1,1,85,0,1.278684," ","integrate(x^3*(b*x+a)*sin(d*x+c),x, algorithm=""fricas"")","-\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) - {\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) - (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
2,1,67,0,1.165086," ","integrate(x^2*(b*x+a)*sin(d*x+c),x, algorithm=""fricas"")","-\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) - {\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) - (3*b*d^2*x^2 + 2*a*d^2*x - 6*b)*sin(d*x + c))/d^4","A",0
3,1,48,0,1.116188," ","integrate(x*(b*x+a)*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b d^{2} x^{2} + a d^{2} x - 2 \, b\right)} \cos\left(d x + c\right) - {\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) - (2*b*d*x + a*d)*sin(d*x + c))/d^3","A",0
4,1,30,0,1.089765," ","integrate((b*x+a)*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b d x + a d\right)} \cos\left(d x + c\right) - b \sin\left(d x + c\right)}{d^{2}}"," ",0,"-((b*d*x + a*d)*cos(d*x + c) - b*sin(d*x + c))/d^2","A",0
5,1,44,0,1.087419," ","integrate((b*x+a)*sin(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, a d \cos\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, b \cos\left(d x + c\right) + {\left(a d \operatorname{Ci}\left(d x\right) + a d \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d}"," ",0,"1/2*(2*a*d*cos(c)*sin_integral(d*x) - 2*b*cos(d*x + c) + (a*d*cos_integral(d*x) + a*d*cos_integral(-d*x))*sin(c))/d","A",0
6,1,75,0,0.792501," ","integrate((b*x+a)*sin(d*x+c)/x^2,x, algorithm=""fricas"")","\frac{{\left(a d x \operatorname{Ci}\left(d x\right) + a d x \operatorname{Ci}\left(-d x\right) + 2 \, b x \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, a \sin\left(d x + c\right) - {\left(2 \, a d x \operatorname{Si}\left(d x\right) - b x \operatorname{Ci}\left(d x\right) - b x \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, x}"," ",0,"1/2*((a*d*x*cos_integral(d*x) + a*d*x*cos_integral(-d*x) + 2*b*x*sin_integral(d*x))*cos(c) - 2*a*sin(d*x + c) - (2*a*d*x*sin_integral(d*x) - b*x*cos_integral(d*x) - b*x*cos_integral(-d*x))*sin(c))/x","A",0
7,1,111,0,0.748751," ","integrate((b*x+a)*sin(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a d x \cos\left(d x + c\right) + 2 \, {\left(a d^{2} x^{2} \operatorname{Si}\left(d x\right) - b d x^{2} \operatorname{Ci}\left(d x\right) - b d x^{2} \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left(2 \, b x + a\right)} \sin\left(d x + c\right) + {\left(a d^{2} x^{2} \operatorname{Ci}\left(d x\right) + a d^{2} x^{2} \operatorname{Ci}\left(-d x\right) + 4 \, b d x^{2} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*a*d*x*cos(d*x + c) + 2*(a*d^2*x^2*sin_integral(d*x) - b*d*x^2*cos_integral(d*x) - b*d*x^2*cos_integral(-d*x))*cos(c) + 2*(2*b*x + a)*sin(d*x + c) + (a*d^2*x^2*cos_integral(d*x) + a*d^2*x^2*cos_integral(-d*x) + 4*b*d*x^2*sin_integral(d*x))*sin(c))/x^2","A",0
8,1,137,0,1.134397," ","integrate((b*x+a)*sin(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b d x^{2} + a d x\right)} \cos\left(d x + c\right) + {\left(a d^{3} x^{3} \operatorname{Ci}\left(d x\right) + a d^{3} x^{3} \operatorname{Ci}\left(-d x\right) + 6 \, b d^{2} x^{3} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, {\left(a d^{2} x^{2} - 3 \, b x - 2 \, a\right)} \sin\left(d x + c\right) - {\left(2 \, a d^{3} x^{3} \operatorname{Si}\left(d x\right) - 3 \, b d^{2} x^{3} \operatorname{Ci}\left(d x\right) - 3 \, b d^{2} x^{3} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*(3*b*d*x^2 + a*d*x)*cos(d*x + c) + (a*d^3*x^3*cos_integral(d*x) + a*d^3*x^3*cos_integral(-d*x) + 6*b*d^2*x^3*sin_integral(d*x))*cos(c) - 2*(a*d^2*x^2 - 3*b*x - 2*a)*sin(d*x + c) - (2*a*d^3*x^3*sin_integral(d*x) - 3*b*d^2*x^3*cos_integral(d*x) - 3*b*d^2*x^3*cos_integral(-d*x))*sin(c))/x^3","A",0
9,1,154,0,0.993448," ","integrate((b*x+a)*sin(d*x+c)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(a d^{3} x^{3} - 4 \, b d x^{2} - 2 \, a d x\right)} \cos\left(d x + c\right) + 2 \, {\left(a d^{4} x^{4} \operatorname{Si}\left(d x\right) - 2 \, b d^{3} x^{4} \operatorname{Ci}\left(d x\right) - 2 \, b d^{3} x^{4} \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left(4 \, b d^{2} x^{3} + a d^{2} x^{2} - 8 \, b x - 6 \, a\right)} \sin\left(d x + c\right) + {\left(a d^{4} x^{4} \operatorname{Ci}\left(d x\right) + a d^{4} x^{4} \operatorname{Ci}\left(-d x\right) + 8 \, b d^{3} x^{4} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right)}{48 \, x^{4}}"," ",0,"1/48*(2*(a*d^3*x^3 - 4*b*d*x^2 - 2*a*d*x)*cos(d*x + c) + 2*(a*d^4*x^4*sin_integral(d*x) - 2*b*d^3*x^4*cos_integral(d*x) - 2*b*d^3*x^4*cos_integral(-d*x))*cos(c) + 2*(4*b*d^2*x^3 + a*d^2*x^2 - 8*b*x - 6*a)*sin(d*x + c) + (a*d^4*x^4*cos_integral(d*x) + a*d^4*x^4*cos_integral(-d*x) + 8*b*d^3*x^4*sin_integral(d*x))*sin(c))/x^4","A",0
10,1,126,0,0.788736," ","integrate(x^2*(b*x+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b^{2} d^{4} x^{4} + 2 \, a b d^{4} x^{3} - 12 \, a b d^{2} x - 2 \, a^{2} d^{2} + {\left(a^{2} d^{4} - 12 \, b^{2} d^{2}\right)} x^{2} + 24 \, b^{2}\right)} \cos\left(d x + c\right) - 2 \, {\left(2 \, b^{2} d^{3} x^{3} + 3 \, a b d^{3} x^{2} - 6 \, a b d + {\left(a^{2} d^{3} - 12 \, b^{2} d\right)} x\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-((b^2*d^4*x^4 + 2*a*b*d^4*x^3 - 12*a*b*d^2*x - 2*a^2*d^2 + (a^2*d^4 - 12*b^2*d^2)*x^2 + 24*b^2)*cos(d*x + c) - 2*(2*b^2*d^3*x^3 + 3*a*b*d^3*x^2 - 6*a*b*d + (a^2*d^3 - 12*b^2*d)*x)*sin(d*x + c))/d^5","A",0
11,1,95,0,1.221763," ","integrate(x*(b*x+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b^{2} d^{3} x^{3} + 2 \, a b d^{3} x^{2} - 4 \, a b d + {\left(a^{2} d^{3} - 6 \, b^{2} d\right)} x\right)} \cos\left(d x + c\right) - {\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 - 4*a*b*d + (a^2*d^3 - 6*b^2*d)*x)*cos(d*x + c) - (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
12,1,63,0,0.990234," ","integrate((b*x+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\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) - 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) - 2*(b^2*d*x + a*b*d)*sin(d*x + c))/d^3","A",0
13,1,78,0,0.996632," ","integrate((b*x+a)^2*sin(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{2} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, b^{2} \sin\left(d x + c\right) - 2 \, {\left(b^{2} d x + 2 \, a b d\right)} \cos\left(d x + c\right) + {\left(a^{2} d^{2} \operatorname{Ci}\left(d x\right) + a^{2} d^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d^{2}}"," ",0,"1/2*(2*a^2*d^2*cos(c)*sin_integral(d*x) + 2*b^2*sin(d*x + c) - 2*(b^2*d*x + 2*a*b*d)*cos(d*x + c) + (a^2*d^2*cos_integral(d*x) + a^2*d^2*cos_integral(-d*x))*sin(c))/d^2","A",0
14,1,111,0,1.175328," ","integrate((b*x+a)^2*sin(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} x \cos\left(d x + c\right) + 2 \, a^{2} d \sin\left(d x + c\right) - {\left(a^{2} d^{2} x \operatorname{Ci}\left(d x\right) + a^{2} d^{2} x \operatorname{Ci}\left(-d x\right) + 4 \, a b d x \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) + 2 \, {\left(a^{2} d^{2} x \operatorname{Si}\left(d x\right) - a b d x \operatorname{Ci}\left(d x\right) - a b d x \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d x}"," ",0,"-1/2*(2*b^2*x*cos(d*x + c) + 2*a^2*d*sin(d*x + c) - (a^2*d^2*x*cos_integral(d*x) + a^2*d^2*x*cos_integral(-d*x) + 4*a*b*d*x*sin_integral(d*x))*cos(c) + 2*(a^2*d^2*x*sin_integral(d*x) - a*b*d*x*cos_integral(d*x) - a*b*d*x*cos_integral(-d*x))*sin(c))/(d*x)","A",0
15,1,147,0,1.005984," ","integrate((b*x+a)^2*sin(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \cos\left(d x + c\right) - 2 \, {\left(2 \, a b d x^{2} \operatorname{Ci}\left(d x\right) + 2 \, a b d x^{2} \operatorname{Ci}\left(-d x\right) - {\left(a^{2} d^{2} - 2 \, b^{2}\right)} x^{2} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) + 2 \, {\left(4 \, a b x + a^{2}\right)} \sin\left(d x + c\right) + {\left(8 \, a b d x^{2} \operatorname{Si}\left(d x\right) + {\left(a^{2} d^{2} - 2 \, b^{2}\right)} x^{2} \operatorname{Ci}\left(d x\right) + {\left(a^{2} d^{2} - 2 \, b^{2}\right)} x^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*a^2*d*x*cos(d*x + c) - 2*(2*a*b*d*x^2*cos_integral(d*x) + 2*a*b*d*x^2*cos_integral(-d*x) - (a^2*d^2 - 2*b^2)*x^2*sin_integral(d*x))*cos(c) + 2*(4*a*b*x + a^2)*sin(d*x + c) + (8*a*b*d*x^2*sin_integral(d*x) + (a^2*d^2 - 2*b^2)*x^2*cos_integral(d*x) + (a^2*d^2 - 2*b^2)*x^2*cos_integral(-d*x))*sin(c))/x^2","A",0
16,1,186,0,0.814035," ","integrate((b*x+a)^2*sin(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a b d x^{2} + a^{2} d x\right)} \cos\left(d x + c\right) + {\left(12 \, a b d^{2} x^{3} \operatorname{Si}\left(d x\right) + {\left(a^{2} d^{3} - 6 \, b^{2} d\right)} x^{3} \operatorname{Ci}\left(d x\right) + {\left(a^{2} d^{3} - 6 \, b^{2} d\right)} x^{3} \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left(6 \, a b x - {\left(a^{2} d^{2} - 6 \, b^{2}\right)} x^{2} + 2 \, a^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left(3 \, a b d^{2} x^{3} \operatorname{Ci}\left(d x\right) + 3 \, a b d^{2} x^{3} \operatorname{Ci}\left(-d x\right) - {\left(a^{2} d^{3} - 6 \, b^{2} d\right)} x^{3} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*(6*a*b*d*x^2 + a^2*d*x)*cos(d*x + c) + (12*a*b*d^2*x^3*sin_integral(d*x) + (a^2*d^3 - 6*b^2*d)*x^3*cos_integral(d*x) + (a^2*d^3 - 6*b^2*d)*x^3*cos_integral(-d*x))*cos(c) + 2*(6*a*b*x - (a^2*d^2 - 6*b^2)*x^2 + 2*a^2)*sin(d*x + c) + 2*(3*a*b*d^2*x^3*cos_integral(d*x) + 3*a*b*d^2*x^3*cos_integral(-d*x) - (a^2*d^3 - 6*b^2*d)*x^3*sin_integral(d*x))*sin(c))/x^3","A",0
17,1,222,0,0.902011," ","integrate((b*x+a)^2*sin(d*x+c)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a b d x^{2} + 2 \, a^{2} d x - {\left(a^{2} d^{3} - 12 \, b^{2} d\right)} x^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(4 \, a b d^{3} x^{4} \operatorname{Ci}\left(d x\right) + 4 \, a b d^{3} x^{4} \operatorname{Ci}\left(-d x\right) - {\left(a^{2} d^{4} - 12 \, b^{2} d^{2}\right)} x^{4} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, {\left(8 \, a b d^{2} x^{3} - 16 \, a b x + {\left(a^{2} d^{2} - 12 \, b^{2}\right)} x^{2} - 6 \, a^{2}\right)} \sin\left(d x + c\right) - {\left(16 \, a b d^{3} x^{4} \operatorname{Si}\left(d x\right) + {\left(a^{2} d^{4} - 12 \, b^{2} d^{2}\right)} x^{4} \operatorname{Ci}\left(d x\right) + {\left(a^{2} d^{4} - 12 \, b^{2} d^{2}\right)} x^{4} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{48 \, x^{4}}"," ",0,"-1/48*(2*(8*a*b*d*x^2 + 2*a^2*d*x - (a^2*d^3 - 12*b^2*d)*x^3)*cos(d*x + c) + 2*(4*a*b*d^3*x^4*cos_integral(d*x) + 4*a*b*d^3*x^4*cos_integral(-d*x) - (a^2*d^4 - 12*b^2*d^2)*x^4*sin_integral(d*x))*cos(c) - 2*(8*a*b*d^2*x^3 - 16*a*b*x + (a^2*d^2 - 12*b^2)*x^2 - 6*a^2)*sin(d*x + c) - (16*a*b*d^3*x^4*sin_integral(d*x) + (a^2*d^4 - 12*b^2*d^2)*x^4*cos_integral(d*x) + (a^2*d^4 - 12*b^2*d^2)*x^4*cos_integral(-d*x))*sin(c))/x^4","A",0
18,1,213,0,1.246904," ","integrate(x^4*sin(d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, a^{4} d^{4} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) - 2 \, {\left(b^{4} d^{3} x^{3} - a b^{3} d^{3} x^{2} - a^{3} b d^{3} + 2 \, a b^{3} d + {\left(a^{2} b^{2} d^{3} - 6 \, b^{4} d\right)} x\right)} \cos\left(d x + c\right) + 2 \, {\left(3 \, b^{4} d^{2} x^{2} - 2 \, a b^{3} d^{2} x + a^{2} b^{2} d^{2} - 6 \, b^{4}\right)} \sin\left(d x + c\right) - {\left(a^{4} d^{4} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + a^{4} d^{4} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, b^{5} d^{4}}"," ",0,"1/2*(2*a^4*d^4*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) - 2*(b^4*d^3*x^3 - a*b^3*d^3*x^2 - a^3*b*d^3 + 2*a*b^3*d + (a^2*b^2*d^3 - 6*b^4*d)*x)*cos(d*x + c) + 2*(3*b^4*d^2*x^2 - 2*a*b^3*d^2*x + a^2*b^2*d^2 - 6*b^4)*sin(d*x + c) - (a^4*d^4*cos_integral((b*d*x + a*d)/b) + a^4*d^4*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^5*d^4)","A",0
19,1,167,0,1.120031," ","integrate(x^3*sin(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a^{3} d^{3} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 2 \, {\left(b^{3} d^{2} x^{2} - a b^{2} d^{2} x + a^{2} b d^{2} - 2 \, b^{3}\right)} \cos\left(d x + c\right) - 2 \, {\left(2 \, b^{3} d x - a b^{2} d\right)} \sin\left(d x + c\right) - {\left(a^{3} d^{3} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + a^{3} d^{3} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, b^{4} d^{3}}"," ",0,"-1/2*(2*a^3*d^3*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + 2*(b^3*d^2*x^2 - a*b^2*d^2*x + a^2*b*d^2 - 2*b^3)*cos(d*x + c) - 2*(2*b^3*d*x - a*b^2*d)*sin(d*x + c) - (a^3*d^3*cos_integral((b*d*x + a*d)/b) + a^3*d^3*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^4*d^3)","A",0
20,1,133,0,1.196140," ","integrate(x^2*sin(d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 2 \, b^{2} \sin\left(d x + c\right) - 2 \, {\left(b^{2} d x - a b d\right)} \cos\left(d x + c\right) - {\left(a^{2} d^{2} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + a^{2} d^{2} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, b^{3} d^{2}}"," ",0,"1/2*(2*a^2*d^2*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + 2*b^2*sin(d*x + c) - 2*(b^2*d*x - a*b*d)*cos(d*x + c) - (a^2*d^2*cos_integral((b*d*x + a*d)/b) + a^2*d^2*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^3*d^2)","A",0
21,1,99,0,1.093863," ","integrate(x*sin(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a d \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 2 \, b \cos\left(d x + c\right) - {\left(a d \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + a d \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, b^{2} d}"," ",0,"-1/2*(2*a*d*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + 2*b*cos(d*x + c) - (a*d*cos_integral((b*d*x + a*d)/b) + a*d*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^2*d)","A",0
22,1,78,0,1.285008," ","integrate(sin(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{{\left(\operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right) - 2 \, \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right)}{2 \, b}"," ",0,"-1/2*((cos_integral((b*d*x + a*d)/b) + cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b) - 2*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b))/b","A",0
23,1,99,0,1.266729," ","integrate(sin(d*x+c)/x/(b*x+a),x, algorithm=""fricas"")","\frac{{\left(\operatorname{Ci}\left(d x\right) + \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right) + {\left(\operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right) + 2 \, \cos\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right)}{2 \, a}"," ",0,"1/2*((cos_integral(d*x) + cos_integral(-d*x))*sin(c) + (cos_integral((b*d*x + a*d)/b) + cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b) + 2*cos(c)*sin_integral(d*x) - 2*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b))/a","A",0
24,1,157,0,1.126444," ","integrate(sin(d*x+c)/x^2/(b*x+a),x, algorithm=""fricas"")","\frac{2 \, b x \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + {\left(a d x \operatorname{Ci}\left(d x\right) + a d x \operatorname{Ci}\left(-d x\right) - 2 \, b x \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, a \sin\left(d x + c\right) - {\left(2 \, a d x \operatorname{Si}\left(d x\right) + b x \operatorname{Ci}\left(d x\right) + b x \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right) - {\left(b x \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + b x \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, a^{2} x}"," ",0,"1/2*(2*b*x*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + (a*d*x*cos_integral(d*x) + a*d*x*cos_integral(-d*x) - 2*b*x*sin_integral(d*x))*cos(c) - 2*a*sin(d*x + c) - (2*a*d*x*sin_integral(d*x) + b*x*cos_integral(d*x) + b*x*cos_integral(-d*x))*sin(c) - (b*x*cos_integral((b*d*x + a*d)/b) + b*x*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^2*x)","A",0
25,1,245,0,1.035311," ","integrate(sin(d*x+c)/x^3/(b*x+a),x, algorithm=""fricas"")","-\frac{4 \, b^{2} x^{2} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 2 \, a^{2} d x \cos\left(d x + c\right) + 2 \, {\left(a b d x^{2} \operatorname{Ci}\left(d x\right) + a b d x^{2} \operatorname{Ci}\left(-d x\right) + {\left(a^{2} d^{2} - 2 \, b^{2}\right)} x^{2} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, {\left(2 \, a b x - a^{2}\right)} \sin\left(d x + c\right) - {\left(4 \, a b d x^{2} \operatorname{Si}\left(d x\right) - {\left(a^{2} d^{2} - 2 \, b^{2}\right)} x^{2} \operatorname{Ci}\left(d x\right) - {\left(a^{2} d^{2} - 2 \, b^{2}\right)} x^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right) - 2 \, {\left(b^{2} x^{2} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + b^{2} x^{2} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, a^{3} x^{2}}"," ",0,"-1/4*(4*b^2*x^2*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + 2*a^2*d*x*cos(d*x + c) + 2*(a*b*d*x^2*cos_integral(d*x) + a*b*d*x^2*cos_integral(-d*x) + (a^2*d^2 - 2*b^2)*x^2*sin_integral(d*x))*cos(c) - 2*(2*a*b*x - a^2)*sin(d*x + c) - (4*a*b*d*x^2*sin_integral(d*x) - (a^2*d^2 - 2*b^2)*x^2*cos_integral(d*x) - (a^2*d^2 - 2*b^2)*x^2*cos_integral(-d*x))*sin(c) - 2*(b^2*x^2*cos_integral((b*d*x + a*d)/b) + b^2*x^2*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^3*x^2)","A",0
