1,1,51,0,1.104938," ","integrate(x^5*(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{3} x^{6} + 6 \, b d x^{2} \sin\left(d x^{2} + c\right) - 3 \, {\left(b d^{2} x^{4} - 2 \, b\right)} \cos\left(d x^{2} + c\right)}{6 \, d^{3}}"," ",0,"1/6*(a*d^3*x^6 + 6*b*d*x^2*sin(d*x^2 + c) - 3*(b*d^2*x^4 - 2*b)*cos(d*x^2 + c))/d^3","A",0
2,1,40,0,1.005585," ","integrate(x^3*(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d^{2} x^{4} - 2 \, b d x^{2} \cos\left(d x^{2} + c\right) + 2 \, b \sin\left(d x^{2} + c\right)}{4 \, d^{2}}"," ",0,"1/4*(a*d^2*x^4 - 2*b*d*x^2*cos(d*x^2 + c) + 2*b*sin(d*x^2 + c))/d^2","A",0
3,1,23,0,0.999881," ","integrate(x*(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\frac{a d x^{2} - b \cos\left(d x^{2} + c\right)}{2 \, d}"," ",0,"1/2*(a*d*x^2 - b*cos(d*x^2 + c))/d","A",0
4,1,38,0,1.111232," ","integrate((a+b*sin(d*x^2+c))/x,x, algorithm=""fricas"")","\frac{1}{2} \, b \cos\left(c\right) \operatorname{Si}\left(d x^{2}\right) + a \log\left(x\right) + \frac{1}{4} \, {\left(b \operatorname{Ci}\left(d x^{2}\right) + b \operatorname{Ci}\left(-d x^{2}\right)\right)} \sin\left(c\right)"," ",0,"1/2*b*cos(c)*sin_integral(d*x^2) + a*log(x) + 1/4*(b*cos_integral(d*x^2) + b*cos_integral(-d*x^2))*sin(c)","A",0
5,1,65,0,0.841694," ","integrate((a+b*sin(d*x^2+c))/x^3,x, algorithm=""fricas"")","-\frac{2 \, b d x^{2} \sin\left(c\right) \operatorname{Si}\left(d x^{2}\right) - {\left(b d x^{2} \operatorname{Ci}\left(d x^{2}\right) + b d x^{2} \operatorname{Ci}\left(-d x^{2}\right)\right)} \cos\left(c\right) + 2 \, b \sin\left(d x^{2} + c\right) + 2 \, a}{4 \, x^{2}}"," ",0,"-1/4*(2*b*d*x^2*sin(c)*sin_integral(d*x^2) - (b*d*x^2*cos_integral(d*x^2) + b*d*x^2*cos_integral(-d*x^2))*cos(c) + 2*b*sin(d*x^2 + c) + 2*a)/x^2","A",0
6,1,85,0,0.969458," ","integrate((a+b*sin(d*x^2+c))/x^5,x, algorithm=""fricas"")","-\frac{2 \, b d^{2} x^{4} \cos\left(c\right) \operatorname{Si}\left(d x^{2}\right) + 2 \, b d x^{2} \cos\left(d x^{2} + c\right) + 2 \, b \sin\left(d x^{2} + c\right) + {\left(b d^{2} x^{4} \operatorname{Ci}\left(d x^{2}\right) + b d^{2} x^{4} \operatorname{Ci}\left(-d x^{2}\right)\right)} \sin\left(c\right) + 2 \, a}{8 \, x^{4}}"," ",0,"-1/8*(2*b*d^2*x^4*cos(c)*sin_integral(d*x^2) + 2*b*d*x^2*cos(d*x^2 + c) + 2*b*sin(d*x^2 + c) + (b*d^2*x^4*cos_integral(d*x^2) + b*d^2*x^4*cos_integral(-d*x^2))*sin(c) + 2*a)/x^4","A",0
7,1,103,0,1.160601," ","integrate(x^4*(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\frac{8 \, a d^{3} x^{5} - 20 \, b d^{2} x^{3} \cos\left(d x^{2} + c\right) - 15 \, \sqrt{2} \pi b \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) - 15 \, \sqrt{2} \pi b \sqrt{\frac{d}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) + 30 \, b d x \sin\left(d x^{2} + c\right)}{40 \, d^{3}}"," ",0,"1/40*(8*a*d^3*x^5 - 20*b*d^2*x^3*cos(d*x^2 + c) - 15*sqrt(2)*pi*b*sqrt(d/pi)*cos(c)*fresnel_sin(sqrt(2)*x*sqrt(d/pi)) - 15*sqrt(2)*pi*b*sqrt(d/pi)*fresnel_cos(sqrt(2)*x*sqrt(d/pi))*sin(c) + 30*b*d*x*sin(d*x^2 + c))/d^3","A",0
8,1,86,0,0.692415," ","integrate(x^2*(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\frac{4 \, a d^{2} x^{3} + 3 \, \sqrt{2} \pi b \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) - 3 \, \sqrt{2} \pi b \sqrt{\frac{d}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) - 6 \, b d x \cos\left(d x^{2} + c\right)}{12 \, d^{2}}"," ",0,"1/12*(4*a*d^2*x^3 + 3*sqrt(2)*pi*b*sqrt(d/pi)*cos(c)*fresnel_cos(sqrt(2)*x*sqrt(d/pi)) - 3*sqrt(2)*pi*b*sqrt(d/pi)*fresnel_sin(sqrt(2)*x*sqrt(d/pi))*sin(c) - 6*b*d*x*cos(d*x^2 + c))/d^2","A",0
9,1,67,0,1.080749," ","integrate(a+b*sin(d*x^2+c),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi b \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) + \sqrt{2} \pi b \sqrt{\frac{d}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) + 2 \, a d x}{2 \, d}"," ",0,"1/2*(sqrt(2)*pi*b*sqrt(d/pi)*cos(c)*fresnel_sin(sqrt(2)*x*sqrt(d/pi)) + sqrt(2)*pi*b*sqrt(d/pi)*fresnel_cos(sqrt(2)*x*sqrt(d/pi))*sin(c) + 2*a*d*x)/d","A",0
10,1,78,0,1.177357," ","integrate((a+b*sin(d*x^2+c))/x^2,x, algorithm=""fricas"")","\frac{\sqrt{2} \pi b x \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) - \sqrt{2} \pi b x \sqrt{\frac{d}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) - b \sin\left(d x^{2} + c\right) - a}{x}"," ",0,"(sqrt(2)*pi*b*x*sqrt(d/pi)*cos(c)*fresnel_cos(sqrt(2)*x*sqrt(d/pi)) - sqrt(2)*pi*b*x*sqrt(d/pi)*fresnel_sin(sqrt(2)*x*sqrt(d/pi))*sin(c) - b*sin(d*x^2 + c) - a)/x","A",0
11,1,98,0,1.135723," ","integrate((a+b*sin(d*x^2+c))/x^4,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{2} \pi b d x^{3} \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) + 2 \, \sqrt{2} \pi b d x^{3} \sqrt{\frac{d}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) + 2 \, b d x^{2} \cos\left(d x^{2} + c\right) + b \sin\left(d x^{2} + c\right) + a}{3 \, x^{3}}"," ",0,"-1/3*(2*sqrt(2)*pi*b*d*x^3*sqrt(d/pi)*cos(c)*fresnel_sin(sqrt(2)*x*sqrt(d/pi)) + 2*sqrt(2)*pi*b*d*x^3*sqrt(d/pi)*fresnel_cos(sqrt(2)*x*sqrt(d/pi))*sin(c) + 2*b*d*x^2*cos(d*x^2 + c) + b*sin(d*x^2 + c) + a)/x^3","A",0
12,1,121,0,1.279108," ","integrate(x^5*(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} x^{6} - 6 \, b^{2} d x^{2} \cos\left(d x^{2} + c\right)^{2} + 3 \, b^{2} d x^{2} - 24 \, {\left(a b d^{2} x^{4} - 2 \, a b\right)} \cos\left(d x^{2} + c\right) + 3 \, {\left(16 \, a b d x^{2} - {\left(2 \, b^{2} d^{2} x^{4} - b^{2}\right)} \cos\left(d x^{2} + c\right)\right)} \sin\left(d x^{2} + c\right)}{24 \, d^{3}}"," ",0,"1/24*(2*(2*a^2 + b^2)*d^3*x^6 - 6*b^2*d*x^2*cos(d*x^2 + c)^2 + 3*b^2*d*x^2 - 24*(a*b*d^2*x^4 - 2*a*b)*cos(d*x^2 + c) + 3*(16*a*b*d*x^2 - (2*b^2*d^2*x^4 - b^2)*cos(d*x^2 + c))*sin(d*x^2 + c))/d^3","A",0
13,1,84,0,0.895763," ","integrate(x^3*(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d^{2} x^{4} - 8 \, a b d x^{2} \cos\left(d x^{2} + c\right) - b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, {\left(b^{2} d x^{2} \cos\left(d x^{2} + c\right) - 4 \, a b\right)} \sin\left(d x^{2} + c\right)}{8 \, d^{2}}"," ",0,"1/8*((2*a^2 + b^2)*d^2*x^4 - 8*a*b*d*x^2*cos(d*x^2 + c) - b^2*cos(d*x^2 + c)^2 - 2*(b^2*d*x^2*cos(d*x^2 + c) - 4*a*b)*sin(d*x^2 + c))/d^2","A",0
14,1,53,0,1.194799," ","integrate(x*(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d x^{2} - b^{2} \cos\left(d x^{2} + c\right) \sin\left(d x^{2} + c\right) - 4 \, a b \cos\left(d x^{2} + c\right)}{4 \, d}"," ",0,"1/4*((2*a^2 + b^2)*d*x^2 - b^2*cos(d*x^2 + c)*sin(d*x^2 + c) - 4*a*b*cos(d*x^2 + c))/d","A",0
15,1,94,0,1.049698," ","integrate((a+b*sin(d*x^2+c))^2/x,x, algorithm=""fricas"")","\frac{1}{4} \, b^{2} \sin\left(2 \, c\right) \operatorname{Si}\left(2 \, d x^{2}\right) + a b \cos\left(c\right) \operatorname{Si}\left(d x^{2}\right) - \frac{1}{8} \, {\left(b^{2} \operatorname{Ci}\left(2 \, d x^{2}\right) + b^{2} \operatorname{Ci}\left(-2 \, d x^{2}\right)\right)} \cos\left(2 \, c\right) + \frac{1}{2} \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(x\right) + \frac{1}{2} \, {\left(a b \operatorname{Ci}\left(d x^{2}\right) + a b \operatorname{Ci}\left(-d x^{2}\right)\right)} \sin\left(c\right)"," ",0,"1/4*b^2*sin(2*c)*sin_integral(2*d*x^2) + a*b*cos(c)*sin_integral(d*x^2) - 1/8*(b^2*cos_integral(2*d*x^2) + b^2*cos_integral(-2*d*x^2))*cos(2*c) + 1/2*(2*a^2 + b^2)*log(x) + 1/2*(a*b*cos_integral(d*x^2) + a*b*cos_integral(-d*x^2))*sin(c)","A",0
16,1,147,0,1.351671," ","integrate((a+b*sin(d*x^2+c))^2/x^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d x^{2} \cos\left(2 \, c\right) \operatorname{Si}\left(2 \, d x^{2}\right) - 4 \, a b d x^{2} \sin\left(c\right) \operatorname{Si}\left(d x^{2}\right) + 2 \, b^{2} \cos\left(d x^{2} + c\right)^{2} - 4 \, a b \sin\left(d x^{2} + c\right) - 2 \, a^{2} - 2 \, b^{2} + 2 \, {\left(a b d x^{2} \operatorname{Ci}\left(d x^{2}\right) + a b d x^{2} \operatorname{Ci}\left(-d x^{2}\right)\right)} \cos\left(c\right) + {\left(b^{2} d x^{2} \operatorname{Ci}\left(2 \, d x^{2}\right) + b^{2} d x^{2} \operatorname{Ci}\left(-2 \, d x^{2}\right)\right)} \sin\left(2 \, c\right)}{4 \, x^{2}}"," ",0,"1/4*(2*b^2*d*x^2*cos(2*c)*sin_integral(2*d*x^2) - 4*a*b*d*x^2*sin(c)*sin_integral(d*x^2) + 2*b^2*cos(d*x^2 + c)^2 - 4*a*b*sin(d*x^2 + c) - 2*a^2 - 2*b^2 + 2*(a*b*d*x^2*cos_integral(d*x^2) + a*b*d*x^2*cos_integral(-d*x^2))*cos(c) + (b^2*d*x^2*cos_integral(2*d*x^2) + b^2*d*x^2*cos_integral(-2*d*x^2))*sin(2*c))/x^2","A",0
17,1,189,0,0.942365," ","integrate((a+b*sin(d*x^2+c))^2/x^5,x, algorithm=""fricas"")","-\frac{2 \, b^{2} d^{2} x^{4} \sin\left(2 \, c\right) \operatorname{Si}\left(2 \, d x^{2}\right) + 2 \, a b d^{2} x^{4} \cos\left(c\right) \operatorname{Si}\left(d x^{2}\right) + 2 \, a b d x^{2} \cos\left(d x^{2} + c\right) - b^{2} \cos\left(d x^{2} + c\right)^{2} + a^{2} + b^{2} - {\left(b^{2} d^{2} x^{4} \operatorname{Ci}\left(2 \, d x^{2}\right) + b^{2} d^{2} x^{4} \operatorname{Ci}\left(-2 \, d x^{2}\right)\right)} \cos\left(2 \, c\right) + 2 \, {\left(b^{2} d x^{2} \cos\left(d x^{2} + c\right) + a b\right)} \sin\left(d x^{2} + c\right) + {\left(a b d^{2} x^{4} \operatorname{Ci}\left(d x^{2}\right) + a b d^{2} x^{4} \operatorname{Ci}\left(-d x^{2}\right)\right)} \sin\left(c\right)}{4 \, x^{4}}"," ",0,"-1/4*(2*b^2*d^2*x^4*sin(2*c)*sin_integral(2*d*x^2) + 2*a*b*d^2*x^4*cos(c)*sin_integral(d*x^2) + 2*a*b*d*x^2*cos(d*x^2 + c) - b^2*cos(d*x^2 + c)^2 + a^2 + b^2 - (b^2*d^2*x^4*cos_integral(2*d*x^2) + b^2*d^2*x^4*cos_integral(-2*d*x^2))*cos(2*c) + 2*(b^2*d*x^2*cos(d*x^2 + c) + a*b)*sin(d*x^2 + c) + (a*b*d^2*x^4*cos_integral(d*x^2) + a*b*d^2*x^4*cos_integral(-d*x^2))*sin(c))/x^4","A",0
18,1,216,0,1.397706," ","integrate(x^4*(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{32 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} x^{5} - 320 \, a b d^{2} x^{3} \cos\left(d x^{2} + c\right) - 60 \, b^{2} d x \cos\left(d x^{2} + c\right)^{2} - 240 \, \sqrt{2} \pi a b \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) - 240 \, \sqrt{2} \pi a b \sqrt{\frac{d}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) + 15 \, \pi b^{2} \sqrt{\frac{d}{\pi}} \cos\left(2 \, c\right) \operatorname{C}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) - 15 \, \pi b^{2} \sqrt{\frac{d}{\pi}} \operatorname{S}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) \sin\left(2 \, c\right) + 30 \, b^{2} d x - 80 \, {\left(b^{2} d^{2} x^{3} \cos\left(d x^{2} + c\right) - 6 \, a b d x\right)} \sin\left(d x^{2} + c\right)}{320 \, d^{3}}"," ",0,"1/320*(32*(2*a^2 + b^2)*d^3*x^5 - 320*a*b*d^2*x^3*cos(d*x^2 + c) - 60*b^2*d*x*cos(d*x^2 + c)^2 - 240*sqrt(2)*pi*a*b*sqrt(d/pi)*cos(c)*fresnel_sin(sqrt(2)*x*sqrt(d/pi)) - 240*sqrt(2)*pi*a*b*sqrt(d/pi)*fresnel_cos(sqrt(2)*x*sqrt(d/pi))*sin(c) + 15*pi*b^2*sqrt(d/pi)*cos(2*c)*fresnel_cos(2*x*sqrt(d/pi)) - 15*pi*b^2*sqrt(d/pi)*fresnel_sin(2*x*sqrt(d/pi))*sin(2*c) + 30*b^2*d*x - 80*(b^2*d^2*x^3*cos(d*x^2 + c) - 6*a*b*d*x)*sin(d*x^2 + c))/d^3","A",0
19,1,176,0,1.439269," ","integrate(x^2*(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} x^{3} + 24 \, \sqrt{2} \pi a b \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) - 12 \, b^{2} d x \cos\left(d x^{2} + c\right) \sin\left(d x^{2} + c\right) - 24 \, \sqrt{2} \pi a b \sqrt{\frac{d}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) + 3 \, \pi b^{2} \sqrt{\frac{d}{\pi}} \cos\left(2 \, c\right) \operatorname{S}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) + 3 \, \pi b^{2} \sqrt{\frac{d}{\pi}} \operatorname{C}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) \sin\left(2 \, c\right) - 48 \, a b d x \cos\left(d x^{2} + c\right)}{48 \, d^{2}}"," ",0,"1/48*(8*(2*a^2 + b^2)*d^2*x^3 + 24*sqrt(2)*pi*a*b*sqrt(d/pi)*cos(c)*fresnel_cos(sqrt(2)*x*sqrt(d/pi)) - 12*b^2*d*x*cos(d*x^2 + c)*sin(d*x^2 + c) - 24*sqrt(2)*pi*a*b*sqrt(d/pi)*fresnel_sin(sqrt(2)*x*sqrt(d/pi))*sin(c) + 3*pi*b^2*sqrt(d/pi)*cos(2*c)*fresnel_sin(2*x*sqrt(d/pi)) + 3*pi*b^2*sqrt(d/pi)*fresnel_cos(2*x*sqrt(d/pi))*sin(2*c) - 48*a*b*d*x*cos(d*x^2 + c))/d^2","A",0
20,1,134,0,1.342436," ","integrate((a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \pi a b \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) + 4 \, \sqrt{2} \pi a b \sqrt{\frac{d}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) - \pi b^{2} \sqrt{\frac{d}{\pi}} \cos\left(2 \, c\right) \operatorname{C}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) + \pi b^{2} \sqrt{\frac{d}{\pi}} \operatorname{S}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) \sin\left(2 \, c\right) + 2 \, {\left(2 \, a^{2} + b^{2}\right)} d x}{4 \, d}"," ",0,"1/4*(4*sqrt(2)*pi*a*b*sqrt(d/pi)*cos(c)*fresnel_sin(sqrt(2)*x*sqrt(d/pi)) + 4*sqrt(2)*pi*a*b*sqrt(d/pi)*fresnel_cos(sqrt(2)*x*sqrt(d/pi))*sin(c) - pi*b^2*sqrt(d/pi)*cos(2*c)*fresnel_cos(2*x*sqrt(d/pi)) + pi*b^2*sqrt(d/pi)*fresnel_sin(2*x*sqrt(d/pi))*sin(2*c) + 2*(2*a^2 + b^2)*d*x)/d","A",0
21,1,159,0,1.296800," ","integrate((a+b*sin(d*x^2+c))^2/x^2,x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} \pi a b x \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) - 2 \, \sqrt{2} \pi a b x \sqrt{\frac{d}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) + \pi b^{2} x \sqrt{\frac{d}{\pi}} \cos\left(2 \, c\right) \operatorname{S}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) + \pi b^{2} x \sqrt{\frac{d}{\pi}} \operatorname{C}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) \sin\left(2 \, c\right) + b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}{x}"," ",0,"(2*sqrt(2)*pi*a*b*x*sqrt(d/pi)*cos(c)*fresnel_cos(sqrt(2)*x*sqrt(d/pi)) - 2*sqrt(2)*pi*a*b*x*sqrt(d/pi)*fresnel_sin(sqrt(2)*x*sqrt(d/pi))*sin(c) + pi*b^2*x*sqrt(d/pi)*cos(2*c)*fresnel_sin(2*x*sqrt(d/pi)) + pi*b^2*x*sqrt(d/pi)*fresnel_cos(2*x*sqrt(d/pi))*sin(2*c) + b^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2)/x","A",0
22,1,206,0,1.222058," ","integrate((a+b*sin(d*x^2+c))^2/x^4,x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \pi a b d x^{3} \sqrt{\frac{d}{\pi}} \cos\left(c\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) + 4 \, \sqrt{2} \pi a b d x^{3} \sqrt{\frac{d}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{d}{\pi}}\right) \sin\left(c\right) - 4 \, \pi b^{2} d x^{3} \sqrt{\frac{d}{\pi}} \cos\left(2 \, c\right) \operatorname{C}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) + 4 \, \pi b^{2} d x^{3} \sqrt{\frac{d}{\pi}} \operatorname{S}\left(2 \, x \sqrt{\frac{d}{\pi}}\right) \sin\left(2 \, c\right) + 4 \, a b d x^{2} \cos\left(d x^{2} + c\right) - b^{2} \cos\left(d x^{2} + c\right)^{2} + a^{2} + b^{2} + 2 \, {\left(2 \, b^{2} d x^{2} \cos\left(d x^{2} + c\right) + a b\right)} \sin\left(d x^{2} + c\right)}{3 \, x^{3}}"," ",0,"-1/3*(4*sqrt(2)*pi*a*b*d*x^3*sqrt(d/pi)*cos(c)*fresnel_sin(sqrt(2)*x*sqrt(d/pi)) + 4*sqrt(2)*pi*a*b*d*x^3*sqrt(d/pi)*fresnel_cos(sqrt(2)*x*sqrt(d/pi))*sin(c) - 4*pi*b^2*d*x^3*sqrt(d/pi)*cos(2*c)*fresnel_cos(2*x*sqrt(d/pi)) + 4*pi*b^2*d*x^3*sqrt(d/pi)*fresnel_sin(2*x*sqrt(d/pi))*sin(2*c) + 4*a*b*d*x^2*cos(d*x^2 + c) - b^2*cos(d*x^2 + c)^2 + a^2 + b^2 + 2*(2*b^2*d*x^2*cos(d*x^2 + c) + a*b)*sin(d*x^2 + c))/x^3","A",0
23,1,79,0,1.237165," ","integrate(x^5*sin(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{{\left(9 \, b^{2} x^{4} - 2\right)} \cos\left(b x^{2} + a\right)^{3} - 3 \, {\left(9 \, b^{2} x^{4} - 14\right)} \cos\left(b x^{2} + a\right) - 6 \, {\left(b x^{2} \cos\left(b x^{2} + a\right)^{2} - 7 \, b x^{2}\right)} \sin\left(b x^{2} + a\right)}{54 \, b^{3}}"," ",0,"1/54*((9*b^2*x^4 - 2)*cos(b*x^2 + a)^3 - 3*(9*b^2*x^4 - 14)*cos(b*x^2 + a) - 6*(b*x^2*cos(b*x^2 + a)^2 - 7*b*x^2)*sin(b*x^2 + a))/b^3","A",0
24,1,58,0,0.964187," ","integrate(x^3*sin(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{3 \, b x^{2} \cos\left(b x^{2} + a\right)^{3} - 9 \, b x^{2} \cos\left(b x^{2} + a\right) - {\left(\cos\left(b x^{2} + a\right)^{2} - 7\right)} \sin\left(b x^{2} + a\right)}{18 \, b^{2}}"," ",0,"1/18*(3*b*x^2*cos(b*x^2 + a)^3 - 9*b*x^2*cos(b*x^2 + a) - (cos(b*x^2 + a)^2 - 7)*sin(b*x^2 + a))/b^2","A",0
25,1,26,0,1.319254," ","integrate(x*sin(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{\cos\left(b x^{2} + a\right)^{3} - 3 \, \cos\left(b x^{2} + a\right)}{6 \, b}"," ",0,"1/6*(cos(b*x^2 + a)^3 - 3*cos(b*x^2 + a))/b","A",0
26,1,63,0,0.999818," ","integrate(sin(b*x^2+a)^3/x,x, algorithm=""fricas"")","-\frac{1}{16} \, {\left(\operatorname{Ci}\left(3 \, b x^{2}\right) + \operatorname{Ci}\left(-3 \, b x^{2}\right)\right)} \sin\left(3 \, a\right) + \frac{3}{16} \, {\left(\operatorname{Ci}\left(b x^{2}\right) + \operatorname{Ci}\left(-b x^{2}\right)\right)} \sin\left(a\right) - \frac{1}{8} \, \cos\left(3 \, a\right) \operatorname{Si}\left(3 \, b x^{2}\right) + \frac{3}{8} \, \cos\left(a\right) \operatorname{Si}\left(b x^{2}\right)"," ",0,"-1/16*(cos_integral(3*b*x^2) + cos_integral(-3*b*x^2))*sin(3*a) + 3/16*(cos_integral(b*x^2) + cos_integral(-b*x^2))*sin(a) - 1/8*cos(3*a)*sin_integral(3*b*x^2) + 3/8*cos(a)*sin_integral(b*x^2)","A",0
27,1,118,0,1.214571," ","integrate(sin(b*x^2+a)^3/x^3,x, algorithm=""fricas"")","\frac{6 \, b x^{2} \sin\left(3 \, a\right) \operatorname{Si}\left(3 \, b x^{2}\right) - 6 \, b x^{2} \sin\left(a\right) \operatorname{Si}\left(b x^{2}\right) - 3 \, {\left(b x^{2} \operatorname{Ci}\left(3 \, b x^{2}\right) + b x^{2} \operatorname{Ci}\left(-3 \, b x^{2}\right)\right)} \cos\left(3 \, a\right) + 3 \, {\left(b x^{2} \operatorname{Ci}\left(b x^{2}\right) + b x^{2} \operatorname{Ci}\left(-b x^{2}\right)\right)} \cos\left(a\right) + 8 \, {\left(\cos\left(b x^{2} + a\right)^{2} - 1\right)} \sin\left(b x^{2} + a\right)}{16 \, x^{2}}"," ",0,"1/16*(6*b*x^2*sin(3*a)*sin_integral(3*b*x^2) - 6*b*x^2*sin(a)*sin_integral(b*x^2) - 3*(b*x^2*cos_integral(3*b*x^2) + b*x^2*cos_integral(-3*b*x^2))*cos(3*a) + 3*(b*x^2*cos_integral(b*x^2) + b*x^2*cos_integral(-b*x^2))*cos(a) + 8*(cos(b*x^2 + a)^2 - 1)*sin(b*x^2 + a))/x^2","A",0
28,1,147,0,1.245060," ","integrate(x^2*sin(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{24 \, b x \cos\left(b x^{2} + a\right)^{3} - \sqrt{6} \pi \sqrt{\frac{b}{\pi}} \cos\left(3 \, a\right) \operatorname{C}\left(\sqrt{6} x \sqrt{\frac{b}{\pi}}\right) + 27 \, \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) + \sqrt{6} \pi \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{6} x \sqrt{\frac{b}{\pi}}\right) \sin\left(3 \, a\right) - 27 \, \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(a\right) - 72 \, b x \cos\left(b x^{2} + a\right)}{144 \, b^{2}}"," ",0,"1/144*(24*b*x*cos(b*x^2 + a)^3 - sqrt(6)*pi*sqrt(b/pi)*cos(3*a)*fresnel_cos(sqrt(6)*x*sqrt(b/pi)) + 27*sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*x*sqrt(b/pi)) + sqrt(6)*pi*sqrt(b/pi)*fresnel_sin(sqrt(6)*x*sqrt(b/pi))*sin(3*a) - 27*sqrt(2)*pi*sqrt(b/pi)*fresnel_sin(sqrt(2)*x*sqrt(b/pi))*sin(a) - 72*b*x*cos(b*x^2 + a))/b^2","A",0
29,1,120,0,0.838865," ","integrate(sin(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{6} \pi \sqrt{\frac{b}{\pi}} \cos\left(3 \, a\right) \operatorname{S}\left(\sqrt{6} x \sqrt{\frac{b}{\pi}}\right) - 9 \, \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) + \sqrt{6} \pi \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\sqrt{6} x \sqrt{\frac{b}{\pi}}\right) \sin\left(3 \, a\right) - 9 \, \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(a\right)}{24 \, b}"," ",0,"-1/24*(sqrt(6)*pi*sqrt(b/pi)*cos(3*a)*fresnel_sin(sqrt(6)*x*sqrt(b/pi)) - 9*sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_sin(sqrt(2)*x*sqrt(b/pi)) + sqrt(6)*pi*sqrt(b/pi)*fresnel_cos(sqrt(6)*x*sqrt(b/pi))*sin(3*a) - 9*sqrt(2)*pi*sqrt(b/pi)*fresnel_cos(sqrt(2)*x*sqrt(b/pi))*sin(a))/b","A",0
30,1,147,0,0.905985," ","integrate(sin(b*x^2+a)^3/x^2,x, algorithm=""fricas"")","-\frac{\sqrt{6} \pi x \sqrt{\frac{b}{\pi}} \cos\left(3 \, a\right) \operatorname{C}\left(\sqrt{6} x \sqrt{\frac{b}{\pi}}\right) - 3 \, \sqrt{2} \pi x \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) - \sqrt{6} \pi x \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{6} x \sqrt{\frac{b}{\pi}}\right) \sin\left(3 \, a\right) + 3 \, \sqrt{2} \pi x \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(a\right) - 4 \, {\left(\cos\left(b x^{2} + a\right)^{2} - 1\right)} \sin\left(b x^{2} + a\right)}{4 \, x}"," ",0,"-1/4*(sqrt(6)*pi*x*sqrt(b/pi)*cos(3*a)*fresnel_cos(sqrt(6)*x*sqrt(b/pi)) - 3*sqrt(2)*pi*x*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*x*sqrt(b/pi)) - sqrt(6)*pi*x*sqrt(b/pi)*fresnel_sin(sqrt(6)*x*sqrt(b/pi))*sin(3*a) + 3*sqrt(2)*pi*x*sqrt(b/pi)*fresnel_sin(sqrt(2)*x*sqrt(b/pi))*sin(a) - 4*(cos(b*x^2 + a)^2 - 1)*sin(b*x^2 + a))/x","A",0
31,1,51,0,1.165240," ","integrate(x^2*sin(x^2)^3,x, algorithm=""fricas"")","\frac{1}{6} \, x \cos\left(x^{2}\right)^{3} - \frac{1}{2} \, x \cos\left(x^{2}\right) - \frac{1}{144} \, \sqrt{6} \sqrt{\pi} \operatorname{C}\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) + \frac{3}{16} \, \sqrt{2} \sqrt{\pi} \operatorname{C}\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)"," ",0,"1/6*x*cos(x^2)^3 - 1/2*x*cos(x^2) - 1/144*sqrt(6)*sqrt(pi)*fresnel_cos(sqrt(6)*x/sqrt(pi)) + 3/16*sqrt(2)*sqrt(pi)*fresnel_cos(sqrt(2)*x/sqrt(pi))","A",0
32,1,73,0,1.096503," ","integrate(x^4*cos(x^2)*sin(x^2)^2,x, algorithm=""fricas"")","-\frac{1}{12} \, x \cos\left(x^{2}\right)^{3} + \frac{1}{4} \, x \cos\left(x^{2}\right) + \frac{1}{288} \, \sqrt{6} \sqrt{\pi} \operatorname{C}\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \frac{3}{32} \, \sqrt{2} \sqrt{\pi} \operatorname{C}\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right) - \frac{1}{6} \, {\left(x^{3} \cos\left(x^{2}\right)^{2} - x^{3}\right)} \sin\left(x^{2}\right)"," ",0,"-1/12*x*cos(x^2)^3 + 1/4*x*cos(x^2) + 1/288*sqrt(6)*sqrt(pi)*fresnel_cos(sqrt(6)*x/sqrt(pi)) - 3/32*sqrt(2)*sqrt(pi)*fresnel_cos(sqrt(2)*x/sqrt(pi)) - 1/6*(x^3*cos(x^2)^2 - x^3)*sin(x^2)","A",0
33,1,52,0,0.978912," ","integrate(x*sin(b*x^2+a)^7,x, algorithm=""fricas"")","\frac{5 \, \cos\left(b x^{2} + a\right)^{7} - 21 \, \cos\left(b x^{2} + a\right)^{5} + 35 \, \cos\left(b x^{2} + a\right)^{3} - 35 \, \cos\left(b x^{2} + a\right)}{70 \, b}"," ",0,"1/70*(5*cos(b*x^2 + a)^7 - 21*cos(b*x^2 + a)^5 + 35*cos(b*x^2 + a)^3 - 35*cos(b*x^2 + a))/b","A",0
34,1,47,0,1.032003," ","integrate((1+sin(x^2))^2/x^3,x, algorithm=""fricas"")","\frac{x^{2} \operatorname{Ci}\left(-x^{2}\right) + x^{2} \operatorname{Ci}\left(x^{2}\right) + x^{2} \operatorname{Si}\left(2 \, x^{2}\right) + \cos\left(x^{2}\right)^{2} - 2 \, \sin\left(x^{2}\right) - 2}{2 \, x^{2}}"," ",0,"1/2*(x^2*cos_integral(-x^2) + x^2*cos_integral(x^2) + x^2*sin_integral(2*x^2) + cos(x^2)^2 - 2*sin(x^2) - 2)/x^2","A",0
35,1,1439,0,1.503474," ","integrate(x^5/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","-\frac{-4 i \, b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 i \, b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 i \, b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 i \, b d x^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, b c^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, b c^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, b c^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, b c^{2} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d^{2} x^{4} - b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 4 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{8 \, {\left(a^{2} - b^{2}\right)} d^{3}}"," ",0,"-1/8*(-4*I*b*d*x^2*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 4*I*b*d*x^2*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 4*I*b*d*x^2*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 4*I*b*d*x^2*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*b*c^2*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*b*c^2*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*b*c^2*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*b*c^2*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(b*d^2*x^4 - b*c^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^2*x^4 - b*c^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d^2*x^4 - b*c^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d^2*x^4 - b*c^2)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 4*b*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*b*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*b*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*b*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b))/((a^2 - b^2)*d^3)","C",0
36,1,1045,0,1.638676," ","integrate(x^3/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","-\frac{2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b d x^{2} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d x^{2} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d x^{2} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d x^{2} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{8 \, {\left(a^{2} - b^{2}\right)} d^{2}}"," ",0,"-1/8*(2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b*d*x^2 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*x^2 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d*x^2 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*x^2 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2 - b^2)*d^2)","B",0
37,1,208,0,1.234514," ","integrate(x/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x^{2} + c\right) \sin\left(d x^{2} + c\right) + b \cos\left(d x^{2} + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}\right)}{4 \, {\left(a^{2} - b^{2}\right)} d}, -\frac{\arctan\left(-\frac{a \sin\left(d x^{2} + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x^{2} + c\right)}\right)}{2 \, \sqrt{a^{2} - b^{2}} d}\right]"," ",0,"[-1/4*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2 + 2*(a*cos(d*x^2 + c)*sin(d*x^2 + c) + b*cos(d*x^2 + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2))/((a^2 - b^2)*d), -1/2*arctan(-(a*sin(d*x^2 + c) + b)/(sqrt(a^2 - b^2)*cos(d*x^2 + c)))/(sqrt(a^2 - b^2)*d)]","A",0
38,0,0,0,1.121605," ","integrate(1/x/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \sin\left(d x^{2} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sin(d*x^2 + c) + a*x), x)","F",0
39,0,0,0,1.146180," ","integrate(1/x^3/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{3} \sin\left(d x^{2} + c\right) + a x^{3}}, x\right)"," ",0,"integral(1/(b*x^3*sin(d*x^2 + c) + a*x^3), x)","F",0
40,0,0,0,1.193612," ","integrate(x^2/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \sin\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*sin(d*x^2 + c) + a), x)","F",0
41,0,0,0,0.966658," ","integrate(1/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \sin\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral(1/(b*sin(d*x^2 + c) + a), x)","F",0
42,0,0,0,1.179776," ","integrate(1/x^2/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} \sin\left(d x^{2} + c\right) + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*sin(d*x^2 + c) + a*x^2), x)","F",0
43,1,2473,0,1.746636," ","integrate(x^5/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} b - b^{3}\right)} d^{2} x^{4} \cos\left(d x^{2} + c\right) + 4 \, {\left(a b^{2} \sin\left(d x^{2} + c\right) + a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a b^{2} \sin\left(d x^{2} + c\right) + a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a b^{2} \sin\left(d x^{2} + c\right) + a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a b^{2} \sin\left(d x^{2} + c\right) + a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{-i \, a \cos\left(d x^{2} + c\right) + a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + {\left(4 i \, a^{3} - 4 i \, a b^{2} + {\left(4 i \, a^{2} b - 4 i \, b^{3}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(2 i \, a b^{2} d x^{2} \sin\left(d x^{2} + c\right) + 2 i \, a^{2} b d x^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(4 i \, a^{3} - 4 i \, a b^{2} + {\left(4 i \, a^{2} b - 4 i \, b^{3}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(-2 i \, a b^{2} d x^{2} \sin\left(d x^{2} + c\right) - 2 i \, a^{2} b d x^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-4 i \, a^{3} + 4 i \, a b^{2} + {\left(-4 i \, a^{2} b + 4 i \, b^{3}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(-2 i \, a b^{2} d x^{2} \sin\left(d x^{2} + c\right) - 2 i \, a^{2} b d x^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-4 i \, a^{3} + 4 i \, a b^{2} + {\left(-4 i \, a^{2} b + 4 i \, b^{3}\right)} \sin\left(d x^{2} + c\right) + 2 \, {\left(2 i \, a b^{2} d x^{2} \sin\left(d x^{2} + c\right) + 2 i \, a^{2} b d x^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} c + {\left(a b^{2} c^{2} \sin\left(d x^{2} + c\right) + a^{2} b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} c + {\left(a b^{2} c^{2} \sin\left(d x^{2} + c\right) + a^{2} b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) + 2 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} c - {\left(a b^{2} c^{2} \sin\left(d x^{2} + c\right) + a^{2} b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} c \sin\left(d x^{2} + c\right) + 2 \, {\left(a^{3} - a b^{2}\right)} c - {\left(a b^{2} c^{2} \sin\left(d x^{2} + c\right) + a^{2} b c^{2}\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d x^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right) + {\left(a^{2} b d^{2} x^{4} - a^{2} b c^{2} + {\left(a b^{2} d^{2} x^{4} - a b^{2} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d x^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right) - {\left(a^{2} b d^{2} x^{4} - a^{2} b c^{2} + {\left(a b^{2} d^{2} x^{4} - a b^{2} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d x^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right) + {\left(a^{2} b d^{2} x^{4} - a^{2} b c^{2} + {\left(a b^{2} d^{2} x^{4} - a b^{2} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(2 \, {\left(a^{3} - a b^{2}\right)} d x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d x^{2} + {\left(a^{2} b - b^{3}\right)} c\right)} \sin\left(d x^{2} + c\right) - {\left(a^{2} b d^{2} x^{4} - a^{2} b c^{2} + {\left(a b^{2} d^{2} x^{4} - a b^{2} c^{2}\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{8 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sin\left(d x^{2} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)}}"," ",0,"1/8*(4*(a^2*b - b^3)*d^2*x^4*cos(d*x^2 + c) + 4*(a*b^2*sin(d*x^2 + c) + a^2*b)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(a*b^2*sin(d*x^2 + c) + a^2*b)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) + 4*(a*b^2*sin(d*x^2 + c) + a^2*b)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) - 4*(a*b^2*sin(d*x^2 + c) + a^2*b)*sqrt(-(a^2 - b^2)/b^2)*polylog(3, -(-I*a*cos(d*x^2 + c) + a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))/b) + (4*I*a^3 - 4*I*a*b^2 + (4*I*a^2*b - 4*I*b^3)*sin(d*x^2 + c) + 2*(2*I*a*b^2*d*x^2*sin(d*x^2 + c) + 2*I*a^2*b*d*x^2)*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (4*I*a^3 - 4*I*a*b^2 + (4*I*a^2*b - 4*I*b^3)*sin(d*x^2 + c) + 2*(-2*I*a*b^2*d*x^2*sin(d*x^2 + c) - 2*I*a^2*b*d*x^2)*sqrt(-(a^2 - b^2)/b^2))*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-4*I*a^3 + 4*I*a*b^2 + (-4*I*a^2*b + 4*I*b^3)*sin(d*x^2 + c) + 2*(-2*I*a*b^2*d*x^2*sin(d*x^2 + c) - 2*I*a^2*b*d*x^2)*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-4*I*a^3 + 4*I*a*b^2 + (-4*I*a^2*b + 4*I*b^3)*sin(d*x^2 + c) + 2*(2*I*a*b^2*d*x^2*sin(d*x^2 + c) + 2*I*a^2*b*d*x^2)*sqrt(-(a^2 - b^2)/b^2))*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(2*(a^2*b - b^3)*c*sin(d*x^2 + c) + 2*(a^3 - a*b^2)*c + (a*b^2*c^2*sin(d*x^2 + c) + a^2*b*c^2)*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(2*(a^2*b - b^3)*c*sin(d*x^2 + c) + 2*(a^3 - a*b^2)*c + (a*b^2*c^2*sin(d*x^2 + c) + a^2*b*c^2)*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) + 2*(2*(a^2*b - b^3)*c*sin(d*x^2 + c) + 2*(a^3 - a*b^2)*c - (a*b^2*c^2*sin(d*x^2 + c) + a^2*b*c^2)*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*(2*(a^2*b - b^3)*c*sin(d*x^2 + c) + 2*(a^3 - a*b^2)*c - (a*b^2*c^2*sin(d*x^2 + c) + a^2*b*c^2)*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*(2*(a^3 - a*b^2)*d*x^2 + 2*(a^3 - a*b^2)*c + 2*((a^2*b - b^3)*d*x^2 + (a^2*b - b^3)*c)*sin(d*x^2 + c) + (a^2*b*d^2*x^4 - a^2*b*c^2 + (a*b^2*d^2*x^4 - a*b^2*c^2)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^3 - a*b^2)*d*x^2 + 2*(a^3 - a*b^2)*c + 2*((a^2*b - b^3)*d*x^2 + (a^2*b - b^3)*c)*sin(d*x^2 + c) - (a^2*b*d^2*x^4 - a^2*b*c^2 + (a*b^2*d^2*x^4 - a*b^2*c^2)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^3 - a*b^2)*d*x^2 + 2*(a^3 - a*b^2)*c + 2*((a^2*b - b^3)*d*x^2 + (a^2*b - b^3)*c)*sin(d*x^2 + c) + (a^2*b*d^2*x^4 - a^2*b*c^2 + (a*b^2*d^2*x^4 - a*b^2*c^2)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(2*(a^3 - a*b^2)*d*x^2 + 2*(a^3 - a*b^2)*c + 2*((a^2*b - b^3)*d*x^2 + (a^2*b - b^3)*c)*sin(d*x^2 + c) - (a^2*b*d^2*x^4 - a^2*b*c^2 + (a*b^2*d^2*x^4 - a*b^2*c^2)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2))*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^4*b - 2*a^2*b^3 + b^5)*d^3*sin(d*x^2 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d^3)","C",0
