 8*a^2*d^3*tan(1/2*d*x) - 8*a^2*d^3*tan(1/2*c) + 24*b^2*x^3)/(d^3*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^3*x^3*tan(1/2*d*x)^2 + d^3*x^3*tan(1/2*c)^2 + d^3*x^3)","C",0
93,1,1255,0,1.326002," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^5,x, algorithm=""giac"")","-\frac{a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{6} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 2 \, a^{2} d^{6} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} + a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 2 \, a^{2} d^{6} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{6} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{6} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 2 \, a^{2} d^{5} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) + a^{2} d^{6} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) - 2 \, a^{2} d^{6} x^{4} \operatorname{Si}\left(d x\right) + 96 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 96 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 192 \, a b d^{3} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{5} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} - 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} - 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, d x\right)^{2} + 8 \, a^{2} d^{5} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) + 2 \, a^{2} d^{5} x^{3} \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b^{2} d x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + 96 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(d x\right) \right) \tan\left(\frac{1}{2} \, c\right) - 96 \, a b d^{3} x^{4} \Im \left( \operatorname{Ci}\left(-d x\right) \right) \tan\left(\frac{1}{2} \, c\right) + 192 \, a b d^{3} x^{4} \operatorname{Si}\left(d x\right) \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 4 \, a^{2} d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} - 2 \, a^{2} d^{5} x^{3} - 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(d x\right) \right) - 48 \, a b d^{3} x^{4} \Re \left( \operatorname{Ci}\left(-d x\right) \right) - 48 \, b^{2} d x^{5} \tan\left(\frac{1}{2} \, d x\right)^{2} - 192 \, b^{2} d x^{5} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 192 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 48 \, b^{2} d x^{5} \tan\left(\frac{1}{2} \, c\right)^{2} - 192 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} - 4 \, a^{2} d^{4} x^{2} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} d^{4} x^{2} \tan\left(\frac{1}{2} \, c\right) + 96 \, b^{2} x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) + 96 \, b^{2} x^{4} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 48 \, b^{2} d x^{5} + 192 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, d x\right) - 4 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, d x\right)^{2} + 192 \, a b d^{2} x^{3} \tan\left(\frac{1}{2} \, c\right) - 16 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right) - 4 \, a^{2} d^{3} x \tan\left(\frac{1}{2} \, c\right)^{2} - 96 \, b^{2} x^{4} \tan\left(\frac{1}{2} \, d x\right) - 96 \, b^{2} x^{4} \tan\left(\frac{1}{2} \, c\right) - 24 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right) - 24 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, d x\right) \tan\left(\frac{1}{2} \, c\right)^{2} + 4 \, a^{2} d^{3} x + 24 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, d x\right) + 24 \, a^{2} d^{2} \tan\left(\frac{1}{2} \, c\right)}{48 \, {\left(d^{2} x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} x^{4} \tan\left(\frac{1}{2} \, d x\right)^{2} + d^{2} x^{4} \tan\left(\frac{1}{2} \, c\right)^{2} + d^{2} x^{4}\right)}}"," ",0,"-1/48*(a^2*d^6*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 2*a^2*d^6*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c)^2 - 2*a^2*d^6*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 2*a^2*d^6*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) - a^2*d^6*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2 + a^2*d^6*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2 - 2*a^2*d^6*x^4*sin_integral(d*x)*tan(1/2*d*x)^2 + a^2*d^6*x^4*imag_part(cos_integral(d*x))*tan(1/2*c)^2 - a^2*d^6*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c)^2 + 2*a^2*d^6*x^4*sin_integral(d*x)*tan(1/2*c)^2 - 2*a^2*d^6*x^4*real_part(cos_integral(d*x))*tan(1/2*c) - 