26,1,357,0,1.525793," ","integrate(x^4*sin(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{5} d^{2} x^{3} - a b^{4} d^{2} x^{2} + 3 \, a^{3} b^{2} d^{2} - 2 \, a b^{4} + {\left(a^{2} b^{3} d^{2} - 2 \, b^{5}\right)} x\right)} \cos\left(d x + c\right) - {\left({\left(a^{4} b d^{4} x + a^{5} d^{4}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a^{4} b d^{4} x + a^{5} d^{4}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 8 \, {\left(a^{3} b^{2} d^{3} x + a^{4} b d^{3}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(a^{4} b d^{3} - 2 \, b^{5} d x^{2} + 2 \, a^{2} b^{3} d\right)} \sin\left(d x + c\right) - 2 \, {\left(2 \, {\left(a^{3} b^{2} d^{3} x + a^{4} b d^{3}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + 2 \, {\left(a^{3} b^{2} d^{3} x + a^{4} b d^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + {\left(a^{4} b d^{4} x + a^{5} d^{4}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{7} d^{3} x + a b^{6} d^{3}\right)}}"," ",0,"-1/2*(2*(b^5*d^2*x^3 - a*b^4*d^2*x^2 + 3*a^3*b^2*d^2 - 2*a*b^4 + (a^2*b^3*d^2 - 2*b^5)*x)*cos(d*x + c) - ((a^4*b*d^4*x + a^5*d^4)*cos_integral((b*d*x + a*d)/b) + (a^4*b*d^4*x + a^5*d^4)*cos_integral(-(b*d*x + a*d)/b) - 8*(a^3*b^2*d^3*x + a^4*b*d^3)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) + 2*(a^4*b*d^3 - 2*b^5*d*x^2 + 2*a^2*b^3*d)*sin(d*x + c) - 2*(2*(a^3*b^2*d^3*x + a^4*b*d^3)*cos_integral((b*d*x + a*d)/b) + 2*(a^3*b^2*d^3*x + a^4*b*d^3)*cos_integral(-(b*d*x + a*d)/b) + (a^4*b*d^4*x + a^5*d^4)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^7*d^3*x + a*b^6*d^3)","A",0
27,1,316,0,1.245081," ","integrate(x^3*sin(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{4} d x^{2} - a b^{3} d x - 2 \, a^{2} b^{2} d\right)} \cos\left(d x + c\right) + {\left({\left(a^{3} b d^{3} x + a^{4} d^{3}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a^{3} b d^{3} x + a^{4} d^{3}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 6 \, {\left(a^{2} b^{2} d^{2} x + a^{3} b d^{2}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(a^{3} b d^{2} + b^{4} x + a b^{3}\right)} \sin\left(d x + c\right) + {\left(3 \, {\left(a^{2} b^{2} d^{2} x + a^{3} b d^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + 3 \, {\left(a^{2} b^{2} d^{2} x + a^{3} b d^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 2 \, {\left(a^{3} b d^{3} x + a^{4} d^{3}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{6} d^{2} x + a b^{5} d^{2}\right)}}"," ",0,"-1/2*(2*(b^4*d*x^2 - a*b^3*d*x - 2*a^2*b^2*d)*cos(d*x + c) + ((a^3*b*d^3*x + a^4*d^3)*cos_integral((b*d*x + a*d)/b) + (a^3*b*d^3*x + a^4*d^3)*cos_integral(-(b*d*x + a*d)/b) - 6*(a^2*b^2*d^2*x + a^3*b*d^2)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*(a^3*b*d^2 + b^4*x + a*b^3)*sin(d*x + c) + (3*(a^2*b^2*d^2*x + a^3*b*d^2)*cos_integral((b*d*x + a*d)/b) + 3*(a^2*b^2*d^2*x + a^3*b*d^2)*cos_integral(-(b*d*x + a*d)/b) + 2*(a^3*b*d^3*x + a^4*d^3)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^6*d^2*x + a*b^5*d^2)","A",0
28,1,264,0,1.030615," ","integrate(x^2*sin(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b d \sin\left(d x + c\right) + 2 \, {\left(b^{3} x + a b^{2}\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} b d^{2} x + a^{3} d^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a^{2} b d^{2} x + a^{3} d^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 4 \, {\left(a b^{2} d x + a^{2} b d\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left({\left(a b^{2} d x + a^{2} b d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a b^{2} d x + a^{2} b d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + {\left(a^{2} b d^{2} x + a^{3} d^{2}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{5} d x + a b^{4} d\right)}}"," ",0,"-1/2*(2*a^2*b*d*sin(d*x + c) + 2*(b^3*x + a*b^2)*cos(d*x + c) - ((a^2*b*d^2*x + a^3*d^2)*cos_integral((b*d*x + a*d)/b) + (a^2*b*d^2*x + a^3*d^2)*cos_integral(-(b*d*x + a*d)/b) - 4*(a*b^2*d*x + a^2*b*d)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*((a*b^2*d*x + a^2*b*d)*cos_integral((b*d*x + a*d)/b) + (a*b^2*d*x + a^2*b*d)*cos_integral(-(b*d*x + a*d)/b) + (a^2*b*d^2*x + a^3*d^2)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^5*d*x + a*b^4*d)","A",0
29,1,208,0,0.916891," ","integrate(x*sin(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, a b \sin\left(d x + c\right) - {\left({\left(a b d x + a^{2} d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a b d x + a^{2} d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 2 \, {\left(b^{2} x + a b\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - {\left({\left(b^{2} x + a b\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(b^{2} x + a b\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 2 \, {\left(a b d x + a^{2} d\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{4} x + a b^{3}\right)}}"," ",0,"1/2*(2*a*b*sin(d*x + c) - ((a*b*d*x + a^2*d)*cos_integral((b*d*x + a*d)/b) + (a*b*d*x + a^2*d)*cos_integral(-(b*d*x + a*d)/b) - 2*(b^2*x + a*b)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - ((b^2*x + a*b)*cos_integral((b*d*x + a*d)/b) + (b^2*x + a*b)*cos_integral(-(b*d*x + a*d)/b) + 2*(a*b*d*x + a^2*d)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^4*x + a*b^3)","A",0
30,1,123,0,0.935658," ","integrate(sin(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b d x + a d\right)} \sin\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + {\left({\left(b d x + a d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(b d x + a d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, b \sin\left(d x + c\right)}{2 \, {\left(b^{3} x + a b^{2}\right)}}"," ",0,"1/2*(2*(b*d*x + a*d)*sin(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + ((b*d*x + a*d)*cos_integral((b*d*x + a*d)/b) + (b*d*x + a*d)*cos_integral(-(b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*b*sin(d*x + c))/(b^3*x + a*b^2)","A",0
31,1,260,0,1.325160," ","integrate(sin(d*x+c)/x/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, a b \sin\left(d x + c\right) + 2 \, {\left(b^{2} x + a b\right)} \cos\left(c\right) \operatorname{Si}\left(d x\right) - {\left({\left(a b d x + a^{2} d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a b d x + a^{2} d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 2 \, {\left(b^{2} x + a b\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) + {\left({\left(b^{2} x + a b\right)} \operatorname{Ci}\left(d x\right) + {\left(b^{2} x + a b\right)} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right) + {\left({\left(b^{2} x + a b\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(b^{2} x + a b\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 2 \, {\left(a b d x + a^{2} d\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"1/2*(2*a*b*sin(d*x + c) + 2*(b^2*x + a*b)*cos(c)*sin_integral(d*x) - ((a*b*d*x + a^2*d)*cos_integral((b*d*x + a*d)/b) + (a*b*d*x + a^2*d)*cos_integral(-(b*d*x + a*d)/b) + 2*(b^2*x + a*b)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) + ((b^2*x + a*b)*cos_integral(d*x) + (b^2*x + a*b)*cos_integral(-d*x))*sin(c) + ((b^2*x + a*b)*cos_integral((b*d*x + a*d)/b) + (b^2*x + a*b)*cos_integral(-(b*d*x + a*d)/b) - 2*(a*b*d*x + a^2*d)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^2*b^2*x + a^3*b)","A",0
32,1,355,0,1.213848," ","integrate(sin(d*x+c)/x^2/(b*x+a)^2,x, algorithm=""fricas"")","\frac{{\left({\left(a b d x^{2} + a^{2} d x\right)} \operatorname{Ci}\left(d x\right) + {\left(a b d x^{2} + a^{2} d x\right)} \operatorname{Ci}\left(-d x\right) - 4 \, {\left(b^{2} x^{2} + a b x\right)} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) + {\left({\left(a b d x^{2} + a^{2} d x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a b d x^{2} + a^{2} d x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 4 \, {\left(b^{2} x^{2} + a b x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(2 \, a b x + a^{2}\right)} \sin\left(d x + c\right) - 2 \, {\left({\left(b^{2} x^{2} + a b x\right)} \operatorname{Ci}\left(d x\right) + {\left(b^{2} x^{2} + a b x\right)} \operatorname{Ci}\left(-d x\right) + {\left(a b d x^{2} + a^{2} d x\right)} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right) - 2 \, {\left({\left(b^{2} x^{2} + a b x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(b^{2} x^{2} + a b x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - {\left(a b d x^{2} + a^{2} d x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}"," ",0,"1/2*(((a*b*d*x^2 + a^2*d*x)*cos_integral(d*x) + (a*b*d*x^2 + a^2*d*x)*cos_integral(-d*x) - 4*(b^2*x^2 + a*b*x)*sin_integral(d*x))*cos(c) + ((a*b*d*x^2 + a^2*d*x)*cos_integral((b*d*x + a*d)/b) + (a*b*d*x^2 + a^2*d*x)*cos_integral(-(b*d*x + a*d)/b) + 4*(b^2*x^2 + a*b*x)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*(2*a*b*x + a^2)*sin(d*x + c) - 2*((b^2*x^2 + a*b*x)*cos_integral(d*x) + (b^2*x^2 + a*b*x)*cos_integral(-d*x) + (a*b*d*x^2 + a^2*d*x)*sin_integral(d*x))*sin(c) - 2*((b^2*x^2 + a*b*x)*cos_integral((b*d*x + a*d)/b) + (b^2*x^2 + a*b*x)*cos_integral(-(b*d*x + a*d)/b) - (a*b*d*x^2 + a^2*d*x)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^3*b*x^2 + a^4*x)","A",0
33,1,515,0,1.143452," ","integrate(x^3*sin(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{4} b d^{2} - 2 \, b^{5} x^{2} - 2 \, a^{2} b^{3} + {\left(a^{3} b^{2} d^{2} - 4 \, a b^{4}\right)} x\right)} \cos\left(d x + c\right) + 2 \, {\left(3 \, {\left(a^{2} b^{3} d^{2} x^{2} + 2 \, a^{3} b^{2} d^{2} x + a^{4} b d^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + 3 \, {\left(a^{2} b^{3} d^{2} x^{2} + 2 \, a^{3} b^{2} d^{2} x + a^{4} b d^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + {\left(a^{5} d^{3} - 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} - 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} - 6 \, a^{2} b^{3} d\right)} x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(6 \, a^{2} b^{3} d x + 5 \, a^{3} b^{2} d\right)} \sin\left(d x + c\right) - {\left({\left(a^{5} d^{3} - 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} - 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} - 6 \, a^{2} b^{3} d\right)} x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a^{5} d^{3} - 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} - 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} - 6 \, a^{2} b^{3} d\right)} x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 12 \, {\left(a^{2} b^{3} d^{2} x^{2} + 2 \, a^{3} b^{2} d^{2} x + a^{4} b d^{2}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{8} d x^{2} + 2 \, a b^{7} d x + a^{2} b^{6} d\right)}}"," ",0,"1/4*(2*(a^4*b*d^2 - 2*b^5*x^2 - 2*a^2*b^3 + (a^3*b^2*d^2 - 4*a*b^4)*x)*cos(d*x + c) + 2*(3*(a^2*b^3*d^2*x^2 + 2*a^3*b^2*d^2*x + a^4*b*d^2)*cos_integral((b*d*x + a*d)/b) + 3*(a^2*b^3*d^2*x^2 + 2*a^3*b^2*d^2*x + a^4*b*d^2)*cos_integral(-(b*d*x + a*d)/b) + (a^5*d^3 - 6*a^3*b^2*d + (a^3*b^2*d^3 - 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 - 6*a^2*b^3*d)*x)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*(6*a^2*b^3*d*x + 5*a^3*b^2*d)*sin(d*x + c) - ((a^5*d^3 - 6*a^3*b^2*d + (a^3*b^2*d^3 - 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 - 6*a^2*b^3*d)*x)*cos_integral((b*d*x + a*d)/b) + (a^5*d^3 - 6*a^3*b^2*d + (a^3*b^2*d^3 - 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 - 6*a^2*b^3*d)*x)*cos_integral(-(b*d*x + a*d)/b) - 12*(a^2*b^3*d^2*x^2 + 2*a^3*b^2*d^2*x + a^4*b*d^2)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^8*d*x^2 + 2*a*b^7*d*x + a^2*b^6*d)","A",0
34,1,438,0,1.148802," ","integrate(x^2*sin(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} b^{2} d x + a^{3} b d\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, {\left(a b^{3} d x^{2} + 2 \, a^{2} b^{2} d x + a^{3} b d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + 2 \, {\left(a b^{3} d x^{2} + 2 \, a^{2} b^{2} d x + a^{3} b d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a b^{3}\right)} x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(4 \, a b^{3} x + 3 \, a^{2} b^{2}\right)} \sin\left(d x + c\right) - {\left({\left(a^{4} d^{2} - 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a b^{3}\right)} x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a b^{3}\right)} x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 8 \, {\left(a b^{3} d x^{2} + 2 \, a^{2} b^{2} d x + a^{3} b d\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"-1/4*(2*(a^2*b^2*d*x + a^3*b*d)*cos(d*x + c) + 2*(2*(a*b^3*d*x^2 + 2*a^2*b^2*d*x + a^3*b*d)*cos_integral((b*d*x + a*d)/b) + 2*(a*b^3*d*x^2 + 2*a^2*b^2*d*x + a^3*b*d)*cos_integral(-(b*d*x + a*d)/b) + (a^4*d^2 - 2*a^2*b^2 + (a^2*b^2*d^2 - 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a*b^3)*x)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*(4*a*b^3*x + 3*a^2*b^2)*sin(d*x + c) - ((a^4*d^2 - 2*a^2*b^2 + (a^2*b^2*d^2 - 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a*b^3)*x)*cos_integral((b*d*x + a*d)/b) + (a^4*d^2 - 2*a^2*b^2 + (a^2*b^2*d^2 - 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a*b^3)*x)*cos_integral(-(b*d*x + a*d)/b) - 8*(a*b^3*d*x^2 + 2*a^2*b^2*d*x + a^3*b*d)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
35,1,346,0,1.241672," ","integrate(x*sin(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a b^{2} d x + a^{2} b d\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(b^{3} d x^{2} + 2 \, a b^{2} d x + a^{2} b d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(b^{3} d x^{2} + 2 \, a b^{2} d x + a^{2} b d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + {\left(a b^{2} d^{2} x^{2} + 2 \, a^{2} b d^{2} x + a^{3} d^{2}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(2 \, b^{3} x + a b^{2}\right)} \sin\left(d x + c\right) - {\left({\left(a b^{2} d^{2} x^{2} + 2 \, a^{2} b d^{2} x + a^{3} d^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a b^{2} d^{2} x^{2} + 2 \, a^{2} b d^{2} x + a^{3} d^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - 4 \, {\left(b^{3} d x^{2} + 2 \, a b^{2} d x + a^{2} b d\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"1/4*(2*(a*b^2*d*x + a^2*b*d)*cos(d*x + c) + 2*((b^3*d*x^2 + 2*a*b^2*d*x + a^2*b*d)*cos_integral((b*d*x + a*d)/b) + (b^3*d*x^2 + 2*a*b^2*d*x + a^2*b*d)*cos_integral(-(b*d*x + a*d)/b) + (a*b^2*d^2*x^2 + 2*a^2*b*d^2*x + a^3*d^2)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*(2*b^3*x + a*b^2)*sin(d*x + c) - ((a*b^2*d^2*x^2 + 2*a^2*b*d^2*x + a^3*d^2)*cos_integral((b*d*x + a*d)/b) + (a*b^2*d^2*x^2 + 2*a^2*b*d^2*x + a^3*d^2)*cos_integral(-(b*d*x + a*d)/b) - 4*(b^3*d*x^2 + 2*a*b^2*d*x + a^2*b*d)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","A",0
36,1,210,0,1.325139," ","integrate(sin(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{2} \sin\left(d x + c\right) + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \cos\left(-\frac{b c - a d}{b}\right) \operatorname{Si}\left(\frac{b d x + a d}{b}\right) + 2 \, {\left(b^{2} d x + a b d\right)} \cos\left(d x + c\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/4*(2*b^2*sin(d*x + c) + 2*(b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*cos(-(b*c - a*d)/b)*sin_integral((b*d*x + a*d)/b) + 2*(b^2*d*x + a*b*d)*cos(d*x + c) - ((b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*cos_integral((b*d*x + a*d)/b) + (b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*cos_integral(-(b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","B",0