44,1,1509,0,1.613745," ","integrate(x^3/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b - b^{3}\right)} d x^{2} \cos\left(d x^{2} + c\right) + {\left(i \, a b^{2} \sin\left(d x^{2} + c\right) + i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, a b^{2} \sin\left(d x^{2} + c\right) - i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, a b^{2} \sin\left(d x^{2} + c\right) - i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, a b^{2} \sin\left(d x^{2} + c\right) + i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a^{2} b d x^{2} + a^{2} b c + {\left(a b^{2} d x^{2} + a b^{2} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d x^{2} + a^{2} b c + {\left(a b^{2} d x^{2} + a b^{2} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) + i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a^{2} b d x^{2} + a^{2} b c + {\left(a b^{2} d x^{2} + a b^{2} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) + {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d x^{2} + a^{2} b c + {\left(a b^{2} d x^{2} + a b^{2} c\right)} \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{2} + c\right) - a \sin\left(d x^{2} + c\right) - {\left(b \cos\left(d x^{2} + c\right) - i \, b \sin\left(d x^{2} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{2} + c\right) + {\left(a b^{2} c \sin\left(d x^{2} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{2} + c\right) + {\left(a b^{2} c \sin\left(d x^{2} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{2} + c\right) - {\left(a b^{2} c \sin\left(d x^{2} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x^{2} + c\right) + 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{2} + c\right) - {\left(a b^{2} c \sin\left(d x^{2} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x^{2} + c\right) - 2 i \, b \sin\left(d x^{2} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right)}{4 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \sin\left(d x^{2} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2}\right)}}"," ",0,"1/4*(2*(a^2*b - b^3)*d*x^2*cos(d*x^2 + c) + (I*a*b^2*sin(d*x^2 + c) + I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*a*b^2*sin(d*x^2 + c) - I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*a*b^2*sin(d*x^2 + c) - I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*a*b^2*sin(d*x^2 + c) + I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (a^2*b*d*x^2 + a^2*b*c + (a*b^2*d*x^2 + a*b^2*c)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a^2*b*d*x^2 + a^2*b*c + (a*b^2*d*x^2 + a*b^2*c)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) + I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a^2*b*d*x^2 + a^2*b*c + (a*b^2*d*x^2 + a*b^2*c)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) + (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a^2*b*d*x^2 + a^2*b*c + (a*b^2*d*x^2 + a*b^2*c)*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^2 + c) - a*sin(d*x^2 + c) - (b*cos(d*x^2 + c) - I*b*sin(d*x^2 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^2 + c) + (a*b^2*c*sin(d*x^2 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^2 + c) + (a*b^2*c*sin(d*x^2 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^2 + c) - (a*b^2*c*sin(d*x^2 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x^2 + c) + 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^2 + c) - (a*b^2*c*sin(d*x^2 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x^2 + c) - 2*I*b*sin(d*x^2 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a))/((a^4*b - 2*a^2*b^3 + b^5)*d^2*sin(d*x^2 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d^2)","B",0
45,1,366,0,1.229150," ","integrate(x/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a b \sin\left(d x^{2} + c\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x^{2} + c\right) \sin\left(d x^{2} + c\right) + b \cos\left(d x^{2} + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x^{2} + c\right)}{4 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x^{2} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}, -\frac{{\left(a b \sin\left(d x^{2} + c\right) + a^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x^{2} + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x^{2} + c\right)}\right) - {\left(a^{2} b - b^{3}\right)} \cos\left(d x^{2} + c\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x^{2} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}\right]"," ",0,"[1/4*((a*b*sin(d*x^2 + c) + a^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2 - 2*(a*cos(d*x^2 + c)*sin(d*x^2 + c) + b*cos(d*x^2 + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2)) + 2*(a^2*b - b^3)*cos(d*x^2 + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*sin(d*x^2 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d), -1/2*((a*b*sin(d*x^2 + c) + a^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x^2 + c) + b)/(sqrt(a^2 - b^2)*cos(d*x^2 + c))) - (a^2*b - b^3)*cos(d*x^2 + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*sin(d*x^2 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)]","A",0
46,0,0,0,1.177521," ","integrate(1/x/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x \cos\left(d x^{2} + c\right)^{2} - 2 \, a b x \sin\left(d x^{2} + c\right) - {\left(a^{2} + b^{2}\right)} x}, x\right)"," ",0,"integral(-1/(b^2*x*cos(d*x^2 + c)^2 - 2*a*b*x*sin(d*x^2 + c) - (a^2 + b^2)*x), x)","F",0
47,0,0,0,1.124475," ","integrate(1/x^3/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x^{3} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b x^{3} \sin\left(d x^{2} + c\right) - {\left(a^{2} + b^{2}\right)} x^{3}}, x\right)"," ",0,"integral(-1/(b^2*x^3*cos(d*x^2 + c)^2 - 2*a*b*x^3*sin(d*x^2 + c) - (a^2 + b^2)*x^3), x)","F",0
48,0,0,0,1.088690," ","integrate(x^2/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{2}}{b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-x^2/(b^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2), x)","F",0
49,0,0,0,0.841615," ","integrate(1/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-1/(b^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2), x)","F",0
50,0,0,0,0.863520," ","integrate(1/x^2/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b x^{2} \sin\left(d x^{2} + c\right) - {\left(a^{2} + b^{2}\right)} x^{2}}, x\right)"," ",0,"integral(-1/(b^2*x^2*cos(d*x^2 + c)^2 - 2*a*b*x^2*sin(d*x^2 + c) - (a^2 + b^2)*x^2), x)","F",0
51,0,0,0,1.102934," ","integrate((e*x)^m*(a+b*sin(d*x^2+c))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \sin\left(d x^{2} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sin(d*x^2 + c) + a)^p, x)","F",0
52,1,321,0,1.288183," ","integrate((e*x)^m*(a+b*sin(d*x^2+c))^3,x, algorithm=""fricas"")","\frac{24 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \left(e x\right)^{m} d x + {\left(b^{3} e m + b^{3} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(\frac{3 i \, d}{e^{2}}\right) - 3 i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, 3 i \, d x^{2}\right) + {\left(-9 i \, a b^{2} e m - 9 i \, a b^{2} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(\frac{2 i \, d}{e^{2}}\right) - 2 i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, 2 i \, d x^{2}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e m + {\left(4 \, a^{2} b + b^{3}\right)} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(\frac{i \, d}{e^{2}}\right) - i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, i \, d x^{2}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e m + {\left(4 \, a^{2} b + b^{3}\right)} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-\frac{i \, d}{e^{2}}\right) + i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -i \, d x^{2}\right) + {\left(9 i \, a b^{2} e m + 9 i \, a b^{2} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-\frac{2 i \, d}{e^{2}}\right) + 2 i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -2 i \, d x^{2}\right) + {\left(b^{3} e m + b^{3} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-\frac{3 i \, d}{e^{2}}\right) + 3 i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -3 i \, d x^{2}\right)}{48 \, {\left(d m + d\right)}}"," ",0,"1/48*(24*(2*a^3 + 3*a*b^2)*(e*x)^m*d*x + (b^3*e*m + b^3*e)*e^(-1/2*(m - 1)*log(3*I*d/e^2) - 3*I*c)*gamma(1/2*m + 1/2, 3*I*d*x^2) + (-9*I*a*b^2*e*m - 9*I*a*b^2*e)*e^(-1/2*(m - 1)*log(2*I*d/e^2) - 2*I*c)*gamma(1/2*m + 1/2, 2*I*d*x^2) - 9*((4*a^2*b + b^3)*e*m + (4*a^2*b + b^3)*e)*e^(-1/2*(m - 1)*log(I*d/e^2) - I*c)*gamma(1/2*m + 1/2, I*d*x^2) - 9*((4*a^2*b + b^3)*e*m + (4*a^2*b + b^3)*e)*e^(-1/2*(m - 1)*log(-I*d/e^2) + I*c)*gamma(1/2*m + 1/2, -I*d*x^2) + (9*I*a*b^2*e*m + 9*I*a*b^2*e)*e^(-1/2*(m - 1)*log(-2*I*d/e^2) + 2*I*c)*gamma(1/2*m + 1/2, -2*I*d*x^2) + (b^3*e*m + b^3*e)*e^(-1/2*(m - 1)*log(-3*I*d/e^2) + 3*I*c)*gamma(1/2*m + 1/2, -3*I*d*x^2))/(d*m + d)","A",0
53,1,198,0,1.225131," ","integrate((e*x)^m*(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, a^{2} + b^{2}\right)} \left(e x\right)^{m} d x + {\left(-i \, b^{2} e m - i \, b^{2} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(\frac{2 i \, d}{e^{2}}\right) - 2 i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, 2 i \, d x^{2}\right) - 8 \, {\left(a b e m + a b e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(\frac{i \, d}{e^{2}}\right) - i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, i \, d x^{2}\right) - 8 \, {\left(a b e m + a b e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-\frac{i \, d}{e^{2}}\right) + i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -i \, d x^{2}\right) + {\left(i \, b^{2} e m + i \, b^{2} e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-\frac{2 i \, d}{e^{2}}\right) + 2 i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -2 i \, d x^{2}\right)}{16 \, {\left(d m + d\right)}}"," ",0,"1/16*(8*(2*a^2 + b^2)*(e*x)^m*d*x + (-I*b^2*e*m - I*b^2*e)*e^(-1/2*(m - 1)*log(2*I*d/e^2) - 2*I*c)*gamma(1/2*m + 1/2, 2*I*d*x^2) - 8*(a*b*e*m + a*b*e)*e^(-1/2*(m - 1)*log(I*d/e^2) - I*c)*gamma(1/2*m + 1/2, I*d*x^2) - 8*(a*b*e*m + a*b*e)*e^(-1/2*(m - 1)*log(-I*d/e^2) + I*c)*gamma(1/2*m + 1/2, -I*d*x^2) + (I*b^2*e*m + I*b^2*e)*e^(-1/2*(m - 1)*log(-2*I*d/e^2) + 2*I*c)*gamma(1/2*m + 1/2, -2*I*d*x^2))/(d*m + d)","A",0
54,1,98,0,1.215541," ","integrate((e*x)^m*(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","\frac{4 \, \left(e x\right)^{m} a d x - {\left(b e m + b e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(\frac{i \, d}{e^{2}}\right) - i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, i \, d x^{2}\right) - {\left(b e m + b e\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-\frac{i \, d}{e^{2}}\right) + i \, c\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -i \, d x^{2}\right)}{4 \, {\left(d m + d\right)}}"," ",0,"1/4*(4*(e*x)^m*a*d*x - (b*e*m + b*e)*e^(-1/2*(m - 1)*log(I*d/e^2) - I*c)*gamma(1/2*m + 1/2, I*d*x^2) - (b*e*m + b*e)*e^(-1/2*(m - 1)*log(-I*d/e^2) + I*c)*gamma(1/2*m + 1/2, -I*d*x^2))/(d*m + d)","A",0
55,0,0,0,0.740335," ","integrate((e*x)^m/(a+b*sin(d*x^2+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b \sin\left(d x^{2} + c\right) + a}, x\right)"," ",0,"integral((e*x)^m/(b*sin(d*x^2 + c) + a), x)","F",0
56,0,0,0,0.870918," ","integrate((e*x)^m/(a+b*sin(d*x^2+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e x\right)^{m}}{b^{2} \cos\left(d x^{2} + c\right)^{2} - 2 \, a b \sin\left(d x^{2} + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(e*x)^m/(b^2*cos(d*x^2 + c)^2 - 2*a*b*sin(d*x^2 + c) - a^2 - b^2), x)","F",0
57,1,40,0,1.167725," ","integrate(x^5*(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\frac{a d^{2} x^{6} - 2 \, b d x^{3} \cos\left(d x^{3} + c\right) + 2 \, b \sin\left(d x^{3} + c\right)}{6 \, d^{2}}"," ",0,"1/6*(a*d^2*x^6 - 2*b*d*x^3*cos(d*x^3 + c) + 2*b*sin(d*x^3 + c))/d^2","A",0
58,1,23,0,1.150727," ","integrate(x^2*(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\frac{a d x^{3} - b \cos\left(d x^{3} + c\right)}{3 \, d}"," ",0,"1/3*(a*d*x^3 - b*cos(d*x^3 + c))/d","A",0
59,1,38,0,0.955275," ","integrate((a+b*sin(d*x^3+c))/x,x, algorithm=""fricas"")","\frac{1}{3} \, b \cos\left(c\right) \operatorname{Si}\left(d x^{3}\right) + a \log\left(x\right) + \frac{1}{6} \, {\left(b \operatorname{Ci}\left(d x^{3}\right) + b \operatorname{Ci}\left(-d x^{3}\right)\right)} \sin\left(c\right)"," ",0,"1/3*b*cos(c)*sin_integral(d*x^3) + a*log(x) + 1/6*(b*cos_integral(d*x^3) + b*cos_integral(-d*x^3))*sin(c)","A",0
60,1,65,0,1.150403," ","integrate((a+b*sin(d*x^3+c))/x^4,x, algorithm=""fricas"")","-\frac{2 \, b d x^{3} \sin\left(c\right) \operatorname{Si}\left(d x^{3}\right) - {\left(b d x^{3} \operatorname{Ci}\left(d x^{3}\right) + b d x^{3} \operatorname{Ci}\left(-d x^{3}\right)\right)} \cos\left(c\right) + 2 \, b \sin\left(d x^{3} + c\right) + 2 \, a}{6 \, x^{3}}"," ",0,"-1/6*(2*b*d*x^3*sin(c)*sin_integral(d*x^3) - (b*d*x^3*cos_integral(d*x^3) + b*d*x^3*cos_integral(-d*x^3))*cos(c) + 2*b*sin(d*x^3 + c) + 2*a)/x^3","A",0
61,1,70,0,1.249184," ","integrate(x^4*(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\frac{9 \, a d^{2} x^{5} - 15 \, b d x^{2} \cos\left(d x^{3} + c\right) + 5 i \, b \left(i \, d\right)^{\frac{1}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) - 5 i \, b \left(-i \, d\right)^{\frac{1}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)}{45 \, d^{2}}"," ",0,"1/45*(9*a*d^2*x^5 - 15*b*d*x^2*cos(d*x^3 + c) + 5*I*b*(I*d)^(1/3)*e^(-I*c)*gamma(2/3, I*d*x^3) - 5*I*b*(-I*d)^(1/3)*e^(I*c)*gamma(2/3, -I*d*x^3))/d^2","A",0
62,1,53,0,1.693385," ","integrate(x*(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\frac{3 \, a d x^{2} - b \left(i \, d\right)^{\frac{1}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) - b \left(-i \, d\right)^{\frac{1}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right)}{6 \, d}"," ",0,"1/6*(3*a*d*x^2 - b*(I*d)^(1/3)*e^(-I*c)*gamma(2/3, I*d*x^3) - b*(-I*d)^(1/3)*e^(I*c)*gamma(2/3, -I*d*x^3))/d","A",0
63,1,62,0,1.346190," ","integrate((a+b*sin(d*x^3+c))/x^2,x, algorithm=""fricas"")","\frac{i \, b \left(i \, d\right)^{\frac{1}{3}} x e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) - i \, b \left(-i \, d\right)^{\frac{1}{3}} x e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right) - 2 \, b \sin\left(d x^{3} + c\right) - 2 \, a}{2 \, x}"," ",0,"1/2*(I*b*(I*d)^(1/3)*x*e^(-I*c)*gamma(2/3, I*d*x^3) - I*b*(-I*d)^(1/3)*x*e^(I*c)*gamma(2/3, -I*d*x^3) - 2*b*sin(d*x^3 + c) - 2*a)/x","A",0
64,1,83,0,1.124150," ","integrate((a+b*sin(d*x^3+c))/x^5,x, algorithm=""fricas"")","\frac{3 \, b \left(i \, d\right)^{\frac{1}{3}} d x^{4} e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + 3 \, b \left(-i \, d\right)^{\frac{1}{3}} d x^{4} e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right) - 6 \, b d x^{3} \cos\left(d x^{3} + c\right) - 2 \, b \sin\left(d x^{3} + c\right) - 2 \, a}{8 \, x^{4}}"," ",0,"1/8*(3*b*(I*d)^(1/3)*d*x^4*e^(-I*c)*gamma(2/3, I*d*x^3) + 3*b*(-I*d)^(1/3)*d*x^4*e^(I*c)*gamma(2/3, -I*d*x^3) - 6*b*d*x^3*cos(d*x^3 + c) - 2*b*sin(d*x^3 + c) - 2*a)/x^4","A",0
65,1,68,0,1.134315," ","integrate(x^3*(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\frac{9 \, a d^{2} x^{4} - 12 \, b d x \cos\left(d x^{3} + c\right) + 2 i \, b \left(i \, d\right)^{\frac{2}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) - 2 i \, b \left(-i \, d\right)^{\frac{2}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right)}{36 \, d^{2}}"," ",0,"1/36*(9*a*d^2*x^4 - 12*b*d*x*cos(d*x^3 + c) + 2*I*b*(I*d)^(2/3)*e^(-I*c)*gamma(1/3, I*d*x^3) - 2*I*b*(-I*d)^(2/3)*e^(I*c)*gamma(1/3, -I*d*x^3))/d^2","A",0
66,1,49,0,0.822569," ","integrate(a+b*sin(d*x^3+c),x, algorithm=""fricas"")","-\frac{b \left(i \, d\right)^{\frac{2}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + b \left(-i \, d\right)^{\frac{2}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) - 6 \, a d x}{6 \, d}"," ",0,"-1/6*(b*(I*d)^(2/3)*e^(-I*c)*gamma(1/3, I*d*x^3) + b*(-I*d)^(2/3)*e^(I*c)*gamma(1/3, -I*d*x^3) - 6*a*d*x)/d","A",0
67,1,66,0,1.188916," ","integrate((a+b*sin(d*x^3+c))/x^3,x, algorithm=""fricas"")","\frac{i \, b \left(i \, d\right)^{\frac{2}{3}} x^{2} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) - i \, b \left(-i \, d\right)^{\frac{2}{3}} x^{2} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) - 2 \, b \sin\left(d x^{3} + c\right) - 2 \, a}{4 \, x^{2}}"," ",0,"1/4*(I*b*(I*d)^(2/3)*x^2*e^(-I*c)*gamma(1/3, I*d*x^3) - I*b*(-I*d)^(2/3)*x^2*e^(I*c)*gamma(1/3, -I*d*x^3) - 2*b*sin(d*x^3 + c) - 2*a)/x^2","A",0
68,1,83,0,1.336214," ","integrate((a+b*sin(d*x^3+c))/x^6,x, algorithm=""fricas"")","\frac{3 \, b \left(i \, d\right)^{\frac{2}{3}} d x^{5} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + 3 \, b \left(-i \, d\right)^{\frac{2}{3}} d x^{5} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) - 6 \, b d x^{3} \cos\left(d x^{3} + c\right) - 4 \, b \sin\left(d x^{3} + c\right) - 4 \, a}{20 \, x^{5}}"," ",0,"1/20*(3*b*(I*d)^(2/3)*d*x^5*e^(-I*c)*gamma(1/3, I*d*x^3) + 3*b*(-I*d)^(2/3)*d*x^5*e^(I*c)*gamma(1/3, -I*d*x^3) - 6*b*d*x^3*cos(d*x^3 + c) - 4*b*sin(d*x^3 + c) - 4*a)/x^5","A",0
69,1,84,0,0.642468," ","integrate(x^5*(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d^{2} x^{6} - 8 \, a b d x^{3} \cos\left(d x^{3} + c\right) - b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, {\left(b^{2} d x^{3} \cos\left(d x^{3} + c\right) - 4 \, a b\right)} \sin\left(d x^{3} + c\right)}{12 \, d^{2}}"," ",0,"1/12*((2*a^2 + b^2)*d^2*x^6 - 8*a*b*d*x^3*cos(d*x^3 + c) - b^2*cos(d*x^3 + c)^2 - 2*(b^2*d*x^3*cos(d*x^3 + c) - 4*a*b)*sin(d*x^3 + c))/d^2","A",0
70,1,53,0,1.018955," ","integrate(x^2*(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} + b^{2}\right)} d x^{3} - b^{2} \cos\left(d x^{3} + c\right) \sin\left(d x^{3} + c\right) - 4 \, a b \cos\left(d x^{3} + c\right)}{6 \, d}"," ",0,"1/6*((2*a^2 + b^2)*d*x^3 - b^2*cos(d*x^3 + c)*sin(d*x^3 + c) - 4*a*b*cos(d*x^3 + c))/d","A",0
71,1,95,0,1.200994," ","integrate((a+b*sin(d*x^3+c))^2/x,x, algorithm=""fricas"")","\frac{1}{6} \, b^{2} \sin\left(2 \, c\right) \operatorname{Si}\left(2 \, d x^{3}\right) + \frac{2}{3} \, a b \cos\left(c\right) \operatorname{Si}\left(d x^{3}\right) - \frac{1}{12} \, {\left(b^{2} \operatorname{Ci}\left(2 \, d x^{3}\right) + b^{2} \operatorname{Ci}\left(-2 \, d x^{3}\right)\right)} \cos\left(2 \, c\right) + \frac{1}{2} \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(x\right) + \frac{1}{3} \, {\left(a b \operatorname{Ci}\left(d x^{3}\right) + a b \operatorname{Ci}\left(-d x^{3}\right)\right)} \sin\left(c\right)"," ",0,"1/6*b^2*sin(2*c)*sin_integral(2*d*x^3) + 2/3*a*b*cos(c)*sin_integral(d*x^3) - 1/12*(b^2*cos_integral(2*d*x^3) + b^2*cos_integral(-2*d*x^3))*cos(2*c) + 1/2*(2*a^2 + b^2)*log(x) + 1/3*(a*b*cos_integral(d*x^3) + a*b*cos_integral(-d*x^3))*sin(c)","A",0
72,1,147,0,0.806058," ","integrate((a+b*sin(d*x^3+c))^2/x^4,x, algorithm=""fricas"")","\frac{2 \, b^{2} d x^{3} \cos\left(2 \, c\right) \operatorname{Si}\left(2 \, d x^{3}\right) - 4 \, a b d x^{3} \sin\left(c\right) \operatorname{Si}\left(d x^{3}\right) + 2 \, b^{2} \cos\left(d x^{3} + c\right)^{2} - 4 \, a b \sin\left(d x^{3} + c\right) - 2 \, a^{2} - 2 \, b^{2} + 2 \, {\left(a b d x^{3} \operatorname{Ci}\left(d x^{3}\right) + a b d x^{3} \operatorname{Ci}\left(-d x^{3}\right)\right)} \cos\left(c\right) + {\left(b^{2} d x^{3} \operatorname{Ci}\left(2 \, d x^{3}\right) + b^{2} d x^{3} \operatorname{Ci}\left(-2 \, d x^{3}\right)\right)} \sin\left(2 \, c\right)}{6 \, x^{3}}"," ",0,"1/6*(2*b^2*d*x^3*cos(2*c)*sin_integral(2*d*x^3) - 4*a*b*d*x^3*sin(c)*sin_integral(d*x^3) + 2*b^2*cos(d*x^3 + c)^2 - 4*a*b*sin(d*x^3 + c) - 2*a^2 - 2*b^2 + 2*(a*b*d*x^3*cos_integral(d*x^3) + a*b*d*x^3*cos_integral(-d*x^3))*cos(c) + (b^2*d*x^3*cos_integral(2*d*x^3) + b^2*d*x^3*cos_integral(-2*d*x^3))*sin(2*c))/x^3","A",0
73,1,150,0,1.169849," ","integrate(x^4*(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{36 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} x^{5} - 60 \, b^{2} d x^{2} \cos\left(d x^{3} + c\right) \sin\left(d x^{3} + c\right) - 240 \, a b d x^{2} \cos\left(d x^{3} + c\right) - 5 \, b^{2} \left(2 i \, d\right)^{\frac{1}{3}} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) + 80 i \, a b \left(i \, d\right)^{\frac{1}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) - 80 i \, a b \left(-i \, d\right)^{\frac{1}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right) - 5 \, b^{2} \left(-2 i \, d\right)^{\frac{1}{3}} e^{\left(2 i \, c\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right)}{360 \, d^{2}}"," ",0,"1/360*(36*(2*a^2 + b^2)*d^2*x^5 - 60*b^2*d*x^2*cos(d*x^3 + c)*sin(d*x^3 + c) - 240*a*b*d*x^2*cos(d*x^3 + c) - 5*b^2*(2*I*d)^(1/3)*e^(-2*I*c)*gamma(2/3, 2*I*d*x^3) + 80*I*a*b*(I*d)^(1/3)*e^(-I*c)*gamma(2/3, I*d*x^3) - 80*I*a*b*(-I*d)^(1/3)*e^(I*c)*gamma(2/3, -I*d*x^3) - 5*b^2*(-2*I*d)^(1/3)*e^(2*I*c)*gamma(2/3, -2*I*d*x^3))/d^2","A",0
74,1,107,0,1.263588," ","integrate(x*(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{-i \, b^{2} \left(2 i \, d\right)^{\frac{1}{3}} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) - 8 \, a b \left(i \, d\right)^{\frac{1}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) - 8 \, a b \left(-i \, d\right)^{\frac{1}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right) + i \, b^{2} \left(-2 i \, d\right)^{\frac{1}{3}} e^{\left(2 i \, c\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right) + 6 \, {\left(2 \, a^{2} + b^{2}\right)} d x^{2}}{24 \, d}"," ",0,"1/24*(-I*b^2*(2*I*d)^(1/3)*e^(-2*I*c)*gamma(2/3, 2*I*d*x^3) - 8*a*b*(I*d)^(1/3)*e^(-I*c)*gamma(2/3, I*d*x^3) - 8*a*b*(-I*d)^(1/3)*e^(I*c)*gamma(2/3, -I*d*x^3) + I*b^2*(-2*I*d)^(1/3)*e^(2*I*c)*gamma(2/3, -2*I*d*x^3) + 6*(2*a^2 + b^2)*d*x^2)/d","A",0
75,1,131,0,1.196259," ","integrate((a+b*sin(d*x^3+c))^2/x^2,x, algorithm=""fricas"")","-\frac{b^{2} \left(2 i \, d\right)^{\frac{1}{3}} x e^{\left(-2 i \, c\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) - 4 i \, a b \left(i \, d\right)^{\frac{1}{3}} x e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + 4 i \, a b \left(-i \, d\right)^{\frac{1}{3}} x e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right) + b^{2} \left(-2 i \, d\right)^{\frac{1}{3}} x e^{\left(2 i \, c\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right) - 4 \, b^{2} \cos\left(d x^{3} + c\right)^{2} + 8 \, a b \sin\left(d x^{3} + c\right) + 4 \, a^{2} + 4 \, b^{2}}{4 \, x}"," ",0,"-1/4*(b^2*(2*I*d)^(1/3)*x*e^(-2*I*c)*gamma(2/3, 2*I*d*x^3) - 4*I*a*b*(I*d)^(1/3)*x*e^(-I*c)*gamma(2/3, I*d*x^3) + 4*I*a*b*(-I*d)^(1/3)*x*e^(I*c)*gamma(2/3, -I*d*x^3) + b^2*(-2*I*d)^(1/3)*x*e^(2*I*c)*gamma(2/3, -2*I*d*x^3) - 4*b^2*cos(d*x^3 + c)^2 + 8*a*b*sin(d*x^3 + c) + 4*a^2 + 4*b^2)/x","A",0
76,1,180,0,1.281013," ","integrate((a+b*sin(d*x^3+c))^2/x^5,x, algorithm=""fricas"")","\frac{3 i \, b^{2} \left(2 i \, d\right)^{\frac{1}{3}} d x^{4} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{2}{3}, 2 i \, d x^{3}\right) + 6 \, a b \left(i \, d\right)^{\frac{1}{3}} d x^{4} e^{\left(-i \, c\right)} \Gamma\left(\frac{2}{3}, i \, d x^{3}\right) + 6 \, a b \left(-i \, d\right)^{\frac{1}{3}} d x^{4} e^{\left(i \, c\right)} \Gamma\left(\frac{2}{3}, -i \, d x^{3}\right) - 3 i \, b^{2} \left(-2 i \, d\right)^{\frac{1}{3}} d x^{4} e^{\left(2 i \, c\right)} \Gamma\left(\frac{2}{3}, -2 i \, d x^{3}\right) - 12 \, a b d x^{3} \cos\left(d x^{3} + c\right) + 2 \, b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a^{2} - 2 \, b^{2} - 4 \, {\left(3 \, b^{2} d x^{3} \cos\left(d x^{3} + c\right) + a b\right)} \sin\left(d x^{3} + c\right)}{8 \, x^{4}}"," ",0,"1/8*(3*I*b^2*(2*I*d)^(1/3)*d*x^4*e^(-2*I*c)*gamma(2/3, 2*I*d*x^3) + 6*a*b*(I*d)^(1/3)*d*x^4*e^(-I*c)*gamma(2/3, I*d*x^3) + 6*a*b*(-I*d)^(1/3)*d*x^4*e^(I*c)*gamma(2/3, -I*d*x^3) - 3*I*b^2*(-2*I*d)^(1/3)*d*x^4*e^(2*I*c)*gamma(2/3, -2*I*d*x^3) - 12*a*b*d*x^3*cos(d*x^3 + c) + 2*b^2*cos(d*x^3 + c)^2 - 2*a^2 - 2*b^2 - 4*(3*b^2*d*x^3*cos(d*x^3 + c) + a*b)*sin(d*x^3 + c))/x^4","A",0
77,1,146,0,0.921377," ","integrate(x^3*(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{18 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} x^{4} - 24 \, b^{2} d x \cos\left(d x^{3} + c\right) \sin\left(d x^{3} + c\right) - 96 \, a b d x \cos\left(d x^{3} + c\right) - b^{2} \left(2 i \, d\right)^{\frac{2}{3}} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) + 16 i \, a b \left(i \, d\right)^{\frac{2}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) - 16 i \, a b \left(-i \, d\right)^{\frac{2}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) - b^{2} \left(-2 i \, d\right)^{\frac{2}{3}} e^{\left(2 i \, c\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right)}{144 \, d^{2}}"," ",0,"1/144*(18*(2*a^2 + b^2)*d^2*x^4 - 24*b^2*d*x*cos(d*x^3 + c)*sin(d*x^3 + c) - 96*a*b*d*x*cos(d*x^3 + c) - b^2*(2*I*d)^(2/3)*e^(-2*I*c)*gamma(1/3, 2*I*d*x^3) + 16*I*a*b*(I*d)^(2/3)*e^(-I*c)*gamma(1/3, I*d*x^3) - 16*I*a*b*(-I*d)^(2/3)*e^(I*c)*gamma(1/3, -I*d*x^3) - b^2*(-2*I*d)^(2/3)*e^(2*I*c)*gamma(1/3, -2*I*d*x^3))/d^2","A",0
78,1,105,0,0.950920," ","integrate((a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{-i \, b^{2} \left(2 i \, d\right)^{\frac{2}{3}} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) - 8 \, a b \left(i \, d\right)^{\frac{2}{3}} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) - 8 \, a b \left(-i \, d\right)^{\frac{2}{3}} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) + i \, b^{2} \left(-2 i \, d\right)^{\frac{2}{3}} e^{\left(2 i \, c\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right) + 12 \, {\left(2 \, a^{2} + b^{2}\right)} d x}{24 \, d}"," ",0,"1/24*(-I*b^2*(2*I*d)^(2/3)*e^(-2*I*c)*gamma(1/3, 2*I*d*x^3) - 8*a*b*(I*d)^(2/3)*e^(-I*c)*gamma(1/3, I*d*x^3) - 8*a*b*(-I*d)^(2/3)*e^(I*c)*gamma(1/3, -I*d*x^3) + I*b^2*(-2*I*d)^(2/3)*e^(2*I*c)*gamma(1/3, -2*I*d*x^3) + 12*(2*a^2 + b^2)*d*x)/d","A",0
79,1,139,0,1.136655," ","integrate((a+b*sin(d*x^3+c))^2/x^3,x, algorithm=""fricas"")","-\frac{b^{2} \left(2 i \, d\right)^{\frac{2}{3}} x^{2} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) - 4 i \, a b \left(i \, d\right)^{\frac{2}{3}} x^{2} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + 4 i \, a b \left(-i \, d\right)^{\frac{2}{3}} x^{2} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) + b^{2} \left(-2 i \, d\right)^{\frac{2}{3}} x^{2} e^{\left(2 i \, c\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right) - 4 \, b^{2} \cos\left(d x^{3} + c\right)^{2} + 8 \, a b \sin\left(d x^{3} + c\right) + 4 \, a^{2} + 4 \, b^{2}}{8 \, x^{2}}"," ",0,"-1/8*(b^2*(2*I*d)^(2/3)*x^2*e^(-2*I*c)*gamma(1/3, 2*I*d*x^3) - 4*I*a*b*(I*d)^(2/3)*x^2*e^(-I*c)*gamma(1/3, I*d*x^3) + 4*I*a*b*(-I*d)^(2/3)*x^2*e^(I*c)*gamma(1/3, -I*d*x^3) + b^2*(-2*I*d)^(2/3)*x^2*e^(2*I*c)*gamma(1/3, -2*I*d*x^3) - 4*b^2*cos(d*x^3 + c)^2 + 8*a*b*sin(d*x^3 + c) + 4*a^2 + 4*b^2)/x^2","A",0
80,1,181,0,1.295244," ","integrate((a+b*sin(d*x^3+c))^2/x^6,x, algorithm=""fricas"")","\frac{3 i \, b^{2} \left(2 i \, d\right)^{\frac{2}{3}} d x^{5} e^{\left(-2 i \, c\right)} \Gamma\left(\frac{1}{3}, 2 i \, d x^{3}\right) + 6 \, a b \left(i \, d\right)^{\frac{2}{3}} d x^{5} e^{\left(-i \, c\right)} \Gamma\left(\frac{1}{3}, i \, d x^{3}\right) + 6 \, a b \left(-i \, d\right)^{\frac{2}{3}} d x^{5} e^{\left(i \, c\right)} \Gamma\left(\frac{1}{3}, -i \, d x^{3}\right) - 3 i \, b^{2} \left(-2 i \, d\right)^{\frac{2}{3}} d x^{5} e^{\left(2 i \, c\right)} \Gamma\left(\frac{1}{3}, -2 i \, d x^{3}\right) - 12 \, a b d x^{3} \cos\left(d x^{3} + c\right) + 4 \, b^{2} \cos\left(d x^{3} + c\right)^{2} - 4 \, a^{2} - 4 \, b^{2} - 4 \, {\left(3 \, b^{2} d x^{3} \cos\left(d x^{3} + c\right) + 2 \, a b\right)} \sin\left(d x^{3} + c\right)}{20 \, x^{5}}"," ",0,"1/20*(3*I*b^2*(2*I*d)^(2/3)*d*x^5*e^(-2*I*c)*gamma(1/3, 2*I*d*x^3) + 6*a*b*(I*d)^(2/3)*d*x^5*e^(-I*c)*gamma(1/3, I*d*x^3) + 6*a*b*(-I*d)^(2/3)*d*x^5*e^(I*c)*gamma(1/3, -I*d*x^3) - 3*I*b^2*(-2*I*d)^(2/3)*d*x^5*e^(2*I*c)*gamma(1/3, -2*I*d*x^3) - 12*a*b*d*x^3*cos(d*x^3 + c) + 4*b^2*cos(d*x^3 + c)^2 - 4*a^2 - 4*b^2 - 4*(3*b^2*d*x^3*cos(d*x^3 + c) + 2*a*b)*sin(d*x^3 + c))/x^5","A",0