2*a^2*d^6*x^4*real_part(cos_integral(-d*x))*tan(1/2*c) - 2*a^2*d^5*x^3*tan(1/2*d*x)^2*tan(1/2*c)^2 + 48*a*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 + 48*a*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c)^2 - a^2*d^6*x^4*imag_part(cos_integral(d*x)) + a^2*d^6*x^4*imag_part(cos_integral(-d*x)) - 2*a^2*d^6*x^4*sin_integral(d*x) + 96*a*b*d^3*x^4*imag_part(cos_integral(d*x))*tan(1/2*d*x)^2*tan(1/2*c) - 96*a*b*d^3*x^4*imag_part(cos_integral(-d*x))*tan(1/2*d*x)^2*tan(1/2*c) + 192*a*b*d^3*x^4*sin_integral(d*x)*tan(1/2*d*x)^2*tan(1/2*c) + 2*a^2*d^5*x^3*tan(1/2*d*x)^2 - 48*a*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*d*x)^2 - 48*a*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*d*x)^2 + 8*a^2*d^5*x^3*tan(1/2*d*x)*tan(1/2*c) + 2*a^2*d^5*x^3*tan(1/2*c)^2 + 48*a*b*d^3*x^4*real_part(cos_integral(d*x))*tan(1/2*c)^2 + 48*a*b*d^3*x^4*real_part(cos_integral(-d*x))*tan(1/2*c)^2 + 48*b^2*d*x^5*tan(1/2*d*x)^2*tan(1/2*c)^2 + 96*a*b*d^3*x^4*imag_part(cos_integral(d*x))*tan(1/2*c) - 96*a*b*d^3*x^4*imag_part(cos_integral(-d*x))*tan(1/2*c) + 192*a*b*d^3*x^4*sin_integral(d*x)*tan(1/2*c) + 4*a^2*d^4*x^2*tan(1/2*d*x)^2*tan(1/2*c) + 4*a^2*d^4*x^2*tan(1/2*d*x)*tan(1/2*c)^2 - 2*a^2*d^5*x^3 - 48*a*b*d^3*x^4*real_part(cos_integral(d*x)) - 48*a*b*d^3*x^4*real_part(cos_integral(-d*x)) - 48*b^2*d*x^5*tan(1/2*d*x)^2 - 192*b^2*d*x^5*tan(1/2*d*x)*tan(1/2*c) - 192*a*b*d^2*x^3*tan(1/2*d*x)^2*tan(1/2*c) - 48*b^2*d*x^5*tan(1/2*c)^2 - 192*a*b*d^2*x^3*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a^2*d^3*x*tan(1/2*d*x)^2*tan(1/2*c)^2 - 4*a^2*d^4*x^2*tan(1/2*d*x) - 4*a^2*d^4*x^2*tan(1/2*c) + 96*b^2*x^4*tan(1/2*d*x)^2*tan(1/2*c) + 96*b^2*x^4*tan(1/2*d*x)*tan(1/2*c)^2 + 48*b^2*d*x^5 + 192*a*b*d^2*x^3*tan(1/2*d*x) - 4*a^2*d^3*x*tan(1/2*d*x)^2 + 192*a*b*d^2*x^3*tan(1/2*c) - 16*a^2*d^3*x*tan(1/2*d*x)*tan(1/2*c) - 4*a^2*d^3*x*tan(1/2*c)^2 - 96*b^2*x^4*tan(1/2*d*x) - 96*b^2*x^4*tan(1/2*c) - 24*a^2*d^2*tan(1/2*d*x)^2*tan(1/2*c) - 24*a^2*d^2*tan(1/2*d*x)*tan(1/2*c)^2 + 4*a^2*d^3*x + 24*a^2*d^2*tan(1/2*d*x) + 24*a^2*d^2*tan(1/2*c))/(d^2*x^4*tan(1/2*d*x)^2*tan(1/2*c)^2 + d^2*x^4*tan(1/2*d*x)^2 + d^2*x^4*tan(1/2*c)^2 + d^2*x^4)","C",0
94,0,0,0,0.000000," ","integrate(x^4*sin(d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{4} \sin\left(d x + c\right)}{b x^{3} + a}\,{d x}"," ",0,"integrate(x^4*sin(d*x + c)/(b*x^3 + a), x)","F",0
95,0,0,0,0.000000," ","integrate(x^3*sin(d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{3} \sin\left(d x + c\right)}{b x^{3} + a}\,{d x}"," ",0,"integrate(x^3*sin(d*x + c)/(b*x^3 + a), x)","F",0
96,0,0,0,0.000000," ","integrate(x^2*sin(d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\int \frac{x^{2} \sin\left(d x + c\right)}{b x^{3} + a}\,{d x}"," ",0,"integrate(x^2*sin(d*x + c)/(b*x^3 + a), x)","F",0
97,0,0,0,0.000000," ","integrate(x*sin(d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\int \frac{x \sin\left(d x + c\right)}{b x^{3} + a}\,{d x}"," ",0,"integrate(x*sin(d*x + c)/(b*x^3 + a), x)","F",0
98,0,0,0,0.000000," ","integrate(sin(d*x+c)/(b*x^3+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{b x^{3} + a}\,{d x}"," ",0,"integrate(sin(d*x + c)/(b*x^3 + a), x)","F",0
99,0,0,0,0.000000," ","integrate(sin(d*x+c)/x/(b*x^3+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{3} + a\right)} x}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^3 + a)*x), x)","F",0
100,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^2/(b*x^3+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{3} + a\right)} x^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^3 + a)*x^2), x)","F",0
101,0,0,0,0.000000," ","integrate(sin(d*x+c)/x^3/(b*x^3+a),x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{3} + a\right)} x^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^3 + a)*x^3), x)","F",0
102,0,0,0,0.000000," ","integrate(x^3*sin(d*x+c)/(b*x^3+a)^2,x, algorithm=""giac"")","\int \frac{x^{3} \sin\left(d x + c\right)}{{\left(b x^{3} + a\right)}^{2}}\,{d x}"," ",0,"integrate(x^3*sin(d*x + c)/(b*x^3 + a)^2, x)","F",0
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113,0,0,0,0.000000," ","integrate(sin(d*x+c)/x/(b*x^3+a)^3,x, algorithm=""giac"")","\int \frac{\sin\left(d x + c\right)}{{\left(b x^{3} + a\right)}^{3} x}\,{d x}"," ",0,"integrate(sin(d*x + c)/((b*x^3 + a)^3*x), x)","F",0