37,1,532,0,1.231946," ","integrate(sin(d*x+c)/x/(b*x+a)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, {\left(a^{2} b^{2} d x + a^{3} b d\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a b^{3} d x^{2} + 2 \, a^{2} b^{2} d x + a^{3} b d\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a b^{3} d x^{2} + 2 \, a^{2} b^{2} d x + a^{3} b d\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a b^{3}\right)} x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(2 \, a b^{3} x + 3 \, a^{2} b^{2}\right)} \sin\left(d x + c\right) + 2 \, {\left({\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} \operatorname{Ci}\left(d x\right) + {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right) - {\left({\left(a^{4} d^{2} - 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a b^{3}\right)} x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a b^{3}\right)} x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 4 \, {\left(a b^{3} d x^{2} + 2 \, a^{2} b^{2} d x + a^{3} b d\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(a^{3} b^{4} x^{2} + 2 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}"," ",0,"1/4*(4*(b^4*x^2 + 2*a*b^3*x + a^2*b^2)*cos(c)*sin_integral(d*x) + 2*(a^2*b^2*d*x + a^3*b*d)*cos(d*x + c) - 2*((a*b^3*d*x^2 + 2*a^2*b^2*d*x + a^3*b*d)*cos_integral((b*d*x + a*d)/b) + (a*b^3*d*x^2 + 2*a^2*b^2*d*x + a^3*b*d)*cos_integral(-(b*d*x + a*d)/b) - (a^4*d^2 - 2*a^2*b^2 + (a^2*b^2*d^2 - 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a*b^3)*x)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) + 2*(2*a*b^3*x + 3*a^2*b^2)*sin(d*x + c) + 2*((b^4*x^2 + 2*a*b^3*x + a^2*b^2)*cos_integral(d*x) + (b^4*x^2 + 2*a*b^3*x + a^2*b^2)*cos_integral(-d*x))*sin(c) - ((a^4*d^2 - 2*a^2*b^2 + (a^2*b^2*d^2 - 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a*b^3)*x)*cos_integral((b*d*x + a*d)/b) + (a^4*d^2 - 2*a^2*b^2 + (a^2*b^2*d^2 - 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a*b^3)*x)*cos_integral(-(b*d*x + a*d)/b) + 4*(a*b^3*d*x^2 + 2*a^2*b^2*d*x + a^3*b*d)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^3*b^4*x^2 + 2*a^4*b^3*x + a^5*b^2)","B",0
38,1,689,0,1.221297," ","integrate(sin(d*x+c)/x^2/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a b^{3} d x^{3} + 2 \, a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \operatorname{Ci}\left(d x\right) + {\left(a b^{3} d x^{3} + 2 \, a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \operatorname{Ci}\left(-d x\right) - 6 \, {\left(b^{4} x^{3} + 2 \, a b^{3} x^{2} + a^{2} b^{2} x\right)} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, {\left(2 \, {\left(a b^{3} d x^{3} + 2 \, a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + 2 \, {\left(a b^{3} d x^{3} + 2 \, a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - {\left({\left(a^{2} b^{2} d^{2} - 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} - 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} - 6 \, a^{2} b^{2}\right)} x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(6 \, a b^{3} x^{2} + 9 \, a^{2} b^{2} x + 2 \, a^{3} b\right)} \sin\left(d x + c\right) + 2 \, {\left(3 \, {\left(b^{4} x^{3} + 2 \, a b^{3} x^{2} + a^{2} b^{2} x\right)} \operatorname{Ci}\left(d x\right) + 3 \, {\left(b^{4} x^{3} + 2 \, a b^{3} x^{2} + a^{2} b^{2} x\right)} \operatorname{Ci}\left(-d x\right) + 2 \, {\left(a b^{3} d x^{3} + 2 \, a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right) - {\left({\left({\left(a^{2} b^{2} d^{2} - 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} - 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} - 6 \, a^{2} b^{2}\right)} x\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left({\left(a^{2} b^{2} d^{2} - 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} - 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} - 6 \, a^{2} b^{2}\right)} x\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 8 \, {\left(a b^{3} d x^{3} + 2 \, a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(a^{4} b^{3} x^{3} + 2 \, a^{5} b^{2} x^{2} + a^{6} b x\right)}}"," ",0,"-1/4*(2*(a^2*b^2*d*x^2 + a^3*b*d*x)*cos(d*x + c) - 2*((a*b^3*d*x^3 + 2*a^2*b^2*d*x^2 + a^3*b*d*x)*cos_integral(d*x) + (a*b^3*d*x^3 + 2*a^2*b^2*d*x^2 + a^3*b*d*x)*cos_integral(-d*x) - 6*(b^4*x^3 + 2*a*b^3*x^2 + a^2*b^2*x)*sin_integral(d*x))*cos(c) - 2*(2*(a*b^3*d*x^3 + 2*a^2*b^2*d*x^2 + a^3*b*d*x)*cos_integral((b*d*x + a*d)/b) + 2*(a*b^3*d*x^3 + 2*a^2*b^2*d*x^2 + a^3*b*d*x)*cos_integral(-(b*d*x + a*d)/b) - ((a^2*b^2*d^2 - 6*b^4)*x^3 + 2*(a^3*b*d^2 - 6*a*b^3)*x^2 + (a^4*d^2 - 6*a^2*b^2)*x)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) + 2*(6*a*b^3*x^2 + 9*a^2*b^2*x + 2*a^3*b)*sin(d*x + c) + 2*(3*(b^4*x^3 + 2*a*b^3*x^2 + a^2*b^2*x)*cos_integral(d*x) + 3*(b^4*x^3 + 2*a*b^3*x^2 + a^2*b^2*x)*cos_integral(-d*x) + 2*(a*b^3*d*x^3 + 2*a^2*b^2*d*x^2 + a^3*b*d*x)*sin_integral(d*x))*sin(c) - (((a^2*b^2*d^2 - 6*b^4)*x^3 + 2*(a^3*b*d^2 - 6*a*b^3)*x^2 + (a^4*d^2 - 6*a^2*b^2)*x)*cos_integral((b*d*x + a*d)/b) + ((a^2*b^2*d^2 - 6*b^4)*x^3 + 2*(a^3*b*d^2 - 6*a*b^3)*x^2 + (a^4*d^2 - 6*a^2*b^2)*x)*cos_integral(-(b*d*x + a*d)/b) + 8*(a*b^3*d*x^3 + 2*a^2*b^2*d*x^2 + a^3*b*d*x)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^4*b^3*x^3 + 2*a^5*b^2*x^2 + a^6*b*x)","B",0
39,1,816,0,1.433051," ","integrate(sin(d*x+c)/x^3/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} b d x^{2} + a^{4} d x\right)} \cos\left(d x + c\right) + 2 \, {\left(3 \, {\left(a b^{3} d x^{4} + 2 \, a^{2} b^{2} d x^{3} + a^{3} b d x^{2}\right)} \operatorname{Ci}\left(d x\right) + 3 \, {\left(a b^{3} d x^{4} + 2 \, a^{2} b^{2} d x^{3} + a^{3} b d x^{2}\right)} \operatorname{Ci}\left(-d x\right) + {\left({\left(a^{2} b^{2} d^{2} - 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 12 \, a^{2} b^{2}\right)} x^{2}\right)} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) + 2 \, {\left(3 \, {\left(a b^{3} d x^{4} + 2 \, a^{2} b^{2} d x^{3} + a^{3} b d x^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + 3 \, {\left(a b^{3} d x^{4} + 2 \, a^{2} b^{2} d x^{3} + a^{3} b d x^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) - {\left({\left(a^{2} b^{2} d^{2} - 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 12 \, a^{2} b^{2}\right)} x^{2}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \cos\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(12 \, a b^{3} x^{3} + 18 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x - a^{4}\right)} \sin\left(d x + c\right) + {\left({\left({\left(a^{2} b^{2} d^{2} - 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 12 \, a^{2} b^{2}\right)} x^{2}\right)} \operatorname{Ci}\left(d x\right) + {\left({\left(a^{2} b^{2} d^{2} - 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 12 \, a^{2} b^{2}\right)} x^{2}\right)} \operatorname{Ci}\left(-d x\right) - 12 \, {\left(a b^{3} d x^{4} + 2 \, a^{2} b^{2} d x^{3} + a^{3} b d x^{2}\right)} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right) + {\left({\left({\left(a^{2} b^{2} d^{2} - 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 12 \, a^{2} b^{2}\right)} x^{2}\right)} \operatorname{Ci}\left(\frac{b d x + a d}{b}\right) + {\left({\left(a^{2} b^{2} d^{2} - 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 12 \, a^{2} b^{2}\right)} x^{2}\right)} \operatorname{Ci}\left(-\frac{b d x + a d}{b}\right) + 12 \, {\left(a b^{3} d x^{4} + 2 \, a^{2} b^{2} d x^{3} + a^{3} b d x^{2}\right)} \operatorname{Si}\left(\frac{b d x + a d}{b}\right)\right)} \sin\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}"," ",0,"-1/4*(2*(a^3*b*d*x^2 + a^4*d*x)*cos(d*x + c) + 2*(3*(a*b^3*d*x^4 + 2*a^2*b^2*d*x^3 + a^3*b*d*x^2)*cos_integral(d*x) + 3*(a*b^3*d*x^4 + 2*a^2*b^2*d*x^3 + a^3*b*d*x^2)*cos_integral(-d*x) + ((a^2*b^2*d^2 - 12*b^4)*x^4 + 2*(a^3*b*d^2 - 12*a*b^3)*x^3 + (a^4*d^2 - 12*a^2*b^2)*x^2)*sin_integral(d*x))*cos(c) + 2*(3*(a*b^3*d*x^4 + 2*a^2*b^2*d*x^3 + a^3*b*d*x^2)*cos_integral((b*d*x + a*d)/b) + 3*(a*b^3*d*x^4 + 2*a^2*b^2*d*x^3 + a^3*b*d*x^2)*cos_integral(-(b*d*x + a*d)/b) - ((a^2*b^2*d^2 - 12*b^4)*x^4 + 2*(a^3*b*d^2 - 12*a*b^3)*x^3 + (a^4*d^2 - 12*a^2*b^2)*x^2)*sin_integral((b*d*x + a*d)/b))*cos(-(b*c - a*d)/b) - 2*(12*a*b^3*x^3 + 18*a^2*b^2*x^2 + 4*a^3*b*x - a^4)*sin(d*x + c) + (((a^2*b^2*d^2 - 12*b^4)*x^4 + 2*(a^3*b*d^2 - 12*a*b^3)*x^3 + (a^4*d^2 - 12*a^2*b^2)*x^2)*cos_integral(d*x) + ((a^2*b^2*d^2 - 12*b^4)*x^4 + 2*(a^3*b*d^2 - 12*a*b^3)*x^3 + (a^4*d^2 - 12*a^2*b^2)*x^2)*cos_integral(-d*x) - 12*(a*b^3*d*x^4 + 2*a^2*b^2*d*x^3 + a^3*b*d*x^2)*sin_integral(d*x))*sin(c) + (((a^2*b^2*d^2 - 12*b^4)*x^4 + 2*(a^3*b*d^2 - 12*a*b^3)*x^3 + (a^4*d^2 - 12*a^2*b^2)*x^2)*cos_integral((b*d*x + a*d)/b) + ((a^2*b^2*d^2 - 12*b^4)*x^4 + 2*(a^3*b*d^2 - 12*a*b^3)*x^3 + (a^4*d^2 - 12*a^2*b^2)*x^2)*cos_integral(-(b*d*x + a*d)/b) + 12*(a*b^3*d*x^4 + 2*a^2*b^2*d*x^3 + a^3*b*d*x^2)*sin_integral((b*d*x + a*d)/b))*sin(-(b*c - a*d)/b))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)","B",0
40,1,95,0,1.178104," ","integrate(x^3*(b*x^2+a)*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b d^{5} x^{5} + {\left(a d^{5} - 20 \, b d^{3}\right)} x^{3} - 6 \, {\left(a d^{3} - 20 \, b d\right)} x\right)} \cos\left(d x + c\right) - {\left(5 \, b d^{4} x^{4} - 6 \, a d^{2} + 3 \, {\left(a d^{4} - 20 \, b d^{2}\right)} x^{2} + 120 \, b\right)} \sin\left(d x + c\right)}{d^{6}}"," ",0,"-((b*d^5*x^5 + (a*d^5 - 20*b*d^3)*x^3 - 6*(a*d^3 - 20*b*d)*x)*cos(d*x + c) - (5*b*d^4*x^4 - 6*a*d^2 + 3*(a*d^4 - 20*b*d^2)*x^2 + 120*b)*sin(d*x + c))/d^6","A",0
41,1,77,0,1.189348," ","integrate(x^2*(b*x^2+a)*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b d^{4} x^{4} - 2 \, a d^{2} + {\left(a d^{4} - 12 \, b d^{2}\right)} x^{2} + 24 \, b\right)} \cos\left(d x + c\right) - 2 \, {\left(2 \, b d^{3} x^{3} + {\left(a d^{3} - 12 \, b d\right)} x\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-((b*d^4*x^4 - 2*a*d^2 + (a*d^4 - 12*b*d^2)*x^2 + 24*b)*cos(d*x + c) - 2*(2*b*d^3*x^3 + (a*d^3 - 12*b*d)*x)*sin(d*x + c))/d^5","A",0
42,1,60,0,1.052651," ","integrate(x*(b*x^2+a)*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b d^{3} x^{3} + {\left(a d^{3} - 6 \, b d\right)} x\right)} \cos\left(d x + c\right) - {\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 - 6*b*d)*x)*cos(d*x + c) - (3*b*d^2*x^2 + a*d^2 - 6*b)*sin(d*x + c))/d^4","A",0
43,1,41,0,1.318977," ","integrate((b*x^2+a)*sin(d*x+c),x, algorithm=""fricas"")","\frac{2 \, b d x \sin\left(d x + c\right) - {\left(b d^{2} x^{2} + a d^{2} - 2 \, b\right)} \cos\left(d x + c\right)}{d^{3}}"," ",0,"(2*b*d*x*sin(d*x + c) - (b*d^2*x^2 + a*d^2 - 2*b)*cos(d*x + c))/d^3","A",0
44,1,61,0,0.884123," ","integrate((b*x^2+a)*sin(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, a d^{2} \cos\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, b d x \cos\left(d x + c\right) + 2 \, b \sin\left(d x + c\right) + {\left(a d^{2} \operatorname{Ci}\left(d x\right) + a d^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d^{2}}"," ",0,"1/2*(2*a*d^2*cos(c)*sin_integral(d*x) - 2*b*d*x*cos(d*x + c) + 2*b*sin(d*x + c) + (a*d^2*cos_integral(d*x) + a*d^2*cos_integral(-d*x))*sin(c))/d^2","A",0
45,1,68,0,0.883809," ","integrate((b*x^2+a)*sin(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a d^{2} x \sin\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, b x \cos\left(d x + c\right) + 2 \, a d \sin\left(d x + c\right) - {\left(a d^{2} x \operatorname{Ci}\left(d x\right) + a d^{2} x \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right)}{2 \, d x}"," ",0,"-1/2*(2*a*d^2*x*sin(c)*sin_integral(d*x) + 2*b*x*cos(d*x + c) + 2*a*d*sin(d*x + c) - (a*d^2*x*cos_integral(d*x) + a*d^2*x*cos_integral(-d*x))*cos(c))/(d*x)","A",0
46,1,85,0,1.236974," ","integrate((b*x^2+a)*sin(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a d^{2} - 2 \, b\right)} x^{2} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, a d x \cos\left(d x + c\right) + 2 \, a \sin\left(d x + c\right) + {\left({\left(a d^{2} - 2 \, b\right)} x^{2} \operatorname{Ci}\left(d x\right) + {\left(a d^{2} - 2 \, b\right)} x^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*(a*d^2 - 2*b)*x^2*cos(c)*sin_integral(d*x) + 2*a*d*x*cos(d*x + c) + 2*a*sin(d*x + c) + ((a*d^2 - 2*b)*x^2*cos_integral(d*x) + (a*d^2 - 2*b)*x^2*cos_integral(-d*x))*sin(c))/x^2","A",0
47,1,105,0,1.318491," ","integrate((b*x^2+a)*sin(d*x+c)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(a d^{3} - 6 \, b d\right)} x^{3} \sin\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, a d x \cos\left(d x + c\right) - {\left({\left(a d^{3} - 6 \, b d\right)} x^{3} \operatorname{Ci}\left(d x\right) + {\left(a d^{3} - 6 \, b d\right)} x^{3} \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left({\left(a d^{2} - 6 \, b\right)} x^{2} - 2 \, a\right)} \sin\left(d x + c\right)}{12 \, x^{3}}"," ",0,"1/12*(2*(a*d^3 - 6*b*d)*x^3*sin(c)*sin_integral(d*x) - 2*a*d*x*cos(d*x + c) - ((a*d^3 - 6*b*d)*x^3*cos_integral(d*x) + (a*d^3 - 6*b*d)*x^3*cos_integral(-d*x))*cos(c) + 2*((a*d^2 - 6*b)*x^2 - 2*a)*sin(d*x + c))/x^3","A",0
48,1,127,0,1.115177," ","integrate((b*x^2+a)*sin(d*x+c)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(a d^{4} - 12 \, b d^{2}\right)} x^{4} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, {\left({\left(a d^{3} - 12 \, b d\right)} x^{3} - 2 \, a d x\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(a d^{2} - 12 \, b\right)} x^{2} - 6 \, a\right)} \sin\left(d x + c\right) + {\left({\left(a d^{4} - 12 \, b d^{2}\right)} x^{4} \operatorname{Ci}\left(d x\right) + {\left(a d^{4} - 12 \, b d^{2}\right)} x^{4} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{48 \, x^{4}}"," ",0,"1/48*(2*(a*d^4 - 12*b*d^2)*x^4*cos(c)*sin_integral(d*x) + 2*((a*d^3 - 12*b*d)*x^3 - 2*a*d*x)*cos(d*x + c) + 2*((a*d^2 - 12*b)*x^2 - 6*a)*sin(d*x + c) + ((a*d^4 - 12*b*d^2)*x^4*cos_integral(d*x) + (a*d^4 - 12*b*d^2)*x^4*cos_integral(-d*x))*sin(c))/x^4","A",0
49,1,154,0,1.066602," ","integrate(x^2*(b*x^2+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b^{2} d^{6} x^{6} - 2 \, a^{2} d^{4} + 2 \, {\left(a b d^{6} - 15 \, b^{2} d^{4}\right)} x^{4} + 48 \, a b d^{2} + {\left(a^{2} d^{6} - 24 \, a b d^{4} + 360 \, b^{2} d^{2}\right)} x^{2} - 720 \, b^{2}\right)} \cos\left(d x + c\right) - 2 \, {\left(3 \, b^{2} d^{5} x^{5} + 4 \, {\left(a b d^{5} - 15 \, b^{2} d^{3}\right)} x^{3} + {\left(a^{2} d^{5} - 24 \, a b d^{3} + 360 \, b^{2} d\right)} x\right)} \sin\left(d x + c\right)}{d^{7}}"," ",0,"-((b^2*d^6*x^6 - 2*a^2*d^4 + 2*(a*b*d^6 - 15*b^2*d^4)*x^4 + 48*a*b*d^2 + (a^2*d^6 - 24*a*b*d^4 + 360*b^2*d^2)*x^2 - 720*b^2)*cos(d*x + c) - 2*(3*b^2*d^5*x^5 + 4*(a*b*d^5 - 15*b^2*d^3)*x^3 + (a^2*d^5 - 24*a*b*d^3 + 360*b^2*d)*x)*sin(d*x + c))/d^7","A",0
50,1,126,0,0.976223," ","integrate(x*(b*x^2+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b^{2} d^{5} x^{5} + 2 \, {\left(a b d^{5} - 10 \, b^{2} d^{3}\right)} x^{3} + {\left(a^{2} d^{5} - 12 \, a b d^{3} + 120 \, b^{2} d\right)} x\right)} \cos\left(d x + c\right) - {\left(5 \, b^{2} d^{4} x^{4} + a^{2} d^{4} - 12 \, a b d^{2} + 6 \, {\left(a b d^{4} - 10 \, b^{2} d^{2}\right)} x^{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 - 10*b^2*d^3)*x^3 + (a^2*d^5 - 12*a*b*d^3 + 120*b^2*d)*x)*cos(d*x + c) - (5*b^2*d^4*x^4 + a^2*d^4 - 12*a*b*d^2 + 6*(a*b*d^4 - 10*b^2*d^2)*x^2 + 120*b^2)*sin(d*x + c))/d^6","A",0
51,1,97,0,1.112622," ","integrate((b*x^2+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b^{2} d^{4} x^{4} + a^{2} d^{4} - 4 \, a b d^{2} + 2 \, {\left(a b d^{4} - 6 \, b^{2} d^{2}\right)} x^{2} + 24 \, b^{2}\right)} \cos\left(d x + c\right) - 4 \, {\left(b^{2} d^{3} x^{3} + {\left(a b d^{3} - 6 \, b^{2} d\right)} x\right)} \sin\left(d x + c\right)}{d^{5}}"," ",0,"-((b^2*d^4*x^4 + a^2*d^4 - 4*a*b*d^2 + 2*(a*b*d^4 - 6*b^2*d^2)*x^2 + 24*b^2)*cos(d*x + c) - 4*(b^2*d^3*x^3 + (a*b*d^3 - 6*b^2*d)*x)*sin(d*x + c))/d^5","A",0
52,1,114,0,1.241664," ","integrate((b*x^2+a)^2*sin(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{4} \cos\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, {\left(b^{2} d^{3} x^{3} + 2 \, {\left(a b d^{3} - 3 \, b^{2} d\right)} x\right)} \cos\left(d x + c\right) + 2 \, {\left(3 \, b^{2} d^{2} x^{2} + 2 \, a b d^{2} - 6 \, b^{2}\right)} \sin\left(d x + c\right) + {\left(a^{2} d^{4} \operatorname{Ci}\left(d x\right) + a^{2} d^{4} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d^{4}}"," ",0,"1/2*(2*a^2*d^4*cos(c)*sin_integral(d*x) - 2*(b^2*d^3*x^3 + 2*(a*b*d^3 - 3*b^2*d)*x)*cos(d*x + c) + 2*(3*b^2*d^2*x^2 + 2*a*b*d^2 - 6*b^2)*sin(d*x + c) + (a^2*d^4*cos_integral(d*x) + a^2*d^4*cos_integral(-d*x))*sin(c))/d^4","A",0
53,1,113,0,1.387691," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d^{4} x \sin\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, {\left(b^{2} d^{2} x^{3} + 2 \, {\left(a b d^{2} - b^{2}\right)} x\right)} \cos\left(d x + c\right) - {\left(a^{2} d^{4} x \operatorname{Ci}\left(d x\right) + a^{2} d^{4} x \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left(a^{2} d^{3} - 2 \, b^{2} d x^{2}\right)} \sin\left(d x + c\right)}{2 \, d^{3} x}"," ",0,"-1/2*(2*a^2*d^4*x*sin(c)*sin_integral(d*x) + 2*(b^2*d^2*x^3 + 2*(a*b*d^2 - b^2)*x)*cos(d*x + c) - (a^2*d^4*x*cos_integral(d*x) + a^2*d^4*x*cos_integral(-d*x))*cos(c) + 2*(a^2*d^3 - 2*b^2*d*x^2)*sin(d*x + c))/(d^3*x)","A",0