81,1,1045,0,1.066624," ","integrate(x^5/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","-\frac{2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x^{3} + c\right) + 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) + 2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cos\left(d x^{3} + c\right) - 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x^{3} + c\right) + 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - 2 \, b c \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-2 \, b \cos\left(d x^{3} + c\right) - 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 i \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b d x^{3} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d x^{3} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d x^{3} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d x^{3} + b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right)}{12 \, {\left(a^{2} - b^{2}\right)} d^{2}}"," ",0,"-1/12*(2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x^3 + c) + 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) + 2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(2*b*cos(d*x^3 + c) - 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x^3 + c) + 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - 2*b*c*sqrt(-(a^2 - b^2)/b^2)*log(-2*b*cos(d*x^3 + c) - 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - 2*I*b*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + 2*(b*d*x^3 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*x^3 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + 2*(b*d*x^3 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - 2*(b*d*x^3 + b*c)*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b))/((a^2 - b^2)*d^2)","B",0
82,1,208,0,1.401113," ","integrate(x^2/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x^{3} + c\right) \sin\left(d x^{3} + c\right) + b \cos\left(d x^{3} + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2}}\right)}{6 \, {\left(a^{2} - b^{2}\right)} d}, -\frac{\arctan\left(-\frac{a \sin\left(d x^{3} + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x^{3} + c\right)}\right)}{3 \, \sqrt{a^{2} - b^{2}} d}\right]"," ",0,"[-1/6*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2 + 2*(a*cos(d*x^3 + c)*sin(d*x^3 + c) + b*cos(d*x^3 + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2))/((a^2 - b^2)*d), -1/3*arctan(-(a*sin(d*x^3 + c) + b)/(sqrt(a^2 - b^2)*cos(d*x^3 + c)))/(sqrt(a^2 - b^2)*d)]","A",0
83,0,0,0,1.127183," ","integrate(1/x/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \sin\left(d x^{3} + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sin(d*x^3 + c) + a*x), x)","F",0
84,0,0,0,0.982727," ","integrate(1/x^4/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{4} \sin\left(d x^{3} + c\right) + a x^{4}}, x\right)"," ",0,"integral(1/(b*x^4*sin(d*x^3 + c) + a*x^4), x)","F",0
85,0,0,0,1.212593," ","integrate(x/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \sin\left(d x^{3} + c\right) + a}, x\right)"," ",0,"integral(x/(b*sin(d*x^3 + c) + a), x)","F",0
86,0,0,0,0.745176," ","integrate(1/x^2/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} \sin\left(d x^{3} + c\right) + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*sin(d*x^3 + c) + a*x^2), x)","F",0
87,0,0,0,0.907283," ","integrate(1/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \sin\left(d x^{3} + c\right) + a}, x\right)"," ",0,"integral(1/(b*sin(d*x^3 + c) + a), x)","F",0
88,0,0,0,1.135576," ","integrate(1/x^3/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{3} \sin\left(d x^{3} + c\right) + a x^{3}}, x\right)"," ",0,"integral(1/(b*x^3*sin(d*x^3 + c) + a*x^3), x)","F",0
89,1,1509,0,1.247657," ","integrate(x^5/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b - b^{3}\right)} d x^{3} \cos\left(d x^{3} + c\right) + {\left(i \, a b^{2} \sin\left(d x^{3} + c\right) + i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, a b^{2} \sin\left(d x^{3} + c\right) - i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(-i \, a b^{2} \sin\left(d x^{3} + c\right) - i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, a b^{2} \sin\left(d x^{3} + c\right) + i \, a^{2} b\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a^{2} b d x^{3} + a^{2} b c + {\left(a b^{2} d x^{3} + a b^{2} c\right)} \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d x^{3} + a^{2} b c + {\left(a b^{2} d x^{3} + a b^{2} c\right)} \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) + i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a^{2} b d x^{3} + a^{2} b c + {\left(a b^{2} d x^{3} + a b^{2} c\right)} \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) + {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d x^{3} + a^{2} b c + {\left(a b^{2} d x^{3} + a b^{2} c\right)} \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} \log\left(-\frac{-i \, a \cos\left(d x^{3} + c\right) - a \sin\left(d x^{3} + c\right) - {\left(b \cos\left(d x^{3} + c\right) - i \, b \sin\left(d x^{3} + c\right)\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - b}{b}\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{3} + c\right) + {\left(a b^{2} c \sin\left(d x^{3} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x^{3} + c\right) + 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{3} + c\right) + {\left(a b^{2} c \sin\left(d x^{3} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cos\left(d x^{3} + c\right) - 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{3} + c\right) - {\left(a b^{2} c \sin\left(d x^{3} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x^{3} + c\right) + 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} + 2 i \, a\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x^{3} + c\right) - {\left(a b^{2} c \sin\left(d x^{3} + c\right) + a^{2} b c\right)} \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(-2 \, b \cos\left(d x^{3} + c\right) - 2 i \, b \sin\left(d x^{3} + c\right) + 2 \, b \sqrt{-\frac{a^{2} - b^{2}}{b^{2}}} - 2 i \, a\right)}{6 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \sin\left(d x^{3} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2}\right)}}"," ",0,"1/6*(2*(a^2*b - b^3)*d*x^3*cos(d*x^3 + c) + (I*a*b^2*sin(d*x^3 + c) + I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*a*b^2*sin(d*x^3 + c) - I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (-I*a*b^2*sin(d*x^3 + c) - I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) + (I*a*b^2*sin(d*x^3 + c) + I*a^2*b)*sqrt(-(a^2 - b^2)/b^2)*dilog((-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b + 1) - (a^2*b*d*x^3 + a^2*b*c + (a*b^2*d*x^3 + a*b^2*c)*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a^2*b*d*x^3 + a^2*b*c + (a*b^2*d*x^3 + a*b^2*c)*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) + I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a^2*b*d*x^3 + a^2*b*c + (a*b^2*d*x^3 + a*b^2*c)*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) + (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) + (a^2*b*d*x^3 + a^2*b*c + (a*b^2*d*x^3 + a*b^2*c)*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2)*log(-(-I*a*cos(d*x^3 + c) - a*sin(d*x^3 + c) - (b*cos(d*x^3 + c) - I*b*sin(d*x^3 + c))*sqrt(-(a^2 - b^2)/b^2) - b)/b) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^3 + c) + (a*b^2*c*sin(d*x^3 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x^3 + c) + 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^3 + c) + (a*b^2*c*sin(d*x^3 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(2*b*cos(d*x^3 + c) - 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^3 + c) - (a*b^2*c*sin(d*x^3 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x^3 + c) + 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) + 2*I*a) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x^3 + c) - (a*b^2*c*sin(d*x^3 + c) + a^2*b*c)*sqrt(-(a^2 - b^2)/b^2))*log(-2*b*cos(d*x^3 + c) - 2*I*b*sin(d*x^3 + c) + 2*b*sqrt(-(a^2 - b^2)/b^2) - 2*I*a))/((a^4*b - 2*a^2*b^3 + b^5)*d^2*sin(d*x^3 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d^2)","B",0
90,1,366,0,1.440942," ","integrate(x^2/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\left[\frac{{\left(a b \sin\left(d x^{3} + c\right) + a^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x^{3} + c\right) \sin\left(d x^{3} + c\right) + b \cos\left(d x^{3} + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x^{3} + c\right)}{6 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x^{3} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}, -\frac{{\left(a b \sin\left(d x^{3} + c\right) + a^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x^{3} + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x^{3} + c\right)}\right) - {\left(a^{2} b - b^{3}\right)} \cos\left(d x^{3} + c\right)}{3 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x^{3} + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}\right]"," ",0,"[1/6*((a*b*sin(d*x^3 + c) + a^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2 - 2*(a*cos(d*x^3 + c)*sin(d*x^3 + c) + b*cos(d*x^3 + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2)) + 2*(a^2*b - b^3)*cos(d*x^3 + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*sin(d*x^3 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d), -1/3*((a*b*sin(d*x^3 + c) + a^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x^3 + c) + b)/(sqrt(a^2 - b^2)*cos(d*x^3 + c))) - (a^2*b - b^3)*cos(d*x^3 + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*sin(d*x^3 + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)]","A",0
91,0,0,0,1.083963," ","integrate(1/x/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x \cos\left(d x^{3} + c\right)^{2} - 2 \, a b x \sin\left(d x^{3} + c\right) - {\left(a^{2} + b^{2}\right)} x}, x\right)"," ",0,"integral(-1/(b^2*x*cos(d*x^3 + c)^2 - 2*a*b*x*sin(d*x^3 + c) - (a^2 + b^2)*x), x)","F",0
92,0,0,0,1.455234," ","integrate(1/x^4/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x^{4} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b x^{4} \sin\left(d x^{3} + c\right) - {\left(a^{2} + b^{2}\right)} x^{4}}, x\right)"," ",0,"integral(-1/(b^2*x^4*cos(d*x^3 + c)^2 - 2*a*b*x^4*sin(d*x^3 + c) - (a^2 + b^2)*x^4), x)","F",0
93,0,0,0,0.740112," ","integrate(x/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x}{b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-x/(b^2*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2), x)","F",0
94,0,0,0,1.218821," ","integrate(1/x^2/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b x^{2} \sin\left(d x^{3} + c\right) - {\left(a^{2} + b^{2}\right)} x^{2}}, x\right)"," ",0,"integral(-1/(b^2*x^2*cos(d*x^3 + c)^2 - 2*a*b*x^2*sin(d*x^3 + c) - (a^2 + b^2)*x^2), x)","F",0
95,0,0,0,0.836341," ","integrate(1/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-1/(b^2*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2), x)","F",0
96,0,0,0,1.107005," ","integrate(1/x^3/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x^{3} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b x^{3} \sin\left(d x^{3} + c\right) - {\left(a^{2} + b^{2}\right)} x^{3}}, x\right)"," ",0,"integral(-1/(b^2*x^3*cos(d*x^3 + c)^2 - 2*a*b*x^3*sin(d*x^3 + c) - (a^2 + b^2)*x^3), x)","F",0
97,0,0,0,0.979335," ","integrate((e*x)^m*(a+b*sin(d*x^3+c))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \sin\left(d x^{3} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sin(d*x^3 + c) + a)^p, x)","F",0
98,1,345,0,1.143649," ","integrate((e*x)^m*(a+b*sin(d*x^3+c))^3,x, algorithm=""fricas"")","\frac{36 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \left(e x\right)^{m} d x + {\left(b^{3} e^{2} m + b^{3} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(\frac{3 i \, d}{e^{3}}\right) - 3 i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, 3 i \, d x^{3}\right) + {\left(-9 i \, a b^{2} e^{2} m - 9 i \, a b^{2} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(\frac{2 i \, d}{e^{3}}\right) - 2 i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, 2 i \, d x^{3}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e^{2} m + {\left(4 \, a^{2} b + b^{3}\right)} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(\frac{i \, d}{e^{3}}\right) - i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, i \, d x^{3}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} e^{2} m + {\left(4 \, a^{2} b + b^{3}\right)} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(-\frac{i \, d}{e^{3}}\right) + i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, -i \, d x^{3}\right) + {\left(9 i \, a b^{2} e^{2} m + 9 i \, a b^{2} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(-\frac{2 i \, d}{e^{3}}\right) + 2 i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, -2 i \, d x^{3}\right) + {\left(b^{3} e^{2} m + b^{3} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(-\frac{3 i \, d}{e^{3}}\right) + 3 i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, -3 i \, d x^{3}\right)}{72 \, {\left(d m + d\right)}}"," ",0,"1/72*(36*(2*a^3 + 3*a*b^2)*(e*x)^m*d*x + (b^3*e^2*m + b^3*e^2)*e^(-1/3*(m - 2)*log(3*I*d/e^3) - 3*I*c)*gamma(1/3*m + 1/3, 3*I*d*x^3) + (-9*I*a*b^2*e^2*m - 9*I*a*b^2*e^2)*e^(-1/3*(m - 2)*log(2*I*d/e^3) - 2*I*c)*gamma(1/3*m + 1/3, 2*I*d*x^3) - 9*((4*a^2*b + b^3)*e^2*m + (4*a^2*b + b^3)*e^2)*e^(-1/3*(m - 2)*log(I*d/e^3) - I*c)*gamma(1/3*m + 1/3, I*d*x^3) - 9*((4*a^2*b + b^3)*e^2*m + (4*a^2*b + b^3)*e^2)*e^(-1/3*(m - 2)*log(-I*d/e^3) + I*c)*gamma(1/3*m + 1/3, -I*d*x^3) + (9*I*a*b^2*e^2*m + 9*I*a*b^2*e^2)*e^(-1/3*(m - 2)*log(-2*I*d/e^3) + 2*I*c)*gamma(1/3*m + 1/3, -2*I*d*x^3) + (b^3*e^2*m + b^3*e^2)*e^(-1/3*(m - 2)*log(-3*I*d/e^3) + 3*I*c)*gamma(1/3*m + 1/3, -3*I*d*x^3))/(d*m + d)","A",0
99,1,214,0,1.777243," ","integrate((e*x)^m*(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","\frac{12 \, {\left(2 \, a^{2} + b^{2}\right)} \left(e x\right)^{m} d x + {\left(-i \, b^{2} e^{2} m - i \, b^{2} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(\frac{2 i \, d}{e^{3}}\right) - 2 i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, 2 i \, d x^{3}\right) - 8 \, {\left(a b e^{2} m + a b e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(\frac{i \, d}{e^{3}}\right) - i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, i \, d x^{3}\right) - 8 \, {\left(a b e^{2} m + a b e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(-\frac{i \, d}{e^{3}}\right) + i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, -i \, d x^{3}\right) + {\left(i \, b^{2} e^{2} m + i \, b^{2} e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(-\frac{2 i \, d}{e^{3}}\right) + 2 i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, -2 i \, d x^{3}\right)}{24 \, {\left(d m + d\right)}}"," ",0,"1/24*(12*(2*a^2 + b^2)*(e*x)^m*d*x + (-I*b^2*e^2*m - I*b^2*e^2)*e^(-1/3*(m - 2)*log(2*I*d/e^3) - 2*I*c)*gamma(1/3*m + 1/3, 2*I*d*x^3) - 8*(a*b*e^2*m + a*b*e^2)*e^(-1/3*(m - 2)*log(I*d/e^3) - I*c)*gamma(1/3*m + 1/3, I*d*x^3) - 8*(a*b*e^2*m + a*b*e^2)*e^(-1/3*(m - 2)*log(-I*d/e^3) + I*c)*gamma(1/3*m + 1/3, -I*d*x^3) + (I*b^2*e^2*m + I*b^2*e^2)*e^(-1/3*(m - 2)*log(-2*I*d/e^3) + 2*I*c)*gamma(1/3*m + 1/3, -2*I*d*x^3))/(d*m + d)","A",0
100,1,106,0,1.081817," ","integrate((e*x)^m*(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","\frac{6 \, \left(e x\right)^{m} a d x - {\left(b e^{2} m + b e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(\frac{i \, d}{e^{3}}\right) - i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, i \, d x^{3}\right) - {\left(b e^{2} m + b e^{2}\right)} e^{\left(-\frac{1}{3} \, {\left(m - 2\right)} \log\left(-\frac{i \, d}{e^{3}}\right) + i \, c\right)} \Gamma\left(\frac{1}{3} \, m + \frac{1}{3}, -i \, d x^{3}\right)}{6 \, {\left(d m + d\right)}}"," ",0,"1/6*(6*(e*x)^m*a*d*x - (b*e^2*m + b*e^2)*e^(-1/3*(m - 2)*log(I*d/e^3) - I*c)*gamma(1/3*m + 1/3, I*d*x^3) - (b*e^2*m + b*e^2)*e^(-1/3*(m - 2)*log(-I*d/e^3) + I*c)*gamma(1/3*m + 1/3, -I*d*x^3))/(d*m + d)","A",0
101,0,0,0,1.729578," ","integrate((e*x)^m/(a+b*sin(d*x^3+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(e x\right)^{m}}{b \sin\left(d x^{3} + c\right) + a}, x\right)"," ",0,"integral((e*x)^m/(b*sin(d*x^3 + c) + a), x)","F",0
102,0,0,0,0.797245," ","integrate((e*x)^m/(a+b*sin(d*x^3+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(e x\right)^{m}}{b^{2} \cos\left(d x^{3} + c\right)^{2} - 2 \, a b \sin\left(d x^{3} + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(e*x)^m/(b^2*cos(d*x^3 + c)^2 - 2*a*b*sin(d*x^3 + c) - a^2 - b^2), x)","F",0
103,1,79,0,1.358793," ","integrate(x^2*sin(a+b/x),x, algorithm=""fricas"")","-\frac{1}{6} \, b^{3} \sin\left(a\right) \operatorname{Si}\left(\frac{b}{x}\right) + \frac{1}{6} \, b x^{2} \cos\left(\frac{a x + b}{x}\right) + \frac{1}{12} \, {\left(b^{3} \operatorname{Ci}\left(\frac{b}{x}\right) + b^{3} \operatorname{Ci}\left(-\frac{b}{x}\right)\right)} \cos\left(a\right) - \frac{1}{6} \, {\left(b^{2} x - 2 \, x^{3}\right)} \sin\left(\frac{a x + b}{x}\right)"," ",0,"-1/6*b^3*sin(a)*sin_integral(b/x) + 1/6*b*x^2*cos((a*x + b)/x) + 1/12*(b^3*cos_integral(b/x) + b^3*cos_integral(-b/x))*cos(a) - 1/6*(b^2*x - 2*x^3)*sin((a*x + b)/x)","A",0
104,1,69,0,1.187745," ","integrate(x*sin(a+b/x),x, algorithm=""fricas"")","\frac{1}{2} \, b^{2} \cos\left(a\right) \operatorname{Si}\left(\frac{b}{x}\right) + \frac{1}{2} \, b x \cos\left(\frac{a x + b}{x}\right) + \frac{1}{2} \, x^{2} \sin\left(\frac{a x + b}{x}\right) + \frac{1}{4} \, {\left(b^{2} \operatorname{Ci}\left(\frac{b}{x}\right) + b^{2} \operatorname{Ci}\left(-\frac{b}{x}\right)\right)} \sin\left(a\right)"," ",0,"1/2*b^2*cos(a)*sin_integral(b/x) + 1/2*b*x*cos((a*x + b)/x) + 1/2*x^2*sin((a*x + b)/x) + 1/4*(b^2*cos_integral(b/x) + b^2*cos_integral(-b/x))*sin(a)","A",0
105,1,45,0,1.319126," ","integrate(sin(a+b/x),x, algorithm=""fricas"")","b \sin\left(a\right) \operatorname{Si}\left(\frac{b}{x}\right) - \frac{1}{2} \, {\left(b \operatorname{Ci}\left(\frac{b}{x}\right) + b \operatorname{Ci}\left(-\frac{b}{x}\right)\right)} \cos\left(a\right) + x \sin\left(\frac{a x + b}{x}\right)"," ",0,"b*sin(a)*sin_integral(b/x) - 1/2*(b*cos_integral(b/x) + b*cos_integral(-b/x))*cos(a) + x*sin((a*x + b)/x)","A",0
106,1,29,0,0.689857," ","integrate(sin(a+b/x)/x,x, algorithm=""fricas"")","-\frac{1}{2} \, {\left(\operatorname{Ci}\left(\frac{b}{x}\right) + \operatorname{Ci}\left(-\frac{b}{x}\right)\right)} \sin\left(a\right) - \cos\left(a\right) \operatorname{Si}\left(\frac{b}{x}\right)"," ",0,"-1/2*(cos_integral(b/x) + cos_integral(-b/x))*sin(a) - cos(a)*sin_integral(b/x)","A",0
107,1,14,0,1.243938," ","integrate(sin(a+b/x)/x^2,x, algorithm=""fricas"")","\frac{\cos\left(\frac{a x + b}{x}\right)}{b}"," ",0,"cos((a*x + b)/x)/b","A",0
108,1,33,0,1.114910," ","integrate(sin(a+b/x)/x^3,x, algorithm=""fricas"")","\frac{b \cos\left(\frac{a x + b}{x}\right) - x \sin\left(\frac{a x + b}{x}\right)}{b^{2} x}"," ",0,"(b*cos((a*x + b)/x) - x*sin((a*x + b)/x))/(b^2*x)","A",0
109,1,44,0,1.306412," ","integrate(sin(a+b/x)/x^4,x, algorithm=""fricas"")","-\frac{2 \, b x \sin\left(\frac{a x + b}{x}\right) - {\left(b^{2} - 2 \, x^{2}\right)} \cos\left(\frac{a x + b}{x}\right)}{b^{3} x^{2}}"," ",0,"-(2*b*x*sin((a*x + b)/x) - (b^2 - 2*x^2)*cos((a*x + b)/x))/(b^3*x^2)","A",0
110,1,52,0,1.283557," ","integrate(sin(a+b/x)/x^5,x, algorithm=""fricas"")","\frac{{\left(b^{3} - 6 \, b x^{2}\right)} \cos\left(\frac{a x + b}{x}\right) - 3 \, {\left(b^{2} x - 2 \, x^{3}\right)} \sin\left(\frac{a x + b}{x}\right)}{b^{4} x^{3}}"," ",0,"((b^3 - 6*b*x^2)*cos((a*x + b)/x) - 3*(b^2*x - 2*x^3)*sin((a*x + b)/x))/(b^4*x^3)","A",0
111,1,109,0,1.298884," ","integrate(x^2*sin(a+b/x)^2,x, algorithm=""fricas"")","\frac{1}{3} \, b x^{2} \cos\left(\frac{a x + b}{x}\right) \sin\left(\frac{a x + b}{x}\right) + \frac{2}{3} \, b^{3} \cos\left(2 \, a\right) \operatorname{Si}\left(\frac{2 \, b}{x}\right) - \frac{1}{3} \, b^{2} x + \frac{1}{3} \, x^{3} + \frac{1}{3} \, {\left(2 \, b^{2} x - x^{3}\right)} \cos\left(\frac{a x + b}{x}\right)^{2} + \frac{1}{3} \, {\left(b^{3} \operatorname{Ci}\left(\frac{2 \, b}{x}\right) + b^{3} \operatorname{Ci}\left(-\frac{2 \, b}{x}\right)\right)} \sin\left(2 \, a\right)"," ",0,"1/3*b*x^2*cos((a*x + b)/x)*sin((a*x + b)/x) + 2/3*b^3*cos(2*a)*sin_integral(2*b/x) - 1/3*b^2*x + 1/3*x^3 + 1/3*(2*b^2*x - x^3)*cos((a*x + b)/x)^2 + 1/3*(b^3*cos_integral(2*b/x) + b^3*cos_integral(-2*b/x))*sin(2*a)","A",0
112,1,90,0,0.916814," ","integrate(x*sin(a+b/x)^2,x, algorithm=""fricas"")","-\frac{1}{2} \, x^{2} \cos\left(\frac{a x + b}{x}\right)^{2} + b x \cos\left(\frac{a x + b}{x}\right) \sin\left(\frac{a x + b}{x}\right) + b^{2} \sin\left(2 \, a\right) \operatorname{Si}\left(\frac{2 \, b}{x}\right) + \frac{1}{2} \, x^{2} - \frac{1}{2} \, {\left(b^{2} \operatorname{Ci}\left(\frac{2 \, b}{x}\right) + b^{2} \operatorname{Ci}\left(-\frac{2 \, b}{x}\right)\right)} \cos\left(2 \, a\right)"," ",0,"-1/2*x^2*cos((a*x + b)/x)^2 + b*x*cos((a*x + b)/x)*sin((a*x + b)/x) + b^2*sin(2*a)*sin_integral(2*b/x) + 1/2*x^2 - 1/2*(b^2*cos_integral(2*b/x) + b^2*cos_integral(-2*b/x))*cos(2*a)","A",0
113,1,56,0,1.359402," ","integrate(sin(a+b/x)^2,x, algorithm=""fricas"")","-x \cos\left(\frac{a x + b}{x}\right)^{2} - b \cos\left(2 \, a\right) \operatorname{Si}\left(\frac{2 \, b}{x}\right) - \frac{1}{2} \, {\left(b \operatorname{Ci}\left(\frac{2 \, b}{x}\right) + b \operatorname{Ci}\left(-\frac{2 \, b}{x}\right)\right)} \sin\left(2 \, a\right) + x"," ",0,"-x*cos((a*x + b)/x)^2 - b*cos(2*a)*sin_integral(2*b/x) - 1/2*(b*cos_integral(2*b/x) + b*cos_integral(-2*b/x))*sin(2*a) + x","A",0
114,1,39,0,1.113127," ","integrate(sin(a+b/x)^2/x,x, algorithm=""fricas"")","\frac{1}{4} \, {\left(\operatorname{Ci}\left(\frac{2 \, b}{x}\right) + \operatorname{Ci}\left(-\frac{2 \, b}{x}\right)\right)} \cos\left(2 \, a\right) - \frac{1}{2} \, \sin\left(2 \, a\right) \operatorname{Si}\left(\frac{2 \, b}{x}\right) + \frac{1}{2} \, \log\left(x\right)"," ",0,"1/4*(cos_integral(2*b/x) + cos_integral(-2*b/x))*cos(2*a) - 1/2*sin(2*a)*sin_integral(2*b/x) + 1/2*log(x)","A",0
115,1,34,0,1.271032," ","integrate(sin(a+b/x)^2/x^2,x, algorithm=""fricas"")","\frac{x \cos\left(\frac{a x + b}{x}\right) \sin\left(\frac{a x + b}{x}\right) - b}{2 \, b x}"," ",0,"1/2*(x*cos((a*x + b)/x)*sin((a*x + b)/x) - b)/(b*x)","A",0
116,1,60,0,1.382551," ","integrate(sin(a+b/x)^2/x^3,x, algorithm=""fricas"")","\frac{2 \, x^{2} \cos\left(\frac{a x + b}{x}\right)^{2} + 4 \, b x \cos\left(\frac{a x + b}{x}\right) \sin\left(\frac{a x + b}{x}\right) - 2 \, b^{2} - x^{2}}{8 \, b^{2} x^{2}}"," ",0,"1/8*(2*x^2*cos((a*x + b)/x)^2 + 4*b*x*cos((a*x + b)/x)*sin((a*x + b)/x) - 2*b^2 - x^2)/(b^2*x^2)","A",0
117,1,72,0,0.796703," ","integrate(sin(a+b/x)^2/x^4,x, algorithm=""fricas"")","\frac{6 \, b x^{2} \cos\left(\frac{a x + b}{x}\right)^{2} - 2 \, b^{3} - 3 \, b x^{2} + 3 \, {\left(2 \, b^{2} x - x^{3}\right)} \cos\left(\frac{a x + b}{x}\right) \sin\left(\frac{a x + b}{x}\right)}{12 \, b^{3} x^{3}}"," ",0,"1/12*(6*b*x^2*cos((a*x + b)/x)^2 - 2*b^3 - 3*b*x^2 + 3*(2*b^2*x - x^3)*cos((a*x + b)/x)*sin((a*x + b)/x))/(b^3*x^3)","A",0
118,1,90,0,1.387784," ","integrate(sin(a+b/x)^2/x^5,x, algorithm=""fricas"")","-\frac{2 \, b^{4} + 6 \, b^{2} x^{2} - 3 \, x^{4} - 6 \, {\left(2 \, b^{2} x^{2} - x^{4}\right)} \cos\left(\frac{a x + b}{x}\right)^{2} - 4 \, {\left(2 \, b^{3} x - 3 \, b x^{3}\right)} \cos\left(\frac{a x + b}{x}\right) \sin\left(\frac{a x + b}{x}\right)}{16 \, b^{4} x^{4}}"," ",0,"-1/16*(2*b^4 + 6*b^2*x^2 - 3*x^4 - 6*(2*b^2*x^2 - x^4)*cos((a*x + b)/x)^2 - 4*(2*b^3*x - 3*b*x^3)*cos((a*x + b)/x)*sin((a*x + b)/x))/(b^4*x^4)","A",0
119,1,74,0,1.332057," ","integrate(sin(a+b/x^2),x, algorithm=""fricas"")","-\sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{x}\right) + \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{x}\right) \sin\left(a\right) + x \sin\left(\frac{a x^{2} + b}{x^{2}}\right)"," ",0,"-sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*sqrt(b/pi)/x) + sqrt(2)*pi*sqrt(b/pi)*fresnel_sin(sqrt(2)*sqrt(b/pi)/x)*sin(a) + x*sin((a*x^2 + b)/x^2)","A",0
120,1,29,0,1.319437," ","integrate(sin(a+b/x^2)/x,x, algorithm=""fricas"")","-\frac{1}{4} \, {\left(\operatorname{Ci}\left(\frac{b}{x^{2}}\right) + \operatorname{Ci}\left(-\frac{b}{x^{2}}\right)\right)} \sin\left(a\right) - \frac{1}{2} \, \cos\left(a\right) \operatorname{Si}\left(\frac{b}{x^{2}}\right)"," ",0,"-1/4*(cos_integral(b/x^2) + cos_integral(-b/x^2))*sin(a) - 1/2*cos(a)*sin_integral(b/x^2)","A",0
121,1,64,0,1.393994," ","integrate(sin(a+b/x^2)/x^2,x, algorithm=""fricas"")","-\frac{\sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{x}\right) + \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{x}\right) \sin\left(a\right)}{2 \, b}"," ",0,"-1/2*(sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_sin(sqrt(2)*sqrt(b/pi)/x) + sqrt(2)*pi*sqrt(b/pi)*fresnel_cos(sqrt(2)*sqrt(b/pi)/x)*sin(a))/b","A",0
122,1,17,0,0.701180," ","integrate(sin(a+b/x^2)/x^3,x, algorithm=""fricas"")","\frac{\cos\left(\frac{a x^{2} + b}{x^{2}}\right)}{2 \, b}"," ",0,"1/2*cos((a*x^2 + b)/x^2)/b","A",0
123,1,85,0,1.245630," ","integrate(sin(a+b/x^2)/x^4,x, algorithm=""fricas"")","-\frac{\sqrt{2} \pi x \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{x}\right) - \sqrt{2} \pi x \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{x}\right) \sin\left(a\right) - 2 \, b \cos\left(\frac{a x^{2} + b}{x^{2}}\right)}{4 \, b^{2} x}"," ",0,"-1/4*(sqrt(2)*pi*x*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*sqrt(b/pi)/x) - sqrt(2)*pi*x*sqrt(b/pi)*fresnel_sin(sqrt(2)*sqrt(b/pi)/x)*sin(a) - 2*b*cos((a*x^2 + b)/x^2))/(b^2*x)","A",0
124,1,6,0,1.376466," ","integrate(sin(x^(1/2))/x^(1/2),x, algorithm=""fricas"")","-2 \, \cos\left(\sqrt{x}\right)"," ",0,"-2*cos(sqrt(x))","A",0
125,1,15,0,1.287683," ","integrate(sin(x^(1/2))^3/x^(1/2),x, algorithm=""fricas"")","\frac{2}{3} \, \cos\left(\sqrt{x}\right)^{3} - 2 \, \cos\left(\sqrt{x}\right)"," ",0,"2/3*cos(sqrt(x))^3 - 2*cos(sqrt(x))","A",0
126,1,16,0,1.528278," ","integrate(sin(x^(1/2)),x, algorithm=""fricas"")","-2 \, \sqrt{x} \cos\left(\sqrt{x}\right) + 2 \, \sin\left(\sqrt{x}\right)"," ",0,"-2*sqrt(x)*cos(sqrt(x)) + 2*sin(sqrt(x))","A",0
127,1,37,0,1.310105," ","integrate(sin(x^(1/3))^2,x, algorithm=""fricas"")","-\frac{3}{4} \, {\left(2 \, x^{\frac{2}{3}} - 1\right)} \cos\left(x^{\frac{1}{3}}\right) \sin\left(x^{\frac{1}{3}}\right) - \frac{3}{2} \, x^{\frac{1}{3}} \cos\left(x^{\frac{1}{3}}\right)^{2} + \frac{1}{2} \, x + \frac{3}{4} \, x^{\frac{1}{3}}"," ",0,"-3/4*(2*x^(2/3) - 1)*cos(x^(1/3))*sin(x^(1/3)) - 3/2*x^(1/3)*cos(x^(1/3))^2 + 1/2*x + 3/4*x^(1/3)","A",0
128,1,51,0,1.360029," ","integrate(sin(x^(1/3))^3,x, algorithm=""fricas"")","\frac{1}{9} \, {\left(9 \, x^{\frac{2}{3}} - 2\right)} \cos\left(x^{\frac{1}{3}}\right)^{3} - \frac{1}{3} \, {\left(9 \, x^{\frac{2}{3}} - 14\right)} \cos\left(x^{\frac{1}{3}}\right) - \frac{2}{3} \, {\left(x^{\frac{1}{3}} \cos\left(x^{\frac{1}{3}}\right)^{2} - 7 \, x^{\frac{1}{3}}\right)} \sin\left(x^{\frac{1}{3}}\right)"," ",0,"1/9*(9*x^(2/3) - 2)*cos(x^(1/3))^3 - 1/3*(9*x^(2/3) - 14)*cos(x^(1/3)) - 2/3*(x^(1/3)*cos(x^(1/3))^2 - 7*x^(1/3))*sin(x^(1/3))","A",0
129,0,0,0,1.603308," ","integrate((e*x)^m*(b*sin(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \left(b \sin\left(d x^{n} + c\right)\right)^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sin(d*x^n + c))^p, x)","F",0
130,0,0,0,1.353293," ","integrate((e*x)^m*(a+b*sin(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \sin\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sin(d*x^n + c) + a)^p, x)","F",0
131,0,0,0,1.443726," ","integrate((e*x)^(-1+n)*(b*sin(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{n - 1} \left(b \sin\left(d x^{n} + c\right)\right)^{p}, x\right)"," ",0,"integral((e*x)^(n - 1)*(b*sin(d*x^n + c))^p, x)","F",0
132,0,0,0,1.496250," ","integrate((e*x)^(-1+2*n)*(b*sin(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{2 \, n - 1} \left(b \sin\left(d x^{n} + c\right)\right)^{p}, x\right)"," ",0,"integral((e*x)^(2*n - 1)*(b*sin(d*x^n + c))^p, x)","F",0
133,0,0,0,1.403656," ","integrate((e*x)^(-1+n)*(a+b*sin(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{n - 1} {\left(b \sin\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^(n - 1)*(b*sin(d*x^n + c) + a)^p, x)","F",0
134,0,0,0,1.717189," ","integrate((e*x)^(-1+2*n)*(a+b*sin(c+d*x^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{2 \, n - 1} {\left(b \sin\left(d x^{n} + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^(2*n - 1)*(b*sin(d*x^n + c) + a)^p, x)","F",0
135,1,35,0,1.335422," ","integrate(sin(a+b*x^n)/x,x, algorithm=""fricas"")","\frac{\operatorname{Ci}\left(b x^{n}\right) \sin\left(a\right) + \operatorname{Ci}\left(-b x^{n}\right) \sin\left(a\right) + 2 \, \cos\left(a\right) \operatorname{Si}\left(b x^{n}\right)}{2 \, n}"," ",0,"1/2*(cos_integral(b*x^n)*sin(a) + cos_integral(-b*x^n)*sin(a) + 2*cos(a)*sin_integral(b*x^n))/n","A",0
136,1,48,0,1.288644," ","integrate(sin(a+b*x^n)^2/x,x, algorithm=""fricas"")","-\frac{\cos\left(2 \, a\right) \operatorname{Ci}\left(2 \, b x^{n}\right) + \cos\left(2 \, a\right) \operatorname{Ci}\left(-2 \, b x^{n}\right) - 2 \, n \log\left(x\right) - 2 \, \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{n}\right)}{4 \, n}"," ",0,"-1/4*(cos(2*a)*cos_integral(2*b*x^n) + cos(2*a)*cos_integral(-2*b*x^n) - 2*n*log(x) - 2*sin(2*a)*sin_integral(2*b*x^n))/n","A",0
137,1,74,0,1.530541," ","integrate(sin(a+b*x^n)^3/x,x, algorithm=""fricas"")","-\frac{\operatorname{Ci}\left(3 \, b x^{n}\right) \sin\left(3 \, a\right) + \operatorname{Ci}\left(-3 \, b x^{n}\right) \sin\left(3 \, a\right) - 3 \, \operatorname{Ci}\left(b x^{n}\right) \sin\left(a\right) - 3 \, \operatorname{Ci}\left(-b x^{n}\right) \sin\left(a\right) + 2 \, \cos\left(3 \, a\right) \operatorname{Si}\left(3 \, b x^{n}\right) - 6 \, \cos\left(a\right) \operatorname{Si}\left(b x^{n}\right)}{8 \, n}"," ",0,"-1/8*(cos_integral(3*b*x^n)*sin(3*a) + cos_integral(-3*b*x^n)*sin(3*a) - 3*cos_integral(b*x^n)*sin(a) - 3*cos_integral(-b*x^n)*sin(a) + 2*cos(3*a)*sin_integral(3*b*x^n) - 6*cos(a)*sin_integral(b*x^n))/n","A",0
138,1,87,0,1.189253," ","integrate(sin(a+b*x^n)^4/x,x, algorithm=""fricas"")","\frac{\cos\left(4 \, a\right) \operatorname{Ci}\left(4 \, b x^{n}\right) - 4 \, \cos\left(2 \, a\right) \operatorname{Ci}\left(2 \, b x^{n}\right) - 4 \, \cos\left(2 \, a\right) \operatorname{Ci}\left(-2 \, b x^{n}\right) + \cos\left(4 \, a\right) \operatorname{Ci}\left(-4 \, b x^{n}\right) + 6 \, n \log\left(x\right) - 2 \, \sin\left(4 \, a\right) \operatorname{Si}\left(4 \, b x^{n}\right) + 8 \, \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{n}\right)}{16 \, n}"," ",0,"1/16*(cos(4*a)*cos_integral(4*b*x^n) - 4*cos(2*a)*cos_integral(2*b*x^n) - 4*cos(2*a)*cos_integral(-2*b*x^n) + cos(4*a)*cos_integral(-4*b*x^n) + 6*n*log(x) - 2*sin(4*a)*sin_integral(4*b*x^n) + 8*sin(2*a)*sin_integral(2*b*x^n))/n","A",0
139,0,0,0,0.647858," ","integrate(sin(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\sin\left(b x^{n} + a\right), x\right)"," ",0,"integral(sin(b*x^n + a), x)","F",0
140,0,0,0,1.141244," ","integrate(sin(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(-\cos\left(b x^{n} + a\right)^{2} + 1, x\right)"," ",0,"integral(-cos(b*x^n + a)^2 + 1, x)","F",0