54,1,136,0,1.191095," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} d^{4} - 4 \, a b d^{2}\right)} x^{2} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, {\left(a^{2} d^{3} x + 2 \, b^{2} d x^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{2} d^{2} - 2 \, b^{2} x^{2}\right)} \sin\left(d x + c\right) + {\left({\left(a^{2} d^{4} - 4 \, a b d^{2}\right)} x^{2} \operatorname{Ci}\left(d x\right) + {\left(a^{2} d^{4} - 4 \, a b d^{2}\right)} x^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{4 \, d^{2} x^{2}}"," ",0,"-1/4*(2*(a^2*d^4 - 4*a*b*d^2)*x^2*cos(c)*sin_integral(d*x) + 2*(a^2*d^3*x + 2*b^2*d*x^3)*cos(d*x + c) + 2*(a^2*d^2 - 2*b^2*x^2)*sin(d*x + c) + ((a^2*d^4 - 4*a*b*d^2)*x^2*cos_integral(d*x) + (a^2*d^4 - 4*a*b*d^2)*x^2*cos_integral(-d*x))*sin(c))/(d^2*x^2)","A",0
55,1,145,0,1.073260," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^4,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d^{4} - 12 \, a b d^{2}\right)} x^{3} \sin\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, {\left(a^{2} d^{2} x + 6 \, b^{2} x^{3}\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} d^{4} - 12 \, a b d^{2}\right)} x^{3} \operatorname{Ci}\left(d x\right) + {\left(a^{2} d^{4} - 12 \, a b d^{2}\right)} x^{3} \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) - 2 \, {\left(2 \, a^{2} d - {\left(a^{2} d^{3} - 12 \, a b d\right)} x^{2}\right)} \sin\left(d x + c\right)}{12 \, d x^{3}}"," ",0,"1/12*(2*(a^2*d^4 - 12*a*b*d^2)*x^3*sin(c)*sin_integral(d*x) - 2*(a^2*d^2*x + 6*b^2*x^3)*cos(d*x + c) - ((a^2*d^4 - 12*a*b*d^2)*x^3*cos_integral(d*x) + (a^2*d^4 - 12*a*b*d^2)*x^3*cos_integral(-d*x))*cos(c) - 2*(2*a^2*d - (a^2*d^3 - 12*a*b*d)*x^2)*sin(d*x + c))/(d*x^3)","A",0
56,1,162,0,1.339705," ","integrate((b*x^2+a)^2*sin(d*x+c)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d^{4} - 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} \cos\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, {\left(2 \, a^{2} d x - {\left(a^{2} d^{3} - 24 \, a b d\right)} x^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left({\left(a^{2} d^{2} - 24 \, a b\right)} x^{2} - 6 \, a^{2}\right)} \sin\left(d x + c\right) + {\left({\left(a^{2} d^{4} - 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} \operatorname{Ci}\left(d x\right) + {\left(a^{2} d^{4} - 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{48 \, x^{4}}"," ",0,"1/48*(2*(a^2*d^4 - 24*a*b*d^2 + 24*b^2)*x^4*cos(c)*sin_integral(d*x) - 2*(2*a^2*d*x - (a^2*d^3 - 24*a*b*d)*x^3)*cos(d*x + c) + 2*((a^2*d^2 - 24*a*b)*x^2 - 6*a^2)*sin(d*x + c) + ((a^2*d^4 - 24*a*b*d^2 + 24*b^2)*x^4*cos_integral(d*x) + (a^2*d^4 - 24*a*b*d^2 + 24*b^2)*x^4*cos_integral(-d*x))*sin(c))/x^4","A",0
57,1,240,0,1.401009," ","integrate(x^4*sin(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a d^{2}}{b}} a d^{2} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} a d^{2} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + \sqrt{\frac{a d^{2}}{b}} a d^{2} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} a d^{2} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + 8 \, b d x \sin\left(d x + c\right) - 4 \, {\left(b d^{2} x^{2} - a d^{2} - 2 \, b\right)} \cos\left(d x + c\right)}{4 \, b^{2} d^{3}}"," ",0,"1/4*(sqrt(a*d^2/b)*a*d^2*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - sqrt(a*d^2/b)*a*d^2*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + sqrt(a*d^2/b)*a*d^2*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - sqrt(a*d^2/b)*a*d^2*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) + 8*b*d*x*sin(d*x + c) - 4*(b*d^2*x^2 - a*d^2 - 2*b)*cos(d*x + c))/(b^2*d^3)","C",0
58,1,185,0,1.209192," ","integrate(x^3*sin(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{i \, a d^{2} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + i \, a d^{2} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - i \, a d^{2} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - i \, a d^{2} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 4 \, b d x \cos\left(d x + c\right) + 4 \, b \sin\left(d x + c\right)}{4 \, b^{2} d^{2}}"," ",0,"1/4*(I*a*d^2*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + I*a*d^2*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - I*a*d^2*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - I*a*d^2*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 4*b*d*x*cos(d*x + c) + 4*b*sin(d*x + c))/(b^2*d^2)","C",0
59,1,195,0,1.143097," ","integrate(x^2*sin(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{\sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + 4 \, \cos\left(d x + c\right)}{4 \, b d}"," ",0,"-1/4*(sqrt(a*d^2/b)*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - sqrt(a*d^2/b)*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + sqrt(a*d^2/b)*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - sqrt(a*d^2/b)*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) + 4*cos(d*x + c))/(b*d)","C",0
60,1,146,0,1.403818," ","integrate(x*sin(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{-i \, {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - i \, {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + i \, {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + i \, {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)}}{4 \, b}"," ",0,"1/4*(-I*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - I*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + I*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + I*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)))/b","C",0
61,1,187,0,1.354812," ","integrate(sin(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)}}{4 \, a d}"," ",0,"1/4*(sqrt(a*d^2/b)*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - sqrt(a*d^2/b)*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + sqrt(a*d^2/b)*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - sqrt(a*d^2/b)*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)))/(a*d)","C",0
62,1,168,0,1.408857," ","integrate(sin(d*x+c)/x/(b*x^2+a),x, algorithm=""fricas"")","\frac{-2 i \, {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 2 i \, {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + i \, {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + i \, {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - i \, {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - i \, {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)}}{4 \, a}"," ",0,"1/4*(-2*I*Ei(I*d*x)*e^(I*c) + 2*I*Ei(-I*d*x)*e^(-I*c) + I*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + I*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - I*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - I*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)))/a","C",0
63,1,240,0,1.413356," ","integrate(sin(d*x+c)/x^2/(b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, a d^{2} x {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 2 \, a d^{2} x {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} - \sqrt{\frac{a d^{2}}{b}} b x {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + \sqrt{\frac{a d^{2}}{b}} b x {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - \sqrt{\frac{a d^{2}}{b}} b x {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + \sqrt{\frac{a d^{2}}{b}} b x {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 4 \, a d \sin\left(d x + c\right)}{4 \, a^{2} d x}"," ",0,"1/4*(2*a*d^2*x*Ei(I*d*x)*e^(I*c) + 2*a*d^2*x*Ei(-I*d*x)*e^(-I*c) - sqrt(a*d^2/b)*b*x*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + sqrt(a*d^2/b)*b*x*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - sqrt(a*d^2/b)*b*x*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + sqrt(a*d^2/b)*b*x*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 4*a*d*sin(d*x + c))/(a^2*d*x)","C",0
64,1,231,0,1.098799," ","integrate(sin(d*x+c)/x^3/(b*x^2+a),x, algorithm=""fricas"")","\frac{i \, {\left(a d^{2} + 2 \, b\right)} x^{2} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} - i \, {\left(a d^{2} + 2 \, b\right)} x^{2} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} - i \, b x^{2} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - i \, b x^{2} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + i \, b x^{2} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + i \, b x^{2} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 2 \, a d x \cos\left(d x + c\right) - 2 \, a \sin\left(d x + c\right)}{4 \, a^{2} x^{2}}"," ",0,"1/4*(I*(a*d^2 + 2*b)*x^2*Ei(I*d*x)*e^(I*c) - I*(a*d^2 + 2*b)*x^2*Ei(-I*d*x)*e^(-I*c) - I*b*x^2*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - I*b*x^2*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + I*b*x^2*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + I*b*x^2*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 2*a*d*x*cos(d*x + c) - 2*a*sin(d*x + c))/(a^2*x^2)","C",0
65,1,351,0,1.046895," ","integrate(x^4*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, a b d x \sin\left(d x + c\right) - {\left(a b d^{2} x^{2} + a^{2} d^{2} + 3 \, {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} - 3 \, {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} + 3 \, {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} - 3 \, {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 8 \, {\left(b^{2} x^{2} + a b\right)} \cos\left(d x + c\right)}{8 \, {\left(b^{4} d x^{2} + a b^{3} d\right)}}"," ",0,"1/8*(4*a*b*d*x*sin(d*x + c) - (a*b*d^2*x^2 + a^2*d^2 + 3*(b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 - 3*(b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 + 3*(b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 - 3*(b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 8*(b^2*x^2 + a*b)*cos(d*x + c))/(b^4*d*x^2 + a*b^3*d)","C",0
66,1,291,0,1.325057," ","integrate(x^3*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(-4 i \, b x^{2} + 2 \, {\left(-i \, b x^{2} - i \, a\right)} \sqrt{\frac{a d^{2}}{b}} - 4 i \, a\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-4 i \, b x^{2} + 2 \, {\left(i \, b x^{2} + i \, a\right)} \sqrt{\frac{a d^{2}}{b}} - 4 i \, a\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(4 i \, b x^{2} + 2 \, {\left(i \, b x^{2} + i \, a\right)} \sqrt{\frac{a d^{2}}{b}} + 4 i \, a\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(4 i \, b x^{2} + 2 \, {\left(-i \, b x^{2} - i \, a\right)} \sqrt{\frac{a d^{2}}{b}} + 4 i \, a\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + 8 \, a \sin\left(d x + c\right)}{16 \, {\left(b^{3} x^{2} + a b^{2}\right)}}"," ",0,"1/16*((-4*I*b*x^2 + 2*(-I*b*x^2 - I*a)*sqrt(a*d^2/b) - 4*I*a)*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (-4*I*b*x^2 + 2*(I*b*x^2 + I*a)*sqrt(a*d^2/b) - 4*I*a)*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (4*I*b*x^2 + 2*(I*b*x^2 + I*a)*sqrt(a*d^2/b) + 4*I*a)*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (4*I*b*x^2 + 2*(-I*b*x^2 - I*a)*sqrt(a*d^2/b) + 4*I*a)*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) + 8*a*sin(d*x + c))/(b^3*x^2 + a*b^2)","C",0
67,1,333,0,1.093701," ","integrate(x^2*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{4 \, a b d x \sin\left(d x + c\right) - {\left(a b d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} - {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} - {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)}}{8 \, {\left(a b^{3} d x^{2} + a^{2} b^{2} d\right)}}"," ",0,"-1/8*(4*a*b*d*x*sin(d*x + c) - (a*b*d^2*x^2 + a^2*d^2 + (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 - (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 + (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 - (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)))/(a*b^3*d*x^2 + a^2*b^2*d)","C",0
68,1,244,0,1.361252," ","integrate(x*sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(i \, b x^{2} + i \, a\right)} \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-i \, b x^{2} - i \, a\right)} \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-i \, b x^{2} - i \, a\right)} \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(i \, b x^{2} + i \, a\right)} \sqrt{\frac{a d^{2}}{b}} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 4 \, a \sin\left(d x + c\right)}{8 \, {\left(a b^{2} x^{2} + a^{2} b\right)}}"," ",0,"1/8*((I*b*x^2 + I*a)*sqrt(a*d^2/b)*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (-I*b*x^2 - I*a)*sqrt(a*d^2/b)*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (-I*b*x^2 - I*a)*sqrt(a*d^2/b)*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (I*b*x^2 + I*a)*sqrt(a*d^2/b)*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 4*a*sin(d*x + c))/(a*b^2*x^2 + a^2*b)","C",0
69,1,333,0,1.444971," ","integrate(sin(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, a b d x \sin\left(d x + c\right) - {\left(a b d^{2} x^{2} + a^{2} d^{2} - {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} - {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(a b d^{2} x^{2} + a^{2} d^{2} + {\left(b^{2} x^{2} + a b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)}}{8 \, {\left(a^{2} b^{2} d x^{2} + a^{3} b d\right)}}"," ",0,"1/8*(4*a*b*d*x*sin(d*x + c) - (a*b*d^2*x^2 + a^2*d^2 - (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 + (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 - (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - (a*b*d^2*x^2 + a^2*d^2 + (b^2*x^2 + a*b)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)))/(a^2*b^2*d*x^2 + a^3*b*d)","C",0
70,1,330,0,1.286241," ","integrate(sin(d*x+c)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{{\left(-8 i \, b x^{2} - 8 i \, a\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + {\left(8 i \, b x^{2} + 8 i \, a\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(4 i \, b x^{2} + 2 \, {\left(-i \, b x^{2} - i \, a\right)} \sqrt{\frac{a d^{2}}{b}} + 4 i \, a\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(4 i \, b x^{2} + 2 \, {\left(i \, b x^{2} + i \, a\right)} \sqrt{\frac{a d^{2}}{b}} + 4 i \, a\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-4 i \, b x^{2} + 2 \, {\left(i \, b x^{2} + i \, a\right)} \sqrt{\frac{a d^{2}}{b}} - 4 i \, a\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-4 i \, b x^{2} + 2 \, {\left(-i \, b x^{2} - i \, a\right)} \sqrt{\frac{a d^{2}}{b}} - 4 i \, a\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + 8 \, a \sin\left(d x + c\right)}{16 \, {\left(a^{2} b x^{2} + a^{3}\right)}}"," ",0,"1/16*((-8*I*b*x^2 - 8*I*a)*Ei(I*d*x)*e^(I*c) + (8*I*b*x^2 + 8*I*a)*Ei(-I*d*x)*e^(-I*c) + (4*I*b*x^2 + 2*(-I*b*x^2 - I*a)*sqrt(a*d^2/b) + 4*I*a)*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (4*I*b*x^2 + 2*(I*b*x^2 + I*a)*sqrt(a*d^2/b) + 4*I*a)*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (-4*I*b*x^2 + 2*(I*b*x^2 + I*a)*sqrt(a*d^2/b) - 4*I*a)*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (-4*I*b*x^2 + 2*(-I*b*x^2 - I*a)*sqrt(a*d^2/b) - 4*I*a)*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) + 8*a*sin(d*x + c))/(a^2*b*x^2 + a^3)","C",0
71,1,406,0,1.409151," ","integrate(sin(d*x+c)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 4 \, {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(a b d^{2} x^{3} + a^{2} d^{2} x - 3 \, {\left(b^{2} x^{3} + a b x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(a b d^{2} x^{3} + a^{2} d^{2} x + 3 \, {\left(b^{2} x^{3} + a b x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(a b d^{2} x^{3} + a^{2} d^{2} x - 3 \, {\left(b^{2} x^{3} + a b x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(a b d^{2} x^{3} + a^{2} d^{2} x + 3 \, {\left(b^{2} x^{3} + a b x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 4 \, {\left(3 \, a b d x^{2} + 2 \, a^{2} d\right)} \sin\left(d x + c\right)}{8 \, {\left(a^{3} b d x^{3} + a^{4} d x\right)}}"," ",0,"1/8*(4*(a*b*d^2*x^3 + a^2*d^2*x)*Ei(I*d*x)*e^(I*c) + 4*(a*b*d^2*x^3 + a^2*d^2*x)*Ei(-I*d*x)*e^(-I*c) + (a*b*d^2*x^3 + a^2*d^2*x - 3*(b^2*x^3 + a*b*x)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (a*b*d^2*x^3 + a^2*d^2*x + 3*(b^2*x^3 + a*b*x)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (a*b*d^2*x^3 + a^2*d^2*x - 3*(b^2*x^3 + a*b*x)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (a*b*d^2*x^3 + a^2*d^2*x + 3*(b^2*x^3 + a*b*x)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 4*(3*a*b*d*x^2 + 2*a^2*d)*sin(d*x + c))/(a^3*b*d*x^3 + a^4*d*x)","C",0