141,0,0,0,1.244032," ","integrate(sin(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(b x^{n} + a\right)^{2} - 1\right)} \sin\left(b x^{n} + a\right), x\right)"," ",0,"integral(-(cos(b*x^n + a)^2 - 1)*sin(b*x^n + a), x)","F",0
142,0,0,0,1.588347," ","integrate(x^m*sin(a+b*x^n),x, algorithm=""fricas"")","{\rm integral}\left(x^{m} \sin\left(b x^{n} + a\right), x\right)"," ",0,"integral(x^m*sin(b*x^n + a), x)","F",0
143,0,0,0,0.925558," ","integrate(x^m*sin(a+b*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(-x^{m} \cos\left(b x^{n} + a\right)^{2} + x^{m}, x\right)"," ",0,"integral(-x^m*cos(b*x^n + a)^2 + x^m, x)","F",0
144,0,0,0,0.993532," ","integrate(x^m*sin(a+b*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(x^{m} \cos\left(b x^{n} + a\right)^{2} - x^{m}\right)} \sin\left(b x^{n} + a\right), x\right)"," ",0,"integral(-(x^m*cos(b*x^n + a)^2 - x^m)*sin(b*x^n + a), x)","F",0
145,1,32,0,1.142070," ","integrate(x^(-1+2*n)*sin(a+b*x^n),x, algorithm=""fricas"")","-\frac{b x^{n} \cos\left(b x^{n} + a\right) - \sin\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"-(b*x^n*cos(b*x^n + a) - sin(b*x^n + a))/(b^2*n)","A",0
146,1,29,0,1.206593," ","integrate(x^(-1+2*n)*cos(a+b*x^n),x, algorithm=""fricas"")","\frac{b x^{n} \sin\left(b x^{n} + a\right) + \cos\left(b x^{n} + a\right)}{b^{2} n}"," ",0,"(b*x^n*sin(b*x^n + a) + cos(b*x^n + a))/(b^2*n)","A",0
147,1,62,0,1.424619," ","integrate(x^(-1-n)*sin(a+b*x^n),x, algorithm=""fricas"")","\frac{b x^{n} \cos\left(a\right) \operatorname{Ci}\left(b x^{n}\right) + b x^{n} \cos\left(a\right) \operatorname{Ci}\left(-b x^{n}\right) - 2 \, b x^{n} \sin\left(a\right) \operatorname{Si}\left(b x^{n}\right) - 2 \, \sin\left(b x^{n} + a\right)}{2 \, n x^{n}}"," ",0,"1/2*(b*x^n*cos(a)*cos_integral(b*x^n) + b*x^n*cos(a)*cos_integral(-b*x^n) - 2*b*x^n*sin(a)*sin_integral(b*x^n) - 2*sin(b*x^n + a))/(n*x^n)","A",0
148,1,73,0,1.316550," ","integrate(x^(-1-n)*sin(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b x^{n} \operatorname{Ci}\left(2 \, b x^{n}\right) \sin\left(2 \, a\right) + b x^{n} \operatorname{Ci}\left(-2 \, b x^{n}\right) \sin\left(2 \, a\right) + 2 \, b x^{n} \cos\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{n}\right) + 2 \, \cos\left(b x^{n} + a\right)^{2} - 2}{2 \, n x^{n}}"," ",0,"1/2*(b*x^n*cos_integral(2*b*x^n)*sin(2*a) + b*x^n*cos_integral(-2*b*x^n)*sin(2*a) + 2*b*x^n*cos(2*a)*sin_integral(2*b*x^n) + 2*cos(b*x^n + a)^2 - 2)/(n*x^n)","A",0
149,1,127,0,1.516189," ","integrate(x^(-1-n)*sin(a+b*x^n)^3,x, algorithm=""fricas"")","-\frac{3 \, b x^{n} \cos\left(3 \, a\right) \operatorname{Ci}\left(3 \, b x^{n}\right) - 3 \, b x^{n} \cos\left(a\right) \operatorname{Ci}\left(b x^{n}\right) - 3 \, b x^{n} \cos\left(a\right) \operatorname{Ci}\left(-b x^{n}\right) + 3 \, b x^{n} \cos\left(3 \, a\right) \operatorname{Ci}\left(-3 \, b x^{n}\right) - 6 \, b x^{n} \sin\left(3 \, a\right) \operatorname{Si}\left(3 \, b x^{n}\right) + 6 \, b x^{n} \sin\left(a\right) \operatorname{Si}\left(b x^{n}\right) - 8 \, {\left(\cos\left(b x^{n} + a\right)^{2} - 1\right)} \sin\left(b x^{n} + a\right)}{8 \, n x^{n}}"," ",0,"-1/8*(3*b*x^n*cos(3*a)*cos_integral(3*b*x^n) - 3*b*x^n*cos(a)*cos_integral(b*x^n) - 3*b*x^n*cos(a)*cos_integral(-b*x^n) + 3*b*x^n*cos(3*a)*cos_integral(-3*b*x^n) - 6*b*x^n*sin(3*a)*sin_integral(3*b*x^n) + 6*b*x^n*sin(a)*sin_integral(b*x^n) - 8*(cos(b*x^n + a)^2 - 1)*sin(b*x^n + a))/(n*x^n)","A",0
150,1,90,0,1.323859," ","integrate(x^(-1-2*n)*sin(a+b*x^n),x, algorithm=""fricas"")","-\frac{b^{2} x^{2 \, n} \operatorname{Ci}\left(b x^{n}\right) \sin\left(a\right) + b^{2} x^{2 \, n} \operatorname{Ci}\left(-b x^{n}\right) \sin\left(a\right) + 2 \, b^{2} x^{2 \, n} \cos\left(a\right) \operatorname{Si}\left(b x^{n}\right) + 2 \, b x^{n} \cos\left(b x^{n} + a\right) + 2 \, \sin\left(b x^{n} + a\right)}{4 \, n x^{2 \, n}}"," ",0,"-1/4*(b^2*x^(2*n)*cos_integral(b*x^n)*sin(a) + b^2*x^(2*n)*cos_integral(-b*x^n)*sin(a) + 2*b^2*x^(2*n)*cos(a)*sin_integral(b*x^n) + 2*b*x^n*cos(b*x^n + a) + 2*sin(b*x^n + a))/(n*x^(2*n))","A",0
151,1,107,0,1.267141," ","integrate(x^(-1-2*n)*sin(a+b*x^n)^2,x, algorithm=""fricas"")","\frac{b^{2} x^{2 \, n} \cos\left(2 \, a\right) \operatorname{Ci}\left(2 \, b x^{n}\right) + b^{2} x^{2 \, n} \cos\left(2 \, a\right) \operatorname{Ci}\left(-2 \, b x^{n}\right) - 2 \, b^{2} x^{2 \, n} \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{n}\right) - 2 \, b x^{n} \cos\left(b x^{n} + a\right) \sin\left(b x^{n} + a\right) + \cos\left(b x^{n} + a\right)^{2} - 1}{2 \, n x^{2 \, n}}"," ",0,"1/2*(b^2*x^(2*n)*cos(2*a)*cos_integral(2*b*x^n) + b^2*x^(2*n)*cos(2*a)*cos_integral(-2*b*x^n) - 2*b^2*x^(2*n)*sin(2*a)*sin_integral(2*b*x^n) - 2*b*x^n*cos(b*x^n + a)*sin(b*x^n + a) + cos(b*x^n + a)^2 - 1)/(n*x^(2*n))","A",0
152,1,183,0,1.427014," ","integrate(x^(-1-2*n)*sin(a+b*x^n)^3,x, algorithm=""fricas"")","\frac{24 \, b x^{n} \cos\left(b x^{n} + a\right)^{3} + 9 \, b^{2} x^{2 \, n} \operatorname{Ci}\left(3 \, b x^{n}\right) \sin\left(3 \, a\right) + 9 \, b^{2} x^{2 \, n} \operatorname{Ci}\left(-3 \, b x^{n}\right) \sin\left(3 \, a\right) - 3 \, b^{2} x^{2 \, n} \operatorname{Ci}\left(b x^{n}\right) \sin\left(a\right) - 3 \, b^{2} x^{2 \, n} \operatorname{Ci}\left(-b x^{n}\right) \sin\left(a\right) + 18 \, b^{2} x^{2 \, n} \cos\left(3 \, a\right) \operatorname{Si}\left(3 \, b x^{n}\right) - 6 \, b^{2} x^{2 \, n} \cos\left(a\right) \operatorname{Si}\left(b x^{n}\right) - 24 \, b x^{n} \cos\left(b x^{n} + a\right) + 8 \, {\left(\cos\left(b x^{n} + a\right)^{2} - 1\right)} \sin\left(b x^{n} + a\right)}{16 \, n x^{2 \, n}}"," ",0,"1/16*(24*b*x^n*cos(b*x^n + a)^3 + 9*b^2*x^(2*n)*cos_integral(3*b*x^n)*sin(3*a) + 9*b^2*x^(2*n)*cos_integral(-3*b*x^n)*sin(3*a) - 3*b^2*x^(2*n)*cos_integral(b*x^n)*sin(a) - 3*b^2*x^(2*n)*cos_integral(-b*x^n)*sin(a) + 18*b^2*x^(2*n)*cos(3*a)*sin_integral(3*b*x^n) - 6*b^2*x^(2*n)*cos(a)*sin_integral(b*x^n) - 24*b*x^n*cos(b*x^n + a) + 8*(cos(b*x^n + a)^2 - 1)*sin(b*x^n + a))/(n*x^(2*n))","A",0
153,1,255,0,1.117085," ","integrate((f*x+e)^3*sin(b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, d f^{3} \sin\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right) + 3 \, \sqrt{2} \pi {\left(d e f^{2} - c f^{3}\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) + 2 \, \sqrt{2} \pi {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) - 2 \, {\left(b d^{3} f^{3} x^{2} + 3 \, b d^{3} e^{2} f - 3 \, b c d^{2} e f^{2} + b c^{2} d f^{3} + {\left(3 \, b d^{3} e f^{2} - b c d^{2} f^{3}\right)} x\right)} \cos\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)}{4 \, b^{2} d^{5}}"," ",0,"1/4*(2*d*f^3*sin(b*d^2*x^2 + 2*b*c*d*x + b*c^2) + 3*sqrt(2)*pi*(d*e*f^2 - c*f^3)*sqrt(b*d^2/pi)*fresnel_cos(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) + 2*sqrt(2)*pi*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt(b*d^2/pi)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) - 2*(b*d^3*f^3*x^2 + 3*b*d^3*e^2*f - 3*b*c*d^2*e*f^2 + b*c^2*d*f^3 + (3*b*d^3*e*f^2 - b*c*d^2*f^3)*x)*cos(b*d^2*x^2 + 2*b*c*d*x + b*c^2))/(b^2*d^5)","A",0
154,1,162,0,1.414615," ","integrate((f*x+e)^2*sin(b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} f^{2} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) + 2 \, \sqrt{2} \pi {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) - 2 \, {\left(b d^{2} f^{2} x + 2 \, b d^{2} e f - b c d f^{2}\right)} \cos\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)}{4 \, b^{2} d^{4}}"," ",0,"1/4*(sqrt(2)*pi*sqrt(b*d^2/pi)*f^2*fresnel_cos(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) + 2*sqrt(2)*pi*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt(b*d^2/pi)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) - 2*(b*d^2*f^2*x + 2*b*d^2*e*f - b*c*d*f^2)*cos(b*d^2*x^2 + 2*b*c*d*x + b*c^2))/(b^2*d^4)","A",0
155,1,80,0,1.315366," ","integrate((f*x+e)*sin(b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} {\left(d e - c f\right)} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) - d f \cos\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)}{2 \, b d^{3}}"," ",0,"1/2*(sqrt(2)*pi*sqrt(b*d^2/pi)*(d*e - c*f)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) - d*f*cos(b*d^2*x^2 + 2*b*c*d*x + b*c^2))/(b*d^3)","A",0
156,1,45,0,0.924257," ","integrate(sin(b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right)}{2 \, b d^{2}}"," ",0,"1/2*sqrt(2)*pi*sqrt(b*d^2/pi)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d)/(b*d^2)","A",0
157,0,0,0,1.231100," ","integrate(sin(b*(d*x+c)^2)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)}{f x + e}, x\right)"," ",0,"integral(sin(b*d^2*x^2 + 2*b*c*d*x + b*c^2)/(f*x + e), x)","F",0
158,0,0,0,1.125305," ","integrate(sin(b*(d*x+c)^2)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin(b*d^2*x^2 + 2*b*c*d*x + b*c^2)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
159,1,449,0,1.375843," ","integrate((f*x+e)^3*sin(b/(d*x+c)^2),x, algorithm=""fricas"")","\frac{b^{2} f^{3} \operatorname{Si}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 4 \, \sqrt{2} \pi {\left(d^{4} e^{3} - 3 \, c d^{3} e^{2} f + 3 \, c^{2} d^{2} e f^{2} - c^{3} d f^{3}\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) + 8 \, \sqrt{2} \pi {\left(b d^{2} e f^{2} - b c d f^{3}\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{S}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) + {\left(b d^{2} f^{3} x^{2} + 8 \, b c d e f^{2} - 7 \, b c^{2} f^{3} + 2 \, {\left(4 \, b d^{2} e f^{2} - 3 \, b c d f^{3}\right)} x\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left(b d^{2} e^{2} f - 2 \, b c d e f^{2} + b c^{2} f^{3}\right)} \operatorname{Ci}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left(b d^{2} e^{2} f - 2 \, b c d e f^{2} + b c^{2} f^{3}\right)} \operatorname{Ci}\left(-\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + {\left(d^{4} f^{3} x^{4} + 4 \, d^{4} e f^{2} x^{3} + 6 \, d^{4} e^{2} f x^{2} + 4 \, d^{4} e^{3} x + 4 \, c d^{3} e^{3} - 6 \, c^{2} d^{2} e^{2} f + 4 \, c^{3} d e f^{2} - c^{4} f^{3}\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{4 \, d^{4}}"," ",0,"1/4*(b^2*f^3*sin_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) - 4*sqrt(2)*pi*(d^4*e^3 - 3*c*d^3*e^2*f + 3*c^2*d^2*e*f^2 - c^3*d*f^3)*sqrt(b/(pi*d^2))*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) + 8*sqrt(2)*pi*(b*d^2*e*f^2 - b*c*d*f^3)*sqrt(b/(pi*d^2))*fresnel_sin(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) + (b*d^2*f^3*x^2 + 8*b*c*d*e*f^2 - 7*b*c^2*f^3 + 2*(4*b*d^2*e*f^2 - 3*b*c*d*f^3)*x)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)) - 3*(b*d^2*e^2*f - 2*b*c*d*e*f^2 + b*c^2*f^3)*cos_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) - 3*(b*d^2*e^2*f - 2*b*c*d*e*f^2 + b*c^2*f^3)*cos_integral(-b/(d^2*x^2 + 2*c*d*x + c^2)) + (d^4*f^3*x^4 + 4*d^4*e*f^2*x^3 + 6*d^4*e^2*f*x^2 + 4*d^4*e^3*x + 4*c*d^3*e^3 - 6*c^2*d^2*e^2*f + 4*c^3*d*e*f^2 - c^4*f^3)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/d^4","A",0
160,1,300,0,1.148648," ","integrate((f*x+e)^2*sin(b/(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \pi b d f^{2} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{S}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) - 6 \, \sqrt{2} \pi {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) + 4 \, {\left(b d f^{2} x + b c f^{2}\right)} \cos\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left(b d e f - b c f^{2}\right)} \operatorname{Ci}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left(b d e f - b c f^{2}\right)} \operatorname{Ci}\left(-\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 3 \, c d^{2} e^{2} - 3 \, c^{2} d e f + c^{3} f^{2}\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{6 \, d^{3}}"," ",0,"1/6*(4*sqrt(2)*pi*b*d*f^2*sqrt(b/(pi*d^2))*fresnel_sin(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) - 6*sqrt(2)*pi*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*sqrt(b/(pi*d^2))*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) + 4*(b*d*f^2*x + b*c*f^2)*cos(b/(d^2*x^2 + 2*c*d*x + c^2)) - 3*(b*d*e*f - b*c*f^2)*cos_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) - 3*(b*d*e*f - b*c*f^2)*cos_integral(-b/(d^2*x^2 + 2*c*d*x + c^2)) + 2*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 3*c*d^2*e^2 - 3*c^2*d*e*f + c^3*f^2)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/d^3","A",0
161,1,155,0,0.853602," ","integrate((f*x+e)*sin(b/(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \pi {\left(d^{2} e - c d f\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) + b f \operatorname{Ci}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + b f \operatorname{Ci}\left(-\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 2 \, {\left(d^{2} f x^{2} + 2 \, d^{2} e x + 2 \, c d e - c^{2} f\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{4 \, d^{2}}"," ",0,"-1/4*(4*sqrt(2)*pi*(d^2*e - c*d*f)*sqrt(b/(pi*d^2))*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) + b*f*cos_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) + b*f*cos_integral(-b/(d^2*x^2 + 2*c*d*x + c^2)) - 2*(d^2*f*x^2 + 2*d^2*e*x + 2*c*d*e - c^2*f)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/d^2","A",0
162,1,73,0,1.313620," ","integrate(sin(b/(d*x+c)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \pi d \sqrt{\frac{b}{\pi d^{2}}} \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) - {\left(d x + c\right)} \sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d}"," ",0,"-(sqrt(2)*pi*d*sqrt(b/(pi*d^2))*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) - (d*x + c)*sin(b/(d^2*x^2 + 2*c*d*x + c^2)))/d","A",0
163,0,0,0,1.308957," ","integrate(sin(b/(d*x+c)^2)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{f x + e}, x\right)"," ",0,"integral(sin(b/(d^2*x^2 + 2*c*d*x + c^2))/(f*x + e), x)","F",0
164,0,0,0,1.327185," ","integrate(sin(b/(d*x+c)^2)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin(b/(d^2*x^2 + 2*c*d*x + c^2))/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
165,1,328,0,1.321823," ","integrate((f*x+e)^3*sin(a+b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, d f^{3} \sin\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right) + \sqrt{2} {\left(3 \, \pi {\left(d e f^{2} - c f^{3}\right)} \cos\left(a\right) + 2 \, \pi {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sin\left(a\right)\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) + \sqrt{2} {\left(2 \, \pi {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \cos\left(a\right) - 3 \, \pi {\left(d e f^{2} - c f^{3}\right)} \sin\left(a\right)\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) - 2 \, {\left(b d^{3} f^{3} x^{2} + 3 \, b d^{3} e^{2} f - 3 \, b c d^{2} e f^{2} + b c^{2} d f^{3} + {\left(3 \, b d^{3} e f^{2} - b c d^{2} f^{3}\right)} x\right)} \cos\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}{4 \, b^{2} d^{5}}"," ",0,"1/4*(2*d*f^3*sin(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a) + sqrt(2)*(3*pi*(d*e*f^2 - c*f^3)*cos(a) + 2*pi*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sin(a))*sqrt(b*d^2/pi)*fresnel_cos(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) + sqrt(2)*(2*pi*(b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*cos(a) - 3*pi*(d*e*f^2 - c*f^3)*sin(a))*sqrt(b*d^2/pi)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) - 2*(b*d^3*f^3*x^2 + 3*b*d^3*e^2*f - 3*b*c*d^2*e*f^2 + b*c^2*d*f^3 + (3*b*d^3*e*f^2 - b*c*d^2*f^3)*x)*cos(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a))/(b^2*d^5)","A",0
166,1,208,0,1.553925," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(\pi f^{2} \cos\left(a\right) + 2 \, \pi {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sin\left(a\right)\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) - \sqrt{2} {\left(\pi f^{2} \sin\left(a\right) - 2 \, \pi {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cos\left(a\right)\right)} \sqrt{\frac{b d^{2}}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) - 2 \, {\left(b d^{2} f^{2} x + 2 \, b d^{2} e f - b c d f^{2}\right)} \cos\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}{4 \, b^{2} d^{4}}"," ",0,"1/4*(sqrt(2)*(pi*f^2*cos(a) + 2*pi*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sin(a))*sqrt(b*d^2/pi)*fresnel_cos(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) - sqrt(2)*(pi*f^2*sin(a) - 2*pi*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cos(a))*sqrt(b*d^2/pi)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) - 2*(b*d^2*f^2*x + 2*b*d^2*e*f - b*c*d*f^2)*cos(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a))/(b^2*d^4)","A",0
167,1,131,0,1.475241," ","integrate((f*x+e)*sin(a+b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} {\left(d e - c f\right)} \cos\left(a\right) \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) + \sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} {\left(d e - c f\right)} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) \sin\left(a\right) - d f \cos\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}{2 \, b d^{3}}"," ",0,"1/2*(sqrt(2)*pi*sqrt(b*d^2/pi)*(d*e - c*f)*cos(a)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) + sqrt(2)*pi*sqrt(b*d^2/pi)*(d*e - c*f)*fresnel_cos(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d)*sin(a) - d*f*cos(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a))/(b*d^3)","A",0
168,1,89,0,1.345090," ","integrate(sin(a+b*(d*x+c)^2),x, algorithm=""fricas"")","\frac{\sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} \cos\left(a\right) \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) + \sqrt{2} \pi \sqrt{\frac{b d^{2}}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b d^{2}}{\pi}} {\left(d x + c\right)}}{d}\right) \sin\left(a\right)}{2 \, b d^{2}}"," ",0,"1/2*(sqrt(2)*pi*sqrt(b*d^2/pi)*cos(a)*fresnel_sin(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d) + sqrt(2)*pi*sqrt(b*d^2/pi)*fresnel_cos(sqrt(2)*sqrt(b*d^2/pi)*(d*x + c)/d)*sin(a))/(b*d^2)","A",0
169,0,0,0,1.157197," ","integrate(sin(a+b*(d*x+c)^2)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}{f x + e}, x\right)"," ",0,"integral(sin(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)/(f*x + e), x)","F",0
170,0,0,0,1.321726," ","integrate(sin(a+b*(d*x+c)^2)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2} + a\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin(b*d^2*x^2 + 2*b*c*d*x + b*c^2 + a)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
171,1,425,0,1.422512," ","integrate((f*x+e)^3*sin(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{{\left(3 \, b d^{3} e^{3} - 9 \, b c d^{2} e^{2} f + 9 \, b c^{2} d e f^{2} - 3 \, b c^{3} f^{3} - i \, f^{3}\right)} \left(i \, b d^{3}\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + {\left(3 \, b d^{3} e^{3} - 9 \, b c d^{2} e^{2} f + 9 \, b c^{2} d e f^{2} - 3 \, b c^{3} f^{3} + i \, f^{3}\right)} \left(-i \, b d^{3}\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right) + 9 \, {\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} \left(i \, b d^{3}\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + 9 \, {\left(b d^{3} e^{2} f - 2 \, b c d^{2} e f^{2} + b c^{2} d f^{3}\right)} \left(-i \, b d^{3}\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right) + 6 \, {\left(b d^{3} f^{3} x + 3 \, b d^{3} e f^{2} - 2 \, b c d^{2} f^{3}\right)} \cos\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}{18 \, b^{2} d^{6}}"," ",0,"-1/18*((3*b*d^3*e^3 - 9*b*c*d^2*e^2*f + 9*b*c^2*d*e*f^2 - 3*b*c^3*f^3 - I*f^3)*(I*b*d^3)^(2/3)*e^(-I*a)*gamma(1/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + (3*b*d^3*e^3 - 9*b*c*d^2*e^2*f + 9*b*c^2*d*e*f^2 - 3*b*c^3*f^3 + I*f^3)*(-I*b*d^3)^(2/3)*e^(I*a)*gamma(1/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3) + 9*(b*d^3*e^2*f - 2*b*c*d^2*e*f^2 + b*c^2*d*f^3)*(I*b*d^3)^(1/3)*e^(-I*a)*gamma(2/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + 9*(b*d^3*e^2*f - 2*b*c*d^2*e*f^2 + b*c^2*d*f^3)*(-I*b*d^3)^(1/3)*e^(I*a)*gamma(2/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3) + 6*(b*d^3*f^3*x + 3*b*d^3*e*f^2 - 2*b*c*d^2*f^3)*cos(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a))/(b^2*d^6)","A",0
172,1,319,0,1.249205," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{2 \, d^{2} f^{2} \cos\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right) + \left(i \, b d^{3}\right)^{\frac{2}{3}} {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + \left(-i \, b d^{3}\right)^{\frac{2}{3}} {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right) + 2 \, \left(i \, b d^{3}\right)^{\frac{1}{3}} {\left(d^{2} e f - c d f^{2}\right)} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + 2 \, \left(-i \, b d^{3}\right)^{\frac{1}{3}} {\left(d^{2} e f - c d f^{2}\right)} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right)}{6 \, b d^{5}}"," ",0,"-1/6*(2*d^2*f^2*cos(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a) + (I*b*d^3)^(2/3)*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*e^(-I*a)*gamma(1/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + (-I*b*d^3)^(2/3)*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*e^(I*a)*gamma(1/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3) + 2*(I*b*d^3)^(1/3)*(d^2*e*f - c*d*f^2)*e^(-I*a)*gamma(2/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + 2*(-I*b*d^3)^(1/3)*(d^2*e*f - c*d*f^2)*e^(I*a)*gamma(2/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3))/(b*d^5)","A",0
173,1,225,0,1.134020," ","integrate((f*x+e)*sin(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{\left(i \, b d^{3}\right)^{\frac{1}{3}} d f e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + \left(-i \, b d^{3}\right)^{\frac{1}{3}} d f e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right) + \left(i \, b d^{3}\right)^{\frac{2}{3}} {\left(d e - c f\right)} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + \left(-i \, b d^{3}\right)^{\frac{2}{3}} {\left(d e - c f\right)} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right)}{6 \, b d^{4}}"," ",0,"-1/6*((I*b*d^3)^(1/3)*d*f*e^(-I*a)*gamma(2/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + (-I*b*d^3)^(1/3)*d*f*e^(I*a)*gamma(2/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3) + (I*b*d^3)^(2/3)*(d*e - c*f)*e^(-I*a)*gamma(1/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + (-I*b*d^3)^(2/3)*(d*e - c*f)*e^(I*a)*gamma(1/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3))/(b*d^4)","A",0
174,1,107,0,1.476905," ","integrate(sin(a+b*(d*x+c)^3),x, algorithm=""fricas"")","-\frac{\left(i \, b d^{3}\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, i \, b d^{3} x^{3} + 3 i \, b c d^{2} x^{2} + 3 i \, b c^{2} d x + i \, b c^{3}\right) + \left(-i \, b d^{3}\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -i \, b d^{3} x^{3} - 3 i \, b c d^{2} x^{2} - 3 i \, b c^{2} d x - i \, b c^{3}\right)}{6 \, b d^{3}}"," ",0,"-1/6*((I*b*d^3)^(2/3)*e^(-I*a)*gamma(1/3, I*b*d^3*x^3 + 3*I*b*c*d^2*x^2 + 3*I*b*c^2*d*x + I*b*c^3) + (-I*b*d^3)^(2/3)*e^(I*a)*gamma(1/3, -I*b*d^3*x^3 - 3*I*b*c*d^2*x^2 - 3*I*b*c^2*d*x - I*b*c^3))/(b*d^3)","A",0
175,0,0,0,1.405138," ","integrate(sin(a+b*(d*x+c)^3)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}{f x + e}, x\right)"," ",0,"integral(sin(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)/(f*x + e), x)","F",0
176,0,0,0,1.524935," ","integrate(sin(a+b*(d*x+c)^3)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(b d^{3} x^{3} + 3 \, b c d^{2} x^{2} + 3 \, b c^{2} d x + b c^{3} + a\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin(b*d^3*x^3 + 3*b*c*d^2*x^2 + 3*b*c^2*d*x + b*c^3 + a)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
177,1,430,0,1.398057," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(2 \, \pi b d f^{2} \sin\left(a\right) - 3 \, \pi {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \cos\left(a\right)\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) + 2 \, \sqrt{2} {\left(2 \, \pi b d f^{2} \cos\left(a\right) + 3 \, \pi {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} \sin\left(a\right)\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{S}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) + 6 \, {\left(b d e f - b c f^{2}\right)} \sin\left(a\right) \operatorname{Si}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 3 \, {\left({\left(b d e f - b c f^{2}\right)} \operatorname{Ci}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + {\left(b d e f - b c f^{2}\right)} \operatorname{Ci}\left(-\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)\right)} \cos\left(a\right) + 4 \, {\left(b d f^{2} x + b c f^{2}\right)} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 3 \, c d^{2} e^{2} - 3 \, c^{2} d e f + c^{3} f^{2}\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{6 \, d^{3}}"," ",0,"1/6*(2*sqrt(2)*(2*pi*b*d*f^2*sin(a) - 3*pi*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*cos(a))*sqrt(b/(pi*d^2))*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) + 2*sqrt(2)*(2*pi*b*d*f^2*cos(a) + 3*pi*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*sin(a))*sqrt(b/(pi*d^2))*fresnel_sin(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) + 6*(b*d*e*f - b*c*f^2)*sin(a)*sin_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) - 3*((b*d*e*f - b*c*f^2)*cos_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) + (b*d*e*f - b*c*f^2)*cos_integral(-b/(d^2*x^2 + 2*c*d*x + c^2)))*cos(a) + 4*(b*d*f^2*x + b*c*f^2)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)) + 2*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 3*c*d^2*e^2 - 3*c^2*d*e*f + c^3*f^2)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)))/d^3","A",0
178,1,260,0,1.171659," ","integrate((f*x+e)*sin(a+b/(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} \pi {\left(d^{2} e - c d f\right)} \sqrt{\frac{b}{\pi d^{2}}} \cos\left(a\right) \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) - 4 \, \sqrt{2} \pi {\left(d^{2} e - c d f\right)} \sqrt{\frac{b}{\pi d^{2}}} \operatorname{S}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) \sin\left(a\right) - 2 \, b f \sin\left(a\right) \operatorname{Si}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + {\left(b f \operatorname{Ci}\left(\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + b f \operatorname{Ci}\left(-\frac{b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)\right)} \cos\left(a\right) - 2 \, {\left(d^{2} f x^{2} + 2 \, d^{2} e x + 2 \, c d e - c^{2} f\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{4 \, d^{2}}"," ",0,"-1/4*(4*sqrt(2)*pi*(d^2*e - c*d*f)*sqrt(b/(pi*d^2))*cos(a)*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) - 4*sqrt(2)*pi*(d^2*e - c*d*f)*sqrt(b/(pi*d^2))*fresnel_sin(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c))*sin(a) - 2*b*f*sin(a)*sin_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) + (b*f*cos_integral(b/(d^2*x^2 + 2*c*d*x + c^2)) + b*f*cos_integral(-b/(d^2*x^2 + 2*c*d*x + c^2)))*cos(a) - 2*(d^2*f*x^2 + 2*d^2*e*x + 2*c*d*e - c^2*f)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)))/d^2","A",0
179,1,137,0,1.374710," ","integrate(sin(a+b/(d*x+c)^2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \pi d \sqrt{\frac{b}{\pi d^{2}}} \cos\left(a\right) \operatorname{C}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) - \sqrt{2} \pi d \sqrt{\frac{b}{\pi d^{2}}} \operatorname{S}\left(\frac{\sqrt{2} d \sqrt{\frac{b}{\pi d^{2}}}}{d x + c}\right) \sin\left(a\right) - {\left(d x + c\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{d}"," ",0,"-(sqrt(2)*pi*d*sqrt(b/(pi*d^2))*cos(a)*fresnel_cos(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c)) - sqrt(2)*pi*d*sqrt(b/(pi*d^2))*fresnel_sin(sqrt(2)*d*sqrt(b/(pi*d^2))/(d*x + c))*sin(a) - (d*x + c)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2)))/d","A",0
180,0,0,0,1.177097," ","integrate(sin(a+b/(d*x+c)^2)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{f x + e}, x\right)"," ",0,"integral(sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))/(f*x + e), x)","F",0
181,0,0,0,1.347773," ","integrate(sin(a+b/(d*x+c)^2)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + b)/(d^2*x^2 + 2*c*d*x + c^2))/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
182,1,488,0,1.499742," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^3),x, algorithm=""fricas"")","-\frac{b f^{2} {\rm Ei}\left(\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) e^{\left(i \, a\right)} + b f^{2} {\rm Ei}\left(-\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) e^{\left(-i \, a\right)} - {\left(-3 i \, d^{3} e f + 3 i \, c d^{2} f^{2}\right)} \left(\frac{i \, b}{d^{3}}\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) - {\left(3 i \, d^{3} e f - 3 i \, c d^{2} f^{2}\right)} \left(-\frac{i \, b}{d^{3}}\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) - {\left(-3 i \, d^{3} e^{2} + 6 i \, c d^{2} e f - 3 i \, c^{2} d f^{2}\right)} \left(\frac{i \, b}{d^{3}}\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) - {\left(3 i \, d^{3} e^{2} - 6 i \, c d^{2} e f + 3 i \, c^{2} d f^{2}\right)} \left(-\frac{i \, b}{d^{3}}\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) - 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 3 \, c d^{2} e^{2} - 3 \, c^{2} d e f + c^{3} f^{2}\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{6 \, d^{3}}"," ",0,"-1/6*(b*f^2*Ei(I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))*e^(I*a) + b*f^2*Ei(-I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))*e^(-I*a) - (-3*I*d^3*e*f + 3*I*c*d^2*f^2)*(I*b/d^3)^(2/3)*e^(-I*a)*gamma(1/3, I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) - (3*I*d^3*e*f - 3*I*c*d^2*f^2)*(-I*b/d^3)^(2/3)*e^(I*a)*gamma(1/3, -I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) - (-3*I*d^3*e^2 + 6*I*c*d^2*e*f - 3*I*c^2*d*f^2)*(I*b/d^3)^(1/3)*e^(-I*a)*gamma(2/3, I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) - (3*I*d^3*e^2 - 6*I*c*d^2*e*f + 3*I*c^2*d*f^2)*(-I*b/d^3)^(1/3)*e^(I*a)*gamma(2/3, -I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) - 2*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 3*c*d^2*e^2 - 3*c^2*d*e*f + c^3*f^2)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)))/d^3","A",0