72,1,492,0,1.512786," ","integrate(x^3*sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(2 i \, a b^{2} d^{2} x^{4} + 4 i \, a^{2} b d^{2} x^{2} + 2 i \, a^{3} d^{2} + 2 \, {\left(3 i \, b^{3} x^{4} + 6 i \, a b^{2} x^{2} + 3 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(2 i \, a b^{2} d^{2} x^{4} + 4 i \, a^{2} b d^{2} x^{2} + 2 i \, a^{3} d^{2} + 2 \, {\left(-3 i \, b^{3} x^{4} - 6 i \, a b^{2} x^{2} - 3 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-2 i \, a b^{2} d^{2} x^{4} - 4 i \, a^{2} b d^{2} x^{2} - 2 i \, a^{3} d^{2} + 2 \, {\left(-3 i \, b^{3} x^{4} - 6 i \, a b^{2} x^{2} - 3 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-2 i \, a b^{2} d^{2} x^{4} - 4 i \, a^{2} b d^{2} x^{2} - 2 i \, a^{3} d^{2} + 2 \, {\left(3 i \, b^{3} x^{4} + 6 i \, a b^{2} x^{2} + 3 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 8 \, {\left(a b^{2} d x^{3} + a^{2} b d x\right)} \cos\left(d x + c\right) - 16 \, {\left(2 \, a b^{2} x^{2} + a^{2} b\right)} \sin\left(d x + c\right)}{64 \, {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)}}"," ",0,"1/64*((2*I*a*b^2*d^2*x^4 + 4*I*a^2*b*d^2*x^2 + 2*I*a^3*d^2 + 2*(3*I*b^3*x^4 + 6*I*a*b^2*x^2 + 3*I*a^2*b)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (2*I*a*b^2*d^2*x^4 + 4*I*a^2*b*d^2*x^2 + 2*I*a^3*d^2 + 2*(-3*I*b^3*x^4 - 6*I*a*b^2*x^2 - 3*I*a^2*b)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (-2*I*a*b^2*d^2*x^4 - 4*I*a^2*b*d^2*x^2 - 2*I*a^3*d^2 + 2*(-3*I*b^3*x^4 - 6*I*a*b^2*x^2 - 3*I*a^2*b)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (-2*I*a*b^2*d^2*x^4 - 4*I*a^2*b*d^2*x^2 - 2*I*a^3*d^2 + 2*(3*I*b^3*x^4 + 6*I*a*b^2*x^2 + 3*I*a^2*b)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 8*(a*b^2*d*x^3 + a^2*b*d*x)*cos(d*x + c) - 16*(2*a*b^2*x^2 + a^2*b)*sin(d*x + c))/(a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3)","C",0
73,1,604,0,1.343389," ","integrate(x^2*sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2} + {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - b^{3}\right)} x^{4} - a^{2} b + 2 \, {\left(a^{2} b d^{2} - a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - b^{3}\right)} x^{4} - a^{2} b + 2 \, {\left(a^{2} b d^{2} - a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2} + {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - b^{3}\right)} x^{4} - a^{2} b + 2 \, {\left(a^{2} b d^{2} - a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - b^{3}\right)} x^{4} - a^{2} b + 2 \, {\left(a^{2} b d^{2} - a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + 4 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cos\left(d x + c\right) - 4 \, {\left(a b^{2} d x^{3} - a^{2} b d x\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{2} b^{4} d x^{4} + 2 \, a^{3} b^{3} d x^{2} + a^{4} b^{2} d\right)}}"," ",0,"-1/32*((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2 + (a^3*d^2 + (a*b^2*d^2 - b^3)*x^4 - a^2*b + 2*(a^2*b*d^2 - a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2 - (a^3*d^2 + (a*b^2*d^2 - b^3)*x^4 - a^2*b + 2*(a^2*b*d^2 - a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2 + (a^3*d^2 + (a*b^2*d^2 - b^3)*x^4 - a^2*b + 2*(a^2*b*d^2 - a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2 - (a^3*d^2 + (a*b^2*d^2 - b^3)*x^4 - a^2*b + 2*(a^2*b*d^2 - a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) + 4*(a^2*b*d^2*x^2 + a^3*d^2)*cos(d*x + c) - 4*(a*b^2*d*x^3 - a^2*b*d*x)*sin(d*x + c))/(a^2*b^4*d*x^4 + 2*a^3*b^3*d*x^2 + a^4*b^2*d)","C",0
74,1,487,0,1.346294," ","integrate(x*sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{16 \, a^{2} b \sin\left(d x + c\right) - {\left(-2 i \, a b^{2} d^{2} x^{4} - 4 i \, a^{2} b d^{2} x^{2} - 2 i \, a^{3} d^{2} + 2 \, {\left(i \, b^{3} x^{4} + 2 i \, a b^{2} x^{2} + i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(-2 i \, a b^{2} d^{2} x^{4} - 4 i \, a^{2} b d^{2} x^{2} - 2 i \, a^{3} d^{2} + 2 \, {\left(-i \, b^{3} x^{4} - 2 i \, a b^{2} x^{2} - i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(2 i \, a b^{2} d^{2} x^{4} + 4 i \, a^{2} b d^{2} x^{2} + 2 i \, a^{3} d^{2} + 2 \, {\left(-i \, b^{3} x^{4} - 2 i \, a b^{2} x^{2} - i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} - {\left(2 i \, a b^{2} d^{2} x^{4} + 4 i \, a^{2} b d^{2} x^{2} + 2 i \, a^{3} d^{2} + 2 \, {\left(i \, b^{3} x^{4} + 2 i \, a b^{2} x^{2} + i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 8 \, {\left(a b^{2} d x^{3} + a^{2} b d x\right)} \cos\left(d x + c\right)}{64 \, {\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)}}"," ",0,"-1/64*(16*a^2*b*sin(d*x + c) - (-2*I*a*b^2*d^2*x^4 - 4*I*a^2*b*d^2*x^2 - 2*I*a^3*d^2 + 2*(I*b^3*x^4 + 2*I*a*b^2*x^2 + I*a^2*b)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) - (-2*I*a*b^2*d^2*x^4 - 4*I*a^2*b*d^2*x^2 - 2*I*a^3*d^2 + 2*(-I*b^3*x^4 - 2*I*a*b^2*x^2 - I*a^2*b)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) - (2*I*a*b^2*d^2*x^4 + 4*I*a^2*b*d^2*x^2 + 2*I*a^3*d^2 + 2*(-I*b^3*x^4 - 2*I*a*b^2*x^2 - I*a^2*b)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) - (2*I*a*b^2*d^2*x^4 + 4*I*a^2*b*d^2*x^2 + 2*I*a^3*d^2 + 2*(I*b^3*x^4 + 2*I*a*b^2*x^2 + I*a^2*b)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 8*(a*b^2*d*x^3 + a^2*b*d*x)*cos(d*x + c))/(a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2)","C",0
75,1,611,0,1.168448," ","integrate(sin(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a b^{2} d^{2} x^{4} + 6 \, a^{2} b d^{2} x^{2} + 3 \, a^{3} d^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + 3 \, b^{3}\right)} x^{4} + 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} + 3 \, a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(3 \, a b^{2} d^{2} x^{4} + 6 \, a^{2} b d^{2} x^{2} + 3 \, a^{3} d^{2} + {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + 3 \, b^{3}\right)} x^{4} + 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} + 3 \, a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(3 \, a b^{2} d^{2} x^{4} + 6 \, a^{2} b d^{2} x^{2} + 3 \, a^{3} d^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + 3 \, b^{3}\right)} x^{4} + 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} + 3 \, a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(3 \, a b^{2} d^{2} x^{4} + 6 \, a^{2} b d^{2} x^{2} + 3 \, a^{3} d^{2} + {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + 3 \, b^{3}\right)} x^{4} + 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} + 3 \, a b^{2}\right)} x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 4 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cos\left(d x + c\right) - 4 \, {\left(3 \, a b^{2} d x^{3} + 5 \, a^{2} b d x\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{3} b^{3} d x^{4} + 2 \, a^{4} b^{2} d x^{2} + a^{5} b d\right)}}"," ",0,"-1/32*((3*a*b^2*d^2*x^4 + 6*a^2*b*d^2*x^2 + 3*a^3*d^2 - (a^3*d^2 + (a*b^2*d^2 + 3*b^3)*x^4 + 3*a^2*b + 2*(a^2*b*d^2 + 3*a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (3*a*b^2*d^2*x^4 + 6*a^2*b*d^2*x^2 + 3*a^3*d^2 + (a^3*d^2 + (a*b^2*d^2 + 3*b^3)*x^4 + 3*a^2*b + 2*(a^2*b*d^2 + 3*a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (3*a*b^2*d^2*x^4 + 6*a^2*b*d^2*x^2 + 3*a^3*d^2 - (a^3*d^2 + (a*b^2*d^2 + 3*b^3)*x^4 + 3*a^2*b + 2*(a^2*b*d^2 + 3*a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (3*a*b^2*d^2*x^4 + 6*a^2*b*d^2*x^2 + 3*a^3*d^2 + (a^3*d^2 + (a*b^2*d^2 + 3*b^3)*x^4 + 3*a^2*b + 2*(a^2*b*d^2 + 3*a*b^2)*x^2)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 4*(a^2*b*d^2*x^2 + a^3*d^2)*cos(d*x + c) - 4*(3*a*b^2*d*x^3 + 5*a^2*b*d*x)*sin(d*x + c))/(a^3*b^3*d*x^4 + 2*a^4*b^2*d*x^2 + a^5*b*d)","C",0
76,1,645,0,1.253323," ","integrate(sin(d*x+c)/x/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(-32 i \, b^{3} x^{4} - 64 i \, a b^{2} x^{2} - 32 i \, a^{2} b\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + {\left(32 i \, b^{3} x^{4} + 64 i \, a b^{2} x^{2} + 32 i \, a^{2} b\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(2 i \, a^{3} d^{2} + 2 i \, {\left(a b^{2} d^{2} + 8 \, b^{3}\right)} x^{4} + 16 i \, a^{2} b + 4 i \, {\left(a^{2} b d^{2} + 8 \, a b^{2}\right)} x^{2} + 2 \, {\left(-5 i \, b^{3} x^{4} - 10 i \, a b^{2} x^{2} - 5 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(2 i \, a^{3} d^{2} + 2 i \, {\left(a b^{2} d^{2} + 8 \, b^{3}\right)} x^{4} + 16 i \, a^{2} b + 4 i \, {\left(a^{2} b d^{2} + 8 \, a b^{2}\right)} x^{2} + 2 \, {\left(5 i \, b^{3} x^{4} + 10 i \, a b^{2} x^{2} + 5 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-2 i \, a^{3} d^{2} - 2 i \, {\left(a b^{2} d^{2} + 8 \, b^{3}\right)} x^{4} - 16 i \, a^{2} b - 4 i \, {\left(a^{2} b d^{2} + 8 \, a b^{2}\right)} x^{2} + 2 \, {\left(5 i \, b^{3} x^{4} + 10 i \, a b^{2} x^{2} + 5 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-2 i \, a^{3} d^{2} - 2 i \, {\left(a b^{2} d^{2} + 8 \, b^{3}\right)} x^{4} - 16 i \, a^{2} b - 4 i \, {\left(a^{2} b d^{2} + 8 \, a b^{2}\right)} x^{2} + 2 \, {\left(-5 i \, b^{3} x^{4} - 10 i \, a b^{2} x^{2} - 5 i \, a^{2} b\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 8 \, {\left(a b^{2} d x^{3} + a^{2} b d x\right)} \cos\left(d x + c\right) + 16 \, {\left(2 \, a b^{2} x^{2} + 3 \, a^{2} b\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)}}"," ",0,"1/64*((-32*I*b^3*x^4 - 64*I*a*b^2*x^2 - 32*I*a^2*b)*Ei(I*d*x)*e^(I*c) + (32*I*b^3*x^4 + 64*I*a*b^2*x^2 + 32*I*a^2*b)*Ei(-I*d*x)*e^(-I*c) + (2*I*a^3*d^2 + 2*I*(a*b^2*d^2 + 8*b^3)*x^4 + 16*I*a^2*b + 4*I*(a^2*b*d^2 + 8*a*b^2)*x^2 + 2*(-5*I*b^3*x^4 - 10*I*a*b^2*x^2 - 5*I*a^2*b)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (2*I*a^3*d^2 + 2*I*(a*b^2*d^2 + 8*b^3)*x^4 + 16*I*a^2*b + 4*I*(a^2*b*d^2 + 8*a*b^2)*x^2 + 2*(5*I*b^3*x^4 + 10*I*a*b^2*x^2 + 5*I*a^2*b)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (-2*I*a^3*d^2 - 2*I*(a*b^2*d^2 + 8*b^3)*x^4 - 16*I*a^2*b - 4*I*(a^2*b*d^2 + 8*a*b^2)*x^2 + 2*(5*I*b^3*x^4 + 10*I*a*b^2*x^2 + 5*I*a^2*b)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (-2*I*a^3*d^2 - 2*I*(a*b^2*d^2 + 8*b^3)*x^4 - 16*I*a^2*b - 4*I*(a^2*b*d^2 + 8*a*b^2)*x^2 + 2*(-5*I*b^3*x^4 - 10*I*a*b^2*x^2 - 5*I*a^2*b)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 8*(a*b^2*d*x^3 + a^2*b*d*x)*cos(d*x + c) + 16*(2*a*b^2*x^2 + 3*a^2*b)*sin(d*x + c))/(a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)","C",0
77,1,720,0,1.476269," ","integrate(sin(d*x+c)/x^2/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{16 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 16 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(7 \, a b^{2} d^{2} x^{5} + 14 \, a^{2} b d^{2} x^{3} + 7 \, a^{3} d^{2} x - {\left({\left(a b^{2} d^{2} + 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} + 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} + 15 \, a^{2} b\right)} x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(7 \, a b^{2} d^{2} x^{5} + 14 \, a^{2} b d^{2} x^{3} + 7 \, a^{3} d^{2} x + {\left({\left(a b^{2} d^{2} + 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} + 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} + 15 \, a^{2} b\right)} x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(7 \, a b^{2} d^{2} x^{5} + 14 \, a^{2} b d^{2} x^{3} + 7 \, a^{3} d^{2} x - {\left({\left(a b^{2} d^{2} + 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} + 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} + 15 \, a^{2} b\right)} x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(7 \, a b^{2} d^{2} x^{5} + 14 \, a^{2} b d^{2} x^{3} + 7 \, a^{3} d^{2} x + {\left({\left(a b^{2} d^{2} + 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} + 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} + 15 \, a^{2} b\right)} x\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 4 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cos\left(d x + c\right) - 4 \, {\left(15 \, a b^{2} d x^{4} + 25 \, a^{2} b d x^{2} + 8 \, a^{3} d\right)} \sin\left(d x + c\right)}{32 \, {\left(a^{4} b^{2} d x^{5} + 2 \, a^{5} b d x^{3} + a^{6} d x\right)}}"," ",0,"1/32*(16*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*Ei(I*d*x)*e^(I*c) + 16*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*Ei(-I*d*x)*e^(-I*c) + (7*a*b^2*d^2*x^5 + 14*a^2*b*d^2*x^3 + 7*a^3*d^2*x - ((a*b^2*d^2 + 15*b^3)*x^5 + 2*(a^2*b*d^2 + 15*a*b^2)*x^3 + (a^3*d^2 + 15*a^2*b)*x)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (7*a*b^2*d^2*x^5 + 14*a^2*b*d^2*x^3 + 7*a^3*d^2*x + ((a*b^2*d^2 + 15*b^3)*x^5 + 2*(a^2*b*d^2 + 15*a*b^2)*x^3 + (a^3*d^2 + 15*a^2*b)*x)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (7*a*b^2*d^2*x^5 + 14*a^2*b*d^2*x^3 + 7*a^3*d^2*x - ((a*b^2*d^2 + 15*b^3)*x^5 + 2*(a^2*b*d^2 + 15*a*b^2)*x^3 + (a^3*d^2 + 15*a^2*b)*x)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (7*a*b^2*d^2*x^5 + 14*a^2*b*d^2*x^3 + 7*a^3*d^2*x + ((a*b^2*d^2 + 15*b^3)*x^5 + 2*(a^2*b*d^2 + 15*a*b^2)*x^3 + (a^3*d^2 + 15*a^2*b)*x)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 4*(a^2*b*d^2*x^3 + a^3*d^2*x)*cos(d*x + c) - 4*(15*a*b^2*d*x^4 + 25*a^2*b*d*x^2 + 8*a^3*d)*sin(d*x + c))/(a^4*b^2*d*x^5 + 2*a^5*b*d*x^3 + a^6*d*x)","C",0
78,1,766,0,1.217240," ","integrate(sin(d*x+c)/x^3/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(16 i \, {\left(a b^{2} d^{2} + 6 \, b^{3}\right)} x^{6} + 32 i \, {\left(a^{2} b d^{2} + 6 \, a b^{2}\right)} x^{4} + 16 i \, {\left(a^{3} d^{2} + 6 \, a^{2} b\right)} x^{2}\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + {\left(-16 i \, {\left(a b^{2} d^{2} + 6 \, b^{3}\right)} x^{6} - 32 i \, {\left(a^{2} b d^{2} + 6 \, a b^{2}\right)} x^{4} - 16 i \, {\left(a^{3} d^{2} + 6 \, a^{2} b\right)} x^{2}\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(-2 i \, {\left(a b^{2} d^{2} + 24 \, b^{3}\right)} x^{6} - 4 i \, {\left(a^{2} b d^{2} + 24 \, a b^{2}\right)} x^{4} - 2 i \, {\left(a^{3} d^{2} + 24 \, a^{2} b\right)} x^{2} + 2 \, {\left(9 i \, b^{3} x^{6} + 18 i \, a b^{2} x^{4} + 9 i \, a^{2} b x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(-2 i \, {\left(a b^{2} d^{2} + 24 \, b^{3}\right)} x^{6} - 4 i \, {\left(a^{2} b d^{2} + 24 \, a b^{2}\right)} x^{4} - 2 i \, {\left(a^{3} d^{2} + 24 \, a^{2} b\right)} x^{2} + 2 \, {\left(-9 i \, b^{3} x^{6} - 18 i \, a b^{2} x^{4} - 9 i \, a^{2} b x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(2 i \, {\left(a b^{2} d^{2} + 24 \, b^{3}\right)} x^{6} + 4 i \, {\left(a^{2} b d^{2} + 24 \, a b^{2}\right)} x^{4} + 2 i \, {\left(a^{3} d^{2} + 24 \, a^{2} b\right)} x^{2} + 2 \, {\left(-9 i \, b^{3} x^{6} - 18 i \, a b^{2} x^{4} - 9 i \, a^{2} b x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x - \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c + \sqrt{\frac{a d^{2}}{b}}\right)} + {\left(2 i \, {\left(a b^{2} d^{2} + 24 \, b^{3}\right)} x^{6} + 4 i \, {\left(a^{2} b d^{2} + 24 \, a b^{2}\right)} x^{4} + 2 i \, {\left(a^{3} d^{2} + 24 \, a^{2} b\right)} x^{2} + 2 \, {\left(9 i \, b^{3} x^{6} + 18 i \, a b^{2} x^{4} + 9 i \, a^{2} b x^{2}\right)} \sqrt{\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-i \, d x + \sqrt{\frac{a d^{2}}{b}}\right) e^{\left(-i \, c - \sqrt{\frac{a d^{2}}{b}}\right)} - 8 \, {\left(3 \, a b^{2} d x^{5} + 7 \, a^{2} b d x^{3} + 4 \, a^{3} d x\right)} \cos\left(d x + c\right) - 16 \, {\left(6 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}\right)} \sin\left(d x + c\right)}{64 \, {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)}}"," ",0,"1/64*((16*I*(a*b^2*d^2 + 6*b^3)*x^6 + 32*I*(a^2*b*d^2 + 6*a*b^2)*x^4 + 16*I*(a^3*d^2 + 6*a^2*b)*x^2)*Ei(I*d*x)*e^(I*c) + (-16*I*(a*b^2*d^2 + 6*b^3)*x^6 - 32*I*(a^2*b*d^2 + 6*a*b^2)*x^4 - 16*I*(a^3*d^2 + 6*a^2*b)*x^2)*Ei(-I*d*x)*e^(-I*c) + (-2*I*(a*b^2*d^2 + 24*b^3)*x^6 - 4*I*(a^2*b*d^2 + 24*a*b^2)*x^4 - 2*I*(a^3*d^2 + 24*a^2*b)*x^2 + 2*(9*I*b^3*x^6 + 18*I*a*b^2*x^4 + 9*I*a^2*b*x^2)*sqrt(a*d^2/b))*Ei(I*d*x - sqrt(a*d^2/b))*e^(I*c + sqrt(a*d^2/b)) + (-2*I*(a*b^2*d^2 + 24*b^3)*x^6 - 4*I*(a^2*b*d^2 + 24*a*b^2)*x^4 - 2*I*(a^3*d^2 + 24*a^2*b)*x^2 + 2*(-9*I*b^3*x^6 - 18*I*a*b^2*x^4 - 9*I*a^2*b*x^2)*sqrt(a*d^2/b))*Ei(I*d*x + sqrt(a*d^2/b))*e^(I*c - sqrt(a*d^2/b)) + (2*I*(a*b^2*d^2 + 24*b^3)*x^6 + 4*I*(a^2*b*d^2 + 24*a*b^2)*x^4 + 2*I*(a^3*d^2 + 24*a^2*b)*x^2 + 2*(-9*I*b^3*x^6 - 18*I*a*b^2*x^4 - 9*I*a^2*b*x^2)*sqrt(a*d^2/b))*Ei(-I*d*x - sqrt(a*d^2/b))*e^(-I*c + sqrt(a*d^2/b)) + (2*I*(a*b^2*d^2 + 24*b^3)*x^6 + 4*I*(a^2*b*d^2 + 24*a*b^2)*x^4 + 2*I*(a^3*d^2 + 24*a^2*b)*x^2 + 2*(9*I*b^3*x^6 + 18*I*a*b^2*x^4 + 9*I*a^2*b*x^2)*sqrt(a*d^2/b))*Ei(-I*d*x + sqrt(a*d^2/b))*e^(-I*c - sqrt(a*d^2/b)) - 8*(3*a*b^2*d*x^5 + 7*a^2*b*d*x^3 + 4*a^3*d*x)*cos(d*x + c) - 16*(6*a*b^2*x^4 + 9*a^2*b*x^2 + 2*a^3)*sin(d*x + c))/(a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)","C",0
79,1,104,0,0.965540," ","integrate(x^3*(b*x^3+a)*sin(d*x+c),x, algorithm=""fricas"")","-\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) - 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) - 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
80,1,87,0,1.145397," ","integrate(x^2*(b*x^3+a)*sin(d*x+c),x, algorithm=""fricas"")","-\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) - {\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) - (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