183,1,321,0,1.354075," ","integrate((f*x+e)*sin(a+b/(d*x+c)^3),x, algorithm=""fricas"")","\frac{-i \, d^{2} f \left(\frac{i \, b}{d^{3}}\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, \frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + i \, d^{2} f \left(-\frac{i \, b}{d^{3}}\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + {\left(-2 i \, d^{2} e + 2 i \, c d f\right)} \left(\frac{i \, b}{d^{3}}\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + {\left(2 i \, d^{2} e - 2 i \, c d f\right)} \left(-\frac{i \, b}{d^{3}}\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + 2 \, {\left(d^{2} f x^{2} + 2 \, d^{2} e x + 2 \, c d e - c^{2} f\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{4 \, d^{2}}"," ",0,"1/4*(-I*d^2*f*(I*b/d^3)^(2/3)*e^(-I*a)*gamma(1/3, I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + I*d^2*f*(-I*b/d^3)^(2/3)*e^(I*a)*gamma(1/3, -I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + (-2*I*d^2*e + 2*I*c*d*f)*(I*b/d^3)^(1/3)*e^(-I*a)*gamma(2/3, I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + (2*I*d^2*e - 2*I*c*d*f)*(-I*b/d^3)^(1/3)*e^(I*a)*gamma(2/3, -I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + 2*(d^2*f*x^2 + 2*d^2*e*x + 2*c*d*e - c^2*f)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)))/d^2","A",0
184,1,175,0,1.475434," ","integrate(sin(a+b/(d*x+c)^3),x, algorithm=""fricas"")","\frac{-i \, d \left(\frac{i \, b}{d^{3}}\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, \frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + i \, d \left(-\frac{i \, b}{d^{3}}\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{2 \, d}"," ",0,"1/2*(-I*d*(I*b/d^3)^(1/3)*e^(-I*a)*gamma(2/3, I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + I*d*(-I*b/d^3)^(1/3)*e^(I*a)*gamma(2/3, -I*b/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)) + 2*(d*x + c)*sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3)))/d","B",0
185,0,0,0,1.317489," ","integrate(sin(a+b/(d*x+c)^3)/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{f x + e}, x\right)"," ",0,"integral(sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/(f*x + e), x)","F",0
186,0,0,0,1.605535," ","integrate(sin(a+b/(d*x+c)^3)/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d^{3} x^{3} + 3 \, a c d^{2} x^{2} + 3 \, a c^{2} d x + a c^{3} + b}{d^{3} x^{3} + 3 \, c d^{2} x^{2} + 3 \, c^{2} d x + c^{3}}\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin((a*d^3*x^3 + 3*a*c*d^2*x^2 + 3*a*c^2*d*x + a*c^3 + b)/(d^3*x^3 + 3*c*d^2*x^2 + 3*c^2*d*x + c^3))/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
187,1,196,0,1.567803," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(b^{5} d^{2} f^{2} x^{2} + b^{5} d^{2} e^{2} - 12 \, b^{3} d e f - 8 \, {\left(b^{3} c - 15 \, b\right)} f^{2} + 2 \, {\left(b^{5} d^{2} e f - 10 \, b^{3} d f^{2}\right)} x\right)} \sqrt{d x + c} \cos\left(\sqrt{d x + c} b + a\right) - {\left(5 \, b^{4} d^{2} f^{2} x^{2} + b^{4} d^{2} e^{2} + 4 \, {\left(b^{4} c - 3 \, b^{2}\right)} d e f - 24 \, {\left(2 \, b^{2} c - 5\right)} f^{2} + 2 \, {\left(3 \, b^{4} d^{2} e f + 2 \, {\left(b^{4} c - 15 \, b^{2}\right)} d f^{2}\right)} x\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)}}{b^{6} d^{3}}"," ",0,"-2*((b^5*d^2*f^2*x^2 + b^5*d^2*e^2 - 12*b^3*d*e*f - 8*(b^3*c - 15*b)*f^2 + 2*(b^5*d^2*e*f - 10*b^3*d*f^2)*x)*sqrt(d*x + c)*cos(sqrt(d*x + c)*b + a) - (5*b^4*d^2*f^2*x^2 + b^4*d^2*e^2 + 4*(b^4*c - 3*b^2)*d*e*f - 24*(2*b^2*c - 5)*f^2 + 2*(3*b^4*d^2*e*f + 2*(b^4*c - 15*b^2)*d*f^2)*x)*sin(sqrt(d*x + c)*b + a))/(b^6*d^3)","A",0
188,1,86,0,0.858478," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(b^{3} d f x + b^{3} d e - 6 \, b f\right)} \sqrt{d x + c} \cos\left(\sqrt{d x + c} b + a\right) - {\left(3 \, b^{2} d f x + b^{2} d e + 2 \, {\left(b^{2} c - 3\right)} f\right)} \sin\left(\sqrt{d x + c} b + a\right)\right)}}{b^{4} d^{2}}"," ",0,"-2*((b^3*d*f*x + b^3*d*e - 6*b*f)*sqrt(d*x + c)*cos(sqrt(d*x + c)*b + a) - (3*b^2*d*f*x + b^2*d*e + 2*(b^2*c - 3)*f)*sin(sqrt(d*x + c)*b + a))/(b^4*d^2)","A",0
189,1,44,0,1.041932," ","integrate(sin(a+b*(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{2 \, {\left(\sqrt{d x + c} b \cos\left(\sqrt{d x + c} b + a\right) - \sin\left(\sqrt{d x + c} b + a\right)\right)}}{b^{2} d}"," ",0,"-2*(sqrt(d*x + c)*b*cos(sqrt(d*x + c)*b + a) - sin(sqrt(d*x + c)*b + a))/(b^2*d)","A",0
190,1,250,0,1.642667," ","integrate(sin(a+b*(d*x+c)^(1/2))/(f*x+e),x, algorithm=""fricas"")","\frac{-i \, {\rm Ei}\left(i \, \sqrt{d x + c} b - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(i \, a + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} - i \, {\rm Ei}\left(i \, \sqrt{d x + c} b + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(i \, a - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} + i \, {\rm Ei}\left(-i \, \sqrt{d x + c} b - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(-i \, a + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} + i \, {\rm Ei}\left(-i \, \sqrt{d x + c} b + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(-i \, a - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)}}{2 \, f}"," ",0,"1/2*(-I*Ei(I*sqrt(d*x + c)*b - sqrt((b^2*d*e - b^2*c*f)/f))*e^(I*a + sqrt((b^2*d*e - b^2*c*f)/f)) - I*Ei(I*sqrt(d*x + c)*b + sqrt((b^2*d*e - b^2*c*f)/f))*e^(I*a - sqrt((b^2*d*e - b^2*c*f)/f)) + I*Ei(-I*sqrt(d*x + c)*b - sqrt((b^2*d*e - b^2*c*f)/f))*e^(-I*a + sqrt((b^2*d*e - b^2*c*f)/f)) + I*Ei(-I*sqrt(d*x + c)*b + sqrt((b^2*d*e - b^2*c*f)/f))*e^(-I*a - sqrt((b^2*d*e - b^2*c*f)/f)))/f","C",0
191,1,416,0,2.024011," ","integrate(sin(a+b*(d*x+c)^(1/2))/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{{\left(-i \, d f x - i \, d e\right)} \sqrt{\frac{b^{2} d e - b^{2} c f}{f}} {\rm Ei}\left(i \, \sqrt{d x + c} b - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(i \, a + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} + {\left(i \, d f x + i \, d e\right)} \sqrt{\frac{b^{2} d e - b^{2} c f}{f}} {\rm Ei}\left(i \, \sqrt{d x + c} b + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(i \, a - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} + {\left(i \, d f x + i \, d e\right)} \sqrt{\frac{b^{2} d e - b^{2} c f}{f}} {\rm Ei}\left(-i \, \sqrt{d x + c} b - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(-i \, a + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} + {\left(-i \, d f x - i \, d e\right)} \sqrt{\frac{b^{2} d e - b^{2} c f}{f}} {\rm Ei}\left(-i \, \sqrt{d x + c} b + \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right) e^{\left(-i \, a - \sqrt{\frac{b^{2} d e - b^{2} c f}{f}}\right)} + 4 \, {\left(d e - c f\right)} \sin\left(\sqrt{d x + c} b + a\right)}{4 \, {\left(d e^{2} f - c e f^{2} + {\left(d e f^{2} - c f^{3}\right)} x\right)}}"," ",0,"-1/4*((-I*d*f*x - I*d*e)*sqrt((b^2*d*e - b^2*c*f)/f)*Ei(I*sqrt(d*x + c)*b - sqrt((b^2*d*e - b^2*c*f)/f))*e^(I*a + sqrt((b^2*d*e - b^2*c*f)/f)) + (I*d*f*x + I*d*e)*sqrt((b^2*d*e - b^2*c*f)/f)*Ei(I*sqrt(d*x + c)*b + sqrt((b^2*d*e - b^2*c*f)/f))*e^(I*a - sqrt((b^2*d*e - b^2*c*f)/f)) + (I*d*f*x + I*d*e)*sqrt((b^2*d*e - b^2*c*f)/f)*Ei(-I*sqrt(d*x + c)*b - sqrt((b^2*d*e - b^2*c*f)/f))*e^(-I*a + sqrt((b^2*d*e - b^2*c*f)/f)) + (-I*d*f*x - I*d*e)*sqrt((b^2*d*e - b^2*c*f)/f)*Ei(-I*sqrt(d*x + c)*b + sqrt((b^2*d*e - b^2*c*f)/f))*e^(-I*a - sqrt((b^2*d*e - b^2*c*f)/f)) + 4*(d*e - c*f)*sin(sqrt(d*x + c)*b + a))/(d*e^2*f - c*e*f^2 + (d*e*f^2 - c*f^3)*x)","C",0
192,1,276,0,1.409863," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(3/2)),x, algorithm=""fricas"")","\frac{{\left(2 i \, d e f - 2 i \, c f^{2}\right)} \left(i \, b\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, {\left(i \, b d x + i \, b c\right)} \sqrt{d x + c}\right) + {\left(-2 i \, d e f + 2 i \, c f^{2}\right)} \left(-i \, b\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, {\left(-i \, b d x - i \, b c\right)} \sqrt{d x + c}\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \left(i \, b\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, {\left(i \, b d x + i \, b c\right)} \sqrt{d x + c}\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \left(-i \, b\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, {\left(-i \, b d x - i \, b c\right)} \sqrt{d x + c}\right) + 6 \, f^{2} \sin\left({\left(b d x + b c\right)} \sqrt{d x + c} + a\right) - 6 \, {\left(b d f^{2} x + 2 \, b d e f - b c f^{2}\right)} \sqrt{d x + c} \cos\left({\left(b d x + b c\right)} \sqrt{d x + c} + a\right)}{9 \, b^{2} d^{3}}"," ",0,"1/9*((2*I*d*e*f - 2*I*c*f^2)*(I*b)^(2/3)*e^(-I*a)*gamma(1/3, (I*b*d*x + I*b*c)*sqrt(d*x + c)) + (-2*I*d*e*f + 2*I*c*f^2)*(-I*b)^(2/3)*e^(I*a)*gamma(1/3, (-I*b*d*x - I*b*c)*sqrt(d*x + c)) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*(I*b)^(1/3)*e^(-I*a)*gamma(2/3, (I*b*d*x + I*b*c)*sqrt(d*x + c)) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*(-I*b)^(1/3)*e^(I*a)*gamma(2/3, (-I*b*d*x - I*b*c)*sqrt(d*x + c)) + 6*f^2*sin((b*d*x + b*c)*sqrt(d*x + c) + a) - 6*(b*d*f^2*x + 2*b*d*e*f - b*c*f^2)*sqrt(d*x + c)*cos((b*d*x + b*c)*sqrt(d*x + c) + a))/(b^2*d^3)","A",0
193,1,185,0,1.471907," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(3/2)),x, algorithm=""fricas"")","\frac{i \, \left(i \, b\right)^{\frac{2}{3}} f e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, {\left(i \, b d x + i \, b c\right)} \sqrt{d x + c}\right) - i \, \left(-i \, b\right)^{\frac{2}{3}} f e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, {\left(-i \, b d x - i \, b c\right)} \sqrt{d x + c}\right) - 6 \, \sqrt{d x + c} b f \cos\left({\left(b d x + b c\right)} \sqrt{d x + c} + a\right) - 3 \, {\left(b d e - b c f\right)} \left(i \, b\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, {\left(i \, b d x + i \, b c\right)} \sqrt{d x + c}\right) - 3 \, {\left(b d e - b c f\right)} \left(-i \, b\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, {\left(-i \, b d x - i \, b c\right)} \sqrt{d x + c}\right)}{9 \, b^{2} d^{2}}"," ",0,"1/9*(I*(I*b)^(2/3)*f*e^(-I*a)*gamma(1/3, (I*b*d*x + I*b*c)*sqrt(d*x + c)) - I*(-I*b)^(2/3)*f*e^(I*a)*gamma(1/3, (-I*b*d*x - I*b*c)*sqrt(d*x + c)) - 6*sqrt(d*x + c)*b*f*cos((b*d*x + b*c)*sqrt(d*x + c) + a) - 3*(b*d*e - b*c*f)*(I*b)^(1/3)*e^(-I*a)*gamma(2/3, (I*b*d*x + I*b*c)*sqrt(d*x + c)) - 3*(b*d*e - b*c*f)*(-I*b)^(1/3)*e^(I*a)*gamma(2/3, (-I*b*d*x - I*b*c)*sqrt(d*x + c)))/(b^2*d^2)","A",0
194,1,69,0,1.512848," ","integrate(sin(a+b*(d*x+c)^(3/2)),x, algorithm=""fricas"")","-\frac{\left(i \, b\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, {\left(i \, b d x + i \, b c\right)} \sqrt{d x + c}\right) + \left(-i \, b\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, {\left(-i \, b d x - i \, b c\right)} \sqrt{d x + c}\right)}{3 \, b d}"," ",0,"-1/3*((I*b)^(1/3)*e^(-I*a)*gamma(2/3, (I*b*d*x + I*b*c)*sqrt(d*x + c)) + (-I*b)^(1/3)*e^(I*a)*gamma(2/3, (-I*b*d*x - I*b*c)*sqrt(d*x + c)))/(b*d)","A",0
195,0,0,0,1.268335," ","integrate(sin(a+b*(d*x+c)^(3/2))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(b d x + b c\right)} \sqrt{d x + c} + a\right)}{f x + e}, x\right)"," ",0,"integral(sin((b*d*x + b*c)*sqrt(d*x + c) + a)/(f*x + e), x)","F",0
196,0,0,0,1.407592," ","integrate(sin(a+b*(d*x+c)^(3/2))/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(b d x + b c\right)} \sqrt{d x + c} + a\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin((b*d*x + b*c)*sqrt(d*x + c) + a)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
197,1,459,0,1.472230," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{{\left(360 \, b^{2} d^{2} e^{2} - 60 \, {\left(b^{4} + 12 \, b^{2} c\right)} d e f + {\left(b^{6} + 60 \, b^{4} c + 360 \, b^{2} c^{2}\right)} f^{2}\right)} \operatorname{Ci}\left(\frac{b}{\sqrt{d x + c}}\right) \sin\left(a\right) + {\left(360 \, b^{2} d^{2} e^{2} - 60 \, {\left(b^{4} + 12 \, b^{2} c\right)} d e f + {\left(b^{6} + 60 \, b^{4} c + 360 \, b^{2} c^{2}\right)} f^{2}\right)} \operatorname{Ci}\left(-\frac{b}{\sqrt{d x + c}}\right) \sin\left(a\right) + 2 \, {\left(360 \, b^{2} d^{2} e^{2} - 60 \, {\left(b^{4} + 12 \, b^{2} c\right)} d e f + {\left(b^{6} + 60 \, b^{4} c + 360 \, b^{2} c^{2}\right)} f^{2}\right)} \cos\left(a\right) \operatorname{Si}\left(\frac{b}{\sqrt{d x + c}}\right) + 2 \, {\left(24 \, b d^{2} f^{2} x^{2} + 360 \, b d^{2} e^{2} - 60 \, {\left(b^{3} + 10 \, b c\right)} d e f + {\left(b^{5} + 58 \, b^{3} c + 264 \, b c^{2}\right)} f^{2} + 2 \, {\left(60 \, b d^{2} e f - {\left(b^{3} + 36 \, b c\right)} d f^{2}\right)} x\right)} \sqrt{d x + c} \cos\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right) + 2 \, {\left(120 \, d^{3} f^{2} x^{3} + 360 \, c d^{2} e^{2} - 60 \, {\left(b^{2} c + 6 \, c^{2}\right)} d e f + {\left(b^{4} c + 54 \, b^{2} c^{2} + 120 \, c^{3}\right)} f^{2} - 6 \, {\left(b^{2} d^{2} f^{2} - 60 \, d^{3} e f\right)} x^{2} - {\left(60 \, b^{2} d^{2} e f - 360 \, d^{3} e^{2} - {\left(b^{4} + 48 \, b^{2} c\right)} d f^{2}\right)} x\right)} \sin\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right)}{720 \, d^{3}}"," ",0,"1/720*((360*b^2*d^2*e^2 - 60*(b^4 + 12*b^2*c)*d*e*f + (b^6 + 60*b^4*c + 360*b^2*c^2)*f^2)*cos_integral(b/sqrt(d*x + c))*sin(a) + (360*b^2*d^2*e^2 - 60*(b^4 + 12*b^2*c)*d*e*f + (b^6 + 60*b^4*c + 360*b^2*c^2)*f^2)*cos_integral(-b/sqrt(d*x + c))*sin(a) + 2*(360*b^2*d^2*e^2 - 60*(b^4 + 12*b^2*c)*d*e*f + (b^6 + 60*b^4*c + 360*b^2*c^2)*f^2)*cos(a)*sin_integral(b/sqrt(d*x + c)) + 2*(24*b*d^2*f^2*x^2 + 360*b*d^2*e^2 - 60*(b^3 + 10*b*c)*d*e*f + (b^5 + 58*b^3*c + 264*b*c^2)*f^2 + 2*(60*b*d^2*e*f - (b^3 + 36*b*c)*d*f^2)*x)*sqrt(d*x + c)*cos((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)) + 2*(120*d^3*f^2*x^3 + 360*c*d^2*e^2 - 60*(b^2*c + 6*c^2)*d*e*f + (b^4*c + 54*b^2*c^2 + 120*c^3)*f^2 - 6*(b^2*d^2*f^2 - 60*d^3*e*f)*x^2 - (60*b^2*d^2*e*f - 360*d^3*e^2 - (b^4 + 48*b^2*c)*d*f^2)*x)*sin((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)))/d^3","A",0
198,1,241,0,1.599730," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{{\left(12 \, b^{2} d e - {\left(b^{4} + 12 \, b^{2} c\right)} f\right)} \operatorname{Ci}\left(\frac{b}{\sqrt{d x + c}}\right) \sin\left(a\right) + {\left(12 \, b^{2} d e - {\left(b^{4} + 12 \, b^{2} c\right)} f\right)} \operatorname{Ci}\left(-\frac{b}{\sqrt{d x + c}}\right) \sin\left(a\right) + 2 \, {\left(12 \, b^{2} d e - {\left(b^{4} + 12 \, b^{2} c\right)} f\right)} \cos\left(a\right) \operatorname{Si}\left(\frac{b}{\sqrt{d x + c}}\right) + 2 \, {\left(2 \, b d f x + 12 \, b d e - {\left(b^{3} + 10 \, b c\right)} f\right)} \sqrt{d x + c} \cos\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right) + 2 \, {\left(6 \, d^{2} f x^{2} + 12 \, c d e - {\left(b^{2} c + 6 \, c^{2}\right)} f - {\left(b^{2} d f - 12 \, d^{2} e\right)} x\right)} \sin\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right)}{24 \, d^{2}}"," ",0,"1/24*((12*b^2*d*e - (b^4 + 12*b^2*c)*f)*cos_integral(b/sqrt(d*x + c))*sin(a) + (12*b^2*d*e - (b^4 + 12*b^2*c)*f)*cos_integral(-b/sqrt(d*x + c))*sin(a) + 2*(12*b^2*d*e - (b^4 + 12*b^2*c)*f)*cos(a)*sin_integral(b/sqrt(d*x + c)) + 2*(2*b*d*f*x + 12*b*d*e - (b^3 + 10*b*c)*f)*sqrt(d*x + c)*cos((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)) + 2*(6*d^2*f*x^2 + 12*c*d*e - (b^2*c + 6*c^2)*f - (b^2*d*f - 12*d^2*e)*x)*sin((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)))/d^2","A",0
199,1,125,0,1.190017," ","integrate(sin(a+b/(d*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{b^{2} \operatorname{Ci}\left(\frac{b}{\sqrt{d x + c}}\right) \sin\left(a\right) + b^{2} \operatorname{Ci}\left(-\frac{b}{\sqrt{d x + c}}\right) \sin\left(a\right) + 2 \, b^{2} \cos\left(a\right) \operatorname{Si}\left(\frac{b}{\sqrt{d x + c}}\right) + 2 \, \sqrt{d x + c} b \cos\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right)}{2 \, d}"," ",0,"1/2*(b^2*cos_integral(b/sqrt(d*x + c))*sin(a) + b^2*cos_integral(-b/sqrt(d*x + c))*sin(a) + 2*b^2*cos(a)*sin_integral(b/sqrt(d*x + c)) + 2*sqrt(d*x + c)*b*cos((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)) + 2*(d*x + c)*sin((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)))/d","A",0
200,1,314,0,1.546601," ","integrate(sin(a+b/(d*x+c)^(1/2))/(f*x+e),x, algorithm=""fricas"")","\frac{2 i \, {\rm Ei}\left(\frac{i \, b}{\sqrt{d x + c}}\right) e^{\left(i \, a\right)} - 2 i \, {\rm Ei}\left(-\frac{i \, b}{\sqrt{d x + c}}\right) e^{\left(-i \, a\right)} - i \, {\rm Ei}\left(-\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} - i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(i \, a + \sqrt{\frac{b^{2} f}{d e - c f}}\right)} - i \, {\rm Ei}\left(\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} + i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(i \, a - \sqrt{\frac{b^{2} f}{d e - c f}}\right)} + i \, {\rm Ei}\left(-\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} + i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(-i \, a + \sqrt{\frac{b^{2} f}{d e - c f}}\right)} + i \, {\rm Ei}\left(\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} - i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(-i \, a - \sqrt{\frac{b^{2} f}{d e - c f}}\right)}}{2 \, f}"," ",0,"1/2*(2*I*Ei(I*b/sqrt(d*x + c))*e^(I*a) - 2*I*Ei(-I*b/sqrt(d*x + c))*e^(-I*a) - I*Ei(-(sqrt(b^2*f/(d*e - c*f))*(d*x + c) - I*sqrt(d*x + c)*b)/(d*x + c))*e^(I*a + sqrt(b^2*f/(d*e - c*f))) - I*Ei((sqrt(b^2*f/(d*e - c*f))*(d*x + c) + I*sqrt(d*x + c)*b)/(d*x + c))*e^(I*a - sqrt(b^2*f/(d*e - c*f))) + I*Ei(-(sqrt(b^2*f/(d*e - c*f))*(d*x + c) + I*sqrt(d*x + c)*b)/(d*x + c))*e^(-I*a + sqrt(b^2*f/(d*e - c*f))) + I*Ei((sqrt(b^2*f/(d*e - c*f))*(d*x + c) - I*sqrt(d*x + c)*b)/(d*x + c))*e^(-I*a - sqrt(b^2*f/(d*e - c*f))))/f","C",0
201,1,448,0,1.231692," ","integrate(sin(a+b/(d*x+c)^(1/2))/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{{\left(i \, d f x + i \, d e\right)} \sqrt{\frac{b^{2} f}{d e - c f}} {\rm Ei}\left(-\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} - i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(i \, a + \sqrt{\frac{b^{2} f}{d e - c f}}\right)} + {\left(-i \, d f x - i \, d e\right)} \sqrt{\frac{b^{2} f}{d e - c f}} {\rm Ei}\left(\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} + i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(i \, a - \sqrt{\frac{b^{2} f}{d e - c f}}\right)} + {\left(-i \, d f x - i \, d e\right)} \sqrt{\frac{b^{2} f}{d e - c f}} {\rm Ei}\left(-\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} + i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(-i \, a + \sqrt{\frac{b^{2} f}{d e - c f}}\right)} + {\left(i \, d f x + i \, d e\right)} \sqrt{\frac{b^{2} f}{d e - c f}} {\rm Ei}\left(\frac{\sqrt{\frac{b^{2} f}{d e - c f}} {\left(d x + c\right)} - i \, \sqrt{d x + c} b}{d x + c}\right) e^{\left(-i \, a - \sqrt{\frac{b^{2} f}{d e - c f}}\right)} - 4 \, {\left(d f x + c f\right)} \sin\left(\frac{a d x + a c + \sqrt{d x + c} b}{d x + c}\right)}{4 \, {\left(d e^{2} f - c e f^{2} + {\left(d e f^{2} - c f^{3}\right)} x\right)}}"," ",0,"-1/4*((I*d*f*x + I*d*e)*sqrt(b^2*f/(d*e - c*f))*Ei(-(sqrt(b^2*f/(d*e - c*f))*(d*x + c) - I*sqrt(d*x + c)*b)/(d*x + c))*e^(I*a + sqrt(b^2*f/(d*e - c*f))) + (-I*d*f*x - I*d*e)*sqrt(b^2*f/(d*e - c*f))*Ei((sqrt(b^2*f/(d*e - c*f))*(d*x + c) + I*sqrt(d*x + c)*b)/(d*x + c))*e^(I*a - sqrt(b^2*f/(d*e - c*f))) + (-I*d*f*x - I*d*e)*sqrt(b^2*f/(d*e - c*f))*Ei(-(sqrt(b^2*f/(d*e - c*f))*(d*x + c) + I*sqrt(d*x + c)*b)/(d*x + c))*e^(-I*a + sqrt(b^2*f/(d*e - c*f))) + (I*d*f*x + I*d*e)*sqrt(b^2*f/(d*e - c*f))*Ei((sqrt(b^2*f/(d*e - c*f))*(d*x + c) - I*sqrt(d*x + c)*b)/(d*x + c))*e^(-I*a - sqrt(b^2*f/(d*e - c*f))) - 4*(d*f*x + c*f)*sin((a*d*x + a*c + sqrt(d*x + c)*b)/(d*x + c)))/(d*e^2*f - c*e*f^2 + (d*e*f^2 - c*f^3)*x)","C",0
202,1,506,0,1.475679," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(3/2)),x, algorithm=""fricas"")","\frac{-i \, b^{2} f^{2} {\rm Ei}\left(\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) e^{\left(i \, a\right)} + i \, b^{2} f^{2} {\rm Ei}\left(-\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) e^{\left(-i \, a\right)} + {\left(-3 i \, d^{2} e^{2} + 6 i \, c d e f - 3 i \, c^{2} f^{2}\right)} \left(i \, b\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, \frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + {\left(3 i \, d^{2} e^{2} - 6 i \, c d e f + 3 i \, c^{2} f^{2}\right)} \left(-i \, b\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 9 \, {\left(b d e f - b c f^{2}\right)} \left(i \, b\right)^{\frac{1}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, \frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 9 \, {\left(b d e f - b c f^{2}\right)} \left(-i \, b\right)^{\frac{1}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + 2 \, {\left(b d f^{2} x + 9 \, b d e f - 8 \, b c f^{2}\right)} \sqrt{d x + c} \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 3 \, c d^{2} e^{2} - 3 \, c^{2} d e f + c^{3} f^{2}\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{6 \, d^{3}}"," ",0,"1/6*(-I*b^2*f^2*Ei(I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2))*e^(I*a) + I*b^2*f^2*Ei(-I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2))*e^(-I*a) + (-3*I*d^2*e^2 + 6*I*c*d*e*f - 3*I*c^2*f^2)*(I*b)^(2/3)*e^(-I*a)*gamma(1/3, I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) + (3*I*d^2*e^2 - 6*I*c*d*e*f + 3*I*c^2*f^2)*(-I*b)^(2/3)*e^(I*a)*gamma(1/3, -I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) - 9*(b*d*e*f - b*c*f^2)*(I*b)^(1/3)*e^(-I*a)*gamma(2/3, I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) - 9*(b*d*e*f - b*c*f^2)*(-I*b)^(1/3)*e^(I*a)*gamma(2/3, -I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) + 2*(b*d*f^2*x + 9*b*d*e*f - 8*b*c*f^2)*sqrt(d*x + c)*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2)) + 2*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 3*c*d^2*e^2 - 3*c^2*d*e*f + c^3*f^2)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2)))/d^3","A",0
203,1,330,0,1.073158," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(3/2)),x, algorithm=""fricas"")","-\frac{3 \, \left(i \, b\right)^{\frac{1}{3}} b f e^{\left(-i \, a\right)} \Gamma\left(\frac{2}{3}, \frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + 3 \, \left(-i \, b\right)^{\frac{1}{3}} b f e^{\left(i \, a\right)} \Gamma\left(\frac{2}{3}, -\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - {\left(-2 i \, d e + 2 i \, c f\right)} \left(i \, b\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, \frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - {\left(2 i \, d e - 2 i \, c f\right)} \left(-i \, b\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 6 \, \sqrt{d x + c} b f \cos\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) - 2 \, {\left(d^{2} f x^{2} + 2 \, d^{2} e x + 2 \, c d e - c^{2} f\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{4 \, d^{2}}"," ",0,"-1/4*(3*(I*b)^(1/3)*b*f*e^(-I*a)*gamma(2/3, I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) + 3*(-I*b)^(1/3)*b*f*e^(I*a)*gamma(2/3, -I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) - (-2*I*d*e + 2*I*c*f)*(I*b)^(2/3)*e^(-I*a)*gamma(1/3, I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) - (2*I*d*e - 2*I*c*f)*(-I*b)^(2/3)*e^(I*a)*gamma(1/3, -I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) - 6*sqrt(d*x + c)*b*f*cos((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2)) - 2*(d^2*f*x^2 + 2*d^2*e*x + 2*c*d*e - c^2*f)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2)))/d^2","A",0
204,1,144,0,1.531682," ","integrate(sin(a+b/(d*x+c)^(3/2)),x, algorithm=""fricas"")","\frac{-i \, \left(i \, b\right)^{\frac{2}{3}} e^{\left(-i \, a\right)} \Gamma\left(\frac{1}{3}, \frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + i \, \left(-i \, b\right)^{\frac{2}{3}} e^{\left(i \, a\right)} \Gamma\left(\frac{1}{3}, -\frac{i \, \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right) + 2 \, {\left(d x + c\right)} \sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{2 \, d}"," ",0,"1/2*(-I*(I*b)^(2/3)*e^(-I*a)*gamma(1/3, I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) + I*(-I*b)^(2/3)*e^(I*a)*gamma(1/3, -I*sqrt(d*x + c)*b/(d^2*x^2 + 2*c*d*x + c^2)) + 2*(d*x + c)*sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2)))/d","A",0
205,0,0,0,1.304402," ","integrate(sin(a+b/(d*x+c)^(3/2))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{f x + e}, x\right)"," ",0,"integral(sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2))/(f*x + e), x)","F",0
206,0,0,0,1.244800," ","integrate(sin(a+b/(d*x+c)^(3/2))/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + \sqrt{d x + c} b}{d^{2} x^{2} + 2 \, c d x + c^{2}}\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin((a*d^2*x^2 + 2*a*c*d*x + a*c^2 + sqrt(d*x + c)*b)/(d^2*x^2 + 2*c*d*x + c^2))/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
207,1,333,0,1.467839," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(56 \, b^{6} d^{2} f^{2} x^{2} + 2 \, b^{6} d^{2} e^{2} + 36 \, b^{6} c d e f + 18 \, {\left(b^{6} c^{2} - 2240\right)} f^{2} + 8 \, {\left(5 \, b^{6} d^{2} e f + 9 \, b^{6} c d f^{2}\right)} x - {\left(b^{8} d^{2} f^{2} x^{2} + 2 \, b^{8} d^{2} e f x + b^{8} d^{2} e^{2} - 20160 \, b^{2} f^{2}\right)} {\left(d x + c\right)}^{\frac{2}{3}} - 240 \, {\left(7 \, b^{4} d f^{2} x + b^{4} d e f + 6 \, b^{4} c f^{2}\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) + 2 \, {\left(3360 \, b^{3} d f^{2} x + 120 \, b^{3} d e f + 3240 \, b^{3} c f^{2} - 12 \, {\left(14 \, b^{5} d f^{2} x + 5 \, b^{5} d e f + 9 \, b^{5} c f^{2}\right)} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(4 \, b^{7} d^{2} f^{2} x^{2} + b^{7} d^{2} e^{2} + 3 \, b^{7} c d e f - 20160 \, b f^{2} + {\left(5 \, b^{7} d^{2} e f + 3 \, b^{7} c d f^{2}\right)} x\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{9} d^{3}}"," ",0,"3*((56*b^6*d^2*f^2*x^2 + 2*b^6*d^2*e^2 + 36*b^6*c*d*e*f + 18*(b^6*c^2 - 2240)*f^2 + 8*(5*b^6*d^2*e*f + 9*b^6*c*d*f^2)*x - (b^8*d^2*f^2*x^2 + 2*b^8*d^2*e*f*x + b^8*d^2*e^2 - 20160*b^2*f^2)*(d*x + c)^(2/3) - 240*(7*b^4*d*f^2*x + b^4*d*e*f + 6*b^4*c*f^2)*(d*x + c)^(1/3))*cos((d*x + c)^(1/3)*b + a) + 2*(3360*b^3*d*f^2*x + 120*b^3*d*e*f + 3240*b^3*c*f^2 - 12*(14*b^5*d*f^2*x + 5*b^5*d*e*f + 9*b^5*c*f^2)*(d*x + c)^(2/3) + (4*b^7*d^2*f^2*x^2 + b^7*d^2*e^2 + 3*b^7*c*d*e*f - 20160*b*f^2 + (5*b^7*d^2*e*f + 3*b^7*c*d*f^2)*x)*(d*x + c)^(1/3))*sin((d*x + c)^(1/3)*b + a))/(b^9*d^3)","A",0
208,1,142,0,1.404433," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(20 \, b^{3} d f x + 2 \, b^{3} d e + 18 \, b^{3} c f - 120 \, {\left(d x + c\right)}^{\frac{1}{3}} b f - {\left(b^{5} d f x + b^{5} d e\right)} {\left(d x + c\right)}^{\frac{2}{3}}\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - {\left(60 \, {\left(d x + c\right)}^{\frac{2}{3}} b^{2} f - {\left(5 \, b^{4} d f x + 2 \, b^{4} d e + 3 \, b^{4} c f\right)} {\left(d x + c\right)}^{\frac{1}{3}} - 120 \, f\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{6} d^{2}}"," ",0,"3*((20*b^3*d*f*x + 2*b^3*d*e + 18*b^3*c*f - 120*(d*x + c)^(1/3)*b*f - (b^5*d*f*x + b^5*d*e)*(d*x + c)^(2/3))*cos((d*x + c)^(1/3)*b + a) - (60*(d*x + c)^(2/3)*b^2*f - (5*b^4*d*f*x + 2*b^4*d*e + 3*b^4*c*f)*(d*x + c)^(1/3) - 120*f)*sin((d*x + c)^(1/3)*b + a))/(b^6*d^2)","A",0
209,1,58,0,1.495692," ","integrate(sin(a+b*(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left(2 \, {\left(d x + c\right)}^{\frac{1}{3}} b \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{2} - 2\right)} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{3} d}"," ",0,"3*(2*(d*x + c)^(1/3)*b*sin((d*x + c)^(1/3)*b + a) - ((d*x + c)^(2/3)*b^2 - 2)*cos((d*x + c)^(1/3)*b + a))/(b^3*d)","A",0
210,1,448,0,1.083523," ","integrate(sin(a+b*(d*x+c)^(1/3))/(f*x+e),x, algorithm=""fricas"")","\frac{i \, {\rm Ei}\left(-i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(i \, \sqrt{3} + 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} - i \, a\right)} + i \, {\rm Ei}\left(-i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(-i \, \sqrt{3} + 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} - i \, a\right)} - i \, {\rm Ei}\left(i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(i \, \sqrt{3} + 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} + i \, a\right)} - i \, {\rm Ei}\left(i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(-i \, \sqrt{3} + 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} + i \, a\right)} - i \, {\rm Ei}\left(i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(i \, a - \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right)} + i \, {\rm Ei}\left(-i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(-i \, a - \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right)}}{2 \, f}"," ",0,"1/2*(I*Ei(-I*(d*x + c)^(1/3)*b + 1/2*(-I*sqrt(3) - 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3))*e^(1/2*(I*sqrt(3) + 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3) - I*a) + I*Ei(-I*(d*x + c)^(1/3)*b + 1/2*(I*sqrt(3) - 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3))*e^(1/2*(-I*sqrt(3) + 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3) - I*a) - I*Ei(I*(d*x + c)^(1/3)*b + 1/2*(-I*sqrt(3) - 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3))*e^(1/2*(I*sqrt(3) + 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3) + I*a) - I*Ei(I*(d*x + c)^(1/3)*b + 1/2*(I*sqrt(3) - 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3))*e^(1/2*(-I*sqrt(3) + 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3) + I*a) - I*Ei(I*(d*x + c)^(1/3)*b + ((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3))*e^(I*a - ((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3)) + I*Ei(-I*(d*x + c)^(1/3)*b + ((I*b^3*d*e - I*b^3*c*f)/f)^(1/3))*e^(-I*a - ((I*b^3*d*e - I*b^3*c*f)/f)^(1/3)))/f","C",0