81,1,68,0,0.943018," ","integrate(x*(b*x^3+a)*sin(d*x+c),x, algorithm=""fricas"")","-\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) - {\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) - (4*b*d^3*x^3 + a*d^3 - 24*b*d*x)*sin(d*x + c))/d^5","A",0
82,1,52,0,0.829656," ","integrate((b*x^3+a)*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b d^{3} x^{3} + a d^{3} - 6 \, b d x\right)} \cos\left(d x + c\right) - 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) - 3*(b*d^2*x^2 - 2*b)*sin(d*x + c))/d^4","A",0
83,1,72,0,1.080181," ","integrate((b*x^3+a)*sin(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, a d^{3} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 4 \, b d x \sin\left(d x + c\right) - 2 \, {\left(b d^{2} x^{2} - 2 \, b\right)} \cos\left(d x + c\right) + {\left(a d^{3} \operatorname{Ci}\left(d x\right) + a d^{3} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d^{3}}"," ",0,"1/2*(2*a*d^3*cos(c)*sin_integral(d*x) + 4*b*d*x*sin(d*x + c) - 2*(b*d^2*x^2 - 2*b)*cos(d*x + c) + (a*d^3*cos_integral(d*x) + a*d^3*cos_integral(-d*x))*sin(c))/d^3","A",0
84,1,79,0,1.232308," ","integrate((b*x^3+a)*sin(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a d^{3} x \sin\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, b d x^{2} \cos\left(d x + c\right) - {\left(a d^{3} x \operatorname{Ci}\left(d x\right) + a d^{3} x \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left(a d^{2} - b x\right)} \sin\left(d x + c\right)}{2 \, d^{2} x}"," ",0,"-1/2*(2*a*d^3*x*sin(c)*sin_integral(d*x) + 2*b*d*x^2*cos(d*x + c) - (a*d^3*x*cos_integral(d*x) + a*d^3*x*cos_integral(-d*x))*cos(c) + 2*(a*d^2 - b*x)*sin(d*x + c))/(d^2*x)","A",0
85,1,84,0,1.566558," ","integrate((b*x^3+a)*sin(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a d^{3} x^{2} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, a d \sin\left(d x + c\right) + 2 \, {\left(a d^{2} x + 2 \, b x^{2}\right)} \cos\left(d x + c\right) + {\left(a d^{3} x^{2} \operatorname{Ci}\left(d x\right) + a d^{3} x^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{4 \, d x^{2}}"," ",0,"-1/4*(2*a*d^3*x^2*cos(c)*sin_integral(d*x) + 2*a*d*sin(d*x + c) + 2*(a*d^2*x + 2*b*x^2)*cos(d*x + c) + (a*d^3*x^2*cos_integral(d*x) + a*d^3*x^2*cos_integral(-d*x))*sin(c))/(d*x^2)","A",0
86,1,114,0,0.853026," ","integrate((b*x^3+a)*sin(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, a d x \cos\left(d x + c\right) + {\left(a d^{3} x^{3} \operatorname{Ci}\left(d x\right) + a d^{3} x^{3} \operatorname{Ci}\left(-d x\right) - 12 \, b x^{3} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, {\left(a d^{2} x^{2} - 2 \, a\right)} \sin\left(d x + c\right) - 2 \, {\left(a d^{3} x^{3} \operatorname{Si}\left(d x\right) + 3 \, b x^{3} \operatorname{Ci}\left(d x\right) + 3 \, b x^{3} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*a*d*x*cos(d*x + c) + (a*d^3*x^3*cos_integral(d*x) + a*d^3*x^3*cos_integral(-d*x) - 12*b*x^3*sin_integral(d*x))*cos(c) - 2*(a*d^2*x^2 - 2*a)*sin(d*x + c) - 2*(a*d^3*x^3*sin_integral(d*x) + 3*b*x^3*cos_integral(d*x) + 3*b*x^3*cos_integral(-d*x))*sin(c))/x^3","A",0
87,1,161,0,1.065078," ","integrate(x*(b*x^3+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(b^{2} d^{7} x^{7} + 2 \, a b d^{7} x^{4} - 42 \, b^{2} d^{5} x^{5} - 24 \, a b d^{5} x^{2} + 840 \, b^{2} d^{3} x^{3} + 48 \, a b d^{3} + {\left(a^{2} d^{7} - 5040 \, b^{2} d\right)} x\right)} \cos\left(d x + c\right) - {\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 - 24*a*b*d^5*x^2 + 840*b^2*d^3*x^3 + 48*a*b*d^3 + (a^2*d^7 - 5040*b^2*d)*x)*cos(d*x + c) - (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
88,1,129,0,1.023897," ","integrate((b*x^3+a)^2*sin(d*x+c),x, algorithm=""fricas"")","-\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) - 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) - 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
89,1,145,0,1.257125," ","integrate((b*x^3+a)^2*sin(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{6} \cos\left(c\right) \operatorname{Si}\left(d x\right) - 2 \, {\left(b^{2} d^{5} x^{5} + 2 \, a b d^{5} x^{2} - 20 \, b^{2} d^{3} x^{3} - 4 \, a b d^{3} + 120 \, b^{2} d x\right)} \cos\left(d x + c\right) + 2 \, {\left(5 \, b^{2} d^{4} x^{4} + 4 \, a b d^{4} x - 60 \, b^{2} d^{2} x^{2} + 120 \, b^{2}\right)} \sin\left(d x + c\right) + {\left(a^{2} d^{6} \operatorname{Ci}\left(d x\right) + a^{2} d^{6} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{2 \, d^{6}}"," ",0,"1/2*(2*a^2*d^6*cos(c)*sin_integral(d*x) - 2*(b^2*d^5*x^5 + 2*a*b*d^5*x^2 - 20*b^2*d^3*x^3 - 4*a*b*d^3 + 120*b^2*d*x)*cos(d*x + c) + 2*(5*b^2*d^4*x^4 + 4*a*b*d^4*x - 60*b^2*d^2*x^2 + 120*b^2)*sin(d*x + c) + (a^2*d^6*cos_integral(d*x) + a^2*d^6*cos_integral(-d*x))*sin(c))/d^6","A",0
90,1,145,0,1.282640," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d^{6} x \sin\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, {\left(b^{2} d^{4} x^{5} + 2 \, a b d^{4} x^{2} - 12 \, b^{2} d^{2} x^{3} + 24 \, b^{2} x\right)} \cos\left(d x + c\right) - {\left(a^{2} d^{6} x \operatorname{Ci}\left(d x\right) + a^{2} d^{6} x \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) - 2 \, {\left(4 \, b^{2} d^{3} x^{4} - a^{2} d^{5} + 2 \, a b d^{3} x - 24 \, b^{2} d x^{2}\right)} \sin\left(d x + c\right)}{2 \, d^{5} x}"," ",0,"-1/2*(2*a^2*d^6*x*sin(c)*sin_integral(d*x) + 2*(b^2*d^4*x^5 + 2*a*b*d^4*x^2 - 12*b^2*d^2*x^3 + 24*b^2*x)*cos(d*x + c) - (a^2*d^6*x*cos_integral(d*x) + a^2*d^6*x*cos_integral(-d*x))*cos(c) - 2*(4*b^2*d^3*x^4 - a^2*d^5 + 2*a*b*d^3*x - 24*b^2*d*x^2)*sin(d*x + c))/(d^5*x)","A",0
91,1,142,0,1.181239," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d^{6} x^{2} \cos\left(c\right) \operatorname{Si}\left(d x\right) + 2 \, {\left(2 \, b^{2} d^{3} x^{5} + a^{2} d^{5} x + 4 \, a b d^{3} x^{2} - 12 \, b^{2} d x^{3}\right)} \cos\left(d x + c\right) - 2 \, {\left(6 \, b^{2} d^{2} x^{4} - a^{2} d^{4} - 12 \, b^{2} x^{2}\right)} \sin\left(d x + c\right) + {\left(a^{2} d^{6} x^{2} \operatorname{Ci}\left(d x\right) + a^{2} d^{6} x^{2} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{4 \, d^{4} x^{2}}"," ",0,"-1/4*(2*a^2*d^6*x^2*cos(c)*sin_integral(d*x) + 2*(2*b^2*d^3*x^5 + a^2*d^5*x + 4*a*b*d^3*x^2 - 12*b^2*d*x^3)*cos(d*x + c) - 2*(6*b^2*d^2*x^4 - a^2*d^4 - 12*b^2*x^2)*sin(d*x + c) + (a^2*d^6*x^2*cos_integral(d*x) + a^2*d^6*x^2*cos_integral(-d*x))*sin(c))/(d^4*x^2)","A",0
92,1,176,0,1.519826," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, b^{2} d^{2} x^{5} + a^{2} d^{4} x - 12 \, b^{2} x^{3}\right)} \cos\left(d x + c\right) + {\left(a^{2} d^{6} x^{3} \operatorname{Ci}\left(d x\right) + a^{2} d^{6} x^{3} \operatorname{Ci}\left(-d x\right) - 24 \, a b d^{3} x^{3} \operatorname{Si}\left(d x\right)\right)} \cos\left(c\right) - 2 \, {\left(a^{2} d^{5} x^{2} + 12 \, b^{2} d x^{4} - 2 \, a^{2} d^{3}\right)} \sin\left(d x + c\right) - 2 \, {\left(a^{2} d^{6} x^{3} \operatorname{Si}\left(d x\right) + 6 \, a b d^{3} x^{3} \operatorname{Ci}\left(d x\right) + 6 \, a b d^{3} x^{3} \operatorname{Ci}\left(-d x\right)\right)} \sin\left(c\right)}{12 \, d^{3} x^{3}}"," ",0,"-1/12*(2*(6*b^2*d^2*x^5 + a^2*d^4*x - 12*b^2*x^3)*cos(d*x + c) + (a^2*d^6*x^3*cos_integral(d*x) + a^2*d^6*x^3*cos_integral(-d*x) - 24*a*b*d^3*x^3*sin_integral(d*x))*cos(c) - 2*(a^2*d^5*x^2 + 12*b^2*d*x^4 - 2*a^2*d^3)*sin(d*x + c) - 2*(a^2*d^6*x^3*sin_integral(d*x) + 6*a*b*d^3*x^3*cos_integral(d*x) + 6*a*b*d^3*x^3*cos_integral(-d*x))*sin(c))/(d^3*x^3)","A",0
93,1,186,0,1.029853," ","integrate((b*x^3+a)^2*sin(d*x+c)/x^5,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d^{5} x^{3} - 24 \, b^{2} d x^{5} - 2 \, a^{2} d^{3} x\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{2} d^{6} x^{4} \operatorname{Si}\left(d x\right) + 24 \, a b d^{3} x^{4} \operatorname{Ci}\left(d x\right) + 24 \, a b d^{3} x^{4} \operatorname{Ci}\left(-d x\right)\right)} \cos\left(c\right) + 2 \, {\left(a^{2} d^{4} x^{2} - 48 \, a b d^{2} x^{3} + 24 \, b^{2} x^{4} - 6 \, a^{2} d^{2}\right)} \sin\left(d x + c\right) + {\left(a^{2} d^{6} x^{4} \operatorname{Ci}\left(d x\right) + a^{2} d^{6} x^{4} \operatorname{Ci}\left(-d x\right) - 96 \, a b d^{3} x^{4} \operatorname{Si}\left(d x\right)\right)} \sin\left(c\right)}{48 \, d^{2} x^{4}}"," ",0,"1/48*(2*(a^2*d^5*x^3 - 24*b^2*d*x^5 - 2*a^2*d^3*x)*cos(d*x + c) + 2*(a^2*d^6*x^4*sin_integral(d*x) + 24*a*b*d^3*x^4*cos_integral(d*x) + 24*a*b*d^3*x^4*cos_integral(-d*x))*cos(c) + 2*(a^2*d^4*x^2 - 48*a*b*d^2*x^3 + 24*b^2*x^4 - 6*a^2*d^2)*sin(d*x + c) + (a^2*d^6*x^4*cos_integral(d*x) + a^2*d^6*x^4*cos_integral(-d*x) - 96*a*b*d^3*x^4*sin_integral(d*x))*sin(c))/(d^2*x^4)","A",0
94,1,397,0,1.352002," ","integrate(x^4*sin(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{\left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} + i\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} + i\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} - i\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} - i\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - 12 \, d x \cos\left(d x + c\right) + 2 i \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 i \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + 12 \, \sin\left(d x + c\right)}{12 \, b d^{2}}"," ",0,"1/12*((I*a*d^3/b)^(2/3)*(sqrt(3) + I)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) - (-I*a*d^3/b)^(2/3)*(sqrt(3) + I)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) - (I*a*d^3/b)^(2/3)*(sqrt(3) - I)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(2/3)*(sqrt(3) - I)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - 12*d*x*cos(d*x + c) + 2*I*(-I*a*d^3/b)^(2/3)*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*I*(I*a*d^3/b)^(2/3)*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) + 12*sin(d*x + c))/(b*d^2)","C",0
95,1,393,0,1.335007," ","integrate(x^3*sin(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{\left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + 2 \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + 2 \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 12 \, \cos\left(d x + c\right)}{12 \, b d}"," ",0,"1/12*((I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + 2*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + 2*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 12*cos(d*x + c))/(b*d)","C",0
96,1,292,0,1.374266," ","integrate(x^2*sin(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{i \, {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} - i \, {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + i \, {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} - i \, {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - i \, {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + i \, {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{6 \, b}"," ",0,"1/6*(I*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) - I*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + I*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) - I*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - I*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + I*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/b","C",0
97,1,379,0,1.333343," ","integrate(x*sin(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","-\frac{\left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} + i\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} + i\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} - i\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} - i\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + 2 i \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 i \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{12 \, a d^{2}}"," ",0,"-1/12*((I*a*d^3/b)^(2/3)*(sqrt(3) + I)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) - (-I*a*d^3/b)^(2/3)*(sqrt(3) + I)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) - (I*a*d^3/b)^(2/3)*(sqrt(3) - I)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(2/3)*(sqrt(3) - I)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + 2*I*(-I*a*d^3/b)^(2/3)*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*I*(I*a*d^3/b)^(2/3)*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/(a*d^2)","C",0
98,1,385,0,1.424851," ","integrate(sin(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{\left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - 2 \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{12 \, a d}"," ",0,"1/12*((I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - 2*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/(a*d)","C",0
99,1,314,0,1.421362," ","integrate(sin(d*x+c)/x/(b*x^3+a),x, algorithm=""fricas"")","\frac{-i \, {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + i \, {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} - i \, {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + i \, {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - 3 i \, {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 3 i \, {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + i \, {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - i \, {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{6 \, a}"," ",0,"1/6*(-I*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + I*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) - I*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + I*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - 3*I*Ei(I*d*x)*e^(I*c) + 3*I*Ei(-I*d*x)*e^(-I*c) + I*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - I*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/a","C",0
100,1,454,0,1.496699," ","integrate(sin(d*x+c)/x^2/(b*x^3+a),x, algorithm=""fricas"")","\frac{6 \, a d^{3} x {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 6 \, a d^{3} x {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + 2 i \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} b x {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 i \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} b x {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 12 \, a d^{2} \sin\left(d x + c\right) + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} b x + i \, b x\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} b x + i \, b x\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} b x - i \, b x\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{3} b x - i \, b x\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)}}{12 \, a^{2} d^{2} x}"," ",0,"1/12*(6*a*d^3*x*Ei(I*d*x)*e^(I*c) + 6*a*d^3*x*Ei(-I*d*x)*e^(-I*c) + 2*I*(-I*a*d^3/b)^(2/3)*b*x*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*I*(I*a*d^3/b)^(2/3)*b*x*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 12*a*d^2*sin(d*x + c) + (I*a*d^3/b)^(2/3)*(sqrt(3)*b*x + I*b*x)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) - (-I*a*d^3/b)^(2/3)*(sqrt(3)*b*x + I*b*x)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) - (I*a*d^3/b)^(2/3)*(sqrt(3)*b*x - I*b*x)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (-I*a*d^3/b)^(2/3)*(sqrt(3)*b*x - I*b*x)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c))/(a^2*d^2*x)","C",0
101,1,491,0,1.599991," ","integrate(sin(d*x+c)/x^3/(b*x^3+a),x, algorithm=""fricas"")","\frac{3 i \, a d^{3} x^{2} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} - 3 i \, a d^{3} x^{2} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + 2 \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} b x^{2} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + 2 \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} b x^{2} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 6 \, a d^{2} x \cos\left(d x + c\right) + {\left(-i \, \sqrt{3} b x^{2} - b x^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(-i \, \sqrt{3} b x^{2} - b x^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(i \, \sqrt{3} b x^{2} - b x^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(i \, \sqrt{3} b x^{2} - b x^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - 6 \, a d \sin\left(d x + c\right)}{12 \, a^{2} d x^{2}}"," ",0,"1/12*(3*I*a*d^3*x^2*Ei(I*d*x)*e^(I*c) - 3*I*a*d^3*x^2*Ei(-I*d*x)*e^(-I*c) + 2*(-I*a*d^3/b)^(1/3)*b*x^2*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + 2*(I*a*d^3/b)^(1/3)*b*x^2*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 6*a*d^2*x*cos(d*x + c) + (-I*sqrt(3)*b*x^2 - b*x^2)*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (-I*sqrt(3)*b*x^2 - b*x^2)*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (I*sqrt(3)*b*x^2 - b*x^2)*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (I*sqrt(3)*b*x^2 - b*x^2)*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - 6*a*d*sin(d*x + c))/(a^2*d*x^2)","C",0
102,1,670,0,1.356724," ","integrate(x^3*sin(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{12 \, a d x \sin\left(d x + c\right) + {\left({\left(b x^{3} - \sqrt{3} {\left(i \, b x^{3} + i \, a\right)} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(b x^{3} + \sqrt{3} {\left(i \, b x^{3} + i \, a\right)} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(b x^{3} - \sqrt{3} {\left(i \, b x^{3} + i \, a\right)} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(b x^{3} + \sqrt{3} {\left(i \, b x^{3} + i \, a\right)} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left({\left(b x^{3} - \sqrt{3} {\left(-i \, b x^{3} - i \, a\right)} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(b x^{3} + \sqrt{3} {\left(-i \, b x^{3} - i \, a\right)} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(b x^{3} - \sqrt{3} {\left(-i \, b x^{3} - i \, a\right)} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(b x^{3} + \sqrt{3} {\left(-i \, b x^{3} - i \, a\right)} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - 2 \, {\left({\left(b x^{3} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 \, {\left({\left(b x^{3} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(b x^{3} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{36 \, {\left(a b^{2} d x^{3} + a^{2} b d\right)}}"," ",0,"-1/36*(12*a*d*x*sin(d*x + c) + ((b*x^3 - sqrt(3)*(I*b*x^3 + I*a) + a)*(I*a*d^3/b)^(2/3) - (b*x^3 + sqrt(3)*(I*b*x^3 + I*a) + a)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + ((b*x^3 - sqrt(3)*(I*b*x^3 + I*a) + a)*(-I*a*d^3/b)^(2/3) - (b*x^3 + sqrt(3)*(I*b*x^3 + I*a) + a)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + ((b*x^3 - sqrt(3)*(-I*b*x^3 - I*a) + a)*(I*a*d^3/b)^(2/3) - (b*x^3 + sqrt(3)*(-I*b*x^3 - I*a) + a)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + ((b*x^3 - sqrt(3)*(-I*b*x^3 - I*a) + a)*(-I*a*d^3/b)^(2/3) - (b*x^3 + sqrt(3)*(-I*b*x^3 - I*a) + a)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - 2*((b*x^3 + a)*(-I*a*d^3/b)^(2/3) - (b*x^3 + a)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*((b*x^3 + a)*(I*a*d^3/b)^(2/3) - (b*x^3 + a)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/(a*b^2*d*x^3 + a^2*b*d)","C",0
103,1,480,0,1.127770," ","integrate(x^2*sin(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, b x^{3} + \sqrt{3} {\left(b x^{3} + a\right)} - i \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(i \, b x^{3} - \sqrt{3} {\left(b x^{3} + a\right)} + i \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-i \, b x^{3} - \sqrt{3} {\left(b x^{3} + a\right)} - i \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(i \, b x^{3} + \sqrt{3} {\left(b x^{3} + a\right)} + i \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-2 i \, b x^{3} - 2 i \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(2 i \, b x^{3} + 2 i \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 12 \, a \sin\left(d x + c\right)}{36 \, {\left(a b^{2} x^{3} + a^{2} b\right)}}"," ",0,"1/36*((-I*b*x^3 + sqrt(3)*(b*x^3 + a) - I*a)*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (I*b*x^3 - sqrt(3)*(b*x^3 + a) + I*a)*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (-I*b*x^3 - sqrt(3)*(b*x^3 + a) - I*a)*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (I*b*x^3 + sqrt(3)*(b*x^3 + a) + I*a)*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + (-2*I*b*x^3 - 2*I*a)*(-I*a*d^3/b)^(1/3)*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (2*I*b*x^3 + 2*I*a)*(I*a*d^3/b)^(1/3)*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 12*a*sin(d*x + c))/(a*b^2*x^3 + a^2*b)","C",0
104,1,661,0,1.363628," ","integrate(x*sin(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{12 \, a b d^{2} x^{2} \sin\left(d x + c\right) - {\left(2 \, a b d^{3} x^{3} + 2 \, a^{2} d^{3} - {\left(-i \, b^{2} x^{3} - i \, a b - \sqrt{3} {\left(b^{2} x^{3} + a b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} - {\left(2 \, a b d^{3} x^{3} + 2 \, a^{2} d^{3} - {\left(i \, b^{2} x^{3} + i \, a b + \sqrt{3} {\left(b^{2} x^{3} + a b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} - {\left(2 \, a b d^{3} x^{3} + 2 \, a^{2} d^{3} - {\left(-i \, b^{2} x^{3} - i \, a b + \sqrt{3} {\left(b^{2} x^{3} + a b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} - {\left(2 \, a b d^{3} x^{3} + 2 \, a^{2} d^{3} - {\left(i \, b^{2} x^{3} + i \, a b - \sqrt{3} {\left(b^{2} x^{3} + a b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - {\left(2 \, a b d^{3} x^{3} + 2 \, a^{2} d^{3} - {\left(-2 i \, b^{2} x^{3} - 2 i \, a b\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - {\left(2 \, a b d^{3} x^{3} + 2 \, a^{2} d^{3} - {\left(2 i \, b^{2} x^{3} + 2 i \, a b\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{36 \, {\left(a^{2} b^{2} d^{2} x^{3} + a^{3} b d^{2}\right)}}"," ",0,"1/36*(12*a*b*d^2*x^2*sin(d*x + c) - (2*a*b*d^3*x^3 + 2*a^2*d^3 - (-I*b^2*x^3 - I*a*b - sqrt(3)*(b^2*x^3 + a*b))*(I*a*d^3/b)^(2/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) - (2*a*b*d^3*x^3 + 2*a^2*d^3 - (I*b^2*x^3 + I*a*b + sqrt(3)*(b^2*x^3 + a*b))*(-I*a*d^3/b)^(2/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) - (2*a*b*d^3*x^3 + 2*a^2*d^3 - (-I*b^2*x^3 - I*a*b + sqrt(3)*(b^2*x^3 + a*b))*(I*a*d^3/b)^(2/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) - (2*a*b*d^3*x^3 + 2*a^2*d^3 - (I*b^2*x^3 + I*a*b - sqrt(3)*(b^2*x^3 + a*b))*(-I*a*d^3/b)^(2/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - (2*a*b*d^3*x^3 + 2*a^2*d^3 - (-2*I*b^2*x^3 - 2*I*a*b)*(-I*a*d^3/b)^(2/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - (2*a*b*d^3*x^3 + 2*a^2*d^3 - (2*I*b^2*x^3 + 2*I*a*b)*(I*a*d^3/b)^(2/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/(a^2*b^2*d^2*x^3 + a^3*b*d^2)","C",0
105,1,673,0,1.172041," ","integrate(sin(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{12 \, a d x \sin\left(d x + c\right) + {\left({\left(b x^{3} + \sqrt{3} {\left(-i \, b x^{3} - i \, a\right)} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(2 \, b x^{3} + \sqrt{3} {\left(2 i \, b x^{3} + 2 i \, a\right)} + 2 \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(b x^{3} + \sqrt{3} {\left(-i \, b x^{3} - i \, a\right)} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(2 \, b x^{3} + \sqrt{3} {\left(2 i \, b x^{3} + 2 i \, a\right)} + 2 \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left({\left(b x^{3} + \sqrt{3} {\left(i \, b x^{3} + i \, a\right)} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(2 \, b x^{3} + \sqrt{3} {\left(-2 i \, b x^{3} - 2 i \, a\right)} + 2 \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(b x^{3} + \sqrt{3} {\left(i \, b x^{3} + i \, a\right)} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(2 \, b x^{3} + \sqrt{3} {\left(-2 i \, b x^{3} - 2 i \, a\right)} + 2 \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - 2 \, {\left({\left(b x^{3} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 \, {\left({\left(b x^{3} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + 2 \, {\left(b x^{3} + a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)}}{36 \, {\left(a^{2} b d x^{3} + a^{3} d\right)}}"," ",0,"1/36*(12*a*d*x*sin(d*x + c) + ((b*x^3 + sqrt(3)*(-I*b*x^3 - I*a) + a)*(I*a*d^3/b)^(2/3) + (2*b*x^3 + sqrt(3)*(2*I*b*x^3 + 2*I*a) + 2*a)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + ((b*x^3 + sqrt(3)*(-I*b*x^3 - I*a) + a)*(-I*a*d^3/b)^(2/3) + (2*b*x^3 + sqrt(3)*(2*I*b*x^3 + 2*I*a) + 2*a)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + ((b*x^3 + sqrt(3)*(I*b*x^3 + I*a) + a)*(I*a*d^3/b)^(2/3) + (2*b*x^3 + sqrt(3)*(-2*I*b*x^3 - 2*I*a) + 2*a)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + ((b*x^3 + sqrt(3)*(I*b*x^3 + I*a) + a)*(-I*a*d^3/b)^(2/3) + (2*b*x^3 + sqrt(3)*(-2*I*b*x^3 - 2*I*a) + 2*a)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - 2*((b*x^3 + a)*(-I*a*d^3/b)^(2/3) + 2*(b*x^3 + a)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*((b*x^3 + a)*(I*a*d^3/b)^(2/3) + 2*(b*x^3 + a)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)))/(a^2*b*d*x^3 + a^3*d)","C",0
106,1,584,0,1.077929," ","integrate(sin(d*x+c)/x/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left(-6 i \, b x^{3} + {\left(i \, b x^{3} - \sqrt{3} {\left(b x^{3} + a\right)} + i \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} - 6 i \, a\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(6 i \, b x^{3} + {\left(-i \, b x^{3} + \sqrt{3} {\left(b x^{3} + a\right)} - i \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} + 6 i \, a\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-6 i \, b x^{3} + {\left(i \, b x^{3} + \sqrt{3} {\left(b x^{3} + a\right)} + i \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} - 6 i \, a\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(6 i \, b x^{3} + {\left(-i \, b x^{3} - \sqrt{3} {\left(b x^{3} + a\right)} - i \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} + 6 i \, a\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-18 i \, b x^{3} - 18 i \, a\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + {\left(18 i \, b x^{3} + 18 i \, a\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(6 i \, b x^{3} + {\left(2 i \, b x^{3} + 2 i \, a\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} + 6 i \, a\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(-6 i \, b x^{3} + {\left(-2 i \, b x^{3} - 2 i \, a\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} - 6 i \, a\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + 12 \, a \sin\left(d x + c\right)}{36 \, {\left(a^{2} b x^{3} + a^{3}\right)}}"," ",0,"1/36*((-6*I*b*x^3 + (I*b*x^3 - sqrt(3)*(b*x^3 + a) + I*a)*(I*a*d^3/b)^(1/3) - 6*I*a)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (6*I*b*x^3 + (-I*b*x^3 + sqrt(3)*(b*x^3 + a) - I*a)*(-I*a*d^3/b)^(1/3) + 6*I*a)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (-6*I*b*x^3 + (I*b*x^3 + sqrt(3)*(b*x^3 + a) + I*a)*(I*a*d^3/b)^(1/3) - 6*I*a)*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (6*I*b*x^3 + (-I*b*x^3 - sqrt(3)*(b*x^3 + a) - I*a)*(-I*a*d^3/b)^(1/3) + 6*I*a)*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + (-18*I*b*x^3 - 18*I*a)*Ei(I*d*x)*e^(I*c) + (18*I*b*x^3 + 18*I*a)*Ei(-I*d*x)*e^(-I*c) + (6*I*b*x^3 + (2*I*b*x^3 + 2*I*a)*(-I*a*d^3/b)^(1/3) + 6*I*a)*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (-6*I*b*x^3 + (-2*I*b*x^3 - 2*I*a)*(I*a*d^3/b)^(1/3) - 6*I*a)*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) + 12*a*sin(d*x + c))/(a^2*b*x^3 + a^3)","C",0
107,1,722,0,1.246682," ","integrate(sin(d*x+c)/x^2/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{{\left(a b d^{3} x^{4} + a^{2} d^{3} x + {\left(2 i \, b^{2} x^{4} + 2 i \, a b x + 2 \, \sqrt{3} {\left(b^{2} x^{4} + a b x\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(a b d^{3} x^{4} + a^{2} d^{3} x + {\left(-2 i \, b^{2} x^{4} - 2 i \, a b x - 2 \, \sqrt{3} {\left(b^{2} x^{4} + a b x\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(a b d^{3} x^{4} + a^{2} d^{3} x + {\left(2 i \, b^{2} x^{4} + 2 i \, a b x - 2 \, \sqrt{3} {\left(b^{2} x^{4} + a b x\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(a b d^{3} x^{4} + a^{2} d^{3} x + {\left(-2 i \, b^{2} x^{4} - 2 i \, a b x + 2 \, \sqrt{3} {\left(b^{2} x^{4} + a b x\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + 9 \, {\left(a b d^{3} x^{4} + a^{2} d^{3} x\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + 9 \, {\left(a b d^{3} x^{4} + a^{2} d^{3} x\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(a b d^{3} x^{4} + a^{2} d^{3} x + {\left(4 i \, b^{2} x^{4} + 4 i \, a b x\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(a b d^{3} x^{4} + a^{2} d^{3} x + {\left(-4 i \, b^{2} x^{4} - 4 i \, a b x\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 6 \, {\left(4 \, a b d^{2} x^{3} + 3 \, a^{2} d^{2}\right)} \sin\left(d x + c\right)}{18 \, {\left(a^{3} b d^{2} x^{4} + a^{4} d^{2} x\right)}}"," ",0,"1/18*((a*b*d^3*x^4 + a^2*d^3*x + (2*I*b^2*x^4 + 2*I*a*b*x + 2*sqrt(3)*(b^2*x^4 + a*b*x))*(I*a*d^3/b)^(2/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (a*b*d^3*x^4 + a^2*d^3*x + (-2*I*b^2*x^4 - 2*I*a*b*x - 2*sqrt(3)*(b^2*x^4 + a*b*x))*(-I*a*d^3/b)^(2/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (a*b*d^3*x^4 + a^2*d^3*x + (2*I*b^2*x^4 + 2*I*a*b*x - 2*sqrt(3)*(b^2*x^4 + a*b*x))*(I*a*d^3/b)^(2/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (a*b*d^3*x^4 + a^2*d^3*x + (-2*I*b^2*x^4 - 2*I*a*b*x + 2*sqrt(3)*(b^2*x^4 + a*b*x))*(-I*a*d^3/b)^(2/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + 9*(a*b*d^3*x^4 + a^2*d^3*x)*Ei(I*d*x)*e^(I*c) + 9*(a*b*d^3*x^4 + a^2*d^3*x)*Ei(-I*d*x)*e^(-I*c) + (a*b*d^3*x^4 + a^2*d^3*x + (4*I*b^2*x^4 + 4*I*a*b*x)*(-I*a*d^3/b)^(2/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (a*b*d^3*x^4 + a^2*d^3*x + (-4*I*b^2*x^4 - 4*I*a*b*x)*(I*a*d^3/b)^(2/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 6*(4*a*b*d^2*x^3 + 3*a^2*d^2)*sin(d*x + c))/(a^3*b*d^2*x^4 + a^4*d^2*x)","C",0
108,1,916,0,1.062439," ","integrate(sin(d*x+c)/x^3/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{{\left({\left(b^{2} x^{5} + a b x^{2} - \sqrt{3} {\left(i \, b^{2} x^{5} + i \, a b x^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{2} x^{5} + 5 \, a b x^{2} - \sqrt{3} {\left(-5 i \, b^{2} x^{5} - 5 i \, a b x^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(b^{2} x^{5} + a b x^{2} - \sqrt{3} {\left(i \, b^{2} x^{5} + i \, a b x^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{2} x^{5} + 5 \, a b x^{2} - \sqrt{3} {\left(-5 i \, b^{2} x^{5} - 5 i \, a b x^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left({\left(b^{2} x^{5} + a b x^{2} - \sqrt{3} {\left(-i \, b^{2} x^{5} - i \, a b x^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{2} x^{5} + 5 \, a b x^{2} - \sqrt{3} {\left(5 i \, b^{2} x^{5} + 5 i \, a b x^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(b^{2} x^{5} + a b x^{2} - \sqrt{3} {\left(-i \, b^{2} x^{5} - i \, a b x^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{2} x^{5} + 5 \, a b x^{2} - \sqrt{3} {\left(5 i \, b^{2} x^{5} + 5 i \, a b x^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} - {\left(9 i \, a b d^{3} x^{5} + 9 i \, a^{2} d^{3} x^{2}\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} - {\left(-9 i \, a b d^{3} x^{5} - 9 i \, a^{2} d^{3} x^{2}\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} - 2 \, {\left({\left(b^{2} x^{5} + a b x^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + 5 \, {\left(b^{2} x^{5} + a b x^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 2 \, {\left({\left(b^{2} x^{5} + a b x^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + 5 \, {\left(b^{2} x^{5} + a b x^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + 18 \, {\left(a b d^{2} x^{4} + a^{2} d^{2} x\right)} \cos\left(d x + c\right) + 6 \, {\left(5 \, a b d x^{3} + 3 \, a^{2} d\right)} \sin\left(d x + c\right)}{36 \, {\left(a^{3} b d x^{5} + a^{4} d x^{2}\right)}}"," ",0,"-1/36*(((b^2*x^5 + a*b*x^2 - sqrt(3)*(I*b^2*x^5 + I*a*b*x^2))*(I*a*d^3/b)^(2/3) + (5*b^2*x^5 + 5*a*b*x^2 - sqrt(3)*(-5*I*b^2*x^5 - 5*I*a*b*x^2))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + ((b^2*x^5 + a*b*x^2 - sqrt(3)*(I*b^2*x^5 + I*a*b*x^2))*(-I*a*d^3/b)^(2/3) + (5*b^2*x^5 + 5*a*b*x^2 - sqrt(3)*(-5*I*b^2*x^5 - 5*I*a*b*x^2))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + ((b^2*x^5 + a*b*x^2 - sqrt(3)*(-I*b^2*x^5 - I*a*b*x^2))*(I*a*d^3/b)^(2/3) + (5*b^2*x^5 + 5*a*b*x^2 - sqrt(3)*(5*I*b^2*x^5 + 5*I*a*b*x^2))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + ((b^2*x^5 + a*b*x^2 - sqrt(3)*(-I*b^2*x^5 - I*a*b*x^2))*(-I*a*d^3/b)^(2/3) + (5*b^2*x^5 + 5*a*b*x^2 - sqrt(3)*(5*I*b^2*x^5 + 5*I*a*b*x^2))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) - (9*I*a*b*d^3*x^5 + 9*I*a^2*d^3*x^2)*Ei(I*d*x)*e^(I*c) - (-9*I*a*b*d^3*x^5 - 9*I*a^2*d^3*x^2)*Ei(-I*d*x)*e^(-I*c) - 2*((b^2*x^5 + a*b*x^2)*(-I*a*d^3/b)^(2/3) + 5*(b^2*x^5 + a*b*x^2)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) - 2*((b^2*x^5 + a*b*x^2)*(I*a*d^3/b)^(2/3) + 5*(b^2*x^5 + a*b*x^2)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) + 18*(a*b*d^2*x^4 + a^2*d^2*x)*cos(d*x + c) + 6*(5*a*b*d*x^3 + 3*a^2*d)*sin(d*x + c))/(a^3*b*d*x^5 + a^4*d*x^2)","C",0