211,1,728,0,1.710254," ","integrate(sin(a+b*(d*x+c)^(1/3))/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{{\left(i \, d f x + i \, d e - \sqrt{3} {\left(d f x + d e\right)}\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(i \, \sqrt{3} + 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} - i \, a\right)} + {\left(i \, d f x + i \, d e + \sqrt{3} {\left(d f x + d e\right)}\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(-i \, \sqrt{3} + 1\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} - i \, a\right)} + {\left(-i \, d f x - i \, d e + \sqrt{3} {\left(d f x + d e\right)}\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(-i \, \sqrt{3} - 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(i \, \sqrt{3} + 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} + i \, a\right)} + {\left(-i \, d f x - i \, d e - \sqrt{3} {\left(d f x + d e\right)}\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \frac{1}{2} \, {\left(i \, \sqrt{3} - 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(\frac{1}{2} \, {\left(-i \, \sqrt{3} + 1\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} + i \, a\right)} + {\left(2 i \, d f x + 2 i \, d e\right)} \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}} {\rm Ei}\left(i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(i \, a - \left(\frac{-i \, b^{3} d e + i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right)} + {\left(-2 i \, d f x - 2 i \, d e\right)} \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}} {\rm Ei}\left(-i \, {\left(d x + c\right)}^{\frac{1}{3}} b + \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right) e^{\left(-i \, a - \left(\frac{i \, b^{3} d e - i \, b^{3} c f}{f}\right)^{\frac{1}{3}}\right)} + 12 \, {\left(d e - c f\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{12 \, {\left(d e^{2} f - c e f^{2} + {\left(d e f^{2} - c f^{3}\right)} x\right)}}"," ",0,"-1/12*((I*d*f*x + I*d*e - sqrt(3)*(d*f*x + d*e))*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3)*Ei(-I*(d*x + c)^(1/3)*b + 1/2*(-I*sqrt(3) - 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3))*e^(1/2*(I*sqrt(3) + 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3) - I*a) + (I*d*f*x + I*d*e + sqrt(3)*(d*f*x + d*e))*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3)*Ei(-I*(d*x + c)^(1/3)*b + 1/2*(I*sqrt(3) - 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3))*e^(1/2*(-I*sqrt(3) + 1)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3) - I*a) + (-I*d*f*x - I*d*e + sqrt(3)*(d*f*x + d*e))*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3)*Ei(I*(d*x + c)^(1/3)*b + 1/2*(-I*sqrt(3) - 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3))*e^(1/2*(I*sqrt(3) + 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3) + I*a) + (-I*d*f*x - I*d*e - sqrt(3)*(d*f*x + d*e))*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3)*Ei(I*(d*x + c)^(1/3)*b + 1/2*(I*sqrt(3) - 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3))*e^(1/2*(-I*sqrt(3) + 1)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3) + I*a) + (2*I*d*f*x + 2*I*d*e)*((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3)*Ei(I*(d*x + c)^(1/3)*b + ((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3))*e^(I*a - ((-I*b^3*d*e + I*b^3*c*f)/f)^(1/3)) + (-2*I*d*f*x - 2*I*d*e)*((I*b^3*d*e - I*b^3*c*f)/f)^(1/3)*Ei(-I*(d*x + c)^(1/3)*b + ((I*b^3*d*e - I*b^3*c*f)/f)^(1/3))*e^(-I*a - ((I*b^3*d*e - I*b^3*c*f)/f)^(1/3)) + 12*(d*e - c*f)*sin((d*x + c)^(1/3)*b + a))/(d*e^2*f - c*e*f^2 + (d*e*f^2 - c*f^3)*x)","C",0
212,1,308,0,1.860851," ","integrate((f*x+e)^2*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{2} {\left(105 \, \pi f^{2} \sin\left(a\right) + 8 \, \pi {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cos\left(a\right)\right)} \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\sqrt{2} {\left(d x + c\right)}^{\frac{1}{3}} \sqrt{\frac{b}{\pi}}\right) + \sqrt{2} {\left(105 \, \pi f^{2} \cos\left(a\right) - 8 \, \pi {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sin\left(a\right)\right)} \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} {\left(d x + c\right)}^{\frac{1}{3}} \sqrt{\frac{b}{\pi}}\right) + 4 \, {\left(35 \, b^{2} d f^{2} x + 16 \, b^{2} d e f + 19 \, b^{2} c f^{2} - 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + b^{4} d^{2} e^{2}\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - 2 \, {\left(105 \, {\left(d x + c\right)}^{\frac{1}{3}} b f^{2} - 4 \, {\left(7 \, b^{3} d f^{2} x + 8 \, b^{3} d e f - b^{3} c f^{2}\right)} {\left(d x + c\right)}^{\frac{2}{3}}\right)} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)}}{32 \, b^{5} d^{3}}"," ",0,"3/32*(sqrt(2)*(105*pi*f^2*sin(a) + 8*pi*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cos(a))*sqrt(b/pi)*fresnel_cos(sqrt(2)*(d*x + c)^(1/3)*sqrt(b/pi)) + sqrt(2)*(105*pi*f^2*cos(a) - 8*pi*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sin(a))*sqrt(b/pi)*fresnel_sin(sqrt(2)*(d*x + c)^(1/3)*sqrt(b/pi)) + 4*(35*b^2*d*f^2*x + 16*b^2*d*e*f + 19*b^2*c*f^2 - 4*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + b^4*d^2*e^2)*(d*x + c)^(1/3))*cos((d*x + c)^(2/3)*b + a) - 2*(105*(d*x + c)^(1/3)*b*f^2 - 4*(7*b^3*d*f^2*x + 8*b^3*d*e*f - b^3*c*f^2)*(d*x + c)^(2/3))*sin((d*x + c)^(2/3)*b + a))/(b^5*d^3)","A",0
213,1,159,0,0.987995," ","integrate((f*x+e)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{2} \pi {\left(b d e - b c f\right)} \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\sqrt{2} {\left(d x + c\right)}^{\frac{1}{3}} \sqrt{\frac{b}{\pi}}\right) - \sqrt{2} \pi {\left(b d e - b c f\right)} \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} {\left(d x + c\right)}^{\frac{1}{3}} \sqrt{\frac{b}{\pi}}\right) \sin\left(a\right) + 4 \, {\left(d x + c\right)}^{\frac{2}{3}} b f \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - 2 \, {\left({\left(b^{2} d f x + b^{2} d e\right)} {\left(d x + c\right)}^{\frac{1}{3}} - 2 \, f\right)} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)}}{4 \, b^{3} d^{2}}"," ",0,"3/4*(sqrt(2)*pi*(b*d*e - b*c*f)*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*(d*x + c)^(1/3)*sqrt(b/pi)) - sqrt(2)*pi*(b*d*e - b*c*f)*sqrt(b/pi)*fresnel_sin(sqrt(2)*(d*x + c)^(1/3)*sqrt(b/pi))*sin(a) + 4*(d*x + c)^(2/3)*b*f*sin((d*x + c)^(2/3)*b + a) - 2*((b^2*d*f*x + b^2*d*e)*(d*x + c)^(1/3) - 2*f)*cos((d*x + c)^(2/3)*b + a))/(b^3*d^2)","A",0
214,1,98,0,1.421597," ","integrate(sin(a+b*(d*x+c)^(2/3)),x, algorithm=""fricas"")","\frac{3 \, {\left(\sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\sqrt{2} {\left(d x + c\right)}^{\frac{1}{3}} \sqrt{\frac{b}{\pi}}\right) - \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} {\left(d x + c\right)}^{\frac{1}{3}} \sqrt{\frac{b}{\pi}}\right) \sin\left(a\right) - 2 \, {\left(d x + c\right)}^{\frac{1}{3}} b \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)}}{4 \, b^{2} d}"," ",0,"3/4*(sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*(d*x + c)^(1/3)*sqrt(b/pi)) - sqrt(2)*pi*sqrt(b/pi)*fresnel_sin(sqrt(2)*(d*x + c)^(1/3)*sqrt(b/pi))*sin(a) - 2*(d*x + c)^(1/3)*b*cos((d*x + c)^(2/3)*b + a))/(b^2*d)","A",0
215,0,0,0,1.494977," ","integrate(sin(a+b*(d*x+c)^(2/3))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{f x + e}, x\right)"," ",0,"integral(sin((d*x + c)^(2/3)*b + a)/(f*x + e), x)","F",0
216,0,0,0,1.539968," ","integrate(sin(a+b*(d*x+c)^(2/3))/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin((d*x + c)^(2/3)*b + a)/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
217,1,653,0,1.600185," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(1/3)),x, algorithm=""fricas"")","-\frac{2 \, {\left(120 \, b^{3} d^{2} f^{2} x^{2} + 2016 \, b^{3} c d e f - 1896 \, b^{3} c^{2} f^{2} + 48 \, {\left(42 \, b^{3} d^{2} e f - 37 \, b^{3} c d f^{2}\right)} x - {\left(5040 \, b d^{2} f^{2} x^{2} + 60480 \, b d^{2} e^{2} - 96768 \, b c d e f - {\left(b^{7} - 41328 \, b c^{2}\right)} f^{2} + 2016 \, {\left(12 \, b d^{2} e f - 7 \, b c d f^{2}\right)} x\right)} {\left(d x + c\right)}^{\frac{2}{3}} - 6 \, {\left(b^{5} d f^{2} x + 168 \, b^{5} d e f - 167 \, b^{5} c f^{2}\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) - {\left({\left(60480 \, b^{3} d^{2} e^{2} - 120960 \, b^{3} c d e f - {\left(b^{9} - 60480 \, b^{3} c^{2}\right)} f^{2}\right)} \cos\left(a\right) + 1008 \, {\left(b^{6} d e f - b^{6} c f^{2}\right)} \sin\left(a\right)\right)} \operatorname{Ci}\left(\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - {\left({\left(60480 \, b^{3} d^{2} e^{2} - 120960 \, b^{3} c d e f - {\left(b^{9} - 60480 \, b^{3} c^{2}\right)} f^{2}\right)} \cos\left(a\right) + 1008 \, {\left(b^{6} d e f - b^{6} c f^{2}\right)} \sin\left(a\right)\right)} \operatorname{Ci}\left(-\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, {\left(40320 \, d^{3} f^{2} x^{3} + 120960 \, d^{3} e f x^{2} + 120960 \, c d^{2} e^{2} - 120960 \, c^{2} d e f - 2 \, {\left(b^{6} c - 20160 \, c^{3}\right)} f^{2} - 2 \, {\left(b^{6} d f^{2} - 60480 \, d^{3} e^{2}\right)} x + 24 \, {\left(b^{4} d f^{2} x + 42 \, b^{4} d e f - 41 \, b^{4} c f^{2}\right)} {\left(d x + c\right)}^{\frac{2}{3}} - {\left(720 \, b^{2} d^{2} f^{2} x^{2} + 60480 \, b^{2} d^{2} e^{2} - 114912 \, b^{2} c d e f - {\left(b^{8} - 55152 \, b^{2} c^{2}\right)} f^{2} + 288 \, {\left(21 \, b^{2} d^{2} e f - 16 \, b^{2} c d f^{2}\right)} x\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) - 2 \, {\left(1008 \, {\left(b^{6} d e f - b^{6} c f^{2}\right)} \cos\left(a\right) - {\left(60480 \, b^{3} d^{2} e^{2} - 120960 \, b^{3} c d e f - {\left(b^{9} - 60480 \, b^{3} c^{2}\right)} f^{2}\right)} \sin\left(a\right)\right)} \operatorname{Si}\left(\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{241920 \, d^{3}}"," ",0,"-1/241920*(2*(120*b^3*d^2*f^2*x^2 + 2016*b^3*c*d*e*f - 1896*b^3*c^2*f^2 + 48*(42*b^3*d^2*e*f - 37*b^3*c*d*f^2)*x - (5040*b*d^2*f^2*x^2 + 60480*b*d^2*e^2 - 96768*b*c*d*e*f - (b^7 - 41328*b*c^2)*f^2 + 2016*(12*b*d^2*e*f - 7*b*c*d*f^2)*x)*(d*x + c)^(2/3) - 6*(b^5*d*f^2*x + 168*b^5*d*e*f - 167*b^5*c*f^2)*(d*x + c)^(1/3))*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) - ((60480*b^3*d^2*e^2 - 120960*b^3*c*d*e*f - (b^9 - 60480*b^3*c^2)*f^2)*cos(a) + 1008*(b^6*d*e*f - b^6*c*f^2)*sin(a))*cos_integral(b/(d*x + c)^(1/3)) - ((60480*b^3*d^2*e^2 - 120960*b^3*c*d*e*f - (b^9 - 60480*b^3*c^2)*f^2)*cos(a) + 1008*(b^6*d*e*f - b^6*c*f^2)*sin(a))*cos_integral(-b/(d*x + c)^(1/3)) - 2*(40320*d^3*f^2*x^3 + 120960*d^3*e*f*x^2 + 120960*c*d^2*e^2 - 120960*c^2*d*e*f - 2*(b^6*c - 20160*c^3)*f^2 - 2*(b^6*d*f^2 - 60480*d^3*e^2)*x + 24*(b^4*d*f^2*x + 42*b^4*d*e*f - 41*b^4*c*f^2)*(d*x + c)^(2/3) - (720*b^2*d^2*f^2*x^2 + 60480*b^2*d^2*e^2 - 114912*b^2*c*d*e*f - (b^8 - 55152*b^2*c^2)*f^2 + 288*(21*b^2*d^2*e*f - 16*b^2*c*d*f^2)*x)*(d*x + c)^(1/3))*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) - 2*(1008*(b^6*d*e*f - b^6*c*f^2)*cos(a) - (60480*b^3*d^2*e^2 - 120960*b^3*c*d*e*f - (b^9 - 60480*b^3*c^2)*f^2)*sin(a))*sin_integral(b/(d*x + c)^(1/3)))/d^3","A",0
218,1,299,0,1.609854," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{5} f - 2 \, b^{3} d f x - 2 \, b^{3} c f + 24 \, {\left(b d f x + 5 \, b d e - 4 \, b c f\right)} {\left(d x + c\right)}^{\frac{2}{3}}\right)} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) + {\left(b^{6} f \sin\left(a\right) + 120 \, {\left(b^{3} d e - b^{3} c f\right)} \cos\left(a\right)\right)} \operatorname{Ci}\left(\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + {\left(b^{6} f \sin\left(a\right) + 120 \, {\left(b^{3} d e - b^{3} c f\right)} \cos\left(a\right)\right)} \operatorname{Ci}\left(-\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 2 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{4} f + 120 \, d^{2} f x^{2} + 240 \, d^{2} e x + 240 \, c d e - 120 \, c^{2} f - 6 \, {\left(b^{2} d f x + 20 \, b^{2} d e - 19 \, b^{2} c f\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) + 2 \, {\left(b^{6} f \cos\left(a\right) - 120 \, {\left(b^{3} d e - b^{3} c f\right)} \sin\left(a\right)\right)} \operatorname{Si}\left(\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right)}{480 \, d^{2}}"," ",0,"1/480*(2*((d*x + c)^(1/3)*b^5*f - 2*b^3*d*f*x - 2*b^3*c*f + 24*(b*d*f*x + 5*b*d*e - 4*b*c*f)*(d*x + c)^(2/3))*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) + (b^6*f*sin(a) + 120*(b^3*d*e - b^3*c*f)*cos(a))*cos_integral(b/(d*x + c)^(1/3)) + (b^6*f*sin(a) + 120*(b^3*d*e - b^3*c*f)*cos(a))*cos_integral(-b/(d*x + c)^(1/3)) + 2*((d*x + c)^(2/3)*b^4*f + 120*d^2*f*x^2 + 240*d^2*e*x + 240*c*d*e - 120*c^2*f - 6*(b^2*d*f*x + 20*b^2*d*e - 19*b^2*c*f)*(d*x + c)^(1/3))*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) + 2*(b^6*f*cos(a) - 120*(b^3*d*e - b^3*c*f)*sin(a))*sin_integral(b/(d*x + c)^(1/3)))/d^2","A",0
219,1,139,0,1.301473," ","integrate(sin(a+b/(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{b^{3} \cos\left(a\right) \operatorname{Ci}\left(\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + b^{3} \cos\left(a\right) \operatorname{Ci}\left(-\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 2 \, b^{3} \sin\left(a\right) \operatorname{Si}\left(\frac{b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 2 \, {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) - 2 \, {\left({\left(d x + c\right)}^{\frac{1}{3}} b^{2} - 2 \, d x - 2 \, c\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)}{4 \, d}"," ",0,"1/4*(b^3*cos(a)*cos_integral(b/(d*x + c)^(1/3)) + b^3*cos(a)*cos_integral(-b/(d*x + c)^(1/3)) - 2*b^3*sin(a)*sin_integral(b/(d*x + c)^(1/3)) + 2*(d*x + c)^(2/3)*b*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) - 2*((d*x + c)^(1/3)*b^2 - 2*d*x - 2*c)*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)))/d","A",0
220,1,554,0,1.620741," ","integrate(sin(a+b/(d*x+c)^(1/3))/(f*x+e),x, algorithm=""fricas"")","\frac{i \, {\rm Ei}\left(\frac{-2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(-i \, d x - i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, a\right)} - i \, {\rm Ei}\left(\frac{2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(-i \, d x - i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, a\right)} + i \, {\rm Ei}\left(\frac{-2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(i \, d x + i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, a\right)} - i \, {\rm Ei}\left(\frac{2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(i \, d x + i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, a\right)} + 3 i \, {\rm Ei}\left(\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) e^{\left(i \, a\right)} - 3 i \, {\rm Ei}\left(-\frac{i \, b}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) e^{\left(-i \, a\right)} - i \, {\rm Ei}\left(\frac{i \, {\left(d x + c\right)}^{\frac{2}{3}} b + \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) e^{\left(i \, a - \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}}\right)} + i \, {\rm Ei}\left(\frac{-i \, {\left(d x + c\right)}^{\frac{2}{3}} b + \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) e^{\left(-i \, a - \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}}\right)}}{2 \, f}"," ",0,"1/2*(I*Ei(1/2*(-2*I*(d*x + c)^(2/3)*b - (I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(-I*d*x - I*c) + c))/(d*x + c))*e^(1/2*(I*b^3*f/(d*e - c*f))^(1/3)*(I*sqrt(3) + 1) - I*a) - I*Ei(1/2*(2*I*(d*x + c)^(2/3)*b - (-I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(-I*d*x - I*c) + c))/(d*x + c))*e^(1/2*(-I*b^3*f/(d*e - c*f))^(1/3)*(I*sqrt(3) + 1) + I*a) + I*Ei(1/2*(-2*I*(d*x + c)^(2/3)*b - (I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(I*d*x + I*c) + c))/(d*x + c))*e^(1/2*(I*b^3*f/(d*e - c*f))^(1/3)*(-I*sqrt(3) + 1) - I*a) - I*Ei(1/2*(2*I*(d*x + c)^(2/3)*b - (-I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(I*d*x + I*c) + c))/(d*x + c))*e^(1/2*(-I*b^3*f/(d*e - c*f))^(1/3)*(-I*sqrt(3) + 1) + I*a) + 3*I*Ei(I*b/(d*x + c)^(1/3))*e^(I*a) - 3*I*Ei(-I*b/(d*x + c)^(1/3))*e^(-I*a) - I*Ei((I*(d*x + c)^(2/3)*b + (-I*b^3*f/(d*e - c*f))^(1/3)*(d*x + c))/(d*x + c))*e^(I*a - (-I*b^3*f/(d*e - c*f))^(1/3)) + I*Ei((-I*(d*x + c)^(2/3)*b + (I*b^3*f/(d*e - c*f))^(1/3)*(d*x + c))/(d*x + c))*e^(-I*a - (I*b^3*f/(d*e - c*f))^(1/3)))/f","C",0
221,1,796,0,1.891853," ","integrate(sin(a+b/(d*x+c)^(1/3))/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{\left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-i \, d f x - i \, d e + \sqrt{3} {\left(d f x + d e\right)}\right)} {\rm Ei}\left(\frac{-2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(-i \, d x - i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} - i \, a\right)} + \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(i \, d f x + i \, d e - \sqrt{3} {\left(d f x + d e\right)}\right)} {\rm Ei}\left(\frac{2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(-i \, d x - i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + i \, a\right)} + \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-i \, d f x - i \, d e - \sqrt{3} {\left(d f x + d e\right)}\right)} {\rm Ei}\left(\frac{-2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(i \, d x + i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} - i \, a\right)} + \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(i \, d f x + i \, d e + \sqrt{3} {\left(d f x + d e\right)}\right)} {\rm Ei}\left(\frac{2 i \, {\left(d x + c\right)}^{\frac{2}{3}} b - \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x - \sqrt{3} {\left(i \, d x + i \, c\right)} + c\right)}}{2 \, {\left(d x + c\right)}}\right) e^{\left(\frac{1}{2} \, \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-i \, \sqrt{3} + 1\right)} + i \, a\right)} + \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(-2 i \, d f x - 2 i \, d e\right)} {\rm Ei}\left(\frac{i \, {\left(d x + c\right)}^{\frac{2}{3}} b + \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) e^{\left(i \, a - \left(-\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}}\right)} + \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(2 i \, d f x + 2 i \, d e\right)} {\rm Ei}\left(\frac{-i \, {\left(d x + c\right)}^{\frac{2}{3}} b + \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}} {\left(d x + c\right)}}{d x + c}\right) e^{\left(-i \, a - \left(\frac{i \, b^{3} f}{d e - c f}\right)^{\frac{1}{3}}\right)} - 12 \, {\left(d f x + c f\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)}{12 \, {\left(d e^{2} f - c e f^{2} + {\left(d e f^{2} - c f^{3}\right)} x\right)}}"," ",0,"-1/12*((I*b^3*f/(d*e - c*f))^(1/3)*(-I*d*f*x - I*d*e + sqrt(3)*(d*f*x + d*e))*Ei(1/2*(-2*I*(d*x + c)^(2/3)*b - (I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(-I*d*x - I*c) + c))/(d*x + c))*e^(1/2*(I*b^3*f/(d*e - c*f))^(1/3)*(I*sqrt(3) + 1) - I*a) + (-I*b^3*f/(d*e - c*f))^(1/3)*(I*d*f*x + I*d*e - sqrt(3)*(d*f*x + d*e))*Ei(1/2*(2*I*(d*x + c)^(2/3)*b - (-I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(-I*d*x - I*c) + c))/(d*x + c))*e^(1/2*(-I*b^3*f/(d*e - c*f))^(1/3)*(I*sqrt(3) + 1) + I*a) + (I*b^3*f/(d*e - c*f))^(1/3)*(-I*d*f*x - I*d*e - sqrt(3)*(d*f*x + d*e))*Ei(1/2*(-2*I*(d*x + c)^(2/3)*b - (I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(I*d*x + I*c) + c))/(d*x + c))*e^(1/2*(I*b^3*f/(d*e - c*f))^(1/3)*(-I*sqrt(3) + 1) - I*a) + (-I*b^3*f/(d*e - c*f))^(1/3)*(I*d*f*x + I*d*e + sqrt(3)*(d*f*x + d*e))*Ei(1/2*(2*I*(d*x + c)^(2/3)*b - (-I*b^3*f/(d*e - c*f))^(1/3)*(d*x - sqrt(3)*(I*d*x + I*c) + c))/(d*x + c))*e^(1/2*(-I*b^3*f/(d*e - c*f))^(1/3)*(-I*sqrt(3) + 1) + I*a) + (-I*b^3*f/(d*e - c*f))^(1/3)*(-2*I*d*f*x - 2*I*d*e)*Ei((I*(d*x + c)^(2/3)*b + (-I*b^3*f/(d*e - c*f))^(1/3)*(d*x + c))/(d*x + c))*e^(I*a - (-I*b^3*f/(d*e - c*f))^(1/3)) + (I*b^3*f/(d*e - c*f))^(1/3)*(2*I*d*f*x + 2*I*d*e)*Ei((-I*(d*x + c)^(2/3)*b + (I*b^3*f/(d*e - c*f))^(1/3)*(d*x + c))/(d*x + c))*e^(-I*a - (I*b^3*f/(d*e - c*f))^(1/3)) - 12*(d*f*x + c*f)*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)))/(d*e^2*f - c*e*f^2 + (d*e*f^2 - c*f^3)*x)","C",0
222,1,494,0,1.269547," ","integrate((f*x+e)^2*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""fricas"")","\frac{315 \, {\left(b^{3} d e f - b^{3} c f^{2}\right)} \cos\left(a\right) \operatorname{Ci}\left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 315 \, {\left(b^{3} d e f - b^{3} c f^{2}\right)} \cos\left(a\right) \operatorname{Ci}\left(-\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 8 \, \sqrt{2} {\left(8 \, \pi b^{4} f^{2} \cos\left(a\right) - 315 \, \pi {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sin\left(a\right)\right)} \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 8 \, \sqrt{2} {\left(8 \, \pi b^{4} f^{2} \sin\left(a\right) + 315 \, \pi {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cos\left(a\right)\right)} \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) - 630 \, {\left(b^{3} d e f - b^{3} c f^{2}\right)} \sin\left(a\right) \operatorname{Si}\left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 2 \, {\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} c f^{2} - 15 \, {\left(4 \, b d^{2} f^{2} x^{2} + 84 \, b d^{2} e^{2} - 147 \, b c d e f + 67 \, b c^{2} f^{2} + {\left(21 \, b d^{2} e f - 13 \, b c d f^{2}\right)} x\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right) + 2 \, {\left(210 \, d^{3} f^{2} x^{3} + 630 \, d^{3} e f x^{2} + 32 \, {\left(d x + c\right)}^{\frac{1}{3}} b^{4} f^{2} + 630 \, d^{3} e^{2} x + 630 \, c d^{2} e^{2} - 630 \, c^{2} d e f + 210 \, c^{3} f^{2} - 3 \, {\left(8 \, b^{2} d f^{2} x + 105 \, b^{2} d e f - 97 \, b^{2} c f^{2}\right)} {\left(d x + c\right)}^{\frac{2}{3}}\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{1260 \, d^{3}}"," ",0,"1/1260*(315*(b^3*d*e*f - b^3*c*f^2)*cos(a)*cos_integral(b/(d*x + c)^(2/3)) + 315*(b^3*d*e*f - b^3*c*f^2)*cos(a)*cos_integral(-b/(d*x + c)^(2/3)) - 8*sqrt(2)*(8*pi*b^4*f^2*cos(a) - 315*pi*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sin(a))*sqrt(b/pi)*fresnel_cos(sqrt(2)*sqrt(b/pi)/(d*x + c)^(1/3)) + 8*sqrt(2)*(8*pi*b^4*f^2*sin(a) + 315*pi*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cos(a))*sqrt(b/pi)*fresnel_sin(sqrt(2)*sqrt(b/pi)/(d*x + c)^(1/3)) - 630*(b^3*d*e*f - b^3*c*f^2)*sin(a)*sin_integral(b/(d*x + c)^(2/3)) - 2*(16*b^3*d*f^2*x + 16*b^3*c*f^2 - 15*(4*b*d^2*f^2*x^2 + 84*b*d^2*e^2 - 147*b*c*d*e*f + 67*b*c^2*f^2 + (21*b*d^2*e*f - 13*b*c*d*f^2)*x)*(d*x + c)^(1/3))*cos((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)) + 2*(210*d^3*f^2*x^3 + 630*d^3*e*f*x^2 + 32*(d*x + c)^(1/3)*b^4*f^2 + 630*d^3*e^2*x + 630*c*d^2*e^2 - 630*c^2*d*e*f + 210*c^3*f^2 - 3*(8*b^2*d*f^2*x + 105*b^2*d*e*f - 97*b^2*c*f^2)*(d*x + c)^(2/3))*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)))/d^3","A",0
223,1,267,0,1.447480," ","integrate((f*x+e)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""fricas"")","\frac{b^{3} f \cos\left(a\right) \operatorname{Ci}\left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + b^{3} f \cos\left(a\right) \operatorname{Ci}\left(-\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) - 2 \, b^{3} f \sin\left(a\right) \operatorname{Si}\left(\frac{b}{{\left(d x + c\right)}^{\frac{2}{3}}}\right) + 16 \, \sqrt{2} \pi {\left(b d e - b c f\right)} \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 16 \, \sqrt{2} \pi {\left(b d e - b c f\right)} \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) \sin\left(a\right) + 2 \, {\left(b d f x + 8 \, b d e - 7 \, b c f\right)} {\left(d x + c\right)}^{\frac{1}{3}} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right) + 2 \, {\left(2 \, d^{2} f x^{2} + 4 \, d^{2} e x - {\left(d x + c\right)}^{\frac{2}{3}} b^{2} f + 4 \, c d e - 2 \, c^{2} f\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{8 \, d^{2}}"," ",0,"1/8*(b^3*f*cos(a)*cos_integral(b/(d*x + c)^(2/3)) + b^3*f*cos(a)*cos_integral(-b/(d*x + c)^(2/3)) - 2*b^3*f*sin(a)*sin_integral(b/(d*x + c)^(2/3)) + 16*sqrt(2)*pi*(b*d*e - b*c*f)*sqrt(b/pi)*cos(a)*fresnel_sin(sqrt(2)*sqrt(b/pi)/(d*x + c)^(1/3)) + 16*sqrt(2)*pi*(b*d*e - b*c*f)*sqrt(b/pi)*fresnel_cos(sqrt(2)*sqrt(b/pi)/(d*x + c)^(1/3))*sin(a) + 2*(b*d*f*x + 8*b*d*e - 7*b*c*f)*(d*x + c)^(1/3)*cos((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)) + 2*(2*d^2*f*x^2 + 4*d^2*e*x - (d*x + c)^(2/3)*b^2*f + 4*c*d*e - 2*c^2*f)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)))/d^2","A",0
224,1,143,0,1.486990," ","integrate(sin(a+b/(d*x+c)^(2/3)),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} \pi b \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{S}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) + 2 \, \sqrt{2} \pi b \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\frac{\sqrt{2} \sqrt{\frac{b}{\pi}}}{{\left(d x + c\right)}^{\frac{1}{3}}}\right) \sin\left(a\right) + 2 \, {\left(d x + c\right)}^{\frac{1}{3}} b \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right) + {\left(d x + c\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{d}"," ",0,"(2*sqrt(2)*pi*b*sqrt(b/pi)*cos(a)*fresnel_sin(sqrt(2)*sqrt(b/pi)/(d*x + c)^(1/3)) + 2*sqrt(2)*pi*b*sqrt(b/pi)*fresnel_cos(sqrt(2)*sqrt(b/pi)/(d*x + c)^(1/3))*sin(a) + 2*(d*x + c)^(1/3)*b*cos((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)) + (d*x + c)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)))/d","A",0
225,0,0,0,1.169318," ","integrate(sin(a+b/(d*x+c)^(2/3))/(f*x+e),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{f x + e}, x\right)"," ",0,"integral(sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(f*x + e), x)","F",0
226,0,0,0,1.351544," ","integrate(sin(a+b/(d*x+c)^(2/3))/(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{f^{2} x^{2} + 2 \, e f x + e^{2}}, x\right)"," ",0,"integral(sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(f^2*x^2 + 2*e*f*x + e^2), x)","F",0
227,1,234,0,3.103297," ","integrate((d*e*x+c*e)^(4/3)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(30 \, b^{4} d^{2} e x^{2} + 60 \, b^{4} c d e x + 30 \, b^{4} c^{2} e - {\left(b^{6} d^{2} e x^{2} + 2 \, b^{6} c d e x + {\left(b^{6} c^{2} - 720\right)} e\right)} {\left(d x + c\right)}^{\frac{2}{3}} - 360 \, {\left(b^{2} d e x + b^{2} c e\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} {\left(d e x + c e\right)}^{\frac{1}{3}} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) + 6 \, {\left(120 \, b d e x + 120 \, b c e - 20 \, {\left(b^{3} d e x + b^{3} c e\right)} {\left(d x + c\right)}^{\frac{2}{3}} + {\left(b^{5} d^{2} e x^{2} + 2 \, b^{5} c d e x + b^{5} c^{2} e\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} {\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{7} d^{2} x + b^{7} c d}"," ",0,"3*((30*b^4*d^2*e*x^2 + 60*b^4*c*d*e*x + 30*b^4*c^2*e - (b^6*d^2*e*x^2 + 2*b^6*c*d*e*x + (b^6*c^2 - 720)*e)*(d*x + c)^(2/3) - 360*(b^2*d*e*x + b^2*c*e)*(d*x + c)^(1/3))*(d*e*x + c*e)^(1/3)*cos((d*x + c)^(1/3)*b + a) + 6*(120*b*d*e*x + 120*b*c*e - 20*(b^3*d*e*x + b^3*c*e)*(d*x + c)^(2/3) + (b^5*d^2*e*x^2 + 2*b^5*c*d*e*x + b^5*c^2*e)*(d*x + c)^(1/3))*(d*e*x + c*e)^(1/3)*sin((d*x + c)^(1/3)*b + a))/(b^7*d^2*x + b^7*c*d)","A",0
228,1,143,0,3.254745," ","integrate((d*e*x+c*e)^(2/3)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(12 \, b^{2} d x + 12 \, b^{2} c - {\left(b^{4} d x + b^{4} c\right)} {\left(d x + c\right)}^{\frac{2}{3}} - 24 \, {\left(d x + c\right)}^{\frac{1}{3}}\right)} {\left(d e x + c e\right)}^{\frac{2}{3}} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - 4 \, {\left(d e x + c e\right)}^{\frac{2}{3}} {\left(6 \, {\left(d x + c\right)}^{\frac{2}{3}} b - {\left(b^{3} d x + b^{3} c\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{5} d^{2} x + b^{5} c d}"," ",0,"3*((12*b^2*d*x + 12*b^2*c - (b^4*d*x + b^4*c)*(d*x + c)^(2/3) - 24*(d*x + c)^(1/3))*(d*e*x + c*e)^(2/3)*cos((d*x + c)^(1/3)*b + a) - 4*(d*e*x + c*e)^(2/3)*(6*(d*x + c)^(2/3)*b - (b^3*d*x + b^3*c)*(d*x + c)^(1/3))*sin((d*x + c)^(1/3)*b + a))/(b^5*d^2*x + b^5*c*d)","A",0
229,1,128,0,3.167871," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b*(d*x+c)^(1/3)),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(6 \, b d x + 6 \, b c - {\left(b^{3} d x + b^{3} c\right)} {\left(d x + c\right)}^{\frac{2}{3}}\right)} {\left(d e x + c e\right)}^{\frac{1}{3}} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) + 3 \, {\left(d e x + c e\right)}^{\frac{1}{3}} {\left({\left(b^{2} d x + b^{2} c\right)} {\left(d x + c\right)}^{\frac{1}{3}} - 2 \, {\left(d x + c\right)}^{\frac{2}{3}}\right)} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{4} d^{2} x + b^{4} c d}"," ",0,"3*((6*b*d*x + 6*b*c - (b^3*d*x + b^3*c)*(d*x + c)^(2/3))*(d*e*x + c*e)^(1/3)*cos((d*x + c)^(1/3)*b + a) + 3*(d*e*x + c*e)^(1/3)*((b^2*d*x + b^2*c)*(d*x + c)^(1/3) - 2*(d*x + c)^(2/3))*sin((d*x + c)^(1/3)*b + a))/(b^4*d^2*x + b^4*c*d)","A",0
230,1,84,0,3.365318," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(1/3),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(d e x + c e\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right) - {\left(d e x + c e\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)\right)}}{b^{2} d^{2} e x + b^{2} c d e}"," ",0,"-3*((d*e*x + c*e)^(2/3)*(d*x + c)^(2/3)*b*cos((d*x + c)^(1/3)*b + a) - (d*e*x + c*e)^(2/3)*(d*x + c)^(1/3)*sin((d*x + c)^(1/3)*b + a))/(b^2*d^2*e*x + b^2*c*d*e)","A",0
231,1,46,0,1.422183," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(2/3),x, algorithm=""fricas"")","-\frac{3 \, {\left(d e x + c e\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \cos\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{b d^{2} e x + b c d e}"," ",0,"-3*(d*e*x + c*e)^(1/3)*(d*x + c)^(2/3)*cos((d*x + c)^(1/3)*b + a)/(b*d^2*e*x + b*c*d*e)","A",0
232,0,0,0,2.905771," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((d*x + c)^(1/3)*b + a)/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
233,0,0,0,2.948812," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((d*e*x + c*e)^(1/3)*sin((d*x + c)^(1/3)*b + a)/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
234,0,0,0,2.986350," ","integrate(sin(a+b*(d*x+c)^(1/3))/(d*e*x+c*e)^(7/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left({\left(d x + c\right)}^{\frac{1}{3}} b + a\right)}{d^{3} e^{3} x^{3} + 3 \, c d^{2} e^{3} x^{2} + 3 \, c^{2} d e^{3} x + c^{3} e^{3}}, x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((d*x + c)^(1/3)*b + a)/(d^3*e^3*x^3 + 3*c*d^2*e^3*x^2 + 3*c^2*d*e^3*x + c^3*e^3), x)","F",0
235,0,0,0,2.934318," ","integrate((d*e*x+c*e)^(4/3)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d e x + c e\right)}^{\frac{4}{3}} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right), x\right)"," ",0,"integral((d*e*x + c*e)^(4/3)*sin((d*x + c)^(2/3)*b + a), x)","F",0
236,0,0,0,3.007138," ","integrate((d*e*x+c*e)^(2/3)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right), x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((d*x + c)^(2/3)*b + a), x)","F",0
237,1,89,0,3.417277," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b*(d*x+c)^(2/3)),x, algorithm=""fricas"")","-\frac{3 \, {\left({\left(b d x + b c\right)} {\left(d e x + c e\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{1}{3}} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right) - {\left(d e x + c e\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)\right)}}{2 \, {\left(b^{2} d^{2} x + b^{2} c d\right)}}"," ",0,"-3/2*((b*d*x + b*c)*(d*e*x + c*e)^(1/3)*(d*x + c)^(1/3)*cos((d*x + c)^(2/3)*b + a) - (d*e*x + c*e)^(1/3)*(d*x + c)^(2/3)*sin((d*x + c)^(2/3)*b + a))/(b^2*d^2*x + b^2*c*d)","A",0
238,1,46,0,1.124847," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(1/3),x, algorithm=""fricas"")","-\frac{3 \, {\left(d e x + c e\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} \cos\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{2 \, {\left(b d^{2} e x + b c d e\right)}}"," ",0,"-3/2*(d*e*x + c*e)^(2/3)*(d*x + c)^(1/3)*cos((d*x + c)^(2/3)*b + a)/(b*d^2*e*x + b*c*d*e)","A",0
239,0,0,0,3.260020," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{{\left(d e x + c e\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(sin((d*x + c)^(2/3)*b + a)/(d*e*x + c*e)^(2/3), x)","F",0
240,0,0,0,2.386073," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((d*x + c)^(2/3)*b + a)/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
241,0,0,0,2.531059," ","integrate(sin(a+b*(d*x+c)^(2/3))/(d*e*x+c*e)^(5/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left({\left(d x + c\right)}^{\frac{2}{3}} b + a\right)}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((d*e*x + c*e)^(1/3)*sin((d*x + c)^(2/3)*b + a)/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
242,0,0,0,2.376305," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b/(d*x+c)^(1/3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right), x\right)"," ",0,"integral((d*e*x + c*e)^(1/3)*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)), x)","F",0
243,0,0,0,3.011423," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)}{{\left(d e x + c e\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c))/(d*e*x + c*e)^(1/3), x)","F",0
244,0,0,0,2.969033," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)}{{\left(d e x + c e\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c))/(d*e*x + c*e)^(2/3), x)","F",0
245,1,64,0,1.189544," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(4/3),x, algorithm=""fricas"")","\frac{3 \, {\left(d e x + c e\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{1}{3}} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)}{b d^{2} e^{2} x + b c d e^{2}}"," ",0,"3*(d*e*x + c*e)^(2/3)*(d*x + c)^(1/3)*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c))/(b*d^2*e^2*x + b*c*d*e^2)","A",0
246,1,116,0,3.258374," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(5/3),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(d e x + c e\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{1}{3}} b \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) - {\left(d e x + c e\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)\right)}}{b^{2} d^{2} e^{2} x + b^{2} c d e^{2}}"," ",0,"3*((d*e*x + c*e)^(1/3)*(d*x + c)^(1/3)*b*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) - (d*e*x + c*e)^(1/3)*(d*x + c)^(2/3)*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)))/(b^2*d^2*e^2*x + b^2*c*d*e^2)","A",0
247,1,160,0,3.863835," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(7/3),x, algorithm=""fricas"")","\frac{3 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b^{3} - 6 \, b d x - 6 \, b c\right)} {\left(d e x + c e\right)}^{\frac{2}{3}} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) - 3 \, {\left(d e x + c e\right)}^{\frac{2}{3}} {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{2} - 2 \, {\left(d x + c\right)}^{\frac{4}{3}}\right)} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)\right)}}{b^{4} d^{3} e^{3} x^{2} + 2 \, b^{4} c d^{2} e^{3} x + b^{4} c^{2} d e^{3}}"," ",0,"3*(((d*x + c)^(1/3)*b^3 - 6*b*d*x - 6*b*c)*(d*e*x + c*e)^(2/3)*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) - 3*(d*e*x + c*e)^(2/3)*((d*x + c)^(2/3)*b^2 - 2*(d*x + c)^(4/3))*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)))/(b^4*d^3*e^3*x^2 + 2*b^4*c*d^2*e^3*x + b^4*c^2*d*e^3)","A",0
248,1,181,0,3.974506," ","integrate(sin(a+b/(d*x+c)^(1/3))/(d*e*x+c*e)^(8/3),x, algorithm=""fricas"")","\frac{3 \, {\left({\left({\left(d x + c\right)}^{\frac{1}{3}} b^{4} - 12 \, b^{2} d x - 12 \, b^{2} c + 24 \, {\left(d x + c\right)}^{\frac{5}{3}}\right)} {\left(d e x + c e\right)}^{\frac{1}{3}} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right) - 4 \, {\left({\left(d x + c\right)}^{\frac{2}{3}} b^{3} - 6 \, {\left(b d x + b c\right)} {\left(d x + c\right)}^{\frac{1}{3}}\right)} {\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{2}{3}} b}{d x + c}\right)\right)}}{b^{5} d^{3} e^{3} x^{2} + 2 \, b^{5} c d^{2} e^{3} x + b^{5} c^{2} d e^{3}}"," ",0,"3*(((d*x + c)^(1/3)*b^4 - 12*b^2*d*x - 12*b^2*c + 24*(d*x + c)^(5/3))*(d*e*x + c*e)^(1/3)*cos((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)) - 4*((d*x + c)^(2/3)*b^3 - 6*(b*d*x + b*c)*(d*x + c)^(1/3))*(d*e*x + c*e)^(1/3)*sin((a*d*x + a*c + (d*x + c)^(2/3)*b)/(d*x + c)))/(b^5*d^3*e^3*x^2 + 2*b^5*c*d^2*e^3*x + b^5*c^2*d*e^3)","A",0
249,0,0,0,2.863911," ","integrate((d*e*x+c*e)^(4/3)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d e x + c e\right)}^{\frac{4}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right), x\right)"," ",0,"integral((d*e*x + c*e)^(4/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)), x)","F",0
250,0,0,0,2.991621," ","integrate((d*e*x+c*e)^(2/3)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right), x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)), x)","F",0
251,0,0,0,2.786265," ","integrate((d*e*x+c*e)^(1/3)*sin(a+b/(d*x+c)^(2/3)),x, algorithm=""fricas"")","{\rm integral}\left({\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right), x\right)"," ",0,"integral((d*e*x + c*e)^(1/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)), x)","F",0
252,0,0,0,2.606705," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{{\left(d e x + c e\right)}^{\frac{1}{3}}}, x\right)"," ",0,"integral(sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(d*e*x + c*e)^(1/3), x)","F",0
253,0,0,0,2.978716," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{{\left(d e x + c e\right)}^{\frac{2}{3}}}, x\right)"," ",0,"integral(sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(d*e*x + c*e)^(2/3), x)","F",0
254,0,0,0,2.889640," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{d^{2} e^{2} x^{2} + 2 \, c d e^{2} x + c^{2} e^{2}}, x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(d^2*e^2*x^2 + 2*c*d*e^2*x + c^2*e^2), x)","F",0
255,1,64,0,1.236102," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(5/3),x, algorithm=""fricas"")","\frac{3 \, {\left(d e x + c e\right)}^{\frac{1}{3}} {\left(d x + c\right)}^{\frac{2}{3}} \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{2 \, {\left(b d^{2} e^{2} x + b c d e^{2}\right)}}"," ",0,"3/2*(d*e*x + c*e)^(1/3)*(d*x + c)^(2/3)*cos((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(b*d^2*e^2*x + b*c*d*e^2)","A",0
256,1,133,0,3.559741," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(7/3),x, algorithm=""fricas"")","\frac{3 \, {\left({\left(d e x + c e\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{2}{3}} b \cos\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right) - {\left(d e x + c e\right)}^{\frac{2}{3}} {\left(d x + c\right)}^{\frac{4}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)\right)}}{2 \, {\left(b^{2} d^{3} e^{3} x^{2} + 2 \, b^{2} c d^{2} e^{3} x + b^{2} c^{2} d e^{3}\right)}}"," ",0,"3/2*((d*e*x + c*e)^(2/3)*(d*x + c)^(2/3)*b*cos((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)) - (d*e*x + c*e)^(2/3)*(d*x + c)^(4/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c)))/(b^2*d^3*e^3*x^2 + 2*b^2*c*d^2*e^3*x + b^2*c^2*d*e^3)","A",0
257,0,0,0,2.966630," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(8/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{1}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{d^{3} e^{3} x^{3} + 3 \, c d^{2} e^{3} x^{2} + 3 \, c^{2} d e^{3} x + c^{3} e^{3}}, x\right)"," ",0,"integral((d*e*x + c*e)^(1/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(d^3*e^3*x^3 + 3*c*d^2*e^3*x^2 + 3*c^2*d*e^3*x + c^3*e^3), x)","F",0
258,0,0,0,2.754947," ","integrate(sin(a+b/(d*x+c)^(2/3))/(d*e*x+c*e)^(10/3),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d e x + c e\right)}^{\frac{2}{3}} \sin\left(\frac{a d x + a c + {\left(d x + c\right)}^{\frac{1}{3}} b}{d x + c}\right)}{d^{4} e^{4} x^{4} + 4 \, c d^{3} e^{4} x^{3} + 6 \, c^{2} d^{2} e^{4} x^{2} + 4 \, c^{3} d e^{4} x + c^{4} e^{4}}, x\right)"," ",0,"integral((d*e*x + c*e)^(2/3)*sin((a*d*x + a*c + (d*x + c)^(1/3)*b)/(d*x + c))/(d^4*e^4*x^4 + 4*c*d^3*e^4*x^3 + 6*c^2*d^2*e^4*x^2 + 4*c^3*d*e^4*x + c^4*e^4), x)","F",0
259,0,0,0,1.419394," ","integrate((e*x)^m*sin(a+b*(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} \sin\left({\left(d x + c\right)}^{n} b + a\right), x\right)"," ",0,"integral((e*x)^m*sin((d*x + c)^n*b + a), x)","F",0
260,0,0,0,1.553927," ","integrate(x^3*sin(a+b*(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(x^{3} \sin\left({\left(d x + c\right)}^{n} b + a\right), x\right)"," ",0,"integral(x^3*sin((d*x + c)^n*b + a), x)","F",0
261,0,0,0,1.233074," ","integrate(x^2*sin(a+b*(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(x^{2} \sin\left({\left(d x + c\right)}^{n} b + a\right), x\right)"," ",0,"integral(x^2*sin((d*x + c)^n*b + a), x)","F",0
262,0,0,0,0.844161," ","integrate(x*sin(a+b*(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(x \sin\left({\left(d x + c\right)}^{n} b + a\right), x\right)"," ",0,"integral(x*sin((d*x + c)^n*b + a), x)","F",0
263,0,0,0,0.993498," ","integrate(sin(a+b*(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\sin\left({\left(d x + c\right)}^{n} b + a\right), x\right)"," ",0,"integral(sin((d*x + c)^n*b + a), x)","F",0
264,0,0,0,1.449892," ","integrate(sin(a+b*(d*x+c)^n)/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(d x + c\right)}^{n} b + a\right)}{x}, x\right)"," ",0,"integral(sin((d*x + c)^n*b + a)/x, x)","F",0
265,0,0,0,1.467197," ","integrate(sin(a+b*(d*x+c)^n)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left({\left(d x + c\right)}^{n} b + a\right)}{x^{2}}, x\right)"," ",0,"integral(sin((d*x + c)^n*b + a)/x^2, x)","F",0
266,0,0,0,1.450625," ","integrate(x^3*(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{3} \sin\left({\left(g x + f\right)}^{n} d + c\right) + a x^{3}, x\right)"," ",0,"integral(b*x^3*sin((g*x + f)^n*d + c) + a*x^3, x)","F",0
267,0,0,0,1.375063," ","integrate(x^2*(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(b x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right) + a x^{2}, x\right)"," ",0,"integral(b*x^2*sin((g*x + f)^n*d + c) + a*x^2, x)","F",0
268,0,0,0,1.576469," ","integrate(x*(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(b x \sin\left({\left(g x + f\right)}^{n} d + c\right) + a x, x\right)"," ",0,"integral(b*x*sin((g*x + f)^n*d + c) + a*x, x)","F",0
269,0,0,0,0.929398," ","integrate(a+b*sin(c+d*(g*x+f)^n),x, algorithm=""fricas"")","{\rm integral}\left(b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a, x\right)"," ",0,"integral(b*sin((g*x + f)^n*d + c) + a, x)","F",0
270,0,0,0,1.566949," ","integrate((a+b*sin(c+d*(g*x+f)^n))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}{x}, x\right)"," ",0,"integral((b*sin((g*x + f)^n*d + c) + a)/x, x)","F",0
271,0,0,0,1.565400," ","integrate((a+b*sin(c+d*(g*x+f)^n))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}{x^{2}}, x\right)"," ",0,"integral((b*sin((g*x + f)^n*d + c) + a)/x^2, x)","F",0
272,0,0,0,0.913375," ","integrate(x^2*(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-b^{2} x^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 2 \, a b x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} + b^{2}\right)} x^{2}, x\right)"," ",0,"integral(-b^2*x^2*cos((g*x + f)^n*d + c)^2 + 2*a*b*x^2*sin((g*x + f)^n*d + c) + (a^2 + b^2)*x^2, x)","F",0
273,0,0,0,1.274333," ","integrate(x*(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-b^{2} x \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 2 \, a b x \sin\left({\left(g x + f\right)}^{n} d + c\right) + {\left(a^{2} + b^{2}\right)} x, x\right)"," ",0,"integral(-b^2*x*cos((g*x + f)^n*d + c)^2 + 2*a*b*x*sin((g*x + f)^n*d + c) + (a^2 + b^2)*x, x)","F",0
274,0,0,0,1.301053," ","integrate((a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-b^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} + 2 \, a b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a^{2} + b^{2}, x\right)"," ",0,"integral(-b^2*cos((g*x + f)^n*d + c)^2 + 2*a*b*sin((g*x + f)^n*d + c) + a^2 + b^2, x)","F",0
275,0,0,0,1.429092," ","integrate((a+b*sin(c+d*(g*x+f)^n))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b \sin\left({\left(g x + f\right)}^{n} d + c\right) - a^{2} - b^{2}}{x}, x\right)"," ",0,"integral(-(b^2*cos((g*x + f)^n*d + c)^2 - 2*a*b*sin((g*x + f)^n*d + c) - a^2 - b^2)/x, x)","F",0
276,0,0,0,1.535172," ","integrate((a+b*sin(c+d*(g*x+f)^n))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b \sin\left({\left(g x + f\right)}^{n} d + c\right) - a^{2} - b^{2}}{x^{2}}, x\right)"," ",0,"integral(-(b^2*cos((g*x + f)^n*d + c)^2 - 2*a*b*sin((g*x + f)^n*d + c) - a^2 - b^2)/x^2, x)","F",0
277,0,0,0,1.232259," ","integrate(x^2/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}, x\right)"," ",0,"integral(x^2/(b*sin((g*x + f)^n*d + c) + a), x)","F",0
278,0,0,0,1.335336," ","integrate(x/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}, x\right)"," ",0,"integral(x/(b*sin((g*x + f)^n*d + c) + a), x)","F",0
279,0,0,0,1.155119," ","integrate(1/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a}, x\right)"," ",0,"integral(1/(b*sin((g*x + f)^n*d + c) + a), x)","F",0
280,0,0,0,1.308648," ","integrate(1/x/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x \sin\left({\left(g x + f\right)}^{n} d + c\right) + a x}, x\right)"," ",0,"integral(1/(b*x*sin((g*x + f)^n*d + c) + a*x), x)","F",0
281,0,0,0,1.299295," ","integrate(1/x^2/(a+b*sin(c+d*(g*x+f)^n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right) + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*sin((g*x + f)^n*d + c) + a*x^2), x)","F",0
282,0,0,0,1.476313," ","integrate(x^2/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x^{2}}{b^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b \sin\left({\left(g x + f\right)}^{n} d + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-x^2/(b^2*cos((g*x + f)^n*d + c)^2 - 2*a*b*sin((g*x + f)^n*d + c) - a^2 - b^2), x)","F",0
283,0,0,0,1.401491," ","integrate(x/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{x}{b^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b \sin\left({\left(g x + f\right)}^{n} d + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-x/(b^2*cos((g*x + f)^n*d + c)^2 - 2*a*b*sin((g*x + f)^n*d + c) - a^2 - b^2), x)","F",0
284,0,0,0,1.066254," ","integrate(1/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b \sin\left({\left(g x + f\right)}^{n} d + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-1/(b^2*cos((g*x + f)^n*d + c)^2 - 2*a*b*sin((g*x + f)^n*d + c) - a^2 - b^2), x)","F",0
285,0,0,0,1.258821," ","integrate(1/x/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b x \sin\left({\left(g x + f\right)}^{n} d + c\right) - {\left(a^{2} + b^{2}\right)} x}, x\right)"," ",0,"integral(-1/(b^2*x*cos((g*x + f)^n*d + c)^2 - 2*a*b*x*sin((g*x + f)^n*d + c) - (a^2 + b^2)*x), x)","F",0
286,0,0,0,1.480090," ","integrate(1/x^2/(a+b*sin(c+d*(g*x+f)^n))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} x^{2} \cos\left({\left(g x + f\right)}^{n} d + c\right)^{2} - 2 \, a b x^{2} \sin\left({\left(g x + f\right)}^{n} d + c\right) - {\left(a^{2} + b^{2}\right)} x^{2}}, x\right)"," ",0,"integral(-1/(b^2*x^2*cos((g*x + f)^n*d + c)^2 - 2*a*b*x^2*sin((g*x + f)^n*d + c) - (a^2 + b^2)*x^2), x)","F",0
287,0,0,0,0.773899," ","integrate((e*x)^m*(a+b*sin(c+d*(g*x+f)^n))^p,x, algorithm=""fricas"")","{\rm integral}\left(\left(e x\right)^{m} {\left(b \sin\left({\left(g x + f\right)}^{n} d + c\right) + a\right)}^{p}, x\right)"," ",0,"integral((e*x)^m*(b*sin((g*x + f)^n*d + c) + a)^p, x)","F",0
288,1,224,0,1.416050," ","integrate((f*x+e)^2*(a+b*sin(c+d/x)),x, algorithm=""fricas"")","\frac{1}{3} \, a f^{2} x^{3} + a e f x^{2} + a e^{2} x + \frac{1}{12} \, {\left(12 \, b d^{2} e f \operatorname{Si}\left(\frac{d}{x}\right) + {\left(b d^{3} f^{2} - 6 \, b d e^{2}\right)} \operatorname{Ci}\left(\frac{d}{x}\right) + {\left(b d^{3} f^{2} - 6 \, b d e^{2}\right)} \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \cos\left(c\right) + \frac{1}{6} \, {\left(b d f^{2} x^{2} + 6 \, b d e f x\right)} \cos\left(\frac{c x + d}{x}\right) + \frac{1}{6} \, {\left(3 \, b d^{2} e f \operatorname{Ci}\left(\frac{d}{x}\right) + 3 \, b d^{2} e f \operatorname{Ci}\left(-\frac{d}{x}\right) - {\left(b d^{3} f^{2} - 6 \, b d e^{2}\right)} \operatorname{Si}\left(\frac{d}{x}\right)\right)} \sin\left(c\right) + \frac{1}{6} \, {\left(2 \, b f^{2} x^{3} + 6 \, b e f x^{2} - {\left(b d^{2} f^{2} - 6 \, b e^{2}\right)} x\right)} \sin\left(\frac{c x + d}{x}\right)"," ",0,"1/3*a*f^2*x^3 + a*e*f*x^2 + a*e^2*x + 1/12*(12*b*d^2*e*f*sin_integral(d/x) + (b*d^3*f^2 - 6*b*d*e^2)*cos_integral(d/x) + (b*d^3*f^2 - 6*b*d*e^2)*cos_integral(-d/x))*cos(c) + 1/6*(b*d*f^2*x^2 + 6*b*d*e*f*x)*cos((c*x + d)/x) + 1/6*(3*b*d^2*e*f*cos_integral(d/x) + 3*b*d^2*e*f*cos_integral(-d/x) - (b*d^3*f^2 - 6*b*d*e^2)*sin_integral(d/x))*sin(c) + 1/6*(2*b*f^2*x^3 + 6*b*e*f*x^2 - (b*d^2*f^2 - 6*b*e^2)*x)*sin((c*x + d)/x)","A",0
289,1,133,0,1.262639," ","integrate((f*x+e)*(a+b*sin(c+d/x)),x, algorithm=""fricas"")","\frac{1}{2} \, b d f x \cos\left(\frac{c x + d}{x}\right) + \frac{1}{2} \, a f x^{2} + a e x + \frac{1}{2} \, {\left(b d^{2} f \operatorname{Si}\left(\frac{d}{x}\right) - b d e \operatorname{Ci}\left(\frac{d}{x}\right) - b d e \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \cos\left(c\right) + \frac{1}{4} \, {\left(b d^{2} f \operatorname{Ci}\left(\frac{d}{x}\right) + b d^{2} f \operatorname{Ci}\left(-\frac{d}{x}\right) + 4 \, b d e \operatorname{Si}\left(\frac{d}{x}\right)\right)} \sin\left(c\right) + \frac{1}{2} \, {\left(b f x^{2} + 2 \, b e x\right)} \sin\left(\frac{c x + d}{x}\right)"," ",0,"1/2*b*d*f*x*cos((c*x + d)/x) + 1/2*a*f*x^2 + a*e*x + 1/2*(b*d^2*f*sin_integral(d/x) - b*d*e*cos_integral(d/x) - b*d*e*cos_integral(-d/x))*cos(c) + 1/4*(b*d^2*f*cos_integral(d/x) + b*d^2*f*cos_integral(-d/x) + 4*b*d*e*sin_integral(d/x))*sin(c) + 1/2*(b*f*x^2 + 2*b*e*x)*sin((c*x + d)/x)","A",0
290,1,52,0,1.040419," ","integrate(a+b*sin(c+d/x),x, algorithm=""fricas"")","b d \sin\left(c\right) \operatorname{Si}\left(\frac{d}{x}\right) + b x \sin\left(\frac{c x + d}{x}\right) + a x - \frac{1}{2} \, {\left(b d \operatorname{Ci}\left(\frac{d}{x}\right) + b d \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \cos\left(c\right)"," ",0,"b*d*sin(c)*sin_integral(d/x) + b*x*sin((c*x + d)/x) + a*x - 1/2*(b*d*cos_integral(d/x) + b*d*cos_integral(-d/x))*cos(c)","A",0
291,1,133,0,1.399814," ","integrate((a+b*sin(c+d/x))/(f*x+e),x, algorithm=""fricas"")","-\frac{2 \, b \cos\left(c\right) \operatorname{Si}\left(\frac{d}{x}\right) - 2 \, b \cos\left(-\frac{c e - d f}{e}\right) \operatorname{Si}\left(\frac{d f x + d e}{e x}\right) - 2 \, a \log\left(f x + e\right) + {\left(b \operatorname{Ci}\left(\frac{d}{x}\right) + b \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \sin\left(c\right) + {\left(b \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + b \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right)\right)} \sin\left(-\frac{c e - d f}{e}\right)}{2 \, f}"," ",0,"-1/2*(2*b*cos(c)*sin_integral(d/x) - 2*b*cos(-(c*e - d*f)/e)*sin_integral((d*f*x + d*e)/(e*x)) - 2*a*log(f*x + e) + (b*cos_integral(d/x) + b*cos_integral(-d/x))*sin(c) + (b*cos_integral((d*f*x + d*e)/(e*x)) + b*cos_integral(-(d*f*x + d*e)/(e*x)))*sin(-(c*e - d*f)/e))/f","A",0
292,1,164,0,1.192631," ","integrate((a+b*sin(c+d/x))/(f*x+e)^2,x, algorithm=""fricas"")","\frac{2 \, b e f x \sin\left(\frac{c x + d}{x}\right) - 2 \, a e^{2} - 2 \, {\left(b d f^{2} x + b d e f\right)} \sin\left(-\frac{c e - d f}{e}\right) \operatorname{Si}\left(\frac{d f x + d e}{e x}\right) - {\left({\left(b d f^{2} x + b d e f\right)} \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + {\left(b d f^{2} x + b d e f\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right)\right)} \cos\left(-\frac{c e - d f}{e}\right)}{2 \, {\left(e^{2} f^{2} x + e^{3} f\right)}}"," ",0,"1/2*(2*b*e*f*x*sin((c*x + d)/x) - 2*a*e^2 - 2*(b*d*f^2*x + b*d*e*f)*sin(-(c*e - d*f)/e)*sin_integral((d*f*x + d*e)/(e*x)) - ((b*d*f^2*x + b*d*e*f)*cos_integral((d*f*x + d*e)/(e*x)) + (b*d*f^2*x + b*d*e*f)*cos_integral(-(d*f*x + d*e)/(e*x)))*cos(-(c*e - d*f)/e))/(e^2*f^2*x + e^3*f)","A",0
293,1,429,0,1.478689," ","integrate((a+b*sin(c+d/x))/(f*x+e)^3,x, algorithm=""fricas"")","-\frac{2 \, a e^{4} + 2 \, {\left({\left(b d e f^{3} x^{2} + 2 \, b d e^{2} f^{2} x + b d e^{3} f\right)} \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + {\left(b d e f^{3} x^{2} + 2 \, b d e^{2} f^{2} x + b d e^{3} f\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right) + {\left(b d^{2} f^{4} x^{2} + 2 \, b d^{2} e f^{3} x + b d^{2} e^{2} f^{2}\right)} \operatorname{Si}\left(\frac{d f x + d e}{e x}\right)\right)} \cos\left(-\frac{c e - d f}{e}\right) + 2 \, {\left(b d e f^{3} x^{2} + b d e^{2} f^{2} x\right)} \cos\left(\frac{c x + d}{x}\right) - {\left({\left(b d^{2} f^{4} x^{2} + 2 \, b d^{2} e f^{3} x + b d^{2} e^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + {\left(b d^{2} f^{4} x^{2} + 2 \, b d^{2} e f^{3} x + b d^{2} e^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right) - 4 \, {\left(b d e f^{3} x^{2} + 2 \, b d e^{2} f^{2} x + b d e^{3} f\right)} \operatorname{Si}\left(\frac{d f x + d e}{e x}\right)\right)} \sin\left(-\frac{c e - d f}{e}\right) - 2 \, {\left(b e^{2} f^{2} x^{2} + 2 \, b e^{3} f x\right)} \sin\left(\frac{c x + d}{x}\right)}{4 \, {\left(e^{4} f^{3} x^{2} + 2 \, e^{5} f^{2} x + e^{6} f\right)}}"," ",0,"-1/4*(2*a*e^4 + 2*((b*d*e*f^3*x^2 + 2*b*d*e^2*f^2*x + b*d*e^3*f)*cos_integral((d*f*x + d*e)/(e*x)) + (b*d*e*f^3*x^2 + 2*b*d*e^2*f^2*x + b*d*e^3*f)*cos_integral(-(d*f*x + d*e)/(e*x)) + (b*d^2*f^4*x^2 + 2*b*d^2*e*f^3*x + b*d^2*e^2*f^2)*sin_integral((d*f*x + d*e)/(e*x)))*cos(-(c*e - d*f)/e) + 2*(b*d*e*f^3*x^2 + b*d*e^2*f^2*x)*cos((c*x + d)/x) - ((b*d^2*f^4*x^2 + 2*b*d^2*e*f^3*x + b*d^2*e^2*f^2)*cos_integral((d*f*x + d*e)/(e*x)) + (b*d^2*f^4*x^2 + 2*b*d^2*e*f^3*x + b*d^2*e^2*f^2)*cos_integral(-(d*f*x + d*e)/(e*x)) - 4*(b*d*e*f^3*x^2 + 2*b*d*e^2*f^2*x + b*d*e^3*f)*sin_integral((d*f*x + d*e)/(e*x)))*sin(-(c*e - d*f)/e) - 2*(b*e^2*f^2*x^2 + 2*b*e^3*f*x)*sin((c*x + d)/x))/(e^4*f^3*x^2 + 2*e^5*f^2*x + e^6*f)","A",0
294,1,300,0,1.670729," ","integrate((f*x+e)*(a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","a b d f x \cos\left(\frac{c x + d}{x}\right) + \frac{1}{2} \, {\left(a^{2} + b^{2}\right)} f x^{2} + {\left(a^{2} + b^{2}\right)} e x - \frac{1}{2} \, {\left(b^{2} f x^{2} + 2 \, b^{2} e x\right)} \cos\left(\frac{c x + d}{x}\right)^{2} - \frac{1}{2} \, {\left(b^{2} d^{2} f \operatorname{Ci}\left(\frac{2 \, d}{x}\right) + b^{2} d^{2} f \operatorname{Ci}\left(-\frac{2 \, d}{x}\right) + 2 \, b^{2} d e \operatorname{Si}\left(\frac{2 \, d}{x}\right)\right)} \cos\left(2 \, c\right) + {\left(a b d^{2} f \operatorname{Si}\left(\frac{d}{x}\right) - a b d e \operatorname{Ci}\left(\frac{d}{x}\right) - a b d e \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \cos\left(c\right) + \frac{1}{2} \, {\left(2 \, b^{2} d^{2} f \operatorname{Si}\left(\frac{2 \, d}{x}\right) - b^{2} d e \operatorname{Ci}\left(\frac{2 \, d}{x}\right) - b^{2} d e \operatorname{Ci}\left(-\frac{2 \, d}{x}\right)\right)} \sin\left(2 \, c\right) + \frac{1}{2} \, {\left(a b d^{2} f \operatorname{Ci}\left(\frac{d}{x}\right) + a b d^{2} f \operatorname{Ci}\left(-\frac{d}{x}\right) + 4 \, a b d e \operatorname{Si}\left(\frac{d}{x}\right)\right)} \sin\left(c\right) + {\left(b^{2} d f x \cos\left(\frac{c x + d}{x}\right) + a b f x^{2} + 2 \, a b e x\right)} \sin\left(\frac{c x + d}{x}\right)"," ",0,"a*b*d*f*x*cos((c*x + d)/x) + 1/2*(a^2 + b^2)*f*x^2 + (a^2 + b^2)*e*x - 1/2*(b^2*f*x^2 + 2*b^2*e*x)*cos((c*x + d)/x)^2 - 1/2*(b^2*d^2*f*cos_integral(2*d/x) + b^2*d^2*f*cos_integral(-2*d/x) + 2*b^2*d*e*sin_integral(2*d/x))*cos(2*c) + (a*b*d^2*f*sin_integral(d/x) - a*b*d*e*cos_integral(d/x) - a*b*d*e*cos_integral(-d/x))*cos(c) + 1/2*(2*b^2*d^2*f*sin_integral(2*d/x) - b^2*d*e*cos_integral(2*d/x) - b^2*d*e*cos_integral(-2*d/x))*sin(2*c) + 1/2*(a*b*d^2*f*cos_integral(d/x) + a*b*d^2*f*cos_integral(-d/x) + 4*a*b*d*e*sin_integral(d/x))*sin(c) + (b^2*d*f*x*cos((c*x + d)/x) + a*b*f*x^2 + 2*a*b*e*x)*sin((c*x + d)/x)","A",0
295,1,130,0,0.996881," ","integrate((a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","-b^{2} x \cos\left(\frac{c x + d}{x}\right)^{2} - b^{2} d \cos\left(2 \, c\right) \operatorname{Si}\left(\frac{2 \, d}{x}\right) + 2 \, a b d \sin\left(c\right) \operatorname{Si}\left(\frac{d}{x}\right) + 2 \, a b x \sin\left(\frac{c x + d}{x}\right) + {\left(a^{2} + b^{2}\right)} x - {\left(a b d \operatorname{Ci}\left(\frac{d}{x}\right) + a b d \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \cos\left(c\right) - \frac{1}{2} \, {\left(b^{2} d \operatorname{Ci}\left(\frac{2 \, d}{x}\right) + b^{2} d \operatorname{Ci}\left(-\frac{2 \, d}{x}\right)\right)} \sin\left(2 \, c\right)"," ",0,"-b^2*x*cos((c*x + d)/x)^2 - b^2*d*cos(2*c)*sin_integral(2*d/x) + 2*a*b*d*sin(c)*sin_integral(d/x) + 2*a*b*x*sin((c*x + d)/x) + (a^2 + b^2)*x - (a*b*d*cos_integral(d/x) + a*b*d*cos_integral(-d/x))*cos(c) - 1/2*(b^2*d*cos_integral(2*d/x) + b^2*d*cos_integral(-2*d/x))*sin(2*c)","A",0
296,1,288,0,1.615701," ","integrate((a+b*sin(c+d/x))^2/(f*x+e),x, algorithm=""fricas"")","-\frac{2 \, b^{2} \sin\left(2 \, c\right) \operatorname{Si}\left(\frac{2 \, d}{x}\right) + 8 \, a b \cos\left(c\right) \operatorname{Si}\left(\frac{d}{x}\right) + 2 \, b^{2} \sin\left(-\frac{2 \, {\left(c e - d f\right)}}{e}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) - 8 \, a b \cos\left(-\frac{c e - d f}{e}\right) \operatorname{Si}\left(\frac{d f x + d e}{e x}\right) - {\left(b^{2} \operatorname{Ci}\left(\frac{2 \, d}{x}\right) + b^{2} \operatorname{Ci}\left(-\frac{2 \, d}{x}\right)\right)} \cos\left(2 \, c\right) + {\left(b^{2} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) + b^{2} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + d e\right)}}{e x}\right)\right)} \cos\left(-\frac{2 \, {\left(c e - d f\right)}}{e}\right) - 2 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(f x + e\right) + 4 \, {\left(a b \operatorname{Ci}\left(\frac{d}{x}\right) + a b \operatorname{Ci}\left(-\frac{d}{x}\right)\right)} \sin\left(c\right) + 4 \, {\left(a b \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + a b \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right)\right)} \sin\left(-\frac{c e - d f}{e}\right)}{4 \, f}"," ",0,"-1/4*(2*b^2*sin(2*c)*sin_integral(2*d/x) + 8*a*b*cos(c)*sin_integral(d/x) + 2*b^2*sin(-2*(c*e - d*f)/e)*sin_integral(2*(d*f*x + d*e)/(e*x)) - 8*a*b*cos(-(c*e - d*f)/e)*sin_integral((d*f*x + d*e)/(e*x)) - (b^2*cos_integral(2*d/x) + b^2*cos_integral(-2*d/x))*cos(2*c) + (b^2*cos_integral(2*(d*f*x + d*e)/(e*x)) + b^2*cos_integral(-2*(d*f*x + d*e)/(e*x)))*cos(-2*(c*e - d*f)/e) - 2*(2*a^2 + b^2)*log(f*x + e) + 4*(a*b*cos_integral(d/x) + a*b*cos_integral(-d/x))*sin(c) + 4*(a*b*cos_integral((d*f*x + d*e)/(e*x)) + a*b*cos_integral(-(d*f*x + d*e)/(e*x)))*sin(-(c*e - d*f)/e))/f","A",0
297,1,343,0,1.158641," ","integrate((a+b*sin(c+d/x))^2/(f*x+e)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} e f x \cos\left(\frac{c x + d}{x}\right)^{2} - 4 \, a b e f x \sin\left(\frac{c x + d}{x}\right) - b^{2} e f x + {\left(2 \, a^{2} + b^{2}\right)} e^{2} + 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cos\left(-\frac{2 \, {\left(c e - d f\right)}}{e}\right) \operatorname{Si}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) + 4 \, {\left(a b d f^{2} x + a b d e f\right)} \sin\left(-\frac{c e - d f}{e}\right) \operatorname{Si}\left(\frac{d f x + d e}{e x}\right) + 2 \, {\left({\left(a b d f^{2} x + a b d e f\right)} \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + {\left(a b d f^{2} x + a b d e f\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right)\right)} \cos\left(-\frac{c e - d f}{e}\right) - {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + d e\right)}}{e x}\right)\right)} \sin\left(-\frac{2 \, {\left(c e - d f\right)}}{e}\right)}{2 \, {\left(e^{2} f^{2} x + e^{3} f\right)}}"," ",0,"-1/2*(2*b^2*e*f*x*cos((c*x + d)/x)^2 - 4*a*b*e*f*x*sin((c*x + d)/x) - b^2*e*f*x + (2*a^2 + b^2)*e^2 + 2*(b^2*d*f^2*x + b^2*d*e*f)*cos(-2*(c*e - d*f)/e)*sin_integral(2*(d*f*x + d*e)/(e*x)) + 4*(a*b*d*f^2*x + a*b*d*e*f)*sin(-(c*e - d*f)/e)*sin_integral((d*f*x + d*e)/(e*x)) + 2*((a*b*d*f^2*x + a*b*d*e*f)*cos_integral((d*f*x + d*e)/(e*x)) + (a*b*d*f^2*x + a*b*d*e*f)*cos_integral(-(d*f*x + d*e)/(e*x)))*cos(-(c*e - d*f)/e) - ((b^2*d*f^2*x + b^2*d*e*f)*cos_integral(2*(d*f*x + d*e)/(e*x)) + (b^2*d*f^2*x + b^2*d*e*f)*cos_integral(-2*(d*f*x + d*e)/(e*x)))*sin(-2*(c*e - d*f)/e))/(e^2*f^2*x + e^3*f)","A",0
298,1,926,0,1.989330," ","integrate((a+b*sin(c+d/x))^2/(f*x+e)^3,x, algorithm=""fricas"")","\frac{b^{2} e^{2} f^{2} x^{2} + 2 \, b^{2} e^{3} f x - {\left(2 \, a^{2} + b^{2}\right)} e^{4} - 2 \, {\left(b^{2} e^{2} f^{2} x^{2} + 2 \, b^{2} e^{3} f x\right)} \cos\left(\frac{c x + d}{x}\right)^{2} - 4 \, {\left({\left(a b d e f^{3} x^{2} + 2 \, a b d e^{2} f^{2} x + a b d e^{3} f\right)} \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + {\left(a b d e f^{3} x^{2} + 2 \, a b d e^{2} f^{2} x + a b d e^{3} f\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right) + {\left(a b d^{2} f^{4} x^{2} + 2 \, a b d^{2} e f^{3} x + a b d^{2} e^{2} f^{2}\right)} \operatorname{Si}\left(\frac{d f x + d e}{e x}\right)\right)} \cos\left(-\frac{c e - d f}{e}\right) + 2 \, {\left({\left(b^{2} d^{2} f^{4} x^{2} + 2 \, b^{2} d^{2} e f^{3} x + b^{2} d^{2} e^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) + {\left(b^{2} d^{2} f^{4} x^{2} + 2 \, b^{2} d^{2} e f^{3} x + b^{2} d^{2} e^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) - 2 \, {\left(b^{2} d e f^{3} x^{2} + 2 \, b^{2} d e^{2} f^{2} x + b^{2} d e^{3} f\right)} \operatorname{Si}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right)\right)} \cos\left(-\frac{2 \, {\left(c e - d f\right)}}{e}\right) - 4 \, {\left(a b d e f^{3} x^{2} + a b d e^{2} f^{2} x\right)} \cos\left(\frac{c x + d}{x}\right) + 2 \, {\left({\left(a b d^{2} f^{4} x^{2} + 2 \, a b d^{2} e f^{3} x + a b d^{2} e^{2} f^{2}\right)} \operatorname{Ci}\left(\frac{d f x + d e}{e x}\right) + {\left(a b d^{2} f^{4} x^{2} + 2 \, a b d^{2} e f^{3} x + a b d^{2} e^{2} f^{2}\right)} \operatorname{Ci}\left(-\frac{d f x + d e}{e x}\right) - 4 \, {\left(a b d e f^{3} x^{2} + 2 \, a b d e^{2} f^{2} x + a b d e^{3} f\right)} \operatorname{Si}\left(\frac{d f x + d e}{e x}\right)\right)} \sin\left(-\frac{c e - d f}{e}\right) + 2 \, {\left({\left(b^{2} d e f^{3} x^{2} + 2 \, b^{2} d e^{2} f^{2} x + b^{2} d e^{3} f\right)} \operatorname{Ci}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) + {\left(b^{2} d e f^{3} x^{2} + 2 \, b^{2} d e^{2} f^{2} x + b^{2} d e^{3} f\right)} \operatorname{Ci}\left(-\frac{2 \, {\left(d f x + d e\right)}}{e x}\right) + 2 \, {\left(b^{2} d^{2} f^{4} x^{2} + 2 \, b^{2} d^{2} e f^{3} x + b^{2} d^{2} e^{2} f^{2}\right)} \operatorname{Si}\left(\frac{2 \, {\left(d f x + d e\right)}}{e x}\right)\right)} \sin\left(-\frac{2 \, {\left(c e - d f\right)}}{e}\right) + 4 \, {\left(a b e^{2} f^{2} x^{2} + 2 \, a b e^{3} f x - {\left(b^{2} d e f^{3} x^{2} + b^{2} d e^{2} f^{2} x\right)} \cos\left(\frac{c x + d}{x}\right)\right)} \sin\left(\frac{c x + d}{x}\right)}{4 \, {\left(e^{4} f^{3} x^{2} + 2 \, e^{5} f^{2} x + e^{6} f\right)}}"," ",0,"1/4*(b^2*e^2*f^2*x^2 + 2*b^2*e^3*f*x - (2*a^2 + b^2)*e^4 - 2*(b^2*e^2*f^2*x^2 + 2*b^2*e^3*f*x)*cos((c*x + d)/x)^2 - 4*((a*b*d*e*f^3*x^2 + 2*a*b*d*e^2*f^2*x + a*b*d*e^3*f)*cos_integral((d*f*x + d*e)/(e*x)) + (a*b*d*e*f^3*x^2 + 2*a*b*d*e^2*f^2*x + a*b*d*e^3*f)*cos_integral(-(d*f*x + d*e)/(e*x)) + (a*b*d^2*f^4*x^2 + 2*a*b*d^2*e*f^3*x + a*b*d^2*e^2*f^2)*sin_integral((d*f*x + d*e)/(e*x)))*cos(-(c*e - d*f)/e) + 2*((b^2*d^2*f^4*x^2 + 2*b^2*d^2*e*f^3*x + b^2*d^2*e^2*f^2)*cos_integral(2*(d*f*x + d*e)/(e*x)) + (b^2*d^2*f^4*x^2 + 2*b^2*d^2*e*f^3*x + b^2*d^2*e^2*f^2)*cos_integral(-2*(d*f*x + d*e)/(e*x)) - 2*(b^2*d*e*f^3*x^2 + 2*b^2*d*e^2*f^2*x + b^2*d*e^3*f)*sin_integral(2*(d*f*x + d*e)/(e*x)))*cos(-2*(c*e - d*f)/e) - 4*(a*b*d*e*f^3*x^2 + a*b*d*e^2*f^2*x)*cos((c*x + d)/x) + 2*((a*b*d^2*f^4*x^2 + 2*a*b*d^2*e*f^3*x + a*b*d^2*e^2*f^2)*cos_integral((d*f*x + d*e)/(e*x)) + (a*b*d^2*f^4*x^2 + 2*a*b*d^2*e*f^3*x + a*b*d^2*e^2*f^2)*cos_integral(-(d*f*x + d*e)/(e*x)) - 4*(a*b*d*e*f^3*x^2 + 2*a*b*d*e^2*f^2*x + a*b*d*e^3*f)*sin_integral((d*f*x + d*e)/(e*x)))*sin(-(c*e - d*f)/e) + 2*((b^2*d*e*f^3*x^2 + 2*b^2*d*e^2*f^2*x + b^2*d*e^3*f)*cos_integral(2*(d*f*x + d*e)/(e*x)) + (b^2*d*e*f^3*x^2 + 2*b^2*d*e^2*f^2*x + b^2*d*e^3*f)*cos_integral(-2*(d*f*x + d*e)/(e*x)) + 2*(b^2*d^2*f^4*x^2 + 2*b^2*d^2*e*f^3*x + b^2*d^2*e^2*f^2)*sin_integral(2*(d*f*x + d*e)/(e*x)))*sin(-2*(c*e - d*f)/e) + 4*(a*b*e^2*f^2*x^2 + 2*a*b*e^3*f*x - (b^2*d*e*f^3*x^2 + b^2*d*e^2*f^2*x)*cos((c*x + d)/x))*sin((c*x + d)/x))/(e^4*f^3*x^2 + 2*e^5*f^2*x + e^6*f)","A",0