109,1,890,0,1.543387," ","integrate(x^3*sin(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{{\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3} + {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{3} {\left(i \, b^{3} x^{6} + 2 i \, a b^{2} x^{3} + i \, a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3} + {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{3} {\left(i \, b^{3} x^{6} + 2 i \, a b^{2} x^{3} + i \, a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3} + {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{3} {\left(-i \, b^{3} x^{6} - 2 i \, a b^{2} x^{3} - i \, a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3} + {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{3} {\left(-i \, b^{3} x^{6} - 2 i \, a b^{2} x^{3} - i \, a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3} - 2 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3} - 2 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + 6 \, {\left(a b^{2} d^{2} x^{5} + a^{2} b d^{2} x^{2}\right)} \cos\left(d x + c\right) + 6 \, {\left(a b^{2} d x^{4} - 2 \, a^{2} b d x\right)} \sin\left(d x + c\right)}{108 \, {\left(a^{2} b^{4} d x^{6} + 2 \, a^{3} b^{3} d x^{3} + a^{4} b^{2} d\right)}}"," ",0,"1/108*((I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3 + (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(3)*(I*b^3*x^6 + 2*I*a*b^2*x^3 + I*a^2*b))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3 + (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(3)*(I*b^3*x^6 + 2*I*a*b^2*x^3 + I*a^2*b))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3 + (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(3)*(-I*b^3*x^6 - 2*I*a*b^2*x^3 - I*a^2*b))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3 + (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(3)*(-I*b^3*x^6 - 2*I*a*b^2*x^3 - I*a^2*b))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + (-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3 - 2*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3 - 2*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) + 6*(a*b^2*d^2*x^5 + a^2*b*d^2*x^2)*cos(d*x + c) + 6*(a*b^2*d*x^4 - 2*a^2*b*d*x)*sin(d*x + c))/(a^2*b^4*d*x^6 + 2*a^3*b^3*d*x^3 + a^4*b^2*d)","C",0
110,1,929,0,1.277969," ","integrate(x^2*sin(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{{\left({\left(-i \, b^{2} x^{6} - 2 i \, a b x^{3} - i \, a^{2} - \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(-2 i \, b^{2} x^{6} - 4 i \, a b x^{3} - 2 i \, a^{2} + 2 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(i \, b^{2} x^{6} + 2 i \, a b x^{3} + i \, a^{2} + \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(2 i \, b^{2} x^{6} + 4 i \, a b x^{3} + 2 i \, a^{2} - 2 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left({\left(-i \, b^{2} x^{6} - 2 i \, a b x^{3} - i \, a^{2} + \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(-2 i \, b^{2} x^{6} - 4 i \, a b x^{3} - 2 i \, a^{2} - 2 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left({\left(i \, b^{2} x^{6} + 2 i \, a b x^{3} + i \, a^{2} - \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(2 i \, b^{2} x^{6} + 4 i \, a b x^{3} + 2 i \, a^{2} + 2 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left({\left(-2 i \, b^{2} x^{6} - 4 i \, a b x^{3} - 2 i \, a^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(-4 i \, b^{2} x^{6} - 8 i \, a b x^{3} - 4 i \, a^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left({\left(2 i \, b^{2} x^{6} + 4 i \, a b x^{3} + 2 i \, a^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(4 i \, b^{2} x^{6} + 8 i \, a b x^{3} + 4 i \, a^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 36 \, a^{2} \sin\left(d x + c\right) + 12 \, {\left(a b d x^{4} + a^{2} d x\right)} \cos\left(d x + c\right)}{216 \, {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)}}"," ",0,"1/216*(((-I*b^2*x^6 - 2*I*a*b*x^3 - I*a^2 - sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(2/3) + (-2*I*b^2*x^6 - 4*I*a*b*x^3 - 2*I*a^2 + 2*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + ((I*b^2*x^6 + 2*I*a*b*x^3 + I*a^2 + sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(2/3) + (2*I*b^2*x^6 + 4*I*a*b*x^3 + 2*I*a^2 - 2*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + ((-I*b^2*x^6 - 2*I*a*b*x^3 - I*a^2 + sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(2/3) + (-2*I*b^2*x^6 - 4*I*a*b*x^3 - 2*I*a^2 - 2*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + ((I*b^2*x^6 + 2*I*a*b*x^3 + I*a^2 - sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(2/3) + (2*I*b^2*x^6 + 4*I*a*b*x^3 + 2*I*a^2 + 2*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + ((-2*I*b^2*x^6 - 4*I*a*b*x^3 - 2*I*a^2)*(-I*a*d^3/b)^(2/3) + (-4*I*b^2*x^6 - 8*I*a*b*x^3 - 4*I*a^2)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + ((2*I*b^2*x^6 + 4*I*a*b*x^3 + 2*I*a^2)*(I*a*d^3/b)^(2/3) + (4*I*b^2*x^6 + 8*I*a*b*x^3 + 4*I*a^2)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 36*a^2*sin(d*x + c) + 12*(a*b*d*x^4 + a^2*d*x)*cos(d*x + c))/(a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)","C",0
111,1,1321,0,1.542226," ","integrate(x*sin(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{{\left(8 \, a b^{2} d^{3} x^{6} + 16 \, a^{2} b d^{3} x^{3} + 8 \, a^{3} d^{3} - {\left(-4 i \, b^{3} x^{6} - 8 i \, a b^{2} x^{3} - 4 i \, a^{2} b - 4 \, \sqrt{3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{3} {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(8 \, a b^{2} d^{3} x^{6} + 16 \, a^{2} b d^{3} x^{3} + 8 \, a^{3} d^{3} - {\left(4 i \, b^{3} x^{6} + 8 i \, a b^{2} x^{3} + 4 i \, a^{2} b + 4 \, \sqrt{3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{3} {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(8 \, a b^{2} d^{3} x^{6} + 16 \, a^{2} b d^{3} x^{3} + 8 \, a^{3} d^{3} - {\left(-4 i \, b^{3} x^{6} - 8 i \, a b^{2} x^{3} - 4 i \, a^{2} b + 4 \, \sqrt{3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{3} {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(8 \, a b^{2} d^{3} x^{6} + 16 \, a^{2} b d^{3} x^{3} + 8 \, a^{3} d^{3} - {\left(4 i \, b^{3} x^{6} + 8 i \, a b^{2} x^{3} + 4 i \, a^{2} b - 4 \, \sqrt{3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{3} {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(8 \, a b^{2} d^{3} x^{6} + 16 \, a^{2} b d^{3} x^{3} + 8 \, a^{3} d^{3} - {\left(-8 i \, b^{3} x^{6} - 16 i \, a b^{2} x^{3} - 8 i \, a^{2} b\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + 2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(8 \, a b^{2} d^{3} x^{6} + 16 \, a^{2} b d^{3} x^{3} + 8 \, a^{3} d^{3} - {\left(8 i \, b^{3} x^{6} + 16 i \, a b^{2} x^{3} + 8 i \, a^{2} b\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + 2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 12 \, {\left(a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cos\left(d x + c\right) - 12 \, {\left(4 \, a b^{2} d^{2} x^{5} + 7 \, a^{2} b d^{2} x^{2}\right)} \sin\left(d x + c\right)}{216 \, {\left(a^{3} b^{3} d^{2} x^{6} + 2 \, a^{4} b^{2} d^{2} x^{3} + a^{5} b d^{2}\right)}}"," ",0,"-1/216*((8*a*b^2*d^3*x^6 + 16*a^2*b*d^3*x^3 + 8*a^3*d^3 - (-4*I*b^3*x^6 - 8*I*a*b^2*x^3 - 4*I*a^2*b - 4*sqrt(3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*(I*a*d^3/b)^(2/3) - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(3)*(I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (8*a*b^2*d^3*x^6 + 16*a^2*b*d^3*x^3 + 8*a^3*d^3 - (4*I*b^3*x^6 + 8*I*a*b^2*x^3 + 4*I*a^2*b + 4*sqrt(3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*(-I*a*d^3/b)^(2/3) - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(3)*(I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (8*a*b^2*d^3*x^6 + 16*a^2*b*d^3*x^3 + 8*a^3*d^3 - (-4*I*b^3*x^6 - 8*I*a*b^2*x^3 - 4*I*a^2*b + 4*sqrt(3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*(I*a*d^3/b)^(2/3) - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(3)*(-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (8*a*b^2*d^3*x^6 + 16*a^2*b*d^3*x^3 + 8*a^3*d^3 - (4*I*b^3*x^6 + 8*I*a*b^2*x^3 + 4*I*a^2*b - 4*sqrt(3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*(-I*a*d^3/b)^(2/3) - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(3)*(-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + (8*a*b^2*d^3*x^6 + 16*a^2*b*d^3*x^3 + 8*a^3*d^3 - (-8*I*b^3*x^6 - 16*I*a*b^2*x^3 - 8*I*a^2*b)*(-I*a*d^3/b)^(2/3) + 2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (8*a*b^2*d^3*x^6 + 16*a^2*b*d^3*x^3 + 8*a^3*d^3 - (8*I*b^3*x^6 + 16*I*a*b^2*x^3 + 8*I*a^2*b)*(I*a*d^3/b)^(2/3) + 2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 12*(a^2*b*d^3*x^3 + a^3*d^3)*cos(d*x + c) - 12*(4*a*b^2*d^2*x^5 + 7*a^2*b*d^2*x^2)*sin(d*x + c))/(a^3*b^3*d^2*x^6 + 2*a^4*b^2*d^2*x^3 + a^5*b*d^2)","C",0
112,1,1223,0,1.101883," ","integrate(sin(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{{\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3} + {\left(3 \, b^{3} x^{6} + 6 \, a b^{2} x^{3} + 3 \, a^{2} b + \sqrt{3} {\left(-3 i \, b^{3} x^{6} - 6 i \, a b^{2} x^{3} - 3 i \, a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{3} x^{6} + 10 \, a b^{2} x^{3} + 5 \, a^{2} b + \sqrt{3} {\left(5 i \, b^{3} x^{6} + 10 i \, a b^{2} x^{3} + 5 i \, a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3} + {\left(3 \, b^{3} x^{6} + 6 \, a b^{2} x^{3} + 3 \, a^{2} b + \sqrt{3} {\left(-3 i \, b^{3} x^{6} - 6 i \, a b^{2} x^{3} - 3 i \, a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{3} x^{6} + 10 \, a b^{2} x^{3} + 5 \, a^{2} b + \sqrt{3} {\left(5 i \, b^{3} x^{6} + 10 i \, a b^{2} x^{3} + 5 i \, a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3} + {\left(3 \, b^{3} x^{6} + 6 \, a b^{2} x^{3} + 3 \, a^{2} b + \sqrt{3} {\left(3 i \, b^{3} x^{6} + 6 i \, a b^{2} x^{3} + 3 i \, a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{3} x^{6} + 10 \, a b^{2} x^{3} + 5 \, a^{2} b + \sqrt{3} {\left(-5 i \, b^{3} x^{6} - 10 i \, a b^{2} x^{3} - 5 i \, a^{2} b\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3} + {\left(3 \, b^{3} x^{6} + 6 \, a b^{2} x^{3} + 3 \, a^{2} b + \sqrt{3} {\left(3 i \, b^{3} x^{6} + 6 i \, a b^{2} x^{3} + 3 i \, a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(5 \, b^{3} x^{6} + 10 \, a b^{2} x^{3} + 5 \, a^{2} b + \sqrt{3} {\left(-5 i \, b^{3} x^{6} - 10 i \, a b^{2} x^{3} - 5 i \, a^{2} b\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(i \, a b^{2} d^{3} x^{6} + 2 i \, a^{2} b d^{3} x^{3} + i \, a^{3} d^{3} - 6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - 10 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(-i \, a b^{2} d^{3} x^{6} - 2 i \, a^{2} b d^{3} x^{3} - i \, a^{3} d^{3} - 6 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} - 10 \, {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 6 \, {\left(a b^{2} d^{2} x^{5} + a^{2} b d^{2} x^{2}\right)} \cos\left(d x + c\right) + 6 \, {\left(5 \, a b^{2} d x^{4} + 8 \, a^{2} b d x\right)} \sin\left(d x + c\right)}{108 \, {\left(a^{3} b^{3} d x^{6} + 2 \, a^{4} b^{2} d x^{3} + a^{5} b d\right)}}"," ",0,"1/108*((-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3 + (3*b^3*x^6 + 6*a*b^2*x^3 + 3*a^2*b + sqrt(3)*(-3*I*b^3*x^6 - 6*I*a*b^2*x^3 - 3*I*a^2*b))*(I*a*d^3/b)^(2/3) + (5*b^3*x^6 + 10*a*b^2*x^3 + 5*a^2*b + sqrt(3)*(5*I*b^3*x^6 + 10*I*a*b^2*x^3 + 5*I*a^2*b))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3 + (3*b^3*x^6 + 6*a*b^2*x^3 + 3*a^2*b + sqrt(3)*(-3*I*b^3*x^6 - 6*I*a*b^2*x^3 - 3*I*a^2*b))*(-I*a*d^3/b)^(2/3) + (5*b^3*x^6 + 10*a*b^2*x^3 + 5*a^2*b + sqrt(3)*(5*I*b^3*x^6 + 10*I*a*b^2*x^3 + 5*I*a^2*b))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3 + (3*b^3*x^6 + 6*a*b^2*x^3 + 3*a^2*b + sqrt(3)*(3*I*b^3*x^6 + 6*I*a*b^2*x^3 + 3*I*a^2*b))*(I*a*d^3/b)^(2/3) + (5*b^3*x^6 + 10*a*b^2*x^3 + 5*a^2*b + sqrt(3)*(-5*I*b^3*x^6 - 10*I*a*b^2*x^3 - 5*I*a^2*b))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3 + (3*b^3*x^6 + 6*a*b^2*x^3 + 3*a^2*b + sqrt(3)*(3*I*b^3*x^6 + 6*I*a*b^2*x^3 + 3*I*a^2*b))*(-I*a*d^3/b)^(2/3) + (5*b^3*x^6 + 10*a*b^2*x^3 + 5*a^2*b + sqrt(3)*(-5*I*b^3*x^6 - 10*I*a*b^2*x^3 - 5*I*a^2*b))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + (I*a*b^2*d^3*x^6 + 2*I*a^2*b*d^3*x^3 + I*a^3*d^3 - 6*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*(-I*a*d^3/b)^(2/3) - 10*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (-I*a*b^2*d^3*x^6 - 2*I*a^2*b*d^3*x^3 - I*a^3*d^3 - 6*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*(I*a*d^3/b)^(2/3) - 10*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 6*(a*b^2*d^2*x^5 + a^2*b*d^2*x^2)*cos(d*x + c) + 6*(5*a*b^2*d*x^4 + 8*a^2*b*d*x)*sin(d*x + c))/(a^3*b^3*d*x^6 + 2*a^4*b^2*d*x^3 + a^5*b*d)","C",0
113,1,1117,0,1.365187," ","integrate(sin(d*x+c)/x/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{{\left(-36 i \, b^{2} x^{6} - 72 i \, a b x^{3} - 36 i \, a^{2} + {\left(i \, b^{2} x^{6} + 2 i \, a b x^{3} + i \, a^{2} + \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(8 i \, b^{2} x^{6} + 16 i \, a b x^{3} + 8 i \, a^{2} - 8 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(36 i \, b^{2} x^{6} + 72 i \, a b x^{3} + 36 i \, a^{2} + {\left(-i \, b^{2} x^{6} - 2 i \, a b x^{3} - i \, a^{2} - \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(-8 i \, b^{2} x^{6} - 16 i \, a b x^{3} - 8 i \, a^{2} + 8 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-36 i \, b^{2} x^{6} - 72 i \, a b x^{3} - 36 i \, a^{2} + {\left(i \, b^{2} x^{6} + 2 i \, a b x^{3} + i \, a^{2} - \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(8 i \, b^{2} x^{6} + 16 i \, a b x^{3} + 8 i \, a^{2} + 8 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, c\right)} + {\left(36 i \, b^{2} x^{6} + 72 i \, a b x^{3} + 36 i \, a^{2} + {\left(-i \, b^{2} x^{6} - 2 i \, a b x^{3} - i \, a^{2} + \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(-8 i \, b^{2} x^{6} - 16 i \, a b x^{3} - 8 i \, a^{2} - 8 \, \sqrt{3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} - 1\right)}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, c\right)} + {\left(-108 i \, b^{2} x^{6} - 216 i \, a b x^{3} - 108 i \, a^{2}\right)} {\rm Ei}\left(i \, d x\right) e^{\left(i \, c\right)} + {\left(108 i \, b^{2} x^{6} + 216 i \, a b x^{3} + 108 i \, a^{2}\right)} {\rm Ei}\left(-i \, d x\right) e^{\left(-i \, c\right)} + {\left(36 i \, b^{2} x^{6} + 72 i \, a b x^{3} + 36 i \, a^{2} + {\left(2 i \, b^{2} x^{6} + 4 i \, a b x^{3} + 2 i \, a^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(16 i \, b^{2} x^{6} + 32 i \, a b x^{3} + 16 i \, a^{2}\right)} \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(i \, d x + \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(i \, c - \left(-\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} + {\left(-36 i \, b^{2} x^{6} - 72 i \, a b x^{3} - 36 i \, a^{2} + {\left(-2 i \, b^{2} x^{6} - 4 i \, a b x^{3} - 2 i \, a^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{2}{3}} + {\left(-16 i \, b^{2} x^{6} - 32 i \, a b x^{3} - 16 i \, a^{2}\right)} \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} {\rm Ei}\left(-i \, d x + \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right) e^{\left(-i \, c - \left(\frac{i \, a d^{3}}{b}\right)^{\frac{1}{3}}\right)} - 12 \, {\left(a b d x^{4} + a^{2} d x\right)} \cos\left(d x + c\right) + 36 \, {\left(2 \, a b x^{3} + 3 \, a^{2}\right)} \sin\left(d x + c\right)}{216 \, {\left(a^{3} b^{2} x^{6} + 2 \, a^{4} b x^{3} + a^{5}\right)}}"," ",0,"1/216*((-36*I*b^2*x^6 - 72*I*a*b*x^3 - 36*I*a^2 + (I*b^2*x^6 + 2*I*a*b*x^3 + I*a^2 + sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(2/3) + (8*I*b^2*x^6 + 16*I*a*b*x^3 + 8*I*a^2 - 8*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) - I*c) + (36*I*b^2*x^6 + 72*I*a*b*x^3 + 36*I*a^2 + (-I*b^2*x^6 - 2*I*a*b*x^3 - I*a^2 - sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(2/3) + (-8*I*b^2*x^6 - 16*I*a*b*x^3 - 8*I*a^2 + 8*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) + 1) + I*c) + (-36*I*b^2*x^6 - 72*I*a*b*x^3 - 36*I*a^2 + (I*b^2*x^6 + 2*I*a*b*x^3 + I*a^2 - sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(2/3) + (8*I*b^2*x^6 + 16*I*a*b*x^3 + 8*I*a^2 + 8*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + 1/2*(I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) - I*c) + (36*I*b^2*x^6 + 72*I*a*b*x^3 + 36*I*a^2 + (-I*b^2*x^6 - 2*I*a*b*x^3 - I*a^2 + sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(2/3) + (-8*I*b^2*x^6 - 16*I*a*b*x^3 - 8*I*a^2 - 8*sqrt(3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + 1/2*(-I*a*d^3/b)^(1/3)*(I*sqrt(3) - 1))*e^(1/2*(-I*a*d^3/b)^(1/3)*(-I*sqrt(3) + 1) + I*c) + (-108*I*b^2*x^6 - 216*I*a*b*x^3 - 108*I*a^2)*Ei(I*d*x)*e^(I*c) + (108*I*b^2*x^6 + 216*I*a*b*x^3 + 108*I*a^2)*Ei(-I*d*x)*e^(-I*c) + (36*I*b^2*x^6 + 72*I*a*b*x^3 + 36*I*a^2 + (2*I*b^2*x^6 + 4*I*a*b*x^3 + 2*I*a^2)*(-I*a*d^3/b)^(2/3) + (16*I*b^2*x^6 + 32*I*a*b*x^3 + 16*I*a^2)*(-I*a*d^3/b)^(1/3))*Ei(I*d*x + (-I*a*d^3/b)^(1/3))*e^(I*c - (-I*a*d^3/b)^(1/3)) + (-36*I*b^2*x^6 - 72*I*a*b*x^3 - 36*I*a^2 + (-2*I*b^2*x^6 - 4*I*a*b*x^3 - 2*I*a^2)*(I*a*d^3/b)^(2/3) + (-16*I*b^2*x^6 - 32*I*a*b*x^3 - 16*I*a^2)*(I*a*d^3/b)^(1/3))*Ei(-I*d*x + (I*a*d^3/b)^(1/3))*e^(-I*c - (I*a*d^3/b)^(1/3)) - 12*(a*b*d*x^4 + a^2*d*x)*cos(d*x + c) + 36*(2*a*b*x^3 + 3*a^2)*sin(d*x + c))/(a^3*b^2*x^6 + 2*a^4*b*x^3 + a^5)","C",0