299,0,0,0,1.371394," ","integrate((f*x+e)^2/(a+b*sin(c+d/x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{f^{2} x^{2} + 2 \, e f x + e^{2}}{b \sin\left(\frac{c x + d}{x}\right) + a}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)/(b*sin((c*x + d)/x) + a), x)","F",0
300,0,0,0,1.450549," ","integrate((f*x+e)/(a+b*sin(c+d/x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{f x + e}{b \sin\left(\frac{c x + d}{x}\right) + a}, x\right)"," ",0,"integral((f*x + e)/(b*sin((c*x + d)/x) + a), x)","F",0
301,0,0,0,1.346744," ","integrate(1/(a+b*sin(c+d/x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b \sin\left(\frac{c x + d}{x}\right) + a}, x\right)"," ",0,"integral(1/(b*sin((c*x + d)/x) + a), x)","F",0
302,0,0,0,1.191190," ","integrate((f*x+e)/(a+b*sin(c+d/x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{f x + e}{b \sin\left(\frac{c x + d}{x}\right) + a}, x\right)"," ",0,"integral((f*x + e)/(b*sin((c*x + d)/x) + a), x)","F",0
303,0,0,0,1.454122," ","integrate((f*x+e)^2/(a+b*sin(c+d/x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{f^{2} x^{2} + 2 \, e f x + e^{2}}{b \sin\left(\frac{c x + d}{x}\right) + a}, x\right)"," ",0,"integral((f^2*x^2 + 2*e*f*x + e^2)/(b*sin((c*x + d)/x) + a), x)","F",0
304,0,0,0,1.215037," ","integrate((f*x+e)^2/(a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{f^{2} x^{2} + 2 \, e f x + e^{2}}{b^{2} \cos\left(\frac{c x + d}{x}\right)^{2} - 2 \, a b \sin\left(\frac{c x + d}{x}\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(f^2*x^2 + 2*e*f*x + e^2)/(b^2*cos((c*x + d)/x)^2 - 2*a*b*sin((c*x + d)/x) - a^2 - b^2), x)","F",0
305,0,0,0,1.523207," ","integrate((f*x+e)/(a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{f x + e}{b^{2} \cos\left(\frac{c x + d}{x}\right)^{2} - 2 \, a b \sin\left(\frac{c x + d}{x}\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(f*x + e)/(b^2*cos((c*x + d)/x)^2 - 2*a*b*sin((c*x + d)/x) - a^2 - b^2), x)","F",0
306,0,0,0,1.389105," ","integrate(1/(a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{1}{b^{2} \cos\left(\frac{c x + d}{x}\right)^{2} - 2 \, a b \sin\left(\frac{c x + d}{x}\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-1/(b^2*cos((c*x + d)/x)^2 - 2*a*b*sin((c*x + d)/x) - a^2 - b^2), x)","F",0
307,0,0,0,2.090890," ","integrate((f*x+e)/(a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{f x + e}{b^{2} \cos\left(\frac{c x + d}{x}\right)^{2} - 2 \, a b \sin\left(\frac{c x + d}{x}\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(f*x + e)/(b^2*cos((c*x + d)/x)^2 - 2*a*b*sin((c*x + d)/x) - a^2 - b^2), x)","F",0
308,0,0,0,1.487074," ","integrate((f*x+e)^2/(a+b*sin(c+d/x))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{f^{2} x^{2} + 2 \, e f x + e^{2}}{b^{2} \cos\left(\frac{c x + d}{x}\right)^{2} - 2 \, a b \sin\left(\frac{c x + d}{x}\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(f^2*x^2 + 2*e*f*x + e^2)/(b^2*cos((c*x + d)/x)^2 - 2*a*b*sin((c*x + d)/x) - a^2 - b^2), x)","F",0
309,0,0,0,1.525784," ","integrate((f*x+e)^m*(a+b*sin(c+d/x))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(f x + e\right)}^{m} {\left(b \sin\left(\frac{c x + d}{x}\right) + a\right)}^{p}, x\right)"," ",0,"integral((f*x + e)^m*(b*sin((c*x + d)/x) + a)^p, x)","F",0
310,1,80,0,2.129421," ","integrate(x^m*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(e^{\left(-m \log\left(i \, b\right) - i \, a\right)} \Gamma\left(m + 1, i \, b x\right) + e^{\left(-m \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(m + 1, -i \, b x\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{2 \, b \sin\left(b x + a\right)}"," ",0,"-1/2*(e^(-m*log(I*b) - I*a)*gamma(m + 1, I*b*x) + e^(-m*log(-I*b) + I*a)*gamma(m + 1, -I*b*x))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)/(b*sin(b*x + a))","A",0
311,1,74,0,1.429978," ","integrate(x^3*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left({\left(b^{3} x^{3} - 6 \, b x\right)} \cos\left(b x + a\right) - 3 \, {\left(b^{2} x^{2} - 2\right)} \sin\left(b x + a\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{b^{4} \sin\left(b x + a\right)}"," ",0,"-((b^3*x^3 - 6*b*x)*cos(b*x + a) - 3*(b^2*x^2 - 2)*sin(b*x + a))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)/(b^4*sin(b*x + a))","A",0
312,1,64,0,1.465974," ","integrate(x^2*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""fricas"")","\frac{{\left(2 \, b x \sin\left(b x + a\right) - {\left(b^{2} x^{2} - 2\right)} \cos\left(b x + a\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{b^{3} \sin\left(b x + a\right)}"," ",0,"(2*b*x*sin(b*x + a) - (b^2*x^2 - 2)*cos(b*x + a))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)/(b^3*sin(b*x + a))","A",0
313,1,55,0,1.578700," ","integrate(x*(c*sin(b*x+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(b x \cos\left(b x + a\right) - \sin\left(b x + a\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{b^{2} \sin\left(b x + a\right)}"," ",0,"-(b*x*cos(b*x + a) - sin(b*x + a))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)/(b^2*sin(b*x + a))","A",0
314,1,43,0,1.100421," ","integrate((c*sin(b*x+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{\left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}} \cos\left(b x + a\right)}{b \sin\left(b x + a\right)}"," ",0,"-(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)*cos(b*x + a)/(b*sin(b*x + a))","A",0
315,1,80,0,1.349747," ","integrate((c*sin(b*x+a)^3)^(1/3)/x,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(2 \cdot 4^{\frac{2}{3}} \cos\left(a\right) \operatorname{Si}\left(b x\right) + {\left(4^{\frac{2}{3}} \operatorname{Ci}\left(b x\right) + 4^{\frac{2}{3}} \operatorname{Ci}\left(-b x\right)\right)} \sin\left(a\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}} \sin\left(b x + a\right)}{8 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)}}"," ",0,"-1/8*4^(1/3)*(2*4^(2/3)*cos(a)*sin_integral(b*x) + (4^(2/3)*cos_integral(b*x) + 4^(2/3)*cos_integral(-b*x))*sin(a))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)*sin(b*x + a)/(cos(b*x + a)^2 - 1)","A",0
316,1,112,0,1.802097," ","integrate((c*sin(b*x+a)^3)^(1/3)/x^2,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(2 \cdot 4^{\frac{2}{3}} \cos\left(b x + a\right)^{2} - {\left(2 \cdot 4^{\frac{2}{3}} b x \sin\left(a\right) \operatorname{Si}\left(b x\right) - {\left(4^{\frac{2}{3}} b x \operatorname{Ci}\left(b x\right) + 4^{\frac{2}{3}} b x \operatorname{Ci}\left(-b x\right)\right)} \cos\left(a\right)\right)} \sin\left(b x + a\right) - 2 \cdot 4^{\frac{2}{3}}\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{8 \, {\left(x \cos\left(b x + a\right)^{2} - x\right)}}"," ",0,"-1/8*4^(1/3)*(2*4^(2/3)*cos(b*x + a)^2 - (2*4^(2/3)*b*x*sin(a)*sin_integral(b*x) - (4^(2/3)*b*x*cos_integral(b*x) + 4^(2/3)*b*x*cos_integral(-b*x))*cos(a))*sin(b*x + a) - 2*4^(2/3))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)/(x*cos(b*x + a)^2 - x)","A",0
317,1,140,0,1.006035," ","integrate((c*sin(b*x+a)^3)^(1/3)/x^3,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(2 \cdot 4^{\frac{2}{3}} \cos\left(b x + a\right)^{2} - {\left(2 \cdot 4^{\frac{2}{3}} b^{2} x^{2} \cos\left(a\right) \operatorname{Si}\left(b x\right) + 2 \cdot 4^{\frac{2}{3}} b x \cos\left(b x + a\right) + {\left(4^{\frac{2}{3}} b^{2} x^{2} \operatorname{Ci}\left(b x\right) + 4^{\frac{2}{3}} b^{2} x^{2} \operatorname{Ci}\left(-b x\right)\right)} \sin\left(a\right)\right)} \sin\left(b x + a\right) - 2 \cdot 4^{\frac{2}{3}}\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{1}{3}}}{16 \, {\left(x^{2} \cos\left(b x + a\right)^{2} - x^{2}\right)}}"," ",0,"-1/16*4^(1/3)*(2*4^(2/3)*cos(b*x + a)^2 - (2*4^(2/3)*b^2*x^2*cos(a)*sin_integral(b*x) + 2*4^(2/3)*b*x*cos(b*x + a) + (4^(2/3)*b^2*x^2*cos_integral(b*x) + 4^(2/3)*b^2*x^2*cos_integral(-b*x))*sin(a))*sin(b*x + a) - 2*4^(2/3))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(1/3)/(x^2*cos(b*x + a)^2 - x^2)","A",0
318,1,98,0,1.799313," ","integrate(x^m*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(i \, b\right) - i \, a\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, i \, b x^{2}\right) + e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-i \, b\right) + i \, a\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -i \, b x^{2}\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}}}{4 \, b \sin\left(b x^{2} + a\right)}"," ",0,"-1/4*(e^(-1/2*(m - 1)*log(I*b) - I*a)*gamma(1/2*m + 1/2, I*b*x^2) + e^(-1/2*(m - 1)*log(-I*b) + I*a)*gamma(1/2*m + 1/2, -I*b*x^2))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)/(b*sin(b*x^2 + a))","A",0
319,1,67,0,1.540695," ","integrate(x^3*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{{\left(b x^{2} \cos\left(b x^{2} + a\right) - \sin\left(b x^{2} + a\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}}}{2 \, b^{2} \sin\left(b x^{2} + a\right)}"," ",0,"-1/2*(b*x^2*cos(b*x^2 + a) - sin(b*x^2 + a))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)/(b^2*sin(b*x^2 + a))","A",0
320,1,156,0,2.072503," ","integrate(x^2*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(4^{\frac{2}{3}} \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(b x^{2} + a\right) - 4^{\frac{2}{3}} \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(b x^{2} + a\right) \sin\left(a\right) - 2 \cdot 4^{\frac{2}{3}} b x \cos\left(b x^{2} + a\right) \sin\left(b x^{2} + a\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}}}{16 \, {\left(b^{2} \cos\left(b x^{2} + a\right)^{2} - b^{2}\right)}}"," ",0,"-1/16*4^(1/3)*(4^(2/3)*sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*x*sqrt(b/pi))*sin(b*x^2 + a) - 4^(2/3)*sqrt(2)*pi*sqrt(b/pi)*fresnel_sin(sqrt(2)*x*sqrt(b/pi))*sin(b*x^2 + a)*sin(a) - 2*4^(2/3)*b*x*cos(b*x^2 + a)*sin(b*x^2 + a))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)/(b^2*cos(b*x^2 + a)^2 - b^2)","A",0
321,1,51,0,0.883153," ","integrate(x*(c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{\left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}} \cos\left(b x^{2} + a\right)}{2 \, b \sin\left(b x^{2} + a\right)}"," ",0,"-1/2*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)*cos(b*x^2 + a)/(b*sin(b*x^2 + a))","A",0
322,1,128,0,1.717315," ","integrate((c*sin(b*x^2+a)^3)^(1/3),x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(4^{\frac{2}{3}} \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(b x^{2} + a\right) + 4^{\frac{2}{3}} \sqrt{2} \pi \sqrt{\frac{b}{\pi}} \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(b x^{2} + a\right) \sin\left(a\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}}}{8 \, {\left(b \cos\left(b x^{2} + a\right)^{2} - b\right)}}"," ",0,"-1/8*4^(1/3)*(4^(2/3)*sqrt(2)*pi*sqrt(b/pi)*cos(a)*fresnel_sin(sqrt(2)*x*sqrt(b/pi))*sin(b*x^2 + a) + 4^(2/3)*sqrt(2)*pi*sqrt(b/pi)*fresnel_cos(sqrt(2)*x*sqrt(b/pi))*sin(b*x^2 + a)*sin(a))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)/(b*cos(b*x^2 + a)^2 - b)","A",0
323,1,94,0,0.900432," ","integrate((c*sin(b*x^2+a)^3)^(1/3)/x,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(2 \cdot 4^{\frac{2}{3}} \cos\left(a\right) \operatorname{Si}\left(b x^{2}\right) + {\left(4^{\frac{2}{3}} \operatorname{Ci}\left(b x^{2}\right) + 4^{\frac{2}{3}} \operatorname{Ci}\left(-b x^{2}\right)\right)} \sin\left(a\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}} \sin\left(b x^{2} + a\right)}{16 \, {\left(\cos\left(b x^{2} + a\right)^{2} - 1\right)}}"," ",0,"-1/16*4^(1/3)*(2*4^(2/3)*cos(a)*sin_integral(b*x^2) + (4^(2/3)*cos_integral(b*x^2) + 4^(2/3)*cos_integral(-b*x^2))*sin(a))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)*sin(b*x^2 + a)/(cos(b*x^2 + a)^2 - 1)","A",0
324,1,150,0,0.920384," ","integrate((c*sin(b*x^2+a)^3)^(1/3)/x^2,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(4^{\frac{2}{3}} \sqrt{2} \pi x \sqrt{\frac{b}{\pi}} \cos\left(a\right) \operatorname{C}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(b x^{2} + a\right) - 4^{\frac{2}{3}} \sqrt{2} \pi x \sqrt{\frac{b}{\pi}} \operatorname{S}\left(\sqrt{2} x \sqrt{\frac{b}{\pi}}\right) \sin\left(b x^{2} + a\right) \sin\left(a\right) + 4^{\frac{2}{3}} \cos\left(b x^{2} + a\right)^{2} - 4^{\frac{2}{3}}\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}}}{4 \, {\left(x \cos\left(b x^{2} + a\right)^{2} - x\right)}}"," ",0,"-1/4*4^(1/3)*(4^(2/3)*sqrt(2)*pi*x*sqrt(b/pi)*cos(a)*fresnel_cos(sqrt(2)*x*sqrt(b/pi))*sin(b*x^2 + a) - 4^(2/3)*sqrt(2)*pi*x*sqrt(b/pi)*fresnel_sin(sqrt(2)*x*sqrt(b/pi))*sin(b*x^2 + a)*sin(a) + 4^(2/3)*cos(b*x^2 + a)^2 - 4^(2/3))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)/(x*cos(b*x^2 + a)^2 - x)","A",0
325,1,138,0,1.477221," ","integrate((c*sin(b*x^2+a)^3)^(1/3)/x^3,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(2 \cdot 4^{\frac{2}{3}} \cos\left(b x^{2} + a\right)^{2} - {\left(2 \cdot 4^{\frac{2}{3}} b x^{2} \sin\left(a\right) \operatorname{Si}\left(b x^{2}\right) - {\left(4^{\frac{2}{3}} b x^{2} \operatorname{Ci}\left(b x^{2}\right) + 4^{\frac{2}{3}} b x^{2} \operatorname{Ci}\left(-b x^{2}\right)\right)} \cos\left(a\right)\right)} \sin\left(b x^{2} + a\right) - 2 \cdot 4^{\frac{2}{3}}\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{1}{3}}}{16 \, {\left(x^{2} \cos\left(b x^{2} + a\right)^{2} - x^{2}\right)}}"," ",0,"-1/16*4^(1/3)*(2*4^(2/3)*cos(b*x^2 + a)^2 - (2*4^(2/3)*b*x^2*sin(a)*sin_integral(b*x^2) - (4^(2/3)*b*x^2*cos_integral(b*x^2) + 4^(2/3)*b*x^2*cos_integral(-b*x^2))*cos(a))*sin(b*x^2 + a) - 2*4^(2/3))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(1/3)/(x^2*cos(b*x^2 + a)^2 - x^2)","A",0
326,0,0,0,1.542402," ","integrate(x^m*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}} x^{m}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)*x^m, x)","F",0
327,0,0,0,0.942318," ","integrate(x^3*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}} x^{3}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)*x^3, x)","F",0
328,0,0,0,1.045549," ","integrate(x^2*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}} x^{2}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)*x^2, x)","F",0
329,0,0,0,1.445679," ","integrate(x*(c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}} x, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)*x, x)","F",0
330,0,0,0,1.499745," ","integrate((c*sin(a+b*x^n)^3)^(1/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3), x)","F",0
331,1,98,0,0.912003," ","integrate((c*sin(a+b*x^n)^3)^(1/3)/x,x, algorithm=""fricas"")","-\frac{4^{\frac{1}{3}} {\left(4^{\frac{2}{3}} \operatorname{Ci}\left(b x^{n}\right) \sin\left(a\right) + 4^{\frac{2}{3}} \operatorname{Ci}\left(-b x^{n}\right) \sin\left(a\right) + 2 \cdot 4^{\frac{2}{3}} \cos\left(a\right) \operatorname{Si}\left(b x^{n}\right)\right)} \left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}} \sin\left(b x^{n} + a\right)}{8 \, {\left(n \cos\left(b x^{n} + a\right)^{2} - n\right)}}"," ",0,"-1/8*4^(1/3)*(4^(2/3)*cos_integral(b*x^n)*sin(a) + 4^(2/3)*cos_integral(-b*x^n)*sin(a) + 2*4^(2/3)*cos(a)*sin_integral(b*x^n))*(-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)*sin(b*x^n + a)/(n*cos(b*x^n + a)^2 - n)","A",0
332,0,0,0,1.628251," ","integrate((c*sin(a+b*x^n)^3)^(1/3)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}}}{x^{2}}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)/x^2, x)","F",0
333,0,0,0,1.470254," ","integrate((c*sin(a+b*x^n)^3)^(1/3)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{1}{3}}}{x^{3}}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(1/3)/x^3, x)","F",0
334,1,112,0,1.513670," ","integrate(x^m*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(4 \, b x x^{m} - {\left(i \, m + i\right)} e^{\left(-m \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(m + 1, 2 i \, b x\right) - {\left(-i \, m - i\right)} e^{\left(-m \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(m + 1, -2 i \, b x\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{8 \, {\left({\left(b m + b\right)} \cos\left(b x + a\right)^{2} - b m - b\right)}}"," ",0,"-1/8*(4*b*x*x^m - (I*m + I)*e^(-m*log(2*I*b) - 2*I*a)*gamma(m + 1, 2*I*b*x) - (-I*m - I)*e^(-m*log(-2*I*b) + 2*I*a)*gamma(m + 1, -2*I*b*x))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/((b*m + b)*cos(b*x + a)^2 - b*m - b)","A",0
335,1,111,0,1.693824," ","integrate(x^3*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(2 \, b^{4} x^{4} + 6 \, b^{2} x^{2} - 6 \, {\left(2 \, b^{2} x^{2} - 1\right)} \cos\left(b x + a\right)^{2} - 4 \, {\left(2 \, b^{3} x^{3} - 3 \, b x\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) - 3\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{16 \, {\left(b^{4} \cos\left(b x + a\right)^{2} - b^{4}\right)}}"," ",0,"-1/16*(2*b^4*x^4 + 6*b^2*x^2 - 6*(2*b^2*x^2 - 1)*cos(b*x + a)^2 - 4*(2*b^3*x^3 - 3*b*x)*cos(b*x + a)*sin(b*x + a) - 3)*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(b^4*cos(b*x + a)^2 - b^4)","A",0
336,1,95,0,1.467901," ","integrate(x^2*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(2 \, b^{3} x^{3} - 6 \, b x \cos\left(b x + a\right)^{2} - 3 \, {\left(2 \, b^{2} x^{2} - 1\right)} \cos\left(b x + a\right) \sin\left(b x + a\right) + 3 \, b x\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{12 \, {\left(b^{3} \cos\left(b x + a\right)^{2} - b^{3}\right)}}"," ",0,"-1/12*(2*b^3*x^3 - 6*b*x*cos(b*x + a)^2 - 3*(2*b^2*x^2 - 1)*cos(b*x + a)*sin(b*x + a) + 3*b*x)*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(b^3*cos(b*x + a)^2 - b^3)","A",0
337,1,82,0,1.570196," ","integrate(x*(c*sin(b*x+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(2 \, b^{2} x^{2} - 4 \, b x \cos\left(b x + a\right) \sin\left(b x + a\right) - 2 \, \cos\left(b x + a\right)^{2} + 1\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{8 \, {\left(b^{2} \cos\left(b x + a\right)^{2} - b^{2}\right)}}"," ",0,"-1/8*(2*b^2*x^2 - 4*b*x*cos(b*x + a)*sin(b*x + a) - 2*cos(b*x + a)^2 + 1)*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(b^2*cos(b*x + a)^2 - b^2)","A",0
338,1,60,0,1.465551," ","integrate((c*sin(b*x+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(b x - \cos\left(b x + a\right) \sin\left(b x + a\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{2 \, {\left(b \cos\left(b x + a\right)^{2} - b\right)}}"," ",0,"-1/2*(b*x - cos(b*x + a)*sin(b*x + a))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(b*cos(b*x + a)^2 - b)","A",0
339,1,88,0,1.317610," ","integrate((c*sin(b*x+a)^3)^(2/3)/x,x, algorithm=""fricas"")","-\frac{4^{\frac{2}{3}} {\left(2 \cdot 4^{\frac{1}{3}} \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x\right) - {\left(4^{\frac{1}{3}} \operatorname{Ci}\left(2 \, b x\right) + 4^{\frac{1}{3}} \operatorname{Ci}\left(-2 \, b x\right)\right)} \cos\left(2 \, a\right) + 2 \cdot 4^{\frac{1}{3}} \log\left(x\right)\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{16 \, {\left(\cos\left(b x + a\right)^{2} - 1\right)}}"," ",0,"-1/16*4^(2/3)*(2*4^(1/3)*sin(2*a)*sin_integral(2*b*x) - (4^(1/3)*cos_integral(2*b*x) + 4^(1/3)*cos_integral(-2*b*x))*cos(2*a) + 2*4^(1/3)*log(x))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(cos(b*x + a)^2 - 1)","A",0
340,1,108,0,1.561548," ","integrate((c*sin(b*x+a)^3)^(2/3)/x^2,x, algorithm=""fricas"")","-\frac{4^{\frac{2}{3}} {\left(2 \cdot 4^{\frac{1}{3}} b x \cos\left(2 \, a\right) \operatorname{Si}\left(2 \, b x\right) + 2 \cdot 4^{\frac{1}{3}} \cos\left(b x + a\right)^{2} + {\left(4^{\frac{1}{3}} b x \operatorname{Ci}\left(2 \, b x\right) + 4^{\frac{1}{3}} b x \operatorname{Ci}\left(-2 \, b x\right)\right)} \sin\left(2 \, a\right) - 2 \cdot 4^{\frac{1}{3}}\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{8 \, {\left(x \cos\left(b x + a\right)^{2} - x\right)}}"," ",0,"-1/8*4^(2/3)*(2*4^(1/3)*b*x*cos(2*a)*sin_integral(2*b*x) + 2*4^(1/3)*cos(b*x + a)^2 + (4^(1/3)*b*x*cos_integral(2*b*x) + 4^(1/3)*b*x*cos_integral(-2*b*x))*sin(2*a) - 2*4^(1/3))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(x*cos(b*x + a)^2 - x)","A",0
341,1,142,0,1.937288," ","integrate((c*sin(b*x+a)^3)^(2/3)/x^3,x, algorithm=""fricas"")","\frac{4^{\frac{2}{3}} {\left(2 \cdot 4^{\frac{1}{3}} b^{2} x^{2} \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x\right) + 2 \cdot 4^{\frac{1}{3}} b x \cos\left(b x + a\right) \sin\left(b x + a\right) - 4^{\frac{1}{3}} \cos\left(b x + a\right)^{2} - {\left(4^{\frac{1}{3}} b^{2} x^{2} \operatorname{Ci}\left(2 \, b x\right) + 4^{\frac{1}{3}} b^{2} x^{2} \operatorname{Ci}\left(-2 \, b x\right)\right)} \cos\left(2 \, a\right) + 4^{\frac{1}{3}}\right)} \left(-{\left(c \cos\left(b x + a\right)^{2} - c\right)} \sin\left(b x + a\right)\right)^{\frac{2}{3}}}{8 \, {\left(x^{2} \cos\left(b x + a\right)^{2} - x^{2}\right)}}"," ",0,"1/8*4^(2/3)*(2*4^(1/3)*b^2*x^2*sin(2*a)*sin_integral(2*b*x) + 2*4^(1/3)*b*x*cos(b*x + a)*sin(b*x + a) - 4^(1/3)*cos(b*x + a)^2 - (4^(1/3)*b^2*x^2*cos_integral(2*b*x) + 4^(1/3)*b^2*x^2*cos_integral(-2*b*x))*cos(2*a) + 4^(1/3))*(-(c*cos(b*x + a)^2 - c)*sin(b*x + a))^(2/3)/(x^2*cos(b*x + a)^2 - x^2)","A",0
342,1,130,0,1.566889," ","integrate(x^m*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(8 \, b x x^{m} - {\left(i \, m + i\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(2 i \, b\right) - 2 i \, a\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, 2 i \, b x^{2}\right) - {\left(-i \, m - i\right)} e^{\left(-\frac{1}{2} \, {\left(m - 1\right)} \log\left(-2 i \, b\right) + 2 i \, a\right)} \Gamma\left(\frac{1}{2} \, m + \frac{1}{2}, -2 i \, b x^{2}\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{16 \, {\left({\left(b m + b\right)} \cos\left(b x^{2} + a\right)^{2} - b m - b\right)}}"," ",0,"-1/16*(8*b*x*x^m - (I*m + I)*e^(-1/2*(m - 1)*log(2*I*b) - 2*I*a)*gamma(1/2*m + 1/2, 2*I*b*x^2) - (-I*m - I)*e^(-1/2*(m - 1)*log(-2*I*b) + 2*I*a)*gamma(1/2*m + 1/2, -2*I*b*x^2))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/((b*m + b)*cos(b*x^2 + a)^2 - b*m - b)","A",0
343,1,96,0,1.606494," ","integrate(x^3*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(2 \, b^{2} x^{4} - 4 \, b x^{2} \cos\left(b x^{2} + a\right) \sin\left(b x^{2} + a\right) - 2 \, \cos\left(b x^{2} + a\right)^{2} + 1\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{16 \, {\left(b^{2} \cos\left(b x^{2} + a\right)^{2} - b^{2}\right)}}"," ",0,"-1/16*(2*b^2*x^4 - 4*b*x^2*cos(b*x^2 + a)*sin(b*x^2 + a) - 2*cos(b*x^2 + a)^2 + 1)*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(b^2*cos(b*x^2 + a)^2 - b^2)","A",0
344,1,146,0,1.475969," ","integrate(x^2*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{4^{\frac{2}{3}} {\left(8 \cdot 4^{\frac{1}{3}} b^{2} x^{3} - 12 \cdot 4^{\frac{1}{3}} b x \cos\left(b x^{2} + a\right) \sin\left(b x^{2} + a\right) + 3 \cdot 4^{\frac{1}{3}} \pi \sqrt{\frac{b}{\pi}} \cos\left(2 \, a\right) \operatorname{S}\left(2 \, x \sqrt{\frac{b}{\pi}}\right) + 3 \cdot 4^{\frac{1}{3}} \pi \sqrt{\frac{b}{\pi}} \operatorname{C}\left(2 \, x \sqrt{\frac{b}{\pi}}\right) \sin\left(2 \, a\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{192 \, {\left(b^{2} \cos\left(b x^{2} + a\right)^{2} - b^{2}\right)}}"," ",0,"-1/192*4^(2/3)*(8*4^(1/3)*b^2*x^3 - 12*4^(1/3)*b*x*cos(b*x^2 + a)*sin(b*x^2 + a) + 3*4^(1/3)*pi*sqrt(b/pi)*cos(2*a)*fresnel_sin(2*x*sqrt(b/pi)) + 3*4^(1/3)*pi*sqrt(b/pi)*fresnel_cos(2*x*sqrt(b/pi))*sin(2*a))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(b^2*cos(b*x^2 + a)^2 - b^2)","A",0
345,1,72,0,1.645294," ","integrate(x*(c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""fricas"")","-\frac{{\left(b x^{2} - \cos\left(b x^{2} + a\right) \sin\left(b x^{2} + a\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{4 \, {\left(b \cos\left(b x^{2} + a\right)^{2} - b\right)}}"," ",0,"-1/4*(b*x^2 - cos(b*x^2 + a)*sin(b*x^2 + a))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(b*cos(b*x^2 + a)^2 - b)","A",0
346,1,114,0,1.631560," ","integrate((c*sin(b*x^2+a)^3)^(2/3),x, algorithm=""fricas"")","\frac{4^{\frac{2}{3}} {\left(4^{\frac{1}{3}} \pi \sqrt{\frac{b}{\pi}} \cos\left(2 \, a\right) \operatorname{C}\left(2 \, x \sqrt{\frac{b}{\pi}}\right) - 4^{\frac{1}{3}} \pi \sqrt{\frac{b}{\pi}} \operatorname{S}\left(2 \, x \sqrt{\frac{b}{\pi}}\right) \sin\left(2 \, a\right) - 2 \cdot 4^{\frac{1}{3}} b x\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{16 \, {\left(b \cos\left(b x^{2} + a\right)^{2} - b\right)}}"," ",0,"1/16*4^(2/3)*(4^(1/3)*pi*sqrt(b/pi)*cos(2*a)*fresnel_cos(2*x*sqrt(b/pi)) - 4^(1/3)*pi*sqrt(b/pi)*fresnel_sin(2*x*sqrt(b/pi))*sin(2*a) - 2*4^(1/3)*b*x)*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(b*cos(b*x^2 + a)^2 - b)","A",0
347,1,100,0,1.811263," ","integrate((c*sin(b*x^2+a)^3)^(2/3)/x,x, algorithm=""fricas"")","-\frac{4^{\frac{2}{3}} {\left(2 \cdot 4^{\frac{1}{3}} \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{2}\right) - {\left(4^{\frac{1}{3}} \operatorname{Ci}\left(2 \, b x^{2}\right) + 4^{\frac{1}{3}} \operatorname{Ci}\left(-2 \, b x^{2}\right)\right)} \cos\left(2 \, a\right) + 4 \cdot 4^{\frac{1}{3}} \log\left(x\right)\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{32 \, {\left(\cos\left(b x^{2} + a\right)^{2} - 1\right)}}"," ",0,"-1/32*4^(2/3)*(2*4^(1/3)*sin(2*a)*sin_integral(2*b*x^2) - (4^(1/3)*cos_integral(2*b*x^2) + 4^(1/3)*cos_integral(-2*b*x^2))*cos(2*a) + 4*4^(1/3)*log(x))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(cos(b*x^2 + a)^2 - 1)","A",0
348,1,127,0,1.407554," ","integrate((c*sin(b*x^2+a)^3)^(2/3)/x^2,x, algorithm=""fricas"")","-\frac{4^{\frac{2}{3}} {\left(4^{\frac{1}{3}} \pi x \sqrt{\frac{b}{\pi}} \cos\left(2 \, a\right) \operatorname{S}\left(2 \, x \sqrt{\frac{b}{\pi}}\right) + 4^{\frac{1}{3}} \pi x \sqrt{\frac{b}{\pi}} \operatorname{C}\left(2 \, x \sqrt{\frac{b}{\pi}}\right) \sin\left(2 \, a\right) + 4^{\frac{1}{3}} \cos\left(b x^{2} + a\right)^{2} - 4^{\frac{1}{3}}\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{4 \, {\left(x \cos\left(b x^{2} + a\right)^{2} - x\right)}}"," ",0,"-1/4*4^(2/3)*(4^(1/3)*pi*x*sqrt(b/pi)*cos(2*a)*fresnel_sin(2*x*sqrt(b/pi)) + 4^(1/3)*pi*x*sqrt(b/pi)*fresnel_cos(2*x*sqrt(b/pi))*sin(2*a) + 4^(1/3)*cos(b*x^2 + a)^2 - 4^(1/3))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(x*cos(b*x^2 + a)^2 - x)","A",0
349,1,132,0,1.053234," ","integrate((c*sin(b*x^2+a)^3)^(2/3)/x^3,x, algorithm=""fricas"")","-\frac{4^{\frac{2}{3}} {\left(2 \cdot 4^{\frac{1}{3}} b x^{2} \cos\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{2}\right) + 2 \cdot 4^{\frac{1}{3}} \cos\left(b x^{2} + a\right)^{2} + {\left(4^{\frac{1}{3}} b x^{2} \operatorname{Ci}\left(2 \, b x^{2}\right) + 4^{\frac{1}{3}} b x^{2} \operatorname{Ci}\left(-2 \, b x^{2}\right)\right)} \sin\left(2 \, a\right) - 2 \cdot 4^{\frac{1}{3}}\right)} \left(-{\left(c \cos\left(b x^{2} + a\right)^{2} - c\right)} \sin\left(b x^{2} + a\right)\right)^{\frac{2}{3}}}{16 \, {\left(x^{2} \cos\left(b x^{2} + a\right)^{2} - x^{2}\right)}}"," ",0,"-1/16*4^(2/3)*(2*4^(1/3)*b*x^2*cos(2*a)*sin_integral(2*b*x^2) + 2*4^(1/3)*cos(b*x^2 + a)^2 + (4^(1/3)*b*x^2*cos_integral(2*b*x^2) + 4^(1/3)*b*x^2*cos_integral(-2*b*x^2))*sin(2*a) - 2*4^(1/3))*(-(c*cos(b*x^2 + a)^2 - c)*sin(b*x^2 + a))^(2/3)/(x^2*cos(b*x^2 + a)^2 - x^2)","A",0
350,0,0,0,1.473278," ","integrate(x^m*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}} x^{m}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)*x^m, x)","F",0
351,0,0,0,1.907591," ","integrate(x^3*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}} x^{3}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)*x^3, x)","F",0
352,0,0,0,1.540046," ","integrate(x^2*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}} x^{2}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)*x^2, x)","F",0
353,0,0,0,1.542413," ","integrate(x*(c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}} x, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)*x, x)","F",0
354,0,0,0,1.695236," ","integrate((c*sin(a+b*x^n)^3)^(2/3),x, algorithm=""fricas"")","{\rm integral}\left(\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3), x)","F",0
355,1,106,0,2.069049," ","integrate((c*sin(a+b*x^n)^3)^(2/3)/x,x, algorithm=""fricas"")","\frac{4^{\frac{2}{3}} {\left(4^{\frac{1}{3}} \cos\left(2 \, a\right) \operatorname{Ci}\left(2 \, b x^{n}\right) + 4^{\frac{1}{3}} \cos\left(2 \, a\right) \operatorname{Ci}\left(-2 \, b x^{n}\right) - 2 \cdot 4^{\frac{1}{3}} n \log\left(x\right) - 2 \cdot 4^{\frac{1}{3}} \sin\left(2 \, a\right) \operatorname{Si}\left(2 \, b x^{n}\right)\right)} \left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}}}{16 \, {\left(n \cos\left(b x^{n} + a\right)^{2} - n\right)}}"," ",0,"1/16*4^(2/3)*(4^(1/3)*cos(2*a)*cos_integral(2*b*x^n) + 4^(1/3)*cos(2*a)*cos_integral(-2*b*x^n) - 2*4^(1/3)*n*log(x) - 2*4^(1/3)*sin(2*a)*sin_integral(2*b*x^n))*(-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)/(n*cos(b*x^n + a)^2 - n)","A",0
356,0,0,0,1.450516," ","integrate((c*sin(a+b*x^n)^3)^(2/3)/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}}}{x^{2}}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)/x^2, x)","F",0
357,0,0,0,1.958881," ","integrate((c*sin(a+b*x^n)^3)^(2/3)/x^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(-{\left(c \cos\left(b x^{n} + a\right)^{2} - c\right)} \sin\left(b x^{n} + a\right)\right)^{\frac{2}{3}}}{x^{3}}, x\right)"," ",0,"integral((-(c*cos(b*x^n + a)^2 - c)*sin(b*x^n + a))^(2/3)/x^3, x)","F",0